Defect-induced ferromagnetism in SiC - Qucosa - TU Dresden

Institut für Ionenstrahlphysik und MaterialforschungHelmholtz-Zentrum Dresden-Rossendorf

Defect-induced ferromagnetism in SiC

Dissertation

zur Erlangung des akademischen Grades

Doctor rerum naturalium (Dr. rer. nat.)

vorgelegt der Fakultät Mathematik und Naturwissenschaften

der Technischen Universistät Dresden

von

Yutian Wang

geboren am 29.03.1984 in China

Eingereicht am 15.10.2014

Verteidigt am 30.01.2015

Gutachter:

1. Prof. Dr. Manfred Helm (TU-Dresden and HZDR)

2. Prof. Dr. Pablo Esquinazi (Uni. Leipzig)

Acknowledgements

I would like to thank my supervisor Prof. Manfred Helm for providing me the precious

opportunity to work in this world leading institute. His guidance and critical reading of this

thesis helped me a lot to overcome many troubles. This is a precious life experience which

lets me have a chance to understand excellent researchers and their work in a total dierent

culture system. I also benet a lot from discussing with Prof. Sibylle Gemming. Here, I

also want to express my highly appreciation for her creative ideas and pertinent comments

for our several manuscripts.

I would like to express my great gratitude to Dr. Shengqiang Zhou for his constant and

patient supervising all the details of my work from the academic English writing to basic

experimental skills. It is a great please for me to study and work in his team during the

past three years. I can never forget those over mid-night beam-time that we did experiments

in several synchrotron centers around the world for better understanding the physics in a

series of diluted magnetic semiconductors. I can also never forget those weekly illuminating

discussions which always trigger my courage and inspiration to ght with these hopeless

data and poor academic writing without any reservation. How can I forget those nice BBQ,

Chinese big dinners, and special gifts in Chinese or German festivals which often warm my

heart.

I want to thank the ion implantation group in HZDR for their excellent technique sup-

port, Dr. F. Munnik for PIXE, Dr. C. Baehtz and Dr. A. Shalimov for XRD. Our ex-

ternal cooperative partners also bring me important help, such as, Dr. E. Weschke (Bessy,

Berlin), Dr. Catherine A. Jenkins (ALS, USA), Dr. E. Arenholz (ALS, USA) and Dr. E.

Wendler(Uni-Jena, Jena). I would like to express my sincere gratitude to all of them.

I am also indebted to my colleagues, Kun, Dr. Khalid, Slawek, Ye, Fang, Yu, Yanda and

other colleagues in FWIM. I can not nish this thesis without their help.

Above all I thank my father and my mother. Their love encourages me to overcome all

the diculties in life and work.

I want to thanks the China Scholarship Council (CSC) to provide generous scholarship

for my study in Germany.

At last, thank to my future wife. Her absence let me have enough time to carefully and

systemically think of meaning of science, art, life, family and world. I am waiting for her to

share these treasures.

Yutian Wang

Abstract

Defect-induced ferromagnetism is attracting intensive research interest. It not only chal-

lenges the traditional opinions about ferromagnetism, but also has some potential appli-

cations in spin-electronics. SiC is a new candidate for the investigation of defect-induced

ferromagnetism after graphitic materials and oxides due to its high material purity and

crystalline quality.

In this thesis, we made a comprehensive investigation on the structural and magnetic

properties of ion implanted and neutron irradiated SiC sample. In combination with X-ray

absorption spectroscopy and rst-principles calculations, we try to understand the mecha-

nism in a microscopic picture.

For neon or xenon ion implanted SiC, we identify a multi-magnetic-phase nature. The

magnetization of SiC can be decomposed into paramagnetic, superparamagnetic and ferro-

magnetic contributions. The ferromagnetic contribution persists well above room tempera-

ture and exhibits a pronounced magnetic anisotropy. We qualitatively explain the magnetic

properties as a result of the intrinsic clustering tendency of defects. By combining X-ray

magnetic circular dichroism and rst-principles calculations, we clarify that p electrons of

the nearest-neighbor carbon atoms around divacancies are mainly responsible for the long-

range ferromagnetic coupling. Thus, we provide a direct correlation between the collective

magnetic phenomena and the specic electrons/orbitals.

With the aim to verify if the defect-induced magnetization can be increased by orders of

magnitude, i.e., if a sample containing defects through its bulk volume can persist ferromag-

netic coupling, we applied neutron irradiation to introduce defects into SiC. Besides a weak

ferromagnetic contribution, we observe a strong paramagnetism, scaling up with the neu-

tron uence. The ferromagnetic contribution induced by neutron irradiation only occurs in a

narrow uence window or after annealing. It seems non-realistic to make the bulk specimens

ferromagnetic by introducing defects. Instead, we speculate that defect-induced ferromag-

netism rather locally appears in particular regions, like surface/interface/grain boundaries.

A comparable investigation on neutron irradiated graphite supports the same conclusion.

Contents

1 Introduction 1

1.1 Defect-induced ferromagnetism . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Oxides . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.3 Carbon-Based materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

1.4 Silicon carbide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

1.5 Organization of this thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2 Experimental Methods 15

2.1 Ion Implantation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.1.1 Energy loss . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.1.2 Stopping and Range of Ions in Matter . . . . . . . . . . . . . . . . . . 16

2.1.3 Direct beam eect: Collision cascade and primary defects . . . . . . . 16

2.1.4 Indirect beam eect: Beyond the primary defects . . . . . . . . . . . . 17

2.1.5 Displacement per atom (DPA) . . . . . . . . . . . . . . . . . . . . . . 18

2.2 Neutron irradiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

2.2.1 Dierence between ion implantation and neutron irradiation . . . . . . 19

2.3 Contamination test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

2.3.1 Particle-induced X-ray emission . . . . . . . . . . . . . . . . . . . . . . 21

2.4 SQUID-VSM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

2.5 X-ray absorption spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

2.5.1 XANES and EXAFS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

2.5.2 Collection mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

2.5.3 XMCD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

2.5.4 The tricks for measuring and processing XAS from the Carbon K-edge 25

3 Structural and magnetic properties of defective SiC 27

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

3.2 Experimental methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

3.3 Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

3.3.1 Magnetic properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

3.3.2 Contamination test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

3.3.3 XRD and RBS Channeling . . . . . . . . . . . . . . . . . . . . . . . . 30

3.3.4 Correlation between ferromagnetism and structural parameters . . . . 32

vii

4 Disentangling defect-induced ferromagnetism in SiC 35

4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35


4.3 Paramagnetism in virgin SiC . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

4.4 Magnetic phases in Ne irradiated SiC . . . . . . . . . . . . . . . . . . . . . . . 39

4.5 Magnetic anisotropy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

4.6 Summary and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

5 Carbon p Electron Ferromagnetism in SiC Single Crystal 49

5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49


5.2.1 Sample preparation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

5.2.2 Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

5.2.3 Calculation parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

5.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

5.3.1 Structural properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

5.3.2 Divacancy identied in the ion implanted sample . . . . . . . . . . . . 52


5.3.4 Direct evidence for the origin of magnetism . . . . . . . . . . . . . . . 55

5.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

5.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

6 Why is the ferromagnetism weak? 59

6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

6.2 Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

6.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

6.3.1 Virgin vs. irradiated SiC . . . . . . . . . . . . . . . . . . . . . . . . . . 61

6.3.2 Structural properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

6.3.3 Paramagnetism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

6.3.4 Ferromagnetism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

6.3.5 Why is the ferromagnetism weak? . . . . . . . . . . . . . . . . . . . . 69

6.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

7 Revisiting defect-induced magnetism in graphite through neutron irradi-

ation 75

7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75


7.3 Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77


7.3.2 Raman spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

7.3.3 X-ray absorption spectroscopy . . . . . . . . . . . . . . . . . . . . . . . 84

7.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

7.4.1 The origin of the paramagnetism . . . . . . . . . . . . . . . . . . . . . 86

7.4.2 The role of trans-planar defects . . . . . . . . . . . . . . . . . . . . . . 87

7.4.3 Why is the magnetic interaction missing? . . . . . . . . . . . . . . . . 89

7.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90

8 Summary and outlook 91

8.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

8.2 Outlook: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

A Publications 109

A.1 Paper published or accepted . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

A.2 Paper submitted or in preparation . . . . . . . . . . . . . . . . . . . . . . . . 109

B Curriculum vitae 111

B.1 Personal data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111

B.2 Education . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111

B.3 Short-term advanced school . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111

Chapter 1

Introduction

1.1 Defect-induced ferromagnetism

Defects have played an important role for modication of the electrical or optical properties

of semiconductors. An unexpected high-temperature ferromagnetism has been discovered

in a series of materials in the past ten years [1, 2, 3, 4]. These materials do not contain

ions with partially lled 3d or 4f band, so the magnetic order observed in such cases is

also called d0 ferromagnetism. It is believed that the defects in those materials can induce

hybridization at the Fermi level and thereby give rise to a long-range ferromagnetic coupling.

Defect-induced ferromagnetism provides a new way for preparing spintronic materials with

high Curie temperature [5]. Further investigations on the mechanism of defect-induced

ferromagnetism present new challenges. Controversial reports accompany this topic from its

birth. This is due to several aspects:

• Contaminations from the sample fabrication or magnetization measurement are hardly

avoided. The typical magnetic moment in reports of defect-induced ferromagnetism

is around 10−5- 10−6 emu in thin lm samples. Such a weak magnetic moment can

also be created by steel tweezers [6], articial eects or measurement errors in Su-

perconducting Quantum Interference Device Magnetic Property Measurement System

(SQUID-MPMS) [7].

• The used substrates for the fabrication of the lms are not well controlled. There are

various publications reporting unknown contamination especially in oxide substrates

[8, 9, 10].

• The poor reproducibility: Most researchers in this specic topic are material scientists

and the defects in their samples are generally controlled by reduced growth or anneal-

ing condition. Experimental conditions can be dierent from lab to lab. M. Roever et

al. [11] systematically investigated defect-induced ferromagnetism in GaN:Gd materi-

als grown by molecular beam epitaxy. They produced around 100 GaN:Gd samples.

However, they found that the reproducibility of the magnetic properties is poor. They

claimed that the uncontrolled parameters seem to be responsible for the ferromagnetic

properties.

1

2 CHAPTER 1. INTRODUCTION

In this chapter, we shortly review the research status for two kinds of materials: oxides

and carbon based materials, which are intensely investigated with respect to defect-induced

ferromagnetism.

1.2 Oxides

Oxides are intensively investigated materials since they are predicted to have high Curie

temperature (Tc) if doped with transition metal ions. As one method to fabricate diluted

magnetic oxides, transition metal ions were implanted into the wide bandgap oxides, such

as ZnO or TiO2. However the continuous disagreements about explaining the source of

ferromagnetism hampered the progress [12, 13, 14]. Later some evidences indicate that

defects also have some contribution to the high TC magnetic order. For instance, undoped

ZnO was reported to be ferromagnetic at room temperature [15]. Borges et al. implanted

Ar+ into ZnO and observed ferromagnetism at room temperature, which can be greatly

suppressed by annealing above 637 K [16]. For TiO2, Zhou et al. used 2 MeV oxygen

implantation to avoid potential foreign elements eect [17]. The magnetic properties of TiO2

before and after implantation at 300 K are shown in Fig. 1.1(a). At 300 K the irradiated

sample shows a hysteresis loop superimposed on the diamagnetic background. The coercive

eld of the loop is around 100 Oe and the saturation magnetization is 10−5 emu, which is

much larger than the sensitivity limit of SQUID magnetometry. Fig. 1.1(b) shows that the

implantation-uence aects the magnetic moment of TiO2. The magnetic moment rst rises

drastically with increasing uence. When the uence is above 5×1015 cm−2, the magnetic

moment begins to decrease signicantly. For the sample with a uence of 5×1015 cm−2 (withthe largest magnetic moment) the dependence of hysteresis loops on temperature is shown

in Fig. 1.1(c). The loops are weakly temperature dependent, which is also a feature of the

reported defect-induced ferromagnetism.

The source of ferromagnetism in defective TiO2 is proposed to be due to Ti3+ ions

[17]. We know that the stoichiometric TiO2 contains only Ti4+ ions and is non-magnetic,

but unpaired 3d electrons in Ti3+ ions can potentially cause magnetism, which recently

has been conrmed by X-ray absorption spectroscopies [18]. In TiO2, oxygen vacancies

induced by ion implantation create a charge imbalance and, therefore, a deviation from

stoichiometric TiO2 with the potential to generate Ti3+. To form Ti3+, the Ti ions are

stripped of electrons from the s band and one from the 3d band, resulting in Ti3+ ions

having 3d1 electronic conguration. By combining X-ray diraction, Raman scattering, and

electron spin resonance spectroscopy, the Zhou et al. [17] do identify a defect complex, i.e.

Ti3+ ions on the substitutional sites accompanied by oxygen vacancies in irradiated TiO2.

This kind of defect complex results in a local (TiO6−x) stretching Raman mode. Therefore,

it is elucidated that Ti3+ ions with one unpaired 3d electron provide the local magnetic

moment. However, it is unclear how the long-range ferromagnetic coupling is established.

Later an investigation on the stability of defect-induced ferromagnetism in TiO2 was

reported by Curz et al. [19]. They implanted Ar+ and N+ into TiO2. The uence was

1×1017 and 2×1017 n/cm2, respectively, and the implantation energy was 100 keV. Both

irradiated samples show induced ferromagnetism with a high Curie temperature above 380

1.2. OXIDES 3

-600 -400 -200 0 200 400 600

-4

-2

0

2

4M

om

en

t(1

0-5

em

u)

Field (mT)

Virgin

5E15

(a)

-1000 -500 0 500 1000-4

-2

0

2

4

Field (mT)

Virgin

1E15

2.5E15

5E15

7.5E15

5E16

(b)

0 5000 10000-2

0

2

4

Ma

gn

etiza

tio

n(1

0-5

em

u)

Field (Oe)

5 K

10 K

100 K

200 K

300 K

(c) sample 5E15

Figure 1.1: TiO2 (a) Magnetic moment in TiO2 measured at 300 K as a function of magneticeld before and after irradiation. The number 5E15 means the irradiation uence of 5×1015cm−2. (b) Magnetic moment at 300 K for samples with an equal sample size and dierention uences. The linear paramagnetic background has been subtracted. (c) Magnetizationof sample 5E15 at temperatures 5 K, 10 K, 100 K, 200 K, 300 K. The gure is from ref. [17].

K. When annealing temperature raised to 1073 K, the saturated magnetization is reduced

greatly in the Ar+ implanted sample but not in the N+ implanted sample. It indicates that

chemically active ions can stabilize the defects and the defect-induced ferromagnetism. The

appearance of Ti3+ in ion implanted TiO2 has also been reported by other groups [20, 21, 22].

In the same period, ion implantation was also used for other oxides. K. Potzger et al.

used Ar+, N+, and H+ ions with energies from 600 eV to 170 keV to implant into SrTiO3 [23].

They also realized room temperature ferromagnetism. The structure of implanted SrTiO3

sample is rather complicated. Polycrystalline SrTiO3, Sr2Ti6O13 or Ruddlesden-Popper like

secondary phases have been observed in the irradiated region. But the magnetization mea-

surement revealed only one magnetic phase, which cannot be due to the above-mentioned

secondary phases. Therefore, it is assumed that defects are responsible for the observed

ferromagnetism. Another case is 200 MeV Xe14+ irradiated CeO2 with uences from 5×1012

n/cm2 to 4×1013 n/cm2 [24]. The saturation magnetization increases with increasing the

uence and reaches a maximum at a specic uence, and then decreases. The X-ray photo-

electron spectroscopy result reveals the presence of oxygen vacancies after irradiation. The

magnetic moments are assigned to the localized 4f electrons on Ce3+ atoms, which are

related to the oxygen vacancies.

Experiments show that dilute magnetic oxides (DMOs) have some particular properties:

• Defects have a great inuence on the magnetism. The well crystallized samples do

not show ferromagnetism [25]. Figure 1.2 shows some possible distributions of defects

in oxides. In these distributions, only small fractions of the total matrix could be

the source of magnetism. One example is Mn-doped ZnO which showed that the

magnetization happens at grain boundaries [26].

• Existing exchange models can not explain the Curie temperature above room temper-

ature by non-uniformly distributed magnetic ions in the matrix.

• No extra experiments support that these defective doped or undoped oxides have sim-

ilar properties like III-V:Mn dilute magnetic semiconductors, such as anomalous Hall


eect, anisotropic magnetoresistance, and Faraday eect.

• In some cases, the experimental evidences show that the ferromagnetism has no cor-

relation with the transition metal dopants in oxides [27].

Figure 1.2: Possible distribution of defects in oxide lms: (a) Point defects are randomlydistributed in the defect region; (b) spinodal decomposition; (c) defects are located at theinterface; (d) defects are located at the grain boundary. Figure is from Ref. [28].

Based on these experiments, J. M. D. Coey et. al. proposed a model by spin-split band

theory [28]. It is also called charge transfer model which includes three components:

• In the vicinity of Fermi level, there is a defect-based band with a high density of states.

• Two transition metal ions with dierent 3d valence conguration compose a charge

container. But the charge reservoir can also be the surface of particles or thin lms

coated with a molecule which acts as an electron donor or acceptor.

• Electrons can easily be transfered in this container. There is an eective exchange

integral I with related to the defect states.

In the traditional Stoner model, uniform magnetization and Stoner criterion satisfaction

are two required conditions. But for the charge transfer model, when the Stoner criterion

satisfaction happens in the high density states of defective, the ferromagnetism will arise

when:

IN(EF ) > 1, (1.1)

where N(EF ) is the density of states in the unsplit band at Fermi level. In the charge

transfer model, the Fermi level is near the maximum of the density of states but is not needed

to merge in the unsplit band like the traditional Stoner model. When the integral I is su-

ciently large, the exchange splitting will generate energy which is not only enough to com-

pensate the cost of splitting, but also to compensate the energy cost of charge-transferring

1.2. OXIDES 5

in the charge reservoir. Figure 1.3 shows schematically the physical mechanism of the charge

transfer model. Electrons are from container to the defect band, so that N(E) increases to

satisfy the Stoner criterion.

Figure 1.3: Schematic of charge transfer model. To satisfy the Stoner criterion, electronsare transfered from or to the charge container and nally to the defect band. The gure isfrom Ref. [28]

To quantitatively describe the model, three parameters I/W, U/W, and Ntot/W need

to be set as the input parameters, where the Stoner integral in the defect band is dened

as I, W is the bandwidth of defects, Ntot is the total number of electrons (electrons in the

container and band ), and U is the parameter characterizing the container which functions as

the on-site Coulomb energy for an electron transferring between cation (i.e Fe3+ to Fe2+).

To simplify the calculation, only a two-peaked defect density of states N(E) is presented

here. N(E) is dened as:

N(E) = (15/4)[8(E −W )2/W 3][1− 4[(E −W )2]/W 2] for 0 ≤ E ≤ 2W. (1.2)

And the total energy is dened as :

Etot =

∫ E0+ε

0E

′N(E

′)dE

′+

∫ E0−ε

0E

′N(E

′)dE

′ − I(n↑−n↓)2 +U [(n↑+n↓)−n0]2, (1.3)

n↑,↓=

∫ E0±ε

0N(E

′)dE

′, (1.4)

where the 2ε is the splitting of defect +band, n0 is a constant which stands for the 3d

occupancy, and so n0 ∈ [0,2]. The Landau potential (Ω) is:

Ω = Etot − TS − µNtot, (1.5)

Where S is entropy and µ is the system chemical potential. To minimize Ω at 0 K, the

numerically solution for ε and µ is possibly not unique since the initial input values have great


inuence on the result. When the solution satises the Stoner criterion, the ferromagnetic

coupling will happen. Figure 1.4 is an example of the solution, and I/W and n0/W are

xed as 1 and 0.4, respectively, which indicate where the charge-transfer ferromagnetism

occurs and the stability of the region. By varying U/W and Ntot/W and I, the phases of

semiconducting and metallic can be identied.

Figure 1.4: Phase diagram of charge transfer model. Two parameters I/W=1 and n0/W=0.4 are xed. The caption indicates regions of dierent electron structure. The red lineshows the half lling of the impurity band. The gure is from Ref. [28].

1.3 Carbon-Based materials

Defect-induced ferromagnetism had been found in highly oriented pyrolytic graphite (HOPG)

earlier than in oxides [29]. Esquinazi et al. designed an experiment to investigate proton

implanted graphite. Protons were implanted into the same sample area for several times and

the implantation uence of each time was dierent. The corresponding magnetic properties

were measured. In Figure 1.5, a strong dierence between the irradiated region and unir-

radiated region of the same irrdiated spot was revealed by measurements of magnetic force

microscopy (MFM) and atomic force microscopy (AFM). These results conrmed that the

ferromagnetism comes from defects.

By SQUID magnetometry, the measured magnetic saturation strongly depends on the

proton uence [29]. The maximum saturation magnetization is 4.5×10−6 emu, but the

maximum did not occur in the highest uence sample. This indicates that formation of fer-

romagnetic coupling needs sucient defects, but redundant defects also damage the magnetic

order. How to nd the optimal experimental parameters for maximizing ferromagnetism is

1.3. CARBON-BASED MATERIALS 7

Figure 1.5: AFM and MFM images of a spot on the graphite irradiated with a 2.25 MeVproton beam and a uence of 50 nC/µm2. The AFM image reveals the beam impact area. Aline scan through its center reveals a deepening of about 70 nm in 5 µm distance. The MFMimage suggests a magnetic ring around the impact area. The measurements were done atambient conditions using a low moment tip and without applying any magnetic eld. Thegures are from Ref. [30].

a long-term problem for this topic.

After the publication of ferromagnetic graphite, some researchers have focused on deter-

mining the defect types and the coupling mechanism. Yang et al. used 12C+ to irradiate

graphite (uence 1×1015cm−2, energy 70 keV) [31]. Their positron annihilation spectroscopy

(PAS) results revealed that defects are vacancies and vacancy clusters. Their calculation us-

ing density functional of theory (DFT) also suggests the magnetic moments are from the

vacancies. Almost of the same time J. Cervenka et al. provided another evidence of defect-

induced ferromagnetism [32]. Their results of AFM, MFM, and electrostatic force microscopy

(EFM) show a certain boundary state which can lead to ferromagnetic coupling. However,

this coupling cannot introduce a magnetization as strong as in their SQUID measurement.

So they proposed a new 3D model to explain this paradox. When the direction of a grain

boundary has a slight displacement of the armchair edge, two possible congurations can

lead to ferromagnetism (Fig. 1.6). (a) a long armchair and short zigzag edge or (b) a long

zigzag and short armchair edge. Only the zigzag edge is able to generate magnetic order

since it has peculiar localized state [33]. If those boundary states are composed as shown

in Fig. 1.6(c), strong ferromagnetic coupling occurs at the boundary. To some extent, this

mode not only reveals the mechanism of ferromagnetism but also shows one possibility of

ferromagnetic coupling in the bulk graphite.

To further probe the coupling mechanism in a microscopic view, Ohldag et al. measured

the proton irradiated, ferromagnetic graphite by X-ray magnetic circular dichroism (XMCD)

[30]. The advantage of XMCD is its element-specic nature, since the core electrons of each

element have an unique energy to be excited to certain outer shell levels. Assuming that the

ferromagnetism originates from carbon-related defects, such as vacancies, the carbon related

X-ray absorption should show a XMCD eect. Two ways were used to collect the XMCD


Figure 1.6: Defect congurations in graphite : (a) A long armchair conguration, (b) a longZigzag conguration, (c) 3D model for 2D in-plane magnetized grain boundary. The guresare from Ref. [32].

signal. One is to x the applied eld, and then change the polarization of the incident light.

The other one is to x the polarization of incident light, and then change the direction of

the applied eld.

As shown in Figure 1.7, three typical energies were selected: 280 eV, 284 eV and 291 eV.

These energy ranges correspond to the pre-edge, π? resonance, and σ? resonance, respec-

tively. µ and σ stand for the direction of applied eld (µ± =± 600 Oe) and helicity (σ±=±1), respectively. The signal has the strongest contrast at 284 eV, so the ferromagnetism

should come from the π? electron. In 2010, Ohlag et al. subsequently reported on the

XMCD measurements of proton irradiated graphite and also pointed out that the hydrogen

absorption on the graphite surface probably plays a key role [34].

Defect-induced ferromagnetism in both graphite and graphene has been intensively in-

vestigated theoretically. Structural defects, in general, can give rise to localized electronic

states. It is well accepted that the in-plane vacancies are the origin of the local magnetic

moment [35]. Upon removal of one atom, each of the three neighboring atoms has one sp2

dangling bond. Two of them can form a pentagon, leaving one bond unsaturated. This

remaining dangling bond is responsible for the magnetic moment. Moreover, the at bands

associated with defects lead to the increase in the density of states at the Fermi energy.

Lehtinen et al., used spin-polarized DFT and demonstrated that vacancies in graphite are

magnetic [36]. They also found that hydrogen will be strongly absorbed at vacancies in

graphite, maintaining the magnetic moment of the defect. Zhang et al. [37] have conrmed

that the local moments appear near the vacancies and with increasing vacancy accumulation

the magnetization decreases nonmonotonically. Using a combination of mean-eld Hubbard

1.3. CARBON-BASED MATERIALS 9

Figure 1.7: Carbon K-edge absorption spectrum (right) obtained from graphite irradiatedat room temperature (black curve) and at 560 C substrate temperature (red curve). Thearrows indicate the photon energies at which the STXM images (left) were recorded for aspot irradiated at 50 nC/µm2 in the sample. The helicity (σ) of the X-rays was reversedbetween the rst and the second row of images (left images in the gure). For the third rowthe direction (µ) of the applied eld was reversed compared to the second row. For the rstand the third rows, both polarization and applied eld are opposite. Images recorded at theπ? resonance (284.0 eV) exhibit a clear XMCD signal. The gures are from Ref. [30].

model and rst principles calculations, Yazyev also conrmed that vacancies in graphite and

graphene can result in net magnetic moment [38]. However, the preserved stacking order

of graphene layers is shown to be a necessary condition for achieving a nite net magnetic

moment of irradiated graphite. In most calculations, the moment per vacancy is sizeable

up to 12 µB [36, 37]. Indeed, by scanning tunneling microscopy experiments, Ugeda et al.

have observed a sharp electronic resonance at the Fermi energy around a single vacancy in

graphite, which can be associated with the formation of local magnetic moments [39].

Also since the report by Esquinazi et al. [29], the debates on ferromagnetic (Fe, Co,

or Ni containing partially lled 3d orbitals) contamination began, since transition metal

nano-inclusions can also create such weak ferromagnetic signal. Esquinazi et al. did the

purity test by Rutherford Backscattering Spectrometry (RBS) and Particle-induced X-ray

emission (PIXE), and the results show that the trace contamination of 3d element can not

introduce such strong magnetic moment [40, 41]. However, the virgin graphite samples are

found hardly pure and are often ferromagnetic without proton irradiation (Supplementary

Materials of ref. [35]).

Nair et al. [35] applied two methods to introduce defects into graphene: (1) Fluoridation

of graphene from a few percent to approaching 100 percent by increasing the number of F

adatoms. (2) Implantation of protons or carbon ions (350-400 keV) into graphene. They

did not detect any ferromagnetism in their graphene samples prepared by both methods.

However, only paramagnetism is measurable and the paramagnetism increases with defect

concentration as shown in Fig. 1.8. They claimed that the ferromagnetism in irradiated


graphite is due to Fe contamination on the boundaries after carefully checking dierent

graphite suppliers (as shown in Fig. 1.9).

Figure 1.8: (left) a and b: Optical images of starting (a) and fully uorinated (b) graphenelaminates. The scale bar is 2 cm. The laminates consist of 1050 nm graphene crystallites,predominantly mono and bilayers, aligned parallel to each other (as seen in a scanningelectron microscope), rotationally disordered and, consequently, electronically decoupled.(right) Magnetic moment ∆M (after subtracting the linear diamagnetic background) as afunction of parallel eld H for dierent F/C ratios. Symbols are the measurements and solidcurves are ts to the Brillouin function with S = 1/2 and assuming g = 2. The gures arefrom Ref. [35]

.

Ney et al.. investigated vertically aligned graphene nanoakes. They introduced defects

by He ion implantation (Energy: 100 keV and Fluence: 1011 - 1017 cm−2) [42]. There is

no ferromagnetism detected in their samples. The observed paramagnetism depends on the

implantation uence, similar to Nair's report [35]. For other carbon-based materials, Höhne

et al. investigated the magnetic properties of diamond implanted with boron, uorine, and

iron [43]. All the implanted diamonds are still diamagnetic, however some paramagnetic cen-

ters indeed induced by the implanted impurities. After subtracting diamagnetic background,

the ferromagnetic-like loop was too weak to be identied.

1.4 Silicon carbide

SiC is another kind of carbon-based materials, which was very recently found to be ferro-

magnetic upon introducing defects by ion implantation and neutron irradiation [44, 45]. SiC

has several advantages in comparison to other carbon materials. First, high-purity SiC is

available on the market [46, 47]. SiC has much lower impurity concentrations compared with

graphite [48]. Second, SiC has been widely used in electronics industry and it has better

compatibility with microelectronics than other carbon-based materials. A brief review of

defect-induced magnetism in SiC will be presented as the background before discussing our

results.

1.4. SILICON CARBIDE 11

Figure 1.9: (a) SEM images of graphite A (top) and sample H (bottom) samples in back-scattering mode. Small white particles are clearly visible in both images, with typical sep-arations between the particles of 100 µm for sample A and 240 µm for sample H. Insetsshow zoomed-up images of the particles indicated by arrows; both particles are around 2µm in diameter. (b) SEM images of the same particle found in a sample B sample taken inbackscattering (top) and secondary electron (bottom) modes. Surface features are clearlyvisible in the SE image while BS is mostly sensitive to chemical composition. The contrastaround the particle in the SE mode is due to a raised surface in this place. (The gures arefrom ref. [35] and its supplementary materials.)

In the experiments from our group [44], the commercial 6H-SiC ((0001) single crystal

wafer from the KMT Corporation, Hefei, China) was implanted with Ne+ ions at an energy

of 140 keV. The uences were 5×1013, 1×1014, 5×1014, and 1×1015 n/cm−2. As shown in

Fig. 1.10, pronounced ferromagnetic hysteresis loops were observed after implantation. The

maximum moment occurred at the sample with the uence of 1×1014 n/cm−2. The high-

uence irradiation deteriorates the crystalline quality, therefore, decreases the saturation

magnetic moment. Corresponding Raman spectra are shown in Figure 1.11. The intensity

of Raman models decrease with uence increasing. The sample irradiated with the highest

uence is totally amorphous. The origin of the magnetism was tentatively attributed to

SiV CV divacancies.

Another work appeared regarding the ferromagnetism in Cu-implanted 6H-SiC by Zheng

et al. [49]. 200 keV Cu+ ions were implanted into 6H-SiC single crystal at room tempera-

ture with uence of 8×1015 cm−2. After implantation, ferromagnetism has been observed at

room temperature. The authors also performed detailed structural characterization by dif-

ferent methods. By high-resolution X-ray diraction and X-ray photoelectron spectroscopy,

they could exclude any ferromagnetism-related secondary phase. However, their positron

annihilation lifetime spectroscopy results show that the main defect type is silicon vacancy

and the concentration of it increases after Cu implantation. With the help of rst-principles

calculations, they conclude that the magnetic moments come from the 2p orbitals of C atoms

and 3d orbitals of Cu dopant.

Before the defect-induced magnetism was found in SiC, irradiation induced defects in SiC

had been intensively investigated by several research groups. N. T. Son et al. investigated


-5000 -2500 0 2500 5000

-3

-2

-1

0

1

2

3

Field (Oe)

Mag

netiz

atio

n (e

mu/

g) 5E13 1E14 5E14 1E15

@ 5 K

Figure 1.10: Neon implanted SiC: Magnetization vs. eld was measured at 5 K and thediamagnetic background has been removed. All the samples are from the same wafer. Theresult has been published in ref. [44].

Figure 1.11: Raman spectra of Ne+ irradiated SiC sample (This gure is from ref. [44]).

1.5. ORGANIZATION OF THIS THESIS 13

an on-axis VSi-VC defect in 4H-SiC (in Fig. 1.12) by electron spin resonance (ESR) [50].

This conguration corresponds to C3v symmetry [50]. Three dangling Si bonds surround

VC and three dangling C bonds surround VSi. Their rst-principles calculation shows that

the ground and charge states of the divacancy is the high spin state (S=1). Two electron

levels arise due to this defect in the band gap. One is below the mid-gap and is generated by

dangling bonds of VSi. Two electrons occupy this level and their spins are parallel with each

other. The other electron level is above the mid-gap and is generated by dangling bonds of

VC . Divacancy can also be charged. In 4H-SiC, three electrons can occupy the upper defect

level which is localized at the carbon vacancy. Positively charged states were also reported.

The corresponding ESR signal was found at 77 K; however, at 293 K only a weak signal has

been detected in dark [51]. This eect implies that high temperature can thermally ionize

the charged defect states into the neutral states.

Slow positron implantation spectroscopy (SPIS) is another method to investigate defects

and defect clusters with open volume. Li et al. reported that the charged defect should

be di-vacancy by tting S parameters [44]. Defects are distributed in a surface layer and

the maximum depth is about 460±25 nm. They also found the S curves are similar for the

uence below 1×1015 n/cm−2. When the uence is 1×1015 n/cm−2, the defective region of

the sample is shrinked into 120 nm. This indicates that defects begin to agglomerate when

the uence is high, which is in coincidence with Raman data and it can also explain the

weakening of ferromagnetism with increasing the uence.

There are few theoretical reports of defect-induced ferromagnetism in SiC. Y. Liu et al.

[45] made rst-principles calculations and found that defect states induce local moments and

the extended tails of defect wave functions favor long-range spin couplings. They considered

three charge congurations of the nearest divacancies: (0,0) (+,+) (-,-). Only the charged

cases can form a stable ferromagnetism coupling.

On the one hand, none of the published works about SiC, there is any experimental

evidences that the magnetic order could occur uniformly in the whole matrix.

1.5 Organization of this thesis

As shown in this short introduction, the controversy and wide scattering in experimental

observations for defect-induced ferromagnetism still remains.

1. Summarizing the experimental reports, the 2p states of C, N and O atoms appear to be

necessary for the defect-induced magnetism. The strongly localized nature of defect

states can lead to spontaneous spin polarization and local moment formation [52].

Therefore, to investigate such a phenomena, one should select materials containing C,

N, or O elements.

2. To investigate defect-induced magnetism in graphite or graphene, one should be careful

with the sample quality and the substrates. At least from recent communications

[53, 54], the graphite samples supplied from dierent companies could be dierent.

3. For nitride materials, special caution should be paid to the substrates since it is com-


Figure 1.12: Si and C neighbors of divacancy in the axial conguration. The gure is fromRef. [50].

mon to use sapphire or SiC as the substrates, both of which actually can be ferromag-

netic [9, 44].

Therfore, to our knowledge, the best test-bed for defect-induced magnetism could be

single crystalline SiC, which can be prepared in microelectronics grade and can be supplied

at large quantity.

In this thesis we will focus on the formation of point defects and on the building of a

correlation between ferromagnetism and defect type/concentration in SiC. Defects will be

introduced by ion implantation and by neutron irradiation so as to stay in the low dpa

(displace per atom, see chpater 2) (<0.1) range. The defective SiC will be characterised

by various spectroscopic techniques and the magnetic properties will be studied. The main

scientic objectives include:

1. To reveal the structural modication in ferromagnetic SiC upon ion implantation

(Chapter 3);

2. To characterize the magnetic properties in detail, e.g. the magnetic phases and

anisotropy (Chapter 4);

3. To make an one-to-one correlation between magnetism and defects (Chapter 5);

4. To examine if the defect-induced ferromagnetism can occur in bulk samples (Chapters

6 and 7).

Chapter 2

Experimental Methods

In this chapter, I describe the main experimental techniques used in my thesis work. Ion im-

plantation and neutron irradiation were used to introduce defects into samples. A supercon-

ducting quantum interference device - Vibrating Sample Magnetometery (SQUID-VSM) was

used to characterize the magnetic properties by varying the external eld and temperature.

Particle induced X-ray emission spectroscopy was performed for detecting contamination.

2.1 Ion Implantation

Ion implantation is a material engineering process. Ions are accelerated in an applied electri-

cal eld and then are implanted into the target materials. This process is used to modify or

even change the chemical and electrical properties of the target materials. In 1952, Ohl [55]

reported that the electrical characteristics of silicon point-contact diodes can be improved by

bombarding the surface with dierent gas ions. In 1954 W. Shockley′s patent Forming Semi-

conductive Devices by Ionic Bombardment" was an milestone for this technique [56]. Until

1998 more than 8000 implantation machines have been under operation in semiconductor

industry.

For defect-induced ferromagnetism, the primary issue is to maximize the magnetization

by optimizing parameters, such as defect type, concentration and distribution in target

materials. It is important to understand how these parameters are inuenced by the ion

energies and uences in the process of ion implantation and neutron irradiation.

2.1.1 Energy loss

When a high energy ion is implanted into a target material, the ion will be slowed down

by a series of collisions with target atom nuclei and electrons. In this process, the incident

ion transfers a part of its energy to the target matrix. The stopping force is dened as the

energy loss per unit path length:

S(E) =dE

dr(2.1)

where E is the kinetic energy of the incident particle, and r is the path length.

The physical meaning of S(E) is the average delivered energy when summed over all

15

16 CHAPTER 2. EXPERIMENTAL METHODS

probabilities of each scattering process. Since dierent materials have unique S(E), S(E) is

used to characterize the property of the target materials.

2.1.2 Stopping and Range of Ions in Matter

Stopping and Range of Ions in Matter (SRIM) is a collection of software packages [57].

This software can be used to calculate many parameters of the transport of ions in matter

by Monte Carlo simulation. In this thesis, SRIM is used to calculate the depth prole of

defects in ion implanted SiC. The depth proles for 500 keV Xe ions implanted in SiC is

shown in Figure 2.1. A mean depth and a standard deviation are obtained by tting the

implantation depth proles with a Gaussian function. In SRIM, the mean depth and the

standard deviation are dened as projected range ( Rp in Figure 2.1) and straggle ( σ in

Figure 2.1), respectively. In this case Rp is about 130 nm. As a rst approximation, Rp and

σ increase linearly with increasing implantation energy. The typical lateral dimensions of

the implanted samples are in wafer scale because the beam usually sweeps over the whole

area. Thus the lateral ion distribution can be treated as uniform.

0 500 1000 1500 2000 2500-2

0

2

4

6

8

10

12

14

16

Depth (Å)

TRIM Xe depth profile

Gaussion

sam

ple

surfa

ce

Rp

Rp = 1300 ÅÅ

(ATO

MS

/cm

3 )/(A

TOM

S/c

m2 )

10

4

Figure 2.1: Xe ion prole from a SRIM simulation for 500 KeV Xe implantation in SiC atan angle of 15o: the Xe depth prole and a Gaussian curve with the project range (Rp) andstandard deviation (σ).

In general, SRIM simulations are well conrmed by experiment, but there are some

exceptions. For example, if the implanted ions are mobile during the implantation, the ions

will diuse into the matrix. So the real Rp is larger than the simulated value.

2.1.3 Direct beam eect: Collision cascade and primary defects

Some basic parameters should be claried before discussing collision cascades and primary

defects.

2.1. ION IMPLANTATION 17

• Threshold displacement energy (TDE)

In a solid, TDE means the minimum energy needed to permanently displace an atom

from its original lattice site to form a defect [58]. The typical value in semiconductors

are about 15 eV, and 25 eV for metals.

• Lattice binding energy (LBE)

Each recoiling target atom loses energy (LBE) when it leaves its original site or recoils

in the target matrix. Typical values are 1-3 eV, but for most of compounds, this value

is unclear.

When an ion is implanted into a solid, the ion will induce a set of energetic collisions

with adjacent atoms. In a collision, if the host atoms obtain a kinetic energy higher than

the TDE of the target material, the host atoms can permanently leave their lattice sites

and form defects. These displaced atoms can further displace other adjacent atoms. This

process is called "collision cascade". These collision cascades mainly create damage during

ion implantation in metals and in semiconductors. The simplest defects generated in col-

lision cascades are primary defects, for example, a Frenkel pair of vacancy and interstitial.

Empirically, the maximum damage distribution of these primary defects is nearer to the

surface than the dopant distribution. Figure 2.2 shows an example of vacancies which are

created by Xe ions and recoiled-ions in SiC, respectively.

Mazzone simulated the defects distribution in ion-implanted Si by Monte-Carlo method

[59]. In his results, the dominated defects are Frenkel pairs, and the defect region can be

clearly divided into two parts according to the depth proles. The region from surface

to 0.8Rp is the vacancy rich region while the region between Rp to 2Rp is the interstitial

rich region. Especially, for low and medium energy irradiation (about a few hundred keV )

interstitials are the dominant point defects because the nature of ion implantation is non-

conservative. That means the number of incident ions will be far in excess of the available

unoccupied lattice sites. For the vacancy rich region, a small tensile strain can be detected by

X-ray diraction. This agrees with the most reported experimental results of defect-induced

ferromagnetism by ion implantation.

2.1.4 Indirect beam eect: Beyond the primary defects

Beside primary defects, other complex defects or amorphization are also considered in this

topic. There are two main mechanisms relating to these defects' diusion and annealing. In

some cases the interstitials diuse towards the surface, and recombine with vacancies. In

other cases, diusion will lead interstitials to aggregate into a bigger defect complex. This

situation also happens in vacancies, i.e vacancies can also aggregate.

When the defect regions are heavily overlapping, amorphization can happen. Meanwhile

for a sample to remain amorphized it also needs to overcome the dynamic annealing. The

time scale of a collision cascade is 10−11 s. The disorder will be kept, if the discrete defects

are immobile after collision. But if the defects are mobile at the implantation temperature,

pronounced dynamic annealing will happen. This process accompanies the whole implanta-

tion procedure .


0 1000 2000 30000.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

sam

ple

surfa

ce

Depth (Å)

Num

ber/(

Angs

trom

-Ion) C target vacancies

Si target vacancies

Figure 2.2: Distribution of Si and C vacancies in SiC which are created by Xe ions (500 keV)and recoiled-ions, respectively.

The eciency of dynamic annealing greatly depends on various factors, for example the

target materials, implanted ions, ion uence, energy, ux and incident angle. For some

materials the dynamic annealing is strong enough to suppress amorphization of the target

materials. Normally, the dynamic annealing eect is stronger at higher implantation tem-

perature. In some cases, the implantation is performed at liquid nitrogen temperature to

avoid dynamic annealing.

2.1.5 Displacement per atom (DPA)

One quantitative parameter to characterize the amount of defects is the displacement per

atom (DPA). The denation of DPA is the number of times that an atom in the target is

displaced at a given uence. DPA can be calculated by the SRIM code. In previous reports

about defect-induced ferromagnetic SiC, the optimized peak DPA is mostly less than 10−1.

For details about ion implantation, please refer to the published book [60].

2.2 Neutron irradiation

Neutron irradiation is a process of using free neutrons to ionize target materials. Compared

with ion implantation, neutron irradiation has two major features. Firstly, neutron irradi-

ation does not introduce ingredient ions into the matrix. Secondly, neutron has a stronger

capability to penetrate the target sample. So the induced defects are distributed in the

whole sample matrix, but are only at the surface region in ion implantated samples. Neu-

tron irradiation could provide the possibility to realize stronger defect-induced magnetism

in the bulk sample.

2.2. NEUTRON IRRADIATION 19

The disadvantage of neutron irradiation is the limited access to neutron sources. There

are three basic types of neutron sources.

Radionuclide neutron source

Radionuclide is the earliest neutron source. The neutrons have a short lifetime and the

ux is also weak. These characteristics make radionuclide still widely applicable in biology

and medical science.

Spallation neutron source

The spallation neutron source has been in use since 1980s. A typical spallation neutron

source includes several parts. First, a high energy accelerator generates high ux protons

of around 1 GeV. Then the protons bombard a target material which is usually made up

of heavy elements, such as uranium and tungsten. After that, nuclear reactions happen in

the target material and neutrons are released at the same time. Compared with ssion,

spallation can generate a higher pulse neutron ux (1×1017 n/cm2s−1 ) in a relatively small

volume and it has a wider energetic spectrum.

Nuclear ssion neutron source

Fission is currently the most widely used neutron source in the world. Neutrons come

from the ssion of isotope 235U. The limitation of heat dissipation in the reactor leads to a

smaller ux than spallation. Taking the example of the BER II (Helmholtz-Zentrum Berlin),

the neutron ux is about 1 to 2×1014 n/cm2·s−1. All our neutron irradiated samples in this

thesis were prepared at this source. Neutron temperature is also named as neutron energy

which indicates the kinetic energy of a free neutron. The energy distribution obeys Maxwell's

distribution. A higher temperature of the reactor generates higher kinetic-energy neutrons.

The wavelength of the free neutrons satisfy De Broglie's relation.

Usually neutrons can be classied by neutron energy, and table 1.1 shows a classication

:

Table 2.1: Neutron temperature [61]

Energy Range Name

0-0.025 eV Cold neutron0.025 eV Thermal neutron0.025-0.4 eV Epithermal neutron0.4-0.6 eV Cadmium neutron0.6-1.0 eV Epicadmium neutron1-10 eV Slow neutron10-300 eV Resonance neutron300eV -1 MeV Intermediate neutron1 MeV-20 MeV Fast neutron> 20 MeV Relativistic neutron

2.2.1 Dierence between ion implantation and neutron irradiation

A comparison between neutron irradiation and ion implantation has been done in Si and Ge

in 1978 by M.L. Swansonet et al. [62]. Before this report, it was known that the high ux


neutrons generated from ssion can amorphize Si if the irradiation time is long enough.

In the experiment by Swansonet, n-type Ge and p-type Si were used as targets. These

samples were irradiated with neutrons at low uence (5×1016, 5×1017, 2.5×1018 n/cm2,

ux 5×1012 n/(cm2·sec) and high uence (8×1019, 5×1020 n/cm2, ux 6×1013 n/(cm2·sec)Fission is currently the most widely used neutron source in the w·sec)), respectively. Dur-

ing neutron irradiation, the ambient temperature was about 50 C. The energy of primary

knock-on collision of ssion neutron irradiation was similar to 20-200 keV Si ion bombard-

ment. With the highest neutron uence (5×1020 n/cm2) the irradiated Si does not become

amorphous as evidenced from structure measurements. The average distance of primary

knock-on collisions of a sample with neutron uence of 5×1020 n/cm2 is 24 Å. Therefore the

damaged region overlap is large enough that the sample should be amorphous. However,

a transmission electron microscopy measurement (TEM) showed that the damaged regions

were still crystalline. They also annealed the sample (450 oC, 1 hour) and again analyzed

it using TEM. The results revealed the sample as microcrystalline with dierent crystalline

orientations. On the other hand for 100 keV Si ion self-implantation at room temperature,

silicon becomes amorphous when the uence reaches, 1×1016 n/cm2 [63].

In general, when the damaged regions begin to overlap, the cascade damage process will

lead to a high defect concentration. The high defect concentration reduces the chain length

of collision and then the energy is harder to deliver to the damage region in the form of a

collision. When the defect concentration goes beyond a critical value, the sample becomes

amorphized. Over the whole process, the ambient temperature should not be high, since a

higher temperature leads to stronger annealing eects.

Amorphization in solid requires the two key factors: ux and temperature. For ux, the

energy deposition rate of neutrons is 10−5 of the rate of ion bombardments. So neutrons

need a larger uence to get the same damage level as ions. It is one of the reasons why it is

hard to form amorphous structures by neutron irradiation. For temperature, in Swansonet's

experiment, the entire process of irradiation and annealing was carried out at 50 oC. At this

temperature most of defects were mobile and easily diuse out of the defect region and can

recombine.

This case provides us with several clues when we use ion and neutron irradiation to

investigate defect-induced magnetism. First, both methods could create a similar defect

state. However, ion implantation is the more eective method: generally the same uence

of ions will generate more defects. Second, with neutron irradiation it is dicult to achieve

amorphization. The limited ux, the lower energy deposition rate and the strong dynamic

annealing eect during neutron irradiation result in much longer processing time than ion

implantation to achieve the same damage level. But in most of reports about defect-induced

magnetism in SiC, ferromagnetism was only observed in samples with low ion uences.

That means a slightly damaged region with a low defect concentration. Therefore neutron

irradiation could be a better method to create this required damage across the whole matrix

and extend the defect-induced ferromagnetism from the surface layer to the bulk.

2.3. CONTAMINATION TEST 21

Figure 2.3: A typical PIXE spectrum for ZYA grade HOPG from Advanced Ceramicsrecorded with a collected ptoton charge of 4.98 C. The green curve is the measured data, theviolet and red curves are the background simulation and t to the data, respectively. Theextracted concentrations as well as minimum detecion limits are given and the correspondingX-ray lines from the detected elements are indicated. This gure is from Ref. [41].

2.3 Contamination test

2.3.1 Particle-induced X-ray emission

Particle-induced X-ray emission (PXIE) was used for trace element detection as a bulk

sensitive method [64]. It can detect an element in the ppm range whose atomic number is

larger than 12. In a typical PIXE setup, the ion source generates an ion beam, for example,

protons. These ions are accelerated to high energy, typically 2-3 MeV. Then they pass

through a bending magnet and collimator. Finally, they arrive at a high vacuum chamber

and bombard the target sample. The core electrons are excited by the injected ions and

are ejected out of the atom and leave a hole. Then the core will be relled by outer shell

electrons and will release energy in the form of an X−ray. The composition of the target

can be identied by measuring the energy spectrum of the emitted X−rays. Figure 2.3

shows a typical PIXE spectrum for ZYA grade HOPG. As one can see, even in the best

HOPG, Fe, CO, Ni contaminations are detectable by PIXE. On the other hand, Fe/Co/Ni

contaminations in SiC are below the detection limit of PIXE as shown in Figure 2.4.

2.4 SQUID-VSM

In this work, all the magnetic properties are measured by a superconducting quantum inter-

ference device vibrating Sample Magnetometer (SQUID VSM). Compared with a SQUID-

MPMS, SQUID-VSM has three improvements. First the liquid helium cost is about 5 L per

day which is mush less than for SQUID-MPMS. Second, less than 30 mins are required to

bring the temperature from 300 K down to 5 K. This is also much faster than MPMS. Third,

the measurement speed is 5-6 times faster while keeping the same sensitivity.

Figure 1.4 illustrates a simplied process of detection for SQUID-VSM. The supercon-

ducting detection coils are composed of a second-order gradiometer. The center part of the

detecting coils is a counterwound outer loop which can conceal the inuence of linear mag-


1 2 3 4 5 6 7 8 9 10101

102

103

104

105

NiCoIn

tens

ity (c

ount

s)

Energy (keV)

4H-SiC, Cree 6H-SiC, Hefei 6H-SiC, Shanghai

Fe

Figure 2.4: A typical PIXE spectrum from 6H-SiC used in this thesis. As shown in thespectrum, within the detection limit of our device, there is no Fe/Co/Ni contamination.

netic eld gradients and uniform magnetic elds. Only an induced current by a disturbance

of corresponding uniform magnetic eld will be detected. Then, the current is coupled to

SQUID for measurement. The SQUID converts the current to voltage with high sensitiv-

ity. For measuring the magnetization of the sample, the signal can be expressed with the

following equation.

V (t) = AB2 sin2(ωt), (2.2)

where ω is the vibration angular frequency, A is a scaling factor related to the magnetic

moment, B is the amplitude of vibration. Because sin2(ωt)=(1/2)-(1/2)cos(2ωt), if a lock-in

amplier is used to isolate the signal occurring at 2ω, most of the noise signal can be avoided

and the small disturbance at 2ω can be detected.

However, there are some external parameters that inuence the SQUID-VSM measure-

ment. For data interpretation, we should pay attention to these eects.

• Sample geometry eects

The standard sample is somehow a point-like sample. When the measured sample is

not point-like, the measurement can be less accurate. Especially, if the sample is longer

than the reference sample, more magnetic ux will be generated at either end of the

sample. The extra ux will be picked up by the counterwound detection coils in order

to reduce the magnetic moment. On the contrary, if the sample is smaller than the

reference sample, the spatial response curve is taller and generates a stronger magnetic

moment.

• Sample holder eects

2.4. SQUID-VSM 23

Figure 2.5: VSM working principles and Quantum Design SQUID-VSM system [65].

Sometimes the sample holder also induces some errors in the measurement, so it is

better to measure the sample holder and judge its contribution. For our SQUID-VSM

system, two kinds of holders are available, brass and quartz. The quartz holders are

fragile and brittle and are used for the high sensitivity and accuracy measurements,

otherwise the brass sample holder is easier to handle.

• Vibration amplitude and frequency eect

For the vibration amplitude, according to equation 1.3, the output voltage quadrati-

cally depends on the amplitude of vibration. We should increase the vibration ampli-

tude if the signal is too weak.

For the vibration frequency, in comparison with copper-detection-coil vibrating sample

magnetometers (CDC-VSM), a change of magnetic ux does not directly generate a

signal in SQUID-VSM but it is used to create an input signal for the lock-in amplier

to separate the signal from instrumental artifacts. The vibration frequency does not

determine the strength of the signal and increasing frequency can not improve the

signal-to-noise ratio. In most cases, there is no reason to change the default frequency.

However, if the VSM is strongly inuenced by additional noise, for example, electro-

magnetic or mechanical resonances in the lab, the frequency setting can be adjusted

to oset these noises.

• Sampling time and precision

In general, increasing meassurement time can signicantly improve the sensitivity. In

theory, if the signal is weaker than 1×10−9 emu, we need more than 100 seconds to

measure each data point. In practice, the precision is about 1×10−8 emu. Then,

when the signal is larger than 1×10−8 emu, 0.25 second is adequate for a precise

measurement. In our experiments, we usually use 4 seconds to measure one data

point.


2.5 X-ray absorption spectroscopy

For X-ray absorption spectroscopy, here we describe several basic concepts and practical

factors for experiments which are related to this thesis. Refs. [66] and [67] can provide more

detailed information.

X-ray absorption spectroscopy (XAS) is a widely used technique for detecting the local

electronic structure of materials. This technique requires an intense and tunable X-ray beam

and it is generally preformed at synchrotron radiation light sources. The high-energy X-ray

beam excites core electrons into the outer shells or directly out of the sample surface. The

electrons coming out of the surface will produce a current in an applied electric eld and

the outer shell electrons will go back to the core and emit uorescence. So XAS data can

be recorded through the current or by the uorescence. Since each element has dierent

energy levels, this technique is element specic. Samples for XAS can be liquid, gas-phase,

or solids. For this thesis, the main concern are the electronic congurations of defects in SiC

and graphite .

2.5.1 XANES and EXAFS

According to the energy range of the incident X-rays, a XAS spectrum can be divided into two

parts. These are the X-ray Absorption Near Edge Structure (XANES, also called NEXAFS:

near edge X-ray absorption ne structure) and Extended X-Ray Absorption Fine Structure

(EXAFS), as shown in Figure 2.6. If we set the jump edge as the 0 point, XANES is the

part of spectrum whose energy range is from -50 eV to 50 eV or 100 eV. The part of spectrum

higher than this range is EXAFS. XANES and EXAFS provide dierent information. For

EXAFS, the multi-scattering mode can be used to extract several physical parameters, such

as the Debye-Waller factor and conguration of neighboring atoms. XANES can be used

as a ngerprint technique to identify the presence of chemical species. Moreover, XANES

is weakly temperature dependent and so the in-situ monitoring of chemical reactions is

possible.

Figure 2.6: Regime of XANES and EXAFS of molybdenum metal. The gure is from Ref.[68]

In previous reports, XANES was performed to investigate the bonding states of defects in

2.5. X-RAY ABSORPTION SPECTROSCOPY 25

irradiated graphite [34]. So in chapter 5 and chapter 6, we also present the XANES spectra

for investigating the bonding states of defects in SiC and graphite.

2.5.2 Collection mode

As mentioned above, there are two main modes for signal collection: Electron yield mode

(EY) and uorescence yield mode (FY). Here, we just briey introduce the electron yield

mode. Electron yield mode has three types: Auger electron yield (AEY), partial electron

yield (PEY), and total electron yield (TEY). The TEY is the simplest detection technique

of the three. It only needs to collect all electrons which are excited out of the sample.

Comparing with the other two, the signal-to-background ratio of TEY is also the worst

one. However, since the device set-up is relatively easy, the TEY is widely used. In our

experiments, we mainly use the TEY mode.

2.5.3 XMCD

X-ray magnetic circular dichroism (XMCD) is the dierence of two XANES spectra which

are excited by incident X-ray beams with dierent circular polarization. The two spectra are

measured in a xed magnetic eld or in magnetic remanence condition. There is a two-step

mode to illuminate the basic principle. For 3d elements, XMCD is usually used to investigate

the transition from the L shell to the conduction d band. As Figure 2.7 shows, more spin

up (spin down) electrons in 2p3/2 are excited by the left (right) circularly polarized X-rays.

For the 2p1/2 states, the situation is opposite. This is the rst step. For the second step, the

transition obeys a selection rule [66] and photoelectrons will be excited into the valence shell

of the d band which can be treated as a spin detector. When the sample is ferromagnetic,

an imbalance of spin-up and spin-down states will appear in the valence shell.

To maximize the dichroic eect, the light wave vector has to parallel to the applied eld.

Otherwise a small angle Θ exists between them, the XMCD signal should be amended by

cosΘ. XMCD of Fe, Co, Ni normally will be processed by a sum rule to calculate the spin and

orbital contribution. However, sum rule is not suitable for carbon since the carbon 1s initial

state is non-spin-orbit split, so the XMCD can only be used to calculate the orbital moment

[71][72][34]. In addition, most of our carbon XMCD signals are too weak or too noisy to

calculate the orbital contribution. In this thesis, the XMCD is only used for detecting the

source of magnetism and for comparison with other reported defect-induced ferromagnetism

in graphite [34].

2.5.4 The tricks for measuring and processing XAS from the Carbon K-

edge

For a beam scientist, carbon is the most undesired element to be measured, because carbon

contamination can be hardly avoided, especially the contamination on the gold mesh which

is used for accounting the incoming photon ux I0. The contamination can absorb X-rays,

and nally it leads to additional peaks on the spectra.

There are two ways to prevent this problem:


Figure 2.7: Illustration of the two-step model for XMCD [69]. In the rst step the spin-polarized electrons are generated. In the second step they are detected by the spin-splitnal states. The gure is from Ref. [70].

• Clean the gold mesh before the measurement. Some groups have developed a gold

evaporator which helps to reduce the residual carbon signal. However, the thickness

of gold should not be too thick in order to have enough transmission.

• Before measuring the sample, record a TEY spectrum of a carbon-free surface which

can be used as the reference of I0. This reference sample only is used for identifying

the unexpected peaks. Beware, the I0 reference could be subjected to changes when

the time of a single measurement is too long because carbon will again accumulate.

Chapter 3

Structural and magnetic properties of

defective SiC

This chapter has been published:

Yutian Wang, Xuliang Chen, Lin Li, A. Shalimov, Wei Tong, S. Prucnal, F. Munnik,

Zhaorong Yang, W. Skorupa, M. Helm, Shengqiang Zhou, Structural and magnetic prop-

erties of irradiated SiC. J. Appl. Phys., 115, 17C104 (2014).

In this chapter, we present a comprehensive structural characterization of ferromagnetic SiC

single crystals induced by Ne ion irradiation. The ferromagnetism has been conrmed by

electron spin resonance and possible transition metal impurities can be excluded to be the

origin of the observed ferromagnetism. Using X-ray diraction and Rutherford backscat-

tering/channeling spectroscopy, we estimate the damage to the crystallinity of SiC which

mutually inuences the ferromagnetism in SiC.

3.1 Introduction

Defect-induced ferromagnetism in materials, which do not contain partially lled 3 d or

4f electrons, has recently entered the focus of condensed matter research [28]. It chal-

lenges the mJ paradigm for magnetism, where m stands for the local moment and J stands

for the interaction between the local moments. Experimentally, defect-induced ferromag-

netism was observed in many materials, including graphite [29, 73, 31, 74] and various ox-

ides [75, 76, 2, 77, 78, 79, 80]. SiC single crystals are emerging as another candidate for this

investigation and have been shown to be ferromagnetic after particle irradiation [44, 45]or

after aluminum doping [81]. The magnetization in SiC is found to sensitively depend on

the uence of ion or neutron irradiation. Compared with other materials, SiC is commer-

cially available at large scale with the microelectronic quality grade [48, 82]. In this paper,

we present a systematic structural investigation in correlation with the magnetic properties

of SiC prepared by Ne ion irradiation. A possible Fe, Co, or Ni contamination in SiC is

excluded by particle induced X-ray emission (PIXE) and by Auger electron spectroscopy

(AES) measurements. The appearance of ferromagnetism has been conrmed by electron

spin resonance (ESR) spectroscopy. Measurements of X-ray diraction (XRD) and Ruther-

27

28 CHAPTER 3. STRUCTURAL AND MAGNETIC PROPERTIES

ford backscattering/channeling spectroscopy (RBS/C) reveal the damage to the crystallinity

of SiC, which can extinguish the ferromagnetism in SiC.

3.2 Experimental methods

The 6H-SiC(0001) wafer purchased from KMT corporation (Hefei, China) is one-side polished

and semi-insulating. The same wafer was cut into smaller pieces which were implanted

with Ne ions at an energy of 140 keV. The ion uences were 5×1013, 1×1014 , 5×1014,1×1015 cm−2, and consequently the samples will be named as 5E13, 1E14, 5E14, and 1E15,

respectively. Magnetometry was performed using a MPMS-XL magnetometer from Quantum

Design. The ferromagnetic resonance was measured at 9.46 GHz by an electron paramagnetic

resonance spectrometer (Bruker ELEXSYS E500). PIXE was performed using 3 MeV protons

with a broad beam of 1 mm2, while AES was done by a scanning Auger electron spectrometer

Microlab 310F (Fisons Instruments). In order to evaluate the crystalline variation after ion

irradiation, synchrotron radiation XRD was carried out at the Rossendorf beamline (BM20)

at the ESRF with an X-ray wavelength of 0.1078 nm. As a complementary method, RBS/C

with 1.7 MeV He+ was used to quantitatively determine the ion-implantation-induced atomic

disorder of the Si sublattice in 6H-SiC.

3.3 Results and discussion

The magnetic properties of Ne irradiated samples at dierent temperatures have been re-

ported in the paper [44]. The inset of Fig. 3.1 shows the magnetization at 300K for all sam-

ples after subtracting the diamagnetic background. The virgin SiC only shows diamagnetism,

while sample 5E13 presents a ferromagnetic hysteresis. Fig. 3.1shows the magnetization at

300 K for all samples after subtracting the diamagnetic background. The saturation mag-

netization shows a nonlinear dependence with increasing Ne uence (defect concentration)

and reaches its maximum for sample 1E14.

3.3.1 Magnetic properties

The appearance of the ferromagnetism in ion irradiated SiC is further conrmed by ESR.

We have measured virgin SiC, sample 1E14, and one paramagnetic SiC in a broad eld

range. Only for sample 1E14, a broad ESR peak and a shift of the center of the resonance

at lower temperatures are clearly observed (Fig. 3.2). Even at 300 K, the ESR signal shows

a very large shift from the free-electron position (around 3300 Oe), showing that the sample

is ferromagnetic and has TC above 300 K. The g -factor increases slightly with decreasing

temperatures.

3.3.2 Contamination test

For the investigation of defect-induced ferromagnetism, the crucial issue is to carefully ex-

amine if the ferromagnetic contamination is actually responsible for the observed ferromag-

netism. The magnetization [Fig. 3.1] shows a clear dependence on the ion uence; however,

3.3. RESULTS AND DISCUSSION 29

Figure 3.1: Magnetization vs. eld measured at 300 K for all samples: the diamagneticbackground from the substrate has been subtracted. The magnetization was calculated byassuming a thin layer of 460 nm thickness. The inset shows the magnetization measured forthe virgin sample (black line) and sample 5E13 without subtracting the background.

Figure 3.2: ESR spectra of sample 1E14 at temperatures between 100 and 300 K: a broadresonance peak appears indicating ferromagnetic resonance. The black line indicates theresonance centers, which slightly change with temperature.


Figure 3.3: PIXE spectrum for the 6H-SiC wafer and a ferromagnetic sample by a broadProton beam. Within the detection limit, we donot observe any Fe, Co or Ni contamination.In comparison with graphite, SiC is better controlled in sample quality.

the magnetic contaminations are expected to be random or to increase with ion uence if

they are due to ion implantation. We further applied PIXE and AES to scrutinize Fe/Co/Ni

elements in our studied SiC specimens. Figure 3.3 shows the PIXE spectra for virgin SiC

and 5E13. In the spectrum, the narrow peak is from Si K-line X-ray emission. The broad

peak is due to the Bremsstrahlung background. No transition metal impurities were detected

within the detection limit of around 1 µg/g.

To exclude contamination introduced during implantation and handling of the samples,

we applied the surface sensitive AES method to the ferromagnetic pieces. For most elements,

the detection limit of AES is in the range of 0.01 to 0.1 at.%, which is around 1012 to 1013

atom/cm2 by assuming a detection depth of 2 nm. We measured both the front and back

sides for virgin and ferromagnetic SiC after Ne irradiation and did not observe any signal

from Fe/Co/Ni within the detection limit (not shown).

3.3.3 XRD and RBS Channeling

In order to correlate magnetization with structure, we performed XRD and RBS/C to check

the crystalline deformation and defects.

Figure 3.4 depicts the θ - 2θ scans at SiC(000 12) recorded for Ne ion irradiated 6H-SiC.

A virgin sample is also shown for comparison. All curves show a main sharp diraction peak

at the diraction angle θ = θBragg coming from the sample volume below the irradiated part.

The diraction peaks at the low angle side of the main Bragg peak (θ < θBragg) are the

characteristics of an expansion gradient of the lattice along SiC [0001]. The elastic strain

in the near surface region (∆d/d) can be deduced from the position of this satellite peak.

Except for the largest uence applied here (1E15), a fringe pattern is clearly visible. This

feature is due to the presence of the non-homogeneous lattice expansion along the depth and


Figure 3.4: AES spectra for virgin and Ne irradiated SiC measured on the front side. Thespectra measured on the back side are essentially the same as those measured on the frontside. Fe/Co/Ni contamination can be excluded within the detection limit.

arises from interferences between x-ray beams diracted from regions with the same lattice

spacing. The maximum value of the normal strain (∆d/d)M is estimated to be roughly

proportional to the uence. Furthermore, we also performed the corresponding reciprocal

spacing mapping (RSM) around SiC(000 12) (see Figure 3.5). Only a vertical streak coming

from the irradiated region of the crystals is observed. No broadening in the horizontal

direction (equivalent to a rocking curve) is measured as compared with that obtained from

virgin crystals. These observations indicate that the defects are randomly distributed point

defects or small defect clusters [83].

For the sample irradiated with the largest uence of 1E15 cm−2, the absence of the satel-

lite peak shows that the near-surface region of this sample is heavily damaged, i.e., no more

crystalline. Such a signal is consistent with a strongly defective crystalline lattice charac-

terized by the presence of extended defects: amorphous clusters or layer. The conclusions

from XRD observation are fully consistent with the observation by positron annihilation

spectroscopy, which reveals the clustering of vacancies.

The RBS/C spectra along the SiC[0001] axis are shown in Fig. 3.6 for virgin and for Ne

irradiated samples. The random spectrum is assumed equivalent to a completely amorphized

SiC, while the virgin spectrum corresponds to an essentially damage-free crystal. The min-

imum yield χmin, the ratio of the channeling spectrum to the random spectrum, is 2.3% for

the virgin SiC crystals at the surface region. For sample 5E13 (not shown), the channeling

spectrum is only slightly higher than the virgin sample. A peak in the damage depth around

150 nm is becoming visible for uences 5×1014 and 1×1015/cm2. Note that for sample 1E15

χmin is 93%, indicating the almost full amorphization at the damage peak. This is in agree-

ment with the threshold displacement per atom (DPA) values for amorphization reported in

literature [84]. DPA presents the irradiation eect considering both ion uence and energy

[57].


Figure 3.5: XRD 2θ/θ XRD scans of the virgin and Ne irradiated 6H-SiC recorded in thevicinity of the (000 12) reection. Labels correspond to the ion uences (in cm−2).

3.3.4 Correlation between ferromagnetism and structural parameters

Combining with the structural properties presented here, we are able to conclude a mutual

relation between defects (or defect concentration and type) and magnetization. As shown

in Fig. 3.7 , there is a narrow DPA window, within which the sample is ferromagnetic.

The initial introduction of structural disorder leads to pronounced magnetization. Further

increasing disorder induces the amorphization of the host SiC crystal and therefore decreases

the saturation magnetization. Approching to full amorphization, the saturation magnetiza-

tion nearly drops to zero.


Figure 3.6: Reciprocal space mapping of SiC(000 12). There is no indication of broadeningalong qx.The streak labeled CTR is the crystal truncation rod. The streak labeled PSD isdue to the transmittance function of the position sensitive detector.


Figure 3.7: A sequence of 1.7 MeV He RBS/C spectra 6H-SiC single crystal implanted with140 keV Ne ions at room temperature. A random spectrum and a channeling spectrum froma virgin sample are also included for comparison. The dashed line indicates the position ofthe damage peaks.

0

2

4

D(d

/d0)

(%

)

0

4 0

8 0

(c) Magnetization

at 5 K

(b) Disorder

cm

in(%

)

(a) Strain

0 .0 1 0 .1 10

1

2

M(e

mu

/g)

DPA

Figure 3.8: Evolution of the saturation magnetization, the Si-sublattice disorder, and themaximum strain with DPA. The gray area indicates the DPA range for optimizing theferromagnetism.

Chapter 4

Disentangling defect-induced

ferromagnetism in SiC

This chapter has been published:

Yutian Wang, Lin Li, S. Prucnal, Xuliang Chen, Wei Tong, Shaorong Yang, F. Munnik,

K. Potzger, W. Skorupa, S. Gemming, M. Helm, Shengqiang Zhou, Disentangling defect-

induced ferromagnetism in SiC, Phys. Rev. B., 89, 014417 (2014).

In this chapter, we present a detailed investigation of the magnetic properties in SiC single

crystals bombarded with Neon ions. Through careful measuring the magnetization of virgin

and irradiated SiC, we decompose the magnetization of SiC into paramagnetic, superparam-

agnetic and ferromagnetic contributions. The ferromagnetic contribution persists well above

room temperature and exhibits a pronounced magnetic anisotropy. We qualitatively explain

the magnetic properties as a result of the intrinsic clustering tendency of defects.

4.1 Introduction

Defect-induced ferromagnetism, also referred as d0 ferromagnetism in contrast to tradi-

tional ferromagnets containing partially lled 3d or 4f electrons, is continuously attract-

ing research interest [5, 28]. It not only challenges the basic understanding of ferromag-

netism, but also allows for potential spintronic applications, such as magneto-optics com-

ponents [85]. Defect-induced ferromagnetism was rst observed in carbon-based materials

[86, 29, 87] Ferromagnetism was subsequently reproduced in graphite by dierent groups

[88, 89, 90, 32, 91, 73, 92]and also in other carbon-based materials [93, 94, 95, 96, 97]. Later

on, defect-induced ferromagnetism was observed in various oxide insulators, including HfO2

[75], TiO2 [17, 1], ZnO [2, 98, 99, 100], and, very recently, in MoS2 [101, 102]. However, the

necessary use of thick substrates for growing those oxides makes the interpretation of magne-

tometry data complicated, i.e., one has to exclude any ferromagnetic contamination in their

substrates [9, 10]. For carbon-based material, Ohldag et al. have shown that the magnetic

order originates from the carbon π-electron system in proton irradiated graphite, or from

hydrogen-mediated electronic states in untreated graphite [30, 34]. On the other hand, the

authors conrmed that the main part of the magnetic order exists in the near-surface region

35

36 CHAPTER 4. DISENTANGLING DEFECT-INDUCED FERROMAGNETISM

[34], making the total measured moments smaller [around ( 1-10) × 10−6 emu per sample]

[30].

Very recently, SiC single crystals have been shown to be ferromagnetic after ion and

neutron bombardment [44, 45]or after aluminum doping [81]. Tentatively, it is proposed

that VSiVC divacancies form local magnetic moments arising from sp states which couple

ferromagnetically due to the extended tails of the defect wave functions [45]. As an important

technologic material, SiC is commercially available at large scale and with high quality at

the microelectronic grade [46, 47]. The impurity concentration of Fe or Ni is of the range

of 1014 atoms/cm3, which corresponds to 0.015 µg/g [48]. This impurity level is around one

order of magnitude lower than that of the purest graphite samples [82], for which the origin

of the defect-induced magnetism is still under intensive discussion [53, 54, 103]. Therefore,

SiC presents a suitable model system for studying defect-induced ferromagnetism in addition

to carbon-based materials.

In this chapter, we present a systematic magnetic investigation of SiC prepared by Ne ion

irradiation. As previous chapter shown, possible Fe, Co, or Ni contamination in virgin SiC

is excluded by particle induced x-ray emission (PIXE) detection. By carefully measuring

the magnetization of virgin and irradiated SiC, the induced magnetization in SiC can be

decomposed into paramagnetic, superparamagnetic, and ferromagnetic contributions. The

ferromagnetic contribution persists well above room temperature. Those results could pro-

mote further understanding of defect induced ferromagnetism.


To examine the impurities in the virgin wafer, we applied the PIXE technique using 2 MeV

protons with a broad beam of 1 mm2. As stated in Ref. [82], PIXE is accurate enough

to detect trace impurities in bulk volume that can lead to ferromagnetism larger than that

induced by the irradiation procedure. We used this technique to examine SiC wafers from

dierent suppliers (Cree and KMT Corporation). Within the detection limit, transition

metal impurities (Fe, Co, and Ni) can be excluded from all examined wafers. In this study,

we present the result based on one 6H-SiC wafer purchased from KMT Corporation. The

same wafer was cut into smaller pieces of 10×10 mm2 for further experiments. Therefore,

the starting materials in this paper are well controlled and free of variations. During the

irradiation experiment, the samples were pasted on a Si wafer by carbon tapes to avoid the

usage of metal clamps. After irradiation, the samples were carefully cleaned by rinsing with

acetone, isopropanol, and deionized water. During the whole procedure (cutting, irradiation,

and measurement), special cautions, such as only using ceramic or plastic tools, were paid

to avoid metal contamination. Moreover, in order to exclude possible contamination during

implantation, we applied Auger electron spectroscopy (AES), which is a surface sensitive

technique, to measure the samples at both the front and the back sides of the irradiated

samples. For most elements, the detection limit of AES is in the range 0.010.1 at. %,

which is around 1012 1013 atoms/cm2 by assuming a detection depth of 2 nm. Within the

detection limit, contamination by Fe, Co, or Ni can be excluded. For more details about the

PIXE and AES results, see Ref. [104].

4.3. PARAMAGNETISM IN VIRGIN SIC 37

The 10×10 mm2 SiC specimens with thickness of 0.5 mm were implanted with Ne ions at

an energy of 140 keV. The implantation was done at room temperature without heating or

cooling the sample holder. The details of the implantation and the magnetization dependence

on the ion uence were reported in Ref. [44]. In this paper, we select two sample with large

magnetization. The implantation uences were 5×10 13cm−2 to 1×1014 cm −2; thereafter thesamples are referred to 5E13 and 1E14, respectively. The implantation induced maximum

displacement per atom (dpa) was calculated using SRIM2003 [57] and is shown in Fig.

4.1. The dpa numbers have been estimated by using a mass density of 3.21 g/cm3 and a

displacement energy of 25 eV for both Si and C. In SRIM calculation the heating eect was

not taken into account. Magnetometry was performed using a SQUID-MPMS or SQUID-

VSM magnetometer from Quantum Design. The electron spin resonance (ESR) spectroscopy

was performed at 9.4 GHz using a Bruker spectrometer (Bruker ELEXSYS E500).

0 50 100 150 200 250 300 3500.00

0.02

0.04

0.06

Depth ( nm)

DPA

5E13 1E14

Figure 4.1: SRIM simulation of displacement per atom (dpa) in SiC by 140 keV Ne ionirradiation. The labels indicate the ion uence in cm2

4.3 Paramagnetism in virgin SiC

The eld-dependent magnetization of virgin 6H-SiC at 4.2 K, 5 K, and 300 K is shown in Fig.

4.2.(a). No hysteresis loop is observed at any measured temperature. The measurement at

300 K displays a typical diamagnetic behavior. However, one can observe a clear deviation

from the diamagnetism at 4.2 K or 5 K. The curves are not linear, which can only be

explained by the presence of paramagnetism


-4 -2 0 2 4 6 8

-2x10-5

-1x10-5

0

1x10-5

2x10-5

0 100 200 300

-2.5x10-5

-2.0x10-5

-1.5x10-5

-1.0x10-5

-5.0x10-6

0 1 2 3 4 5 6 7 80.0

2.0x10-6

4.0x10-6

6.0x10-6

8.0x10-6

Virgin 6H-SiC 300 K 5.0 K 4.2 K Fitting results (Curie law)

Mag

netiz

atio

n (e

mu/

mg) (a)

7 T

1 T

4 T

Mag

netiz

atio

n (e

mu/

mg) (b)

Field (T)

Experimental data J = 1/2 J = 1 J = 3/2

Virgin 6H-SiC, at 5 KParamagnetic contribution

Mag

netiz

atio

n (e

mu/

mg)

Field (T)

(C)

Temperature(K)

Figure 4.2: (a) Magnetization of virgin 6H-SiC at dierent temperatures. At larger eldand low temperature, one can see a deviation from the linear behavior: the indication of thepresence of paramagnetism. (b) Temperature-dependent magnetization (open symbols) ofvirgin 6H-SiC measured at dierent applied eld. All curves can be tted well (red solid lines)by considering a paramagnetic contribution with a diamagnetic background. (c) Fitting ofthe paramagnetism by Brillouin function with dierent J.The magnetization is normalizedby the whole sample mass.

4.4. MAGNETIC PHASES IN NE IRRADIATED SIC 39

Figure. 4.2.(b) shows the temperature-dependent magnetization under dierent elds.

For all curves, the large contribution represents the diamagnetic background, which is es-

sentially temperature independent. We t all the curves by Curie's law:

M = χd + CB

T, (4.1)

Where the χd is diamagnetic background, B is applied eld, T is the thermodynamic

temperature, C is the Cuire constant. The ted χd at dierent elds has been plotted in Fig.

4.2.(a) by the star symbols. The three curves in Fig 1 b (at 10000, 40000, and 70000 Oe) fall

into the same line of the eld-dependent magnetization measured at 300 K. Therefore, as a

rst order of approximation the paramagnetic component can be extracted by subtracting the

diamagnetism measured at 300 K, as shown in Fig. 4.2(c). The paramagnetic contribution

can be well tted by the Brillouin function:

M(x) = NJµBgJ [2J + 1

2Jcoth(

2J + 1

2Jx)− 1

2Jcoth(

1

2Jx)], (4.2)

Where gJ is around 2 obtained from electron spin resonance measurement shown in Fig.

4.3, µB is the Bohr magneton, and N is the density of spins. The curve can be well tted

by J= 0.5 corresponding to single electrons and N = 1.04×1018 µB/g. Thus, in the virgin

sample, the paramagnetic part originates from the electron spins, which probably reside

on defect sites. Previous reports have shown that isolated (Vsi,Vc) are dominant intrinsic

paramagnetic defects in SiC [48]. In high purity semi-insulating (HPSI) 4H-SiC, the intrinsic

impurity concentration is of the order of 2×1016 atoms/cm3 [48]. The impurities can induce

Si or C vacancies and antisites. So the defect concentration can be estimated to be 1×1017

atoms/cm3. In HPSI 6H-SiC [105], the impurity concentration is generally higher by one

order of magnitude than in 4H-SiC. Therefore, it is reasonably consider that the spin density

could reach 3.2×1018 µB/cm3 related to defects and impurities.

Paramagnetic centers in the virgin SiC have also been conrmed by ESR. The ESR

spectra exhibit a central line and some hyperne lines. The g factor is calculated to be

around 2.005, which is characteristic of free electron. From the line shape, the defect is very

probably a negatively charged Si vacancy [106].

The denitive identication requires a detailed angular scan to see the anisotropy of

the hyperne lines and a large amount of defects by neutron or electron irradiation [106],

which is beyond the scope of this work. It is worth noting that S=1/2 spins do not exhibit

magnetocrystalline anisotropy as the resonance eld of the central line does not change with

the sample orientation [106].

4.4 Magnetic phases in Ne irradiated SiC

In order to get a more precise picture of the magnetic properties in the Ne irradiated samples,

we have to consider the paramagnetic contribution in the virgin SiC, since most of the volume

remains intact. Figure 4.4(a) shows the comparison of the hysteresis loops measured at 5 K


Figure 4.3: ESR spectra for a virgin 6H-SiC sample used in this study at dierent tempera-ture. The eld is applied parallel to the sample surface[(0001)plane].

for the virgin SiC and for samples 1E14 and 5E13. In Fig. 4.4(b), we show the magnetization

of sample 1E14 after subtracting the diamagnetism and the paramagnetism originating from

the substrate. After this data treatment, the paramagnetic part can be mostly subtracted,

but not all. The slightly increased magnetization at the large-eld part [shown in Figs.

4.4(b)and 4.4(c)] indicates more than one magnetic contribution in the irradiated sample.

Nevertheless, we can estimate roughly the saturation magnetization to be around 0.3-0.4 µBper vacancy calculated from the SRIM simulation (see Fig. 4.1). In reality, this value can

be larger, as we possibly overestimate the amount of vacancies by neglecting the dynamic

annealing eect in the simulation.

Fig. 4.5 shows the hysteresis loops of sample 1E14 measured at dierent temperatures.

One can observe three features: (1) the hysteresis behavior persists above 300 K, (2) there

is only a slight decrease of the saturation magnetization, and (3)the coercivity changes for

dierent temperatures. The coercivity drops from 260 Oe at 5 K to 130 Oe at 50 K, and

then drops slowly with increasing temperatures. These features indicate the coexistence of

ferromagnetism and superparamagnetism [107, 108, 109].

Now we have to nd an approach to separate the superparamagnetic and the ferro-

magnetic contributions in the Ne irradiated SiC. While it is dicult to calculate separate

hysteresis loops for both contributions, the magnetic remanence and coercivity for super-

paramagnetism show distinct behavior compared with ferromagnetism upon increasing tem-

perature. Therefore, we can analyze the temperature-dependent magnetic remanence as

shown in Fig. 4.6 in order to decompose it into dierent components. For superparamag-

netism, the remanence and coercivity are more sensitive to the temperature increase [108].

To measure the remanence, we rst cooled the sample to 5 K at a large eld (10 000 Oe).

Then the eld was set to 10 Oe to compensate a possible small negative eld in the super-

conducting magnet. The remanence was measured during warming up. As shown in Fig.

4.6, the magnetic remanence measured at 10 Oe shows two distinct regimes with increasing

temperature: it decreases rapidly below 50 K and moderately above 50 K. This is consistent

with the coercivity change with increasing temperature shown in Fig. 4.5. The temperature

dependence of magnetization for superparamagnetism and single-phase ferromagnetism can


0 10000 200000.000

0.002

0.004

0.006

0 10000 200000

1

2

3

-10000 -5000 0 5000 10000-0.002

-0.001

0.000

0.001

0.002

(b) Sample 1E14 at 5 K

Subtracting DM and PM

Mag

netiz

atio

n (e

mu/

g) Subtracting DM

Subtracting DM and PMnormalized to the affected volume mass

Mag

netiz

atio

n (e

mu/

g)

Field (Oe)

(c) Sample 1E14 at 5 K

1E14

Virgin

Mag

netiz

atio

n (e

mu/

g)

5E13

(a) 6H-SiC at 5 K

Figure 4.4: (a)Comparison of hysteresis loops measured at 5 K for the virgin SiC and sam-ples 1E14 and 5E13.(b)(c) Magnetization at 5 K of sample 1E14 after subtracting dierentcontributions from the substrate. DM: diamagnetism; PM: paramagnetism. Before and aftersubtracting the diamagnetic background from the substrate, the magnetization is normal-ized by the whole sample mass (a), (b) and by the implanted mass (c), respectively. Theimplanted depth corresponds to around 0.1 % of the sample thickness.


0 1000 2000 3000

-1

0

1

2

100 K50 K

Mag

netiz

atio

n (e

mu/

g)

Field (Oe)

5 K

HC at different temperatures: 5 K: 260 Oe 50 K: 130 Oe100 K: 110 Oe300 K: 80 Oe

300 K

Figure 4.5: Hysteresis loops measured at dierent temperatures for sample 1E14. There isa fast drop of the coercivity from 5 K to 50 K, however, a slower decrease above 50 K. Themagnetization is normalized by the implanted mass corresponding to around 0.1% of thesample.

Table 4.1: Fitting results for samples 1E14 and 5E13 using Eq. 3.

Samples TC MS(0) n µ

1E14 762 K 3.6×1019 µB/g 4.1×1014/g 8.1×104 µB5E13 750 K 1.3×1019 µB/g 5.3×1014/g 4.5×104 µB

be described by their sum [110]:

M = Ms(0)[1− T/Tc]3/2 + nµ[coth(µH/kBT )− kBT/µH] (4.3)

The rst term refers to the spontaneous magnetization of the ferromagnetic contribution

at temperature below the Curie temperature and the second refers to the superparamag-

netism. For the term of ferromagnetism, Tc is the Curie temperature, Ms(0) is spontaneous

magnetization at 0 K, and kB is the Boltzmann constant. For the second term, n is the

density of superparamagnetic clusters and µ is the average magnetic moment of one super-

paramagnetic cluster.

As shown in Fig. 4.6, the temperature-dependent magnetization is well tted by consid-

ering both superparamagnetism and ferromagnetism contributions. The table I shows the

tting result.

For superparamagnetism the spontaneous magnetization can only appear below the

blocking temperature. Basically, for both samples, the contribution from the superpara-


0 50 100 150 200 250 300 350 4000.0

2.0x1019

4.0x1019

6.0x1019

(a) Sample 1E14

Experimental data Fitting result (FM+SPM) Fitting result (only FM) Fitting result (only SPM)

Mag

netiz

atio

n (

B/g

)

Temperature (K)0 50 100 150 200 250 300 350 400

0.0

1.0x1019

2.0x1019

Experimental data Fitting result (FM+SPM) Fitting result (only FM) Fitting result (only SPM)

Mag

netiz

atio

n (

B/g

)

Temperature (K)

(b) Sample 5E13

Figure 4.6: Magnetic remanence of Ne irradiated SiC samples(1E14,5E13):the large dier-ence occur around 50K. The data are shown without correcting for the diamagnetic andparamagnetic background, which is negligible due to the small eld. The solid lines are welltted by equation(3)

magnetic part drops to zero slightly above 50 K. For sample 1E14, the tting shows that

one superparamagnetic cluster contains 8.1×104 µB on average. In the light of a theoretical

calculation [45] each divacancy generates 2 µB . Assuming the magnetic moments arising

from neutral VSiVC divacancies, one magnetic cluster in sample 1E14 contains around 40

000VSiVC divacancies; however, it is dicult to correlate it to a physical cluster size. For

the ferromagnetic contribution, a best tting value of Curie temperature is around 760 K.

Although the saturation magnetization is dierent for samples 5E13 and 1E14 (see Fig. 4.4),

both of them show a similar behavior in the temperature-dependent magnetic remanence.

The ferromagnetic part of sample 5E13 is deduced to also have a TC value around 750

K. That means the magnetic properties in both ion irradiated SiC samples exhibit the same

nature. The interplay between the concentration of defects and the crystallinity results in

a dierent magnitude of magnetization. We will discuss the origin for the coexistence of

dierent magnetic phases in the next section.

The coexistence of dierent magnetic phases can also be evidenced by the zero eld

cooled/eld cooled (ZFC/FC) measurements as shown in Fig. 4.7. The ZFC magnetization

was measured by cooling the sample from 300 K to 5 K with zero eld, then a eld of 100

Oe was applied and the magnetization was measured during warming up. The FC curves

were measured by cooling the sample in a eld of 10 000 Oe, then at 5 K the eld was

decreased to 100 Oe and the magnetization was measured also during warming up. The

ZFC/FC curves for both samples are dierent from those of samples with a single magnetic

phase. For a superparamagnetic system (e.g., magnetic nanoparticles) the ZFC curve would

increase with temperature, peak at a particular temperature range, and nally merge with

the FC magnetization. For a ferromagnetic system, when the coercivity is larger than the

applied eld, the ZFC magnetization can be very small compared with the FC magnetization

and temperature independent below the Curie temperature. When the coercivity is small,

the ZFC curves superimpose on the FC curves [111]. For both SiC samples shown in Fig.

1.6, the ZFC/FC curves cannot be explained by a single magnetic phase. They can only be

understood, if assuming a superparamagnetic phase with blocking temperature around 50


0 50 100 150 200 250 300 3500.1

0.2

0.3

0.4

ZFC (1E14)

ZFC (5E13)Mag

netiz

atio

n (e

mu/

mg)

Temperature (K)

FC (5E13)

FC (1E14)

Figure 4.7: ZFC/FC magnetization for two irradiated SiC samples with Ne ion uences of5×1013/cm2 (5E13) and 1×1014/cm2 (1E14), respectively. The thermal irreversibility hasbeen observed for both samples. The data are shown without correcting for the diamagneticand paramagnetic background which is negligible due to the small eld.

K and a ferromagnetic phase with Curie temperature well above 300 K.

4.5 Magnetic anisotropy

M-H loops were also measured for ferromagnetic SiC with the eld both perpendicular and

parallel to the sample surface. Figure 4.8 shows the comparison of the magnetization along

two directions at 5 K. Note that the diamagnetic and paramagnetic backgrounds have been

subtracted for the magnetization along both directions. Obviously, the in-plane direction is

the easy axis. It is worth noting that we do not observe any signicant dierence in the M-H

loops along the two in-plane directions SiC [1010] and [1120].

Since the implanted layer is a thin layer compared with the bulk substrate(300 nm vs 330

µm), it is reasonable to discuss the anisotropy as a geometric eect, i.e., as due to the shape

anisotropy. We can reasonably assume a demagnetization factor 4π for the ferromagnetic

SiC [112]. The ferromagnetic volume fraction can thus be estimated to be 1.5×10−5, whichis around 5 nm given the sample thickness of around 330µm. The ferromagnetic thickness

is much smaller than the irradiation thickness (see Fig. 4.1) [113]. Due to the dynamic

annealing the vacancies in SiC can recombine with interstitial ions as well as redistribute,

nally resulting in thin planar regions which are ferromagnetic. Of course, we cannot exclude

other anisotropic sources, for instance, anisotropy induced by strain.

4.5. MAGNETIC ANISOTROPY 45

-20000 -10000 0 10000 20000

-0.010

-0.005

0.000

0.005

0.010

Mag

netiz

atio

n (e

mu/

cm3 )

Field (Oe)

H perp. SiC[0001] H para. SiC[0001]

Sample 1E14 at 5 K

4 MS: 580 emu/cm3

Figure 4.8: Magnetization vs. eld measured in-plane (eld perpendicular to the SiC [0001]axis) and out-of-plane (eld parallel to the SiC [0001] axis). A clear magnetic anisotropyis observed. The dashed line is used to approximately obtain the anisotropy eld. Themagnetization is normalized by the whole sample mass (a), (b) and by the implanted mass(c), respectively. The implanted depth corresponds to around 0.1% of the sample thickness.


4.6 Summary and Discussion

We have disentangled defect-induced ferromagnetism in Ne ion irradiated 6H-SiC. The mag-

netization can be decomposed to three contributions: paramagnetism, superparamagnetism,

and ferromagnetism. The ferromagnetism dominates at high temperature and its Curie tem-

perature is estimated to be 760 K. We also observed a pronounced magnetic anisotropy with

the in-plane direction as the easy axis.

Defect-induced ferromagnetism has been observed in graphite and oxides. For all-carbon

systems, various groups have shown that the vacancies are magnetic using spinpolarized

density functional theory (DFT). The moment per vacancy is sizable up to 1-2 µB [36, 37].

Indeed, by scanning tunneling microscopy experiments, Ugeda et al.have observed a sharp

electronic resonance at the Fermi energy around a single vacancy in graphite, which can

be associated with the formation of local magnetic moments [39]. At the same time, the

local environment of the vacancy in graphite is found to strongly inuence the magnetic

state. Mostly, hydrogen and nitrogen are found to play a positive role. Vacancy-nitrogen

or vacancy-hydrogen pairs result in a larger magnetic moment compared with the vacancy

alone.

For ferromagnetic SiC, a theoretical scenario concerning vacancies has been adopted.

First-principles calculations predict high-spin congurations for negatively charged Si va-

cancies in 3C-SiC [114]. For the case of 6H-SiC, DFT-based rst-principles calculations

show that each neutral divacancy (VSiVC , an adjacent Si and C vacancy pair) yields 2µBand the tails of the defect wave functions overlap, resulting in ferromagnetic coupling be-

tween adjacent divacancies [45]. Indeed, such VSiVC divacancies are observed by positron

annihilation spectroscopy in 6H-SiC after neutron and Ne ion irradiation. Considering the

magnetic properties of defective SiC presented in this work, we can envision the following

picture: (1) the defects in SiC are nonhomogenously distributed, (2) the isolated, uncou-

pled defects contribute to the paramagnetism, and (3) the coupled defects result in the

superparamagnetic and ferromagnetic components.

Now we discuss the simultaneous appearance of ferromagnetic and superparamagnetic

components in ion irradiated SiC. In ion irradiated graphite, a paramagnetic component cor-

responding to independent magnetic moments and a ferromagnetic contribution are observed

[115, 116].The ferromagnetic component shows a linear temperature dependence and can be

well explained by a two-dimensional Heisenberg model. Recently, by careful angular depen-

dent near-edge x-ray-absorption ne-structure analysis (NEXAFS), He et al. observed defect

electronic states near the Fermi level, which are extended in the graphite basal plane [117].

In chemically processed graphite, multilevel ferromagnetism was observed and is attributed

to the weak coupling between ferromagnetic regions and to the ferromagnetism inside the

defect regions [118]. Therefore, in ion irradiated SiC the ferromagnetic coupling is expected

to rst arise within regions with proper vacancy concentrations. Some regions are connected

to be big enough and behave as a ferromagnet. Some regions with ferromagnetically coupled

defects are small and behave as superparamagnets. However, the ferromagnetic and super-

paramagnetic components in the two samples irradiated with dierent uences 5E13 and

1E14 (Fig. 4.6 and Fig. 4.7) are very similar regarding the Curie temperature and the su-

4.6. SUMMARY AND DISCUSSION 47

perparamagnetic blocking temperatures. This fact essentially excludes a depth distribution

of defects as the origin of the magnetic inhomogeneity. In a recent work on Gd-doped GaN

using large-scale rst-principles electronic structure calculations [119], Thiess et al.nd that

intrinsically the Ga vacancies tend to cluster, resulting in the coexistence of ferromagnetism

and superparamagnetism, which could also explain the present experimental results in our

SiC.

As a conclusion, we have observed a magnetic inhomogeneity in SiC irradiated by Ne

ions. Three magnetic phases (paramagnetic, superparamagnetic, and ferromagnetic phases)

can be identied by numerical tting. Moreover, the ferromagnetic SiC samples exhibit a

pronounced magnetic anisotropy with the easy axis along the SiC(0001) basal plane. By

comparing with the model and experimental data in literature, we tentatively attribute the

magnetic properties to the inhomogenous distribution of defects in SiC and the preferential

clustering along the basal plane.

Chapter 5

Carbon p Electron Ferromagnetism in

SiC Single Crystal

This chapter has been submitted for publication:

Yutian Wang, Yu Liu, Gang Wang, W. Anwand, C. A. Jenkins, E. Arenholz, F. Munnik,

O. D. Gordan, G. Salvan, Dietrich R. T. Zahn, Xiaolong Chen, S. Gemming, M. Helm,

Shengqiang Zhou, Carbon p Electron Ferromagnetism in SiC Single Crystal, Scien-

tic Reports, submitted (2014).

Ferromagnetism can occur in wide-bandgap semiconductors as well as in carbon-based ma-

terials, when defects are introduced in an appropriate way. It is desirable to establish a

direct relation between such ferromagnetism and defects. Here, we succeed to reveal the

origin of defect-induced ferromagnetism using SiC as a prototypical example. We show

that the long-range ferromagnetic coupling is due to the p electrons of the nearest-neighbor

carbon atoms around VSiVC divacancies. Thus, the ferromagnetism is traced down to its

microscopic, electronic origin. Our results shall deepen the comprehension of defect-induced

ferromagnetism in solids.

5.1 Introduction

Unexpected ferromagnetism in many defective carbon based materials and wide bandgap

semiconductors was observed in highly oriented pyrolytic graphite (HOPG), HfO2, ZnO,

SiC and graphene [29, 75, 98, 45, 120, 121], which provides an alternative opportunity for

organic and semiconductor spintronics. As the origin of the ferromagnetism is dierent

from the conventional, the experimental evidence to reveal its origin will be crucial. So

far, Cervenka et al. [32] demonstrated direct evidence that localized electron states at grain

boundaries were one of origins to induce ferromagnetism in HOPG. Ohldag et al. [34] proved

ferromagnetism found in graphite originated from carbon? - states and hydrogen-mediated

electronic states. Ugeda et al. [39] explained the formation of local magnetic moments from

a single vacancy in graphite. However, in a relatively complicated case, neither Zn nor O

49

50 CHAPTER 5. CARBON P ELECTRON FERROMAGNETISM IN SIC

is conrmed to be responsible for the ferromagnetism in ZnO [122, 123]. Therefore, further

evidence is called to address this issue. Recently, defect-induced ferromagnetism was found

in SiC [98, 81, 44]. Divacancies (VSiVC) are proven to exist in neutron irradiated and neon

implanted SiC [45, 44] which is dierent from the situation of graphite and ZnO. Thus the

question arises whether it is possible to establish a one-to-one correlation between the local

moments and the specic orbitals/electrons in SiC.

On the other hand, SiC has been well known as a kind of economical and practical

abrasive and for its application in high-temperature and high-voltage semiconductor elec-

tronics. Recent studies also reveal that the defects in SiC could also be manipulated in

quantum optics and quantum information [124, 82, 35, 9]. As to our work, the good crys-

talline quality and the low concentrations of impurities (please compare the relevant data

in Ref. [45, 125, 126]) can remove the concerns whether the observed ferromagnetism could

originate from extrinsic factors (e.g. magnetic contamination, see Ref. [127, 128]). More-

over, the dynamics of defects and their charge states in SiC upon ion irradiation can be

obtained by ab initio molecular dynamics simulations [129], which strengths the versatility

of SiC as a test-bed for investigation of defect-induced ferromagnetism. Therefore, a direct

experimental evidence for defect-induced ferromagnetism in SiC will certainly promote the

study of spintronics and other areas related to defects.

In this communication, 6H-SiC single crystals irradiated with xenon ions are investigated

to reveal the origin of its ferromagnetism. We present the results of X-ray absorption near-

edge structure (XANES) and X-ray magnetic circular dichroism (XMCD) at both the silicon

and carbon K-edges in conjunction with sensitive magnetization measurements and rst-

principles calculations. These results show that the p electrons of the nearest-neighbor

carbon atoms of VSiVC are mainly responsible for the long-range ferromagnetic coupling.

Our results provide important evidence for the defect-induced ferromagnetism in SiC.


5.2.1 Sample preparation

A commercial one-side-polished semi-insulating 6H-SiC (0001) single crystal wafer was cut

into pieces for ion irradiation. The concentrations of transition metal impurities (Fe, Co and

Ni) prove to be below the detection limit of particle induced X-ray emission. Four SiC pieces

were implanted by xenon ions with uence of 5×1012, 1×1013, 5×1013, 1×1014 cm−2 at an

energy of 500 keV at room temperature, which were subsequently labelled as 5E12, 1E13,

5E13, and 1E14, respectively. During implantation, the samples were tilted by 7 degrees

to reduce the channelling eect. The corresponding displacements per atom (DPA) values

calculated by Stopping and Range of Ions in Matter (SRIM) [57] to be 0.023, 0.047, 0.23,

and 0.47, respectively. The distribution of irradiation-induced damage predicted by SRIM

for xenon ions is more uniform and closer to the surface than that produced by 140 keV neon

ions [44].

5.2. EXPERIMENTAL METHODS 51

500 750 1000 1250 1500 1750

FLOIn

tens

ity (a

rb. u

nits

)

Raman Shift (cm-1)

pristine 5E12 1E13 5E13 1E14

FTO FLO

FTO

FLA

Figure 5.1: Room temperature UV-Raman spectra of samples 5E12, 1E13, 5E13, 1E14as well as the pristine sample. The folded transverse acoustic (FTA) and optic (FTO) andlongitudinal acoustic (FLA) and optic (FLO) modes in 6H-SiC are identied in these spectra.The peaks at higher wavenumbers are second order modes.

5.2.2 Measurements

All samples were measured by superconductor quantum interference device (SQUID-MPMS

or SQUID-VSM, Quantum Design). The magnetization is calculated according to the total

vacancies calculated using SRIM29. As shown in the inset of Fig. 5.3(a), the pristine sample

only shows diamagnetism, while the sample 5E12 reveals a ferromagnetic contribution at 5

K. Paramagnetism in the implanted samples is also visible in the high magnetic eld region,

as evidenced by the non-linear dependence of the magnetization on the eld. Both XANES

and XMCD spectroscopy at the silicon and carbon K-edges was obtained at the Advanced

Light Source (Berkeley Lab). The spectra of the silicon K-edge were measured at BL6.3.1

under a magnetic eld of -2 and 2 T at 77 K, while the carbon K-edge spectra were measured

at BL4.0.2 with the possibility of using a X-ray photon energy as low as 100 eV (note that

the carbon K-edge is around 285 eV) and applying an external eld of -0.5 and 0.5 T at 300

K. The typical spectral resolution for both beamlines is 5000. In the measurements, total

electron yield (EY) mode is chosen, which usually collects the signal from the topmost 510

nm of the sample [130].

5.2.3 Calculation parameters

First-principles calculations were performed using the Cambridge Serial Total Energy Pack-

age [131]. Spin-polarized electronic structure calculations were performed using the Perdew-

Burke-Ernzerhof functional [132] for the exchange-correlation potential based on the gen-

eralized gradient approximation. The core-valence interaction was described by ultrasoft

pseudopotentials [133], and to represent the self-consistently treated valence electrons the


cuto energy of the plane-wave basis was set to 310 eV. We calculated the total spin-resolved

density of states (DOS) and the partial spin-resolved DOS of silicon atoms and carbon atoms

in a 4×4×1 6H-SiC supercell containing one axial VSiVC [Si95(VSi)C95(VC ]. With the min-

imum distance between adjacent VSiVC larger than 12 Å, this structure allows long-range

ferromagnetic coupling4. The content of the spin polarization contribution is determined by

comparing the integrated DOS below the Fermi level.

5.3 Results

5.3.1 Structural properties

As ion irradiation induces damage only near the surface, UV-Raman spectroscopy with a

He-Cd laser of 325 nm is used to characterize the structure after ion irradiation. Figure

5.1 exhibits UV-Raman spectra measured at room temperature for samples 5E12, 1E13,

5E13, 1E14 and the pristine sample, respectively. The folded transverse acoustic (FTA)

and optic (FTO) and longitudinal acoustic (FLA) and optic (FLO) modes in 6H-SiC are

identied in these spectra. [75] and no secondary phase is detected within the measurement

sensitivity. The strength of the peaks decreases with increasing uence, which indicates

that the crystal structure is damaged upon ion bombardment. The samples 5E12 and 1E13

maintain relatively good crystallinity, while the structures of samples 5E13 and 1E14 suer

too much damage so that the sharp peaks vanish.

5.3.2 Divacancy identied in the ion implanted sample

In order to clarify the nature of defects which were created by the Xe ion implantation,

positron annihilation Doppler broadening spectroscopy (DBS) was applied. DBS is an ex-

cellent technique to detect open volume defects from clusters consisting of several vacancies

down to less than a mono-vacancy. The positron in a crystal lattice is strongly subjected to

repulsion from the positive atom core. Because of the locally reduced atomic density inside

the open volume defects, with a lower local electron density, positrons have a high probabil-

ity to be trapped and to annihilate with electrons in these defects by the emission of two 511

keV photons. Monitoring of the 511 keV annihilation radiation was performed by DBS. The

Doppler broadening of the 511 keV annihilation line is mainly caused by the momentum of

the electron due to the very low momentum of the thermalized positron. There is one main

parameters, S (shape), obtained from the 511 keV annihilation line. The S parameter reects

the fraction of positrons, annihilating with electrons of low momentum (valance electrons).

Therefore, the S parameter is mainly a measure for the open volume in the material. The

S parameter is dened as the ratio of the counts from the central part of the annihilation

peak (here 510.17 keV511.83 keV) to the total number of counts in the whole peak (498

keV524 keV). DBS measurements were carried out with the mono-energetic slow positron

beam "SPONSOR" at HZDR [121] at which a variation of the positron energy E from 30 eV

to 36 keV with a smallest step width of 50 eV, if required, is possible. The energy resolution

of the Ge detector at 511 keV was (1.09 + 0.01) keV, resulting in a high sensitivity to changes

in material properties from surface to depth of several µm.

5.3. RESULTS 53

0 5 10 15 20 25 30 35 400.49

0.50

0.51

0.52

0.53

0.54

0.55

S p

aram

eter

Incident positron energy E (keV)

Sbulk

SSi-C-divacancy

Figure 5.2: S parameter versus incident positron energy of the Xe implanted 6H-SiC sample(5E12).

Figure 5.2 shows the measured S parameter versus the incident positron energy. The

maximum of the S parameter around positron energy of 34 keV corresponds to positron

annihilation in the defects created by ion implantation within a depth of about 200 nm. For

higher positron energies the positron annihilation is shifted more and more to the undamaged

bulk material, the S parameter decreases and nally reaches the bulk value at 20 keV (dash-

dot line in Fig. 5.2). The dierence of the S values between the undamaged bulk Sbulk and

the defects Sdefect is a measure for type and concentration of these defects. Comprehensive

investigations of defects in 6H-SiC were already done in the past. A relation between the S

parameter and the number of agglomerated Si-C divacancies is published in Ref. [32] and

shown as a scaling curve. From this scaling curve the S parameter of the Si-C divacancy

was taken and plotted as a solid line in Fig. 5.2. It is clearly visible that the S parameter

of the defects in the implanted range agrees well with the value of S for the Si-C divacancy

which leads to the conclusion that Si-C divacancies were created by the Xe implantation

into 6H-SiC.


Figure 5.3 exhibits the hysteresis loops of all implanted samples after subtraction of the

weak paramagnetic background. The weak paramagnetic background of the samples be-

fore implantation is due to the unavoidable intrinsic defects during growth. The strongest

magnetization occurs for the sample 5E12, the sample with the lowest uence and the least

damage to the crystallinity. With rising uence, the saturated magnetization (MS) decreases


Figure 5.3: (a) Ferromagnetic hysteresis loops of samples 5E12, 1E13, 5E13, 1E14 at 5 Kafter subtracting the diamagnetic background from the pristine sample. The inset showsmagnetization vs. eld of the sample 5E12 and the pristine sample at 5 K. (b) Hysteresisloops of the sample 5E12 at 5 K and 300 K without the diamagnetic background.

5.4. DISCUSSION 55

from 0.72 µB/vacancy to around 0.02 µB/vacancy. The hysteresis loops of the sample 5E12

without diamagnetic background at 5 K and 300 K are shown in Fig. 5.3(b), indicating MS

at 300 K is still around half of MS at 5 K and the transition temperature is higher than 300

K. Therefore, we focus on the sample 5E12 in the following investigation.

5.3.4 Direct evidence for the origin of magnetism

XMCD spectroscopy as an element-specic technique to measure the magnetic contribution

from dierent elements with partially occupied 3d or 4f subshells [134, 135]. Ohldag et al.

[30] successfully applied this technique to investigate the magnetism at the carbon K-edge

in proton irradiated HOPG. As it is possible to investigate the bonding state in SiC single

crystals using XANES spectroscopy [136], it is also possible to explore the magnetic contri-

bution in defect-induced ferromagnetism in SiC with soft X-ray spectroscopy. Figure 5.4(a)

shows the XANES spectra of the silicon K-edge for selected samples to investigate the source

of the observed ferromagnetism. Comparing with the pristine sample, the peak positions of

samples after implantation are not changed, but the relative strength of the peak at 1848 eV

decreases, which suggests an increase of defect density [136]. As shown in Fig. 5.4(b), the

strength of the XMCD signal is below the detection noise level in both the pristine sample

and the sample 5E12 at the silicon K-edge. We may conclude that no spin-polarized states

close to the Fermi level occur at silicon atoms, and thus silicon centers do not contribute

to the ferromagnetism observed in the sample 5E12. Figure 5.4(c) shows the XANES spec-

tra at the carbon K-edge of the sample 5E12 and the pristine sample measured at 300 K.

Resonances around 285 eV and 290 eV correspond to the transition of carbon 1s core-level

electrons to π∗ and σ∗ bands, respectively [30]. The resonance at 285 eV of the sample

5E12 is sharper than that of the pristine sample, indicating that the orbital hybridization

at carbon is modied from the diamond-like sp3-type carbon in pure SiC towards a more

planar, graphitic sp2-type carbon center, which leaves the orthogonal pz orbital unchanged

and giving rise to the peak of π∗ bands [137]. This reects a change of the local coordination

from the tetrahedrally coordinated carbon atom in pristine SiC to the three-fold bound car-

bon site. In sharp contrast to the silicon K-edge, a clear XMCD signal appears at the carbon

K-edge as shown in Fig. 5.4(d). Therefore, the defect-induced ferromagnetism originates

from a spin-polarized partial occupancy of the pz orbitals at carbon atoms close to defect

sites in SiC.

5.4 Discussion

According to the results provided by positron annihilation spectroscopy (see Figure 5.2),

divacancies VSiVC are the dominated defect type in our samples. Note that the nearest-

neighbor atoms of VSiVC include three carbon atoms as well as three silicon atoms. Why

is the magnetic signal observed only from carbon atoms? To answer these questions, rst-

principles calculations were employed. As shown in Figure 5.5(a), 90% of the spin polariza-

tion is contributed by the valence states of the carbon atoms. This explains why XMCD is

only observable at the carbon K-edge. Further, when comparing the partial spin-resolved


Figure 5.4: X-ray absorption spectra measured in EY (electron yield) mode for the sample5E12 and the pristine sample: (a) XANES of the silicon K-edge at 77 K, (b) XMCD at thesilicon K-edge at 77 K, (c) XANES of the carbon K-edge at 300 K. (d) XMCD at the carbonK-edge at 300 K.

5.4. DISCUSSION 57

Figure 5.5: The electronic structure of Si95(VSi)C95(VC): (a) The total spin-resolved DOSand the partial spin-resolved DOS of silicon atoms and carbon atoms, respectively. (b)Comparison of partial spin-resolved DOS of nearest-neighbor carbon atoms and others. (c)Comparison of the partial spin-resolved DOS of s and p electrons of nearest-neighbor carbonatoms of VSiVC . (d) The structure and spin density isosurface (0.08 e/3, in purple) aroundone of the nearest-neighbor carbon atoms. The carbon atom is in grey in the middle andsilicon atoms are in yellow. The arrows indicate the bond angles of Si-C-Si. The dashed lineand square indicate the direction and the location of the adjacent silicon vacancy part (VSi)within VSiVC , respectively.


DOS of nearest-neighbor carbon atoms with that of other carbon atoms, it is visible [see Fig-

ure 5.5(b)] that 85% magnetic moments are from the three nearest-neighbor carbon atoms.

So the magnetic moments of the nearest-neighbor carbon atoms of VSiVC are mainly respon-

sible for the ferromagnetism. In a Si-C system, as carbon has higher electronegativity than

silicon, unpaired electrons will thus have a tendency to be attracted by carbon atoms with

priority. Spin polarization thus mainly appears at those carbon atoms around the vacan-

cies. According to Fig. 5.5(c), our calculation indicates that most of the magnetic moments

(90%) originate from the p states of nearest-neighbor carbon atoms of VSiVC . Due to the

attraction of the remaining adjacent silicon atoms, the nearest-neighbor carbon atoms will

move away slightly from the VSiVC . This structure change from the unperturbed four-fold

bulk coordination to a more planar three-fold bound state is connected with rehybridizations

at those C atoms in the close vicinity of VSiVC . Concomitantly, that distortion will modify

the electronic structure locally towards a higher degree of sp2 bonding orbitals and a singly

occupied p-type lone pair at the C atoms. Thus their outermost orbitals will acquire a signif-

icant π character and the magnetic moments are mainly contributed by p electrons, as shown

in Fig. 5.5(d). This analysis corroborates our interpretation of the XMCD experiment: the

XMCD signal of SiC after irradiation is thus assigned to p electrons.

5.5 Conclusion

In conclusion, in this work we investigated semi-insulating 6H-SiC after xenon irradiation.

X-ray absorption spectroscopies at both the silicon and carbon K-edges combined with sen-

sitive magnetization measurements and rst-principles calculations are used to understand

the origin of defect-induced ferromagnetism. It proves that the p electrons of the nearest-

neighbor carbon atoms of VSiVC are mainly responsible for the observed ferromagnetism.

These results provide valuable insight to comprehend the phenomena of defect-induced fer-

romagnetism in SiC, graphitic and other carbon-based materials, and will encourage the

exploration of the origin of defect-induced ferromagnetism in other promising materials like

graphene and oxides.

Chapter 6

Why is the ferromagnetism weak?

This chapter in preparation for publication:

Yutian Wang , Yu Liu, E. Wendler, Gang Wang, Xuliang Chen, Wei Tong, Zhaorong Yang,

F. Munnik, G. Bukalis, Xiaolong Chen, S. Gemming, M. Helm, Shengqiang Zhou, Why is

defect induced ferromagnetism weak, in preparation (2014)

Defect-induced ferromagnetism has triggered a lot of investigations and controversies.

The major issue is that the induced ferromagnetism is so weak that it can be accounted

for by trace contamination. Hoping the defect-induced magnetization can be increased by

orders of magnitude, we studied the variation of the magnetic properties of SiC after neutron

irradiation with uence covering four orders of magnitude. A large paramagnetic component

has been induced and scales up with defect concentration, which can be well accounted for

by un-coupled divacancies. However, the ferromagnetic contribution is still weak and only

appears in the low uence range of neutrons or after annealing treatments. First-principles

calculations hint towards a mutually exclusive role of the concentration of defects: A low

defect concentration favors spin polarization but not magnetic interaction. Combining both

experimental and rst-principles calculation results, the defect-induced ferromagnetism can

be understood as a local eect which cannot be scaled up with the volume. Therefore, our

investigation answers the long-standing question why the defect-induced ferromagnetism is

weak.

6.1 Introduction

The magic of magnetism was disclosed since early of 20th century with the development

of quantum mechanics. The discovered Heisenberg model has since then been extremely

successful to understand magnetism and magnetic materials [112]. All previously identied

ferromagnetic materials contain partially lled 3d (4d) or 4f (5f ) shells. A fundamental

question is if materials containing only s or p electrons can be ferromagnetic. For nearly two

decades, there have been various theoretical and experimental studies devoted to clarifying

59

60 CHAPTER 6. WHY IS DEFECT INDUCED FERROMAGNETISM WEAK?

this question [29, 88, 37, 89, 32, 92, 94, 95, 96, 97]. It turns out that materials with completely

lled 3d or 4f shells or with only s or p electrons can be ferromagnetic when they contain

defects. Among those materials, graphite/graphene and oxides attract particular attention

due to experimental evidence reported by various groups [29, 88, 89, 32, 92, 94, 95, 96, 97].

However, the experimentally measured ferromagnetism remains a weak signal being slightly

above the detection limit of sensitive SQUID magnetometry [17, 116, 117, 45, 44, 11]. The

very weak magnetization not only limits the practical applications, but also raises questions

on the fundamentals of defect induced ferromagnetism. On the one hand, measurement

artifacts in SQUID magnetometry may occur: improper mounting of samples and wrong use

of sample holders can easily generate ferromagnetic like signal [6, 7]. On the other hand,

the debate over the purity of graphite and oxide substrates continues in parallel [82, 53, 54,

138, 41]. Pristine graphite and oxides substrates are often ferromagnetic due to dierent

contaminations or due to intrinsic defects [53, 8, 9, 10], which hamper the interpretation of

the observed ferromagnetism. Indeed, Nair et al. reported that there is only paramagnetism

in graphene after introducing adatoms or defects [35].

Therefore, the understanding defect-induced ferromagnetism in materials without par-

tially lled 3d or 4f electron shells is far from satisfaction. It is rather calling for an inves-

tigation in which the following requirements should be fullled.

• The pristine materials should be well controlled with the highest purity grade possible.

• The materials should be supplied in a large quantity with identical properties, such

that one can perform a series of experiments using identical specimens.

• The materials should be free of elements with 3d or 4f electrons.

• The induced eect should exist in a large volume to measure a large enough magnetic

signal [139].

After screening by these facts, Si and SiC are the best candidates. Defect-induced fer-

romagnetism was revealed in SiC after neutron and ion irradiation [45, 44]. Recently, it

was suggested that the p electrons from the carbon atoms are mainly responsible for the

long-range ferromagnetic coupling in SiC after ion irradiation [140], which is similar to the

observation in graphite [34]. In this work, we start with 4H-SiC, high purity semi-insulating

SiC. Neutron irradiation was used to introduce defects in the whole sample volume over a

large range of defect concentrations. The large magnetic volume and well controlled pristine

materials allow for reliable interpretation for the following experimental observations: (1)

paramagnetism increases with neutron uence and saturates at the end; (2) ferromagnetism

only occurs in a narrow uence range although it is weak; (3) thermal annealing paramag-

netic defective SiC can induce weak ferromagnetism. Together with density-functional theory

(DFT), we show that there is an intrinsic limit to increase the ferromagnetic magnetization.

6.2 Experiment

Commercial semi-insulating 4H-SiC single crystal wafers (Cree) were used for our experi-

ment. Particle induced X-ray emission (PIXE) was performed to check magnetic impurities

6.3. RESULTS 61

in the pristine sample. The concentrations of magnetic impurities (Fe, Co and Ni) are

proved to be below the detection limits (shown later). Neutron irradiation was performed

at chambers DBVK and DBVR at the BER II reactor at Helmholtz-Zentrum Berlin at a

temperature less than 50 C. The uxes of DBVK are 1.08×1014 cm−2s−1 of thermal neu-

trons, 7.04×1012 cm−2s−1 of epithermal neutrons, and 5.80×1013 cm−2s−1 of fast neutrons,respectively and those of DBVR are 1.50×1014 cm−2s−1, 6.80×1012 cm−2s−1, 5.10×1013

cm−2s−1, correspondingly. Comparing with epithermal or fast neutrons, thermal neutrons

only produce negligible displacement. Therefore, only epithermal and fast neutrons are ac-

counted for in the uence calculation [141]. The neutron uence spanned a large range

from 3.28×1016 cm−2 to 3.50×1019 cm−2 covering all possibilities from light damage to near

amorphization. It is worthy to note that the applied neutron uence covers the range used in

Ref. [45] and is extended to much higher uence by two orders of magnitude. For structural

characterization, µ-Raman spectroscopy has been performed by using a Nd:YAG Laser with

532 nm wavelength in the scattering geometry using a liquid nitrogen cooled charge-coupled

device camera. The magnetic properties are measured by superconducting quantum inter-

ference device magnetic property measurement system and vibrating sample magnetometers

(SQUID-MPMS and SOUID-VSM, Quantum Design). The electron spin resonance (ESR)

spectroscopy was performed at 9.4 GHz using a Bruker spectrometer (Bruker ELEXSYS

E500).

6.3 Results

6.3.1 Virgin vs. irradiated SiC

Before we start to describe the detailed results, we rst present the key facts for the virgin

SiC substrates employed in our investigation.

To check the trace presence of transition metals (Fe, Co and Ni, etc.) in our SiC sub-

strates, we have performed PIXE using 2 MeV protons with a broad beam of around 1 mm2,

as shown in Figure 6.1. PIXE is a sensitive method to detect trace impurities in bulk volume

without signicant structural destruction [82, 41]. In the spectrum, the sharp peak is the Si

K-line X-ray emission. The broad bump is due to the Secondary Electron Bremsstrahlung

background. For commercially available, purest graphite, there is detectable transition metal

contamination (mainly Ti, V, Fe, Ni) as revealed by PIXE [41]. In sharp contrast, the tran-

sition metal impurity in the SiC we used for this study, if there is, is below the detection

limit (Fig. 6.1).

Figure 6.2 shows a comparison of the magnetic properties measured at 5 K between the

virgin SiC and a specimen irradiated with neutron with a relative low uence of 4.68×1017

cm−2. The results were without any background subtraction but only normalized to the mass

of samples. The dierence between the virgin and irradiated SiC is obviously not trivial: the

virgin SiC shows purely diamagnetic behavior, while the irradiated one shows a paramagnetic

component as revealed by the large deviation from the linear dependence on the magnetic

eld. The inset of Fig. 6.2 shows the zoom of the low eld part. Besides the paramagnetic

component induced by neutron irradiation, a small ferromagnetic contribution also shows


1 2 3 4 5 6 7 8 9 10102

103

104

105

NiCo

Inte

nsity

(cou

nts)

Energy (keV)

4H-SiC, Cree

Fe

Si K-edge

Figure 6.1: PIXE spectrum for the 4H-SiC wafer by a broad Proton beam. Within thedetection limit, no Fe, Co or Ni contamination is observed.

up with its saturation magnetization around 1% of the paramagnetism. The defect-induced

paramagnetism and ferromagnetism are exactly the key facts we are going to discuss in this

manuscript.

6.3.2 Structural properties

The damage to the crystallinity of SiC upon neutron irradiation is veried by Raman spec-

troscopy. Figure 6.3 exemplarily shows the Raman spectra for the virgin sample and the

samples irradiated with dierent neutron uence as indicated in the gure. The typical

Raman scattering modes for 4H-SiC are resolved: folded transverse optic (FTO) and lon-

gitudinal optic (FLO) [142]. Note the dierent scale in the y-axis: with increasing uence,

the intensity of the Raman scattering modes is dramatically reduced, as observed in Refs.

[45, 44]. This behaviour directly reects the increasing disorder of the crystalline material.

For the sample with largest uence, the Raman modes are hardly resolved and the sample

approaches an amorphous state [84, 141].

6.3.3 Paramagnetism

Figure 6.4(a) presents the magnetization [(M(H)] of neutron irradiated SiC after subtracting

the diamagnetic background which is measured for the pristine sample at 300 K. It is clearly

seen that all samples exhibit a paramagnetic component. The magnetization increases with

increasing neutron uence. The paramagnetism can be accurately described by Brillouin

6.3. RESULTS 63

-40000 -20000 0 20000 40000 60000

-0.02

-0.01

0.00

0.01

M

agne

tizat

ion

(em

u/g)

Field (Oe)

4H-SiC, virgin 4.68 1017 cm-2

@ 5 K

-2000 -1000 0 1000 2000

-5

0

5

M (1

0-4 e

mu/

g)

Field (Oe)

Figure 6.2: Comparison of the magnetic properties: virgin vs. neutron irradiated SiC.Inset: the zoom of the low eld part. Neutron irradiation induces signicant, unambiguousmagnetic variation in SiC.

function:

M(α) = NJµBgJ [2J + 1

2Jcoth(

2J + 1

2Jα)− 1

2Jcoth(

α

2J)] (6.1)

where the g factor is about 2 obtained from electron spin resonance measurement (shown

later), µB is Bohr magneton, α = gJµBH/kBT , kB is the the Boltzmann constant and N is

the density of spins. As exemplarily shows in Fig. 6.4(b), the data can be tted nicely by J

= 1. Moreover, a value of J larger or smaller than 1 results in a pronounced deviation from

the experimental data. This tting allows us to conclude that the observed paramagnetism

is due to a single species with moment µ = gJµB = 2µB. This conclusion is in an excellent

agreement with our rst-principles calculation (shown later): the induced magnetism is due

to VSiVC divacancy carrying a magnetic moment of 2 µB.

Figure 6.5 shows the temperature dependent magnetization [M(T)] for samples with

dierent neutron uences under an applied eld of 10000 Oe. As expected, one contribution

represents the diamagnetic background, which is essentially temperature independent and

dominates at higher temperature. The Curie-like paramagnetic component shows a strong

temperature and neutron uence dependence. In a self-consistence, the M(T) cures can be

well tted according to the Curie law (Eq. 6.2) by using the same J and N obtained from

the corresponding M(H) curve tting: J = 1 and N = 1.66×1019/g for the sample shown in

Fig. 6.4(b) and Fig. 6.5(b).


0

500

1000

Ram

an in

tens

ity

Virgin

FLO

FTO

0

100

200

300

3.50 1019 cm-2

6.75 1018 cm-2

1.48 1018 cm-2

6.90 1017 cm-2

0

50

100

150

0

10

20

30

700 800 900 10000

10

20

Raman shift (cm-1)

Figure 6.3: Raman spectra for virgin and neutron irradiated 4H-SiC single crystals. Thefolded transverse optic (FTO) and longitudinal optic (FLO) modes are identied. Withincreasing neutron uence the Raman scattering intensity is decreased.

6.3. RESULTS 65

0 10 20 30 40 500.00

0.05

0.10

0.15

0.20

0.25

0 10 20 30 40 500.0

1.0

2.0

Mag

netiz

atio

n (e

mu/

g)

Field (kOe)

3.50 × 1019 cm-2

8.38 × 1018 cm-2

4.89 × 1018 cm-2

3.21 × 1018 cm-2

1.50 × 1018 cm-2

6.70 × 1017 cm-2

4.68 × 1017 cm-2

3.28 × 1016 cm-2

(a) 4H-SiC at 5 K

Fitting J = 1/2 J = 1 J = 3/2 J = 2 J = 5/2

Mag

netiz

atio

n (1

019B/g

)

Field (kOe)

(b) 3.50 × 1019 cm-2

at 5 K Experimental

Figure 6.4: (a) Magnetization of all irradiated samples measured at 5 K as a function of eld[(M(H)], (b) Fits of the magnetization measured at dierent temperatures for the samplewith a uence of 3.50×1019 cm−2 using the Brillouin function with dierent values of J.


χ =M

H= N

J(J + 1)(gµB)2

3kBT(6.2)

Paramagnetic centers in the neutron irradiated SiC have also been detected by ESR. As

shown in Figure 6.6, in the broad eld range, there is only one sharp resonance peak due to

paramagnetic electrons. Within the detection limit, there is no broad resonance peak, which

could be related with ferromagnetic resonance. The inset shows a narrow scan with smaller

eld step at the paramagnetic resonance peak. The ESR spectrum exhibits a central line

and some weak hyperne lines. The g factor is calculated to be around 2.005, which is the

characteristic of free electrons. From the line shape, the defect is very probably divacancy

in 4H-SiC [50]. The hyperne structure is not well resolved as in the work by Son et al. [50],

which is probably due to the crystalline degradation upon neutron irradiation.

6.3.4 Ferromagnetism

In Refs. [45, 44], a sizeable ferromagnetism was observed for neutron or ion irradiated SiC.

Note that in Ref. [45], the maximum neutron uence (if counting only the fast neutrons)

is around 5.60×1017 cm−2. The authors show magnetization measurements at low eld and

a magnetic hysteresis loop was observed. We also checked our samples carefully whether

a hysteresis appears in the low eld range. Interestingly, besides the large paramagnetic

component we also observe a ferromagnetic hysteresis in samples with uence of around

5.60×1017 cm−2. However, the hysteresis is not resolvable when the uence is higher than

67×1017 cm−2. In Fig. 6.7, we show the detailed magnetization measurements for three

representative samples: sample 431-50 with an intermediate uence 4.68×1017 cm−2, sample

431-56 with the highest uence of 3.50×1019 cm−2 before and after annealing. Sample 431-50

shows a clear hysteresis added on the paramagnetic component (at 5 K) or on the diamagnetic

background (300 K). In contrast, for sample 431-56, at both 5 and 300 K, there is no

hysteresis resolvable and the paramagnetism dominates at low temperature. However, after

annealing at 900 C for 15 min, sample 431-56 shows a ferromagnetic component at 5 and 300

K. The paramagnetic component is drastically reduced to below 10% compared with the non-

annealed sample. Moreover, we also observed a similar ferromagnetic component for several

samples with the uence in the order of 26×1017 cm−2. The saturation magnetization for

the ferromagnetic component in dierent samples is in the range of 15×10−4 emu/g and is

only around 1% of the paramagnetic component.

The appearance or disappearance of the weak ferromagnetic component is conrmed

by zero-eld-cooled and eld-cooled magnetization measurement (ZFC/FC) shown in Fig.

6.7(d, e, f). The ZFC magnetization was measured by cooling the sample from 350 K to 5

K with zero eld, then a eld of 100 Oe was applied and the magnetization was measured

during warming up. The FC curves were measured by cooling the sample in a eld of

100 Oe during cooling. This approach is often used to verify if the measured specimen is

ferromagnetic, paramagnetic or superparamagnetic. If the specimen contains a ferromagnetic

component and if the eld during measurement is smaller than its coercive eld, the ZFC/FC

magnetizations will show an irreversibility with the FC magnetization larger than the ZFC

magnetization. If the specimen contains only paramagnetism, the ZFC/FC magnetization

6.3. RESULTS 67

0.0

0.1

0.2

0.3

0.4

0.5

(b)

Mag

netiz

atio

n (1

0-3 e

mu/

g)

3.50 1019 cm-2

8.38 1018 cm-2

4.89 1018 cm-2

3.21 1018 cm-2

1.50 1018 cm-2

4.68 1017 cm-2

3.68 1017 cm-2

4H-SiC, M(T) at 10000 Oe(a)

0 50 100 150 200 250 3000.0

0.5

1.0

1.5

0 10 20 30 40

Temperature (K)

3.50 1019 cm-2

Experimental data Fitting

Temperature (K)

Figure 6.5: (a) The magnetic moment of all irradiated samples measured at 10000 Oe as afunction of temperature [M(T)]. (b) For the sample irradiated with the largest uence: theblack symbols are experimental data and the red solid curve is the tting result by equation(2).


0 2000 4000 6000 8000

ES

R (a

rb. u

nit)

FIeld (Oe)

8.38 1018 cm-2

@ 2 K

3300 3320 3340 3360 3380 3400

ESR

Field (Oe)

Figure 6.6: ESR spectrum for a 4H-SiC sample irradiated with neutron with a uence of8.38×1018 cm−2. The eld is applied perpendicular to the c-axis. The inset shows thedetailed hyperne structure (indicated by arrows) of the resonance peak.

should overlap with each other. For samples contains superparamagnetic components, a

blocking behavior at low temperature, i.e. an increase in the ZFC magnetization with

temperature, will appear. For samples 431-50 [Fig. 6.7(d)] and 431-56 after annealing [Fig.

6.7(f)], a dierence is observed up to 300 K in the ZFC/FC magnetization, while for sample

431-56 the FC curve superimposes the ZFC curve. Moreover, the data did not indicate any

blocking temperatures that can be associated with superparamagnetic behavior, which was

reported for ion implanted SiC [143].

As shown by our comprehensive investigation on the magnetic properties of 4H-SiC upon

neutron irradiation with a much broader uence range than that used in Ref. [45] (especially

in the large uence range), the paramagnetic component scales up with uence (the concen-

tration of defects), but the weak ferromagnetic contribution appears only for samples with

relatively low uence or after annealing. Figure 6.8 shows the tted paramagnetism depend-

ing on neutron uence. Those samples shown as the red circles and the blue triangle appear

to have a ferromagnetic component. As shown in Refs. [45, 44], the divacancies in SiC are

responsible for the magnetic properties. The scaling between the concentration of paramag-

netic centers and the neutron uence provides a solid evidence that the defects created by

irradiation are directly responsible for the local moments. However, the long-range-coupling

between the local moments is not always favorable. The ferromagnetism only appears when

the defect concentration (represented by the density of paramagnetic center and by the neu-

tron uence) is in a narrow window (as indicated by the grey bars in Fig. 6.8.) This is

consistent with the ferromagnetism observed in ion implanted SiC [44, 104]. Nevertheless,

the saturation magnetization for the ferromagnetic component in dierent samples is much

smaller than the paramagnetic component. In the next section, we employ rst-principles

calculation to understand why the defect-induced ferromagnetism is weak.

6.3. RESULTS 69

-2000 -1000 0 1000 2000-0.5

0.0

0.5

-2000 -1000 0 1000 2000-15

-10

-5

0

5

10

15

-2000 -1000 0 1000 2000-1.0

-0.5

0.0

0.5

1.0

0 100 200 300-0.02

-0.01

0.00

0.01

0.02

0.03

0 100 200 3000.0

0.2

0.4

0.6

0 100 200 300

0.00

0.02

0.04

0.06

(f)(e)(d)

(b)

4.68 1017 cm-2

5 K 300 K

Mag

netiz

atio

n (1

0-3 e

mu/

g)

Field (Oe)

(a)

3.50 1019 cm-2

5 K 300 K

Field (Oe)

(c)

Field (Oe)

3.50 1019 cm-2, Annealed 5 K 300 K

4.68 1017 cm-2

ZFC FC

Temperature (K)

Temperature (K)

3.50 1019 cm-2

ZFC FC

3.50 1019 cm-2, annealed ZFC FC

Temperature (K)

Figure 6.7: Magnetization vs. Field at the low eld range for samples with uences (a)4.68×1017 cm−2, (b) 3.50×1019 cm−2 and (c) 3.50×1019 cm−2 after annealing and ZFC/FCmagnetization for the same set of samples (d-f).

6.3.5 Why is the ferromagnetism weak?

According to literature [45, 44], the divacancy is the most likely origin for the measured

ferromagnetism. Meanwhile, the ferromagnetism only occurs in samples with relatively low

neutron uence or after annealing and is much weak compared with the induced paramag-

netism. These facts motivate us to perform some theory work to understand the puzzle.

First-principles calculations were performed by using the Cambridge Serial Total Energy

Package [131]. Spin-polarized electronic structure calculations were carried out using the

Perdew-Burke-Ernzerhof functional [132] for the exchange-correlation potential based on

the generalized gradient approximation. The core-valence interaction was described by ul-

trasoft pseudopotentials [133]. The cuto energy for the plane-wave basis is set to 310 eV.

Full optimization of the atomic positions and lattice parameters was carried out with con-

vergence threshold of the remanent Hellmann-Feynman force 0.01 eV/Å. 4H-SiC supercells

with various sizes containing one axial divacancy (VSiVC) were built to obtain the variation

of spin polarization and the magnetic coupling depending on the distance between defects.

Actually, the calculation results show no signicant dierence between 4H- and 6H-SiC.

As a hexagonal structure, 4H-SiC has a lattice constant c (out-of-plane) dierent from

a and b (in-plane), so the distance between adjacent VSiVC divacancies in dierent axis

is also dierent from each other. Usually, the magnetic moments couple with each other

preferentially along the shortest distance, which will be chosen as the coupling distance. It

is found that the coupling is along the a-b plane in a SiC supercell, which will be explained


1016 1017 1018 1019 10201017

1018

1019

1020

N (g

-1)

Neutron fluence (cm-2)

Fitted paramagnetic components No ferromagnetism With ferromagnetism With ferromagnetism

after annealing

Figure 6.8: The tted N (the density of paramagnetic centers) for samples with dierentneutron uence and the sample with the highest uence after annealing at 900 C for 15 min.The dashed line is only for guiding eyes to indicate the trend. The grey bars indicate therange of samples with a resolvable ferromagnetic component, regarding to N and neutronuence, respectively.

6.3. RESULTS 71

6 8 10 12 14 16 18

-0.5

0.0

0.56x6x1

5x5x13x3x1

4x4x1

E SP (e

V)

2x2x1

(a)

6 8 10 12 14 16 180

20

40

60

80

100

120

140

(b)

J 0 (m

eV)

dV (Å)

J0 for (-1, -1) -J0 for (+1, +1)

Figure 6.9: (a) Spin-polarization energy ∆Esp as a function of the distance dV between theadjacent vacancies. ∆Esp increases with increasing dV and the critical value is 9.7 Å. (b)The ferromagnetic (or antiferromagnetic) exchange coupling energy between charged (-1, -1)or (+1, +1) divacancies as a function of dV . The corresponding supercell structures withone VSiVC are marked with the numbers and multiply signs.


hereinafter. Therefore, the distance between adjacent VSiVC in the a-b plane is chosen as

the coupling distance (dV ) between them. The spin-polarizing energies ∆Esp (the energy

dierence between the spin-unpolarized and spin-polarized states) of supercells as a function

of dV are shown in Fig. 6.9. It is found that ∆Esp increases when dV increases, indicating

that the spin polarization is stable under low VSiVC concentrations. When dV is larger

than 9.7 Å, ∆Esp changes from negative to positive and the spin polarization becomes

energetically favored. Here, the supercells with dV less than 9.7 Å are designed for obtaining

the critical value of dV switching the sign of ∆Esp. Besides, each VSiVC yields a local

moment of 2.0 µB when VSiVC is more than 12.34 Å. This result is in well agreement with

our experimental data shown in Figs. 6.4 and 6.5. The experimental results show that the

induced paramagnetism is due to a single species with moment of 2 µB.

In order to investigate the magnetic coupling (ferromagnetism or antiferromagnetism)

between these VSiVC-induced local moments, we put two 4H-SiC 4×4×1 supercells side

by side along the a- or along the c- direction. Each 4×4×1 supercell contains one VSiVC .

Note that these antiferromagnetic structures are designed only for obtaining the magnetic

interaction. The energy dierence between the antiferromagnetic and ferromagnetic phases

is EAFM − EFM = 8J0(dV )S2 or EAFM − EFM = 4J0(dV )S2 for size doubling from a or c

directions, respectively, according to the nearest-neighbor Heisenberg model, where J0(dV )

is the nearest-neighbor exchange interaction as a function of dV and S is the net spin of the

VSiVC states. In previous work, it has been shown that the intrinsic defects in high purity

SiC can be neutral, positively or negatively charged [144]. The possible impurities, such as

Boron and Nitrogen (see ref. [48]), with the concentration in the order of 1015−16 cm−3 can

also modify the charge state of VSiVC . Therefore, we calculate the interaction for dierent

charge states. As shown in Table I, VSiVC does not couple with each other along the c

axis, even when dV is as small as 10.11 Å. The exchange interaction is much stronger along

the a axis and strongly depends on the charge state. Neutron or positively charged VSiVCantiferromagnetically couples with a maximal exchange interaction of 125.68 meV when dV

is 12.33 Å. The result is also consistent with the previous report [45], in which the coupling

between neutral VSiVC is also antiferromagnetic. Negatively charged VSiVC divacancies

favor a ferromagnetic coupling. However, the exchange interaction dramatically decreases

from 49.36 meV to 3.71 meV then dV is increased from 12.33 to 18.50 Å.

In Figure 6.9(b), we plot the ferromagnetic exchange interaction energy depending on dV .

As shown in Fig. 6.9(a) and (b), the ferromagnetism induced by divacancies requires that

divacancies are negatively charged with dV in the range from 12.33 Å to 15.42 Å. The required

dV would correspond to a concentration of divacancies in the order of 36×1020 cm−3 (1/d3V ).This concentration is around 1 at.% of SiC and well above the maximum concentration for the

local moments we obtained by neutron irradiation (see Fig. 6.8). However, after irradiation

with the largest neutron uence the sample is approaching amorphous as shown by the

Raman results and the density of paramagnetic centers (N ) starts to saturate. In this sense,

it is unrealistic to expect the ferromagnetic coupling throughout the whole bulk sample. In

principle, it is in agreement with our experimental observation. The experimentally observed

weak ferromagnetism can be understood as a local eect: only some particular regions with

nm or µm dimension can accommodate a high concentration of divacancies. These regions

6.4. CONCLUSION 73

Table 6.1: Magnetic coupling between VSiVC-induced local moments in SiC. The coupling isantiferromagnetic between neutron or positively charged VSiVC while ferromagnetic betweennegatively charged ones. As the arrangement direction of VSiVC is along c axis, the couplingalmost does not exist.

dV (Å) c- or a-axis charge state EAFM -EFM (meV) J0 (meV)10.11 c axis (0, 0) -0.55 -0.1412.33 a axis (0, 0) -39.45 -4.9312.33 a axis (+1 +1) -251.35 -125.6812.33 a axis (-1, -1) 98.73 49.3615.42 a axis (0, 0) -5.77 -0.7215.42 a axis (+1, +1) -179.81 -89.9015.42 a axis (-1, -1) 33.31 16.6618.50 a axis (0, 0) -0.93 -0.1218.50 a axis (+1, +1) -49.75 -24.8818.50 a axis (-1, -1) 7.43 3.71

form ferromagnetic bubbles with very strong interaction (see Table I), leading to the high

Curie temperature. Presumably, these regions could be surface, interface or grain boundary.

However, according to our calculation the spin-polarization will be unfavorable if dV is too

small. Therefore, the narrow uence window of ferromagnetism shown in Fig. 6.8 as well as

in neon implanted SiC [44] can be understood: In the beginning of neutron irradiation, the

defect concentration increases, and some local regions accommodating a larger concentration

of divacancies appear to be ferromagnetic. When dV in the local regions reaches the critical

value of 9.7 Å, the increase of defect concentration will suppress the spin polarization. There

may appear some new local regions with the concentration of divacancies reaching to the

level to induce ferromagnetism, but the damage to the crystalline structure by irradiation will

weaken the coupling. Therefore, the magnetic moments can not be increased by increasing

the uence of irradiation all the time. While, the amount of paramagnetic centers can be

scaled up with neutron uence and show saturation at very large uences.

6.4 Conclusion

To investigate defect-induced magnetism, we applied a broad neutron uence covering four

orders of magnitude to irradiate SiC. A huge paramagnetic contribution is observed and

scaled up with neutron uence. While, ferromagnetism only appears in a certain, rather low

uence range or after annealing treatments. First-principles calculations hints towards a mu-

tually exclusive role of defects: A low defect concentration favors spin-polarization, but leads

to negligible magnetic interaction. Combining both experimental and rst-principles calcu-

lation results, we can conclude that defect-induced ferromagnetism can only be understood

as local eect and cannot be scaled up with the volume. Therefore, our investigation an-

swers the long-standing question why the measured magnetization is low for defect-induced

ferromagnetism.

Chapter 7

Revisiting defect-induced magnetism

in graphite through neutron

irradiation

This chapter is submitted for publication:

Yutian Wang, M. Helm, P. Pochet, C. A. Jenkins, E. Arenholz, G. Bukalis, S. Gemming,

and Shengqiang Zhou,Revisiting defect-induced magnetism in graphite through neu-

tron irradiation, Phys. Res. B., submitted (2014).

We have investigated the variation in the magnetization of highly ordered pyrolytic

graphite (HOPG) after neutron irradiation, which introduces defects in the bulk sample

and consequently gives rise to a large magnetic signal. We observe strong paramagnetism in

HOPG, increasing with the neutron uence. We correlate the induced paramagnetism with

structural defects by comparison with density-functional theory calculations. In addition to

the in-plane vacancies, the trans-planar defects also contribute to the magnetization. The

lack of any magnetic order between the local moments is possibly due to the absence of

hydrogen/nitrogen chemisorption, or the magnetic order cannot be established at all in the

bulk form.

7.1 Introduction

Defect induced magnetism in carbon based materials gives many attractive perspectives in

the fundamental understanding of magnetism as well as in future spintronic applications.

As early as 2003 highly ordered pyrolytic graphite (HOPG) was reported to be ferromag-

netic after proton irradiation [29], which provides an approach to control the defect-induced

magnetism in graphite both concerning strength and in lateral distribution. After that,

successive investigations were performed for testing the reliability of the ferromagnetism in

graphite [88, 89, 32, 90, 91, 73, 92] and for nding other carbon-based ferromagnetic materials

[93, 94, 95, 96, 97]. So far experiments and theory show the following common features:

75

76 CHAPTER 7. REVISITING DEFECT-INDUCED MAGNETISM IN GRAPHITE

1. Paramagnetism can be greatly enhanced by introducing defects in graphite or graphene

[116, 42, 35]. Some research groups conclude that these paramagnetic centers do not

show any magnetic ordering down to 1.8 or 2 K [145, 42, 35].

2. Ferromagnetism only appears under certain defect concentrations, i.e., in a narrow ion

uence window, and the magnetization is weak [17, 116, 117, 45, 44].

3. In a microscopic picture, it has been found both theoretically [37] and experimentally

[117, 39] that defect-induced or disturbed electron states play an important role in

generating local moments in graphite.

4. Foreign (or impurity) atoms, particularly, hydrogen and nitrogen, are helpful in estab-

lishing the ferromagnetic coupling between defects [34, 37, 36].

However, as to our knowledge, the research has focused on thin-lm like samples: ion

implanted graphite with nmµm aected thickness or graphene akes. The as-measured

magnetization is always in the range of 10−610−5 emu per sample [29, 17, 116, 117, 45,

11]. The small magnetization renders data interpretation controversial as shown in a recent

intensive discussion [82, 53, 54, 138, 41]. There is no experimental report about the possible

ferromagnetism in defective bulk-graphite or other semiconductors. In our current work, the

central aim is to search for possible defect induced magnetism, which occurs in the whole

bulk sample and is expected to give a large measurable magnetic moment.

Although ion implantation [146] is commonly used to introduce defects into crystalline

materials for the investigation of defect induced magnetism, this technology poses two un-

avoidable challenges. Firstly, the defect region usually locates in the near-surface region of

several hundred nanometers and it is hard to generate defects in the whole bulk specimens.

Secondly, the implanted ions, especially those, that dier chemically from the substrate,

will stay in the matrix as foreign atoms and an interface will naturally form between the

implanted region and the untouched substrate. Both the interface and the implanted ions

will make it dicult to unambiguously identify the defect type and hamper the interpre-

tation of the mechanism for the observed magnetization. To avoid these problems we use

neutron irradiation. Neutrons have a much stronger penetrating capability than ions and

will generate defects through the whole sample. In this way, the foreign ion eect and the

interface eect can be excluded in the present study. Therefore, the application of neutron

irradiation could be a promising method to clarify the long standing question regarding the

origin of the defect induced magnetism concerning the following aspects:

• To overcome the problem in detecting weak magnetic signals, which often results in

misinterpretation of magnetism from the contamination of samples [10, 9, 53, 103] or

from articial eects in SQUID (superconducting quantum interference device) mag-

netometry [6, 7].

• To verify whether the defect induced magnetism is a bulk eect or only a surface

eect. We nd that in most of reports the defect induced magnetism is caused by the

crystal damage in the surface implanted region or in thin lms or in nanostructures

[147, 29, 17, 116, 117, 100, 98, 45, 11, 2]. Assuming this eect can be extended over

7.2. EXPERIMENTAL METHODS 77

the whole sample, neutron irradiation could turn the whole sample to be magnetic.

We should be able to measure a 100-1000 times larger magnetic moment than that of

ion implanted graphite, which would then correspond to a saturation magnetization of

10−410−2 emu.

Therefore, our work has been performed in the following way. HOPG specimens were

subjected to neutron irradiation, whereby the irradiation uence is varied to induce defects

in graphite from slight damage to near amorphization. We correlate the magnetic and

structural properties and the results are understood by comparing with literature data and

DFT calculations. Our aim is to clarify whether the defect-induced ferromagnetism can

occur in the bulk form in graphite.


In the experiment, the used graphite samples were highly oriented pyrolytic graphite (HOPG)

with a grade of ZYA, which are generally referred as graphite in this manuscript. Neuron ir-

radiation was performed at the reactor BER II (DBVK, Helmholtz-Zentrum Berlin). During

irradiation the temperature of the samples was less than 50 C (see ref. [141]). Four sam-

ples were irradiated with the uences of 6.24×1017, 1.25×1018, 6.24×1018, and 3.12×1019

cm−2, which are named as 3H, 6H, 30H and 150H according to the irradiation time of 3

hours, 6 hours, 30 hours, 150 hours, respectively. Only the epithermal and fast neutrons are

considered in calculating the uence.

Magnetometry was performed using a SQUID-VSM (Quantum Design). The magnetic

properties were measured regarding their dependences on magnetic eld and on temperature.

The structure change is characterized by Raman spectroscopy which is sensitive to defects

in the aromatic ring, the edge state, the hybridization type, the interstitial ions, and also to

the stacking orders, etc [148]. The µ-Raman system is equipped with a 532 nm wavelength

laser and a liquid nitrogen cooled CCD detector working in backscattering geometry. X-ray

absorption spectroscopy (XAS) will further detect the bonding state change resulting from

neutron irradiation. The variations of the magnetization, the Raman scattering and the X-

ray absorption at the carbon K-edge depending on the irradiation uence allow us to clearly

correlate the density of vacancies interstitials with the magnetism in the neutron irradiated

graphite.

7.3 Results and discussion


Figure 7.1 shows the magnetization measurements at 300 K and 1.8 K for the virgin and

irradiated graphite without any background correction. For the virgin graphite, the dia-

magnetic background dominates the magnetic properties. A weak ferromagnetic hysteresis

is observed already in the virgin graphite. It is probably caused by intrinsic defects [34] or

by Fe contamination [53, 54, 103]. Moreover, the ferromagnetic contribution is not changed

signicantly upon neutron irradiation. Therefore, this weak ferromagnetism is not the topic


-40000 -20000 0 20000 40000-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

-2000 -1000 0 1000 2000

-2

0

2

(b) Magnetization at 1.8 K150H

Mag

netiz

atio

n (e

mu/

g)

Field (Oe)

Virgin

6H

150H30H

3H

VirginMag

netiz

atio

n (1

0-3 e

mu/

g)

Field (Oe)

(a) Magnetization at 300 K

Figure 7.1: Magnetization vs. eld (a) the low eld range at 300 K and (b) the large eldrange at 1.8 K.


10000 20000 30000 40000 50000

0.0

0.2

0.4

0.6

Virgin

Mag

netiz

atio

n (e

mu/

g)

Field (Oe)

150H 30H 6H 3H Virgin

0

T = 1.8 K

3H6H

30H

150H

Figure 7.2: The magnetic moments of all irradiated sample measured at 1.8 K as a functionof the applied external eld.

of our study in this manuscript. Besides the marginal change in the ferromagnetic com-

ponent, there is a huge increment of the magnetization at low temperature. Figure 7.1(b)

shows the comparison of the magnetization measurement at 1.8 K for the virgin graphite and

sample 150H. Sample 150H shows a large paramagnetic component which will be discussed

in detail later. Note that the change in the slope of the MH curves in Fig. 7.1(a) is due

to the large increase of the paramagnetism upon irradiation as shown. At low temperature,

the weak ferromagnetism in the irradiated samples is dominated by the paramagnetism and

not resolvable.

The eld dependence of the magnetization at 1.8 K for all samples is shown in Fig. 7.2.

Neutron irradiation leads to strong paramagnetism. The graphite sample is changed com-

pletely from diamagnetic-like to paramagnetic-like with increasing neutron uence. However,

even for the sample with the highest neutron uence, the magnetization is not saturated at

1.8 K up to a eld of 50000 Oe. In our experiment, the measured absolute magnetic mo-

ment for a graphite sample of around 4×4 mm2 is in the range of 0.001-0.01 emu at 1.8 or

5 K. This value is much larger than the previously reported ion implanted samples with a

magnetic moment of around 10−510−6 emu [29, 17, 116, 117] and is far above the sensitiv-

ity of SQUID-VSM. As shown in Fig. 7.3(a), the induced paramagnetism can be precisely

described by the standard Brillouin function after removing the residual diamagnetic back-

ground and the intrinsic paramagnetic contribution from the virgin graphite:

M(α) = NJµBg[2J + 1

2Jcoth(

2J + 1

2Jα)− 1

2Jcoth(

1

2Jα)] (7.1)

where the g factor is about 2 obtained from electron spin resonance measurement (not

shown), µB is Bohr magneton, α = gJµBH/kBT , kB is the the Boltzmann constant and

N is the density of spins. The Brillouin function provides excellent ts for J = 0.5, which


corresponds to single electrons as charge carries and N = 8×1019 µB/mg for sample 150H.

The ts using larger J unequivocally deviate from the shape of the measured M-H curves,

as they give signicantly dierent, sharper changes with faster saturation.

The Curie law

χ =M

H= N

J(J + 1)(gµB)2

3kBT(7.2)

with J = 0.5 and N = 8×1019 µB/mg inferred from Fig. 7.3(a) also gives a good t to

the temperature dependent magnetization as shown in Fig. 7.3(b). The inset of Fig. 7.3(b)

shows the inverse susceptibility versus temperature, revealing a linear, purely paramagnetic

behavior with no indication of magnetic ordering.

Figure 7.6 (shown later in the paper) shows the density of paramagnetic centers obtained

by tting the magnetization measured at 1.8 K for dierent samples as a function of neutron

uence in double logarithmic scale. With increasing neutron uence, i.e. the amount of

defects, more and more paramagnetic centers are generated. This indicates that even the

most strongly irradiated sample is still not totally amorphous.

We also noted the work by Ramos et al. [116] Using ion implantation to introduce defects

into graphite, they reported an anomalous paramagnetic contribution. This contribution

remains independent of temperature up to 100 K, whereas the eld dependent magnetization

shows neither saturation nor any nonlinearity [116]. Meanwhile theoretical calculations also

pointed out that if sucient carbon adatoms were available, they could weakly agglomerate in

graphene and superparamagnetism can be nally observed [149]. However, in our experiment

the magnetic properties for all samples can be well described by spin 1/2 paramagnetism

without superparamagnetic contributions. As expected if the whole volume contributes,

in our experiment the as-measured magnetization signal is as large as 0.0010.01 emu per

sample. The large magnetization signal allows us to draw reliable conclusions and to exclude

any spurious and anomalous paramagnetic contribution.

To further exclude a possible ferromagnetic ordering in our sample we measured the

magnetization vs. eld at dierent temperature to perform an Arrott plot analysis [150].

This method is usually used to accurately determine the Curie temperature TC and to

verify the paramagnetic to ferromagnetic phase transition. Such an analysis is based on the

relationship derived by Wohlfarth [151]

[M(H,T )]2 = [M(0, 0)]2[1− (T/TC)2 + 2χ0H/M(H,T )] (7.3)

Note that this relationship results in parallel lines of the isothermal M2 which cross zero

(H/M = 0) in the vicinity of T = TC ± δ. Figure 7.4 shows the isothermal magnetiza-

tion Arrott plot for sample 150H (irradiated up to the highest uence). The measurement

temperatures range from 1.8 K to 20 K. With increasing temperature, the magnetization

decreases, but none of the lines crosses the zero point (H/M = 0). It conrms that down to

1.8 K no magnetic order appears in this sample. It is purely paramagnetic.


0 10000 20000 30000 40000 500000.0

0.2

0.4

0.6

0 50 100 150 200 250 300

0.00

0.02

0.04

0.06

0.08

Mag

netiz

atio

n (e

mu/

g)

Field (Oe)

at 1.8 K Experiment J=0.5 J=1 J=1.5

(a)

(b)

Mag

netiz

atio

n (e

mu/

g)

Temperature (K)

0.00 0.05 0.10 0.15 0.20

1/T (K -1)

Figure 7.3: (a) The measured magnetization at 1.8 K for sample 150H and the ttingusing Brillouin function with J = 0.5, 1, 1.5. (b) Temperature dependent susceptibilitymeasured under a eld of 10000 Oe. The black symbols are experimental data and the redsolid curve is is the tting result by the equation (2). Inset: Inverse susceptibility versustemperature demonstrating a linear, purely paramagnetic behavior with no indication ofmagnetic ordering.


0 1 2 3 4 5 60.00

0.05

0.10

0.15

0.20

0.25

0.30

20 K

M2 ((

emu/

g)2 )

H/M (105 Oe/(emu/g))

1.8 K

Figure 7.4: Isothermal magnetization an Arrott plot: M2 versusH/M . The lines withdierent color correspond to the measurements in the temperature range 1.8 to 20 K.

7.3.2 Raman spectroscopy

Figure 7.5 shows the Raman spectra of graphite samples after neutron irradiation. From top

to bottom are the virgin sample and samples 3H...150H, respectively. A linear background

has been removed.

The reference sample shows the peaks typical for the high-quality HOPG [148, 152]. The

G peak located at around 1590 cm−1 corresponds to the inherent E 2g mode of the aromatic

ring. The D peak around 1360 cm−1 represents an elastic scattering at defects in crystal

[153, 148, 152, 154].

Upon neutron irradiation, the most pronounced changes occur in the D peak and in

its overtone G' peak (2D peak): the D peak rises with irradiation uence and becomes as

strong as the G peak. Two pronounced changes will be described in the following.

In-plane vacancies

The increase of peak D is generally attributed to the in-plane vacancies in graphite [153,

148, 152, 154]. By independent methods such as X-ray diraction and transmission electron

microscopy, the intensity ratio between D and G peaks has been conrmed as a measure

of the in-plane grain size. Neutron irradiation induces a large number of interstitial and

vacancy pairs (I-V ). Most of I-V defects will recombine simultaneously and the remaining

species can form various defects. Since a high energy barrier blocks the diusion of vacancies,

most vacancies become in-plane vacancies or form vacancy clusters. The interstitial atoms

prefer staying in the region between the layers owing to the energetically highly unfavorable

interstitial in-plane position [155]. In Figure 7.6, we plot the uence dependent ID/IG (the

intensity ratio between D and G peaks). In our samples, the strength of the D peak increases


0

400

800

1200

1600

0

250

500

750

1000

1250

0

250

500

750

1000

1250

0

250

500

750

1000

1000 1250 1500 17500

200

400

600

2500 2750

D1G'

D

G

G

D

Raman shift (cm-1)

Ram

an in

tens

ity (a

rb. u

nit)

G'1

Virgin

G'2

3Hours

6Hours

30Hours

D'

150Hours

Figure 7.5: Raman spectra of graphite after neutron irradiation. From the top to bottomshown are data for virgin graphite and 3 hours to 150 hours irradiated samples, respectively.The peaks were deconvoluted to reveal the detailed variation after neutron irradiation.


with the neutron uence when the irradiation time is less than 30 hours. Further increasing

the neutron uence, ID/IG reaches a saturation value. It indicates that with increasing the

irradiation time from 3 hours to 30 hours the density of vacancies is continuously increasing

until the vacancies reach a saturation density. Such behavior was observed in ion irradiated

or ball milled graphite [153, 154].

Out-of-plane defects

The G' peak around 2720 cm−1 is the overtone of the D peak. It is often referred as the

2D peak and is very sensitive to the c-axis stacking order of graphite. The line shape and

intensity of G' are signatures of the stacking of graphene layers. For bulk graphite consisting

of an ...ABAB...stacking, the G' peak is composed of two peaks. When the stacking is

absent, the interaction between the planes is very weak and they behave as two-dimensional

crystals. For a single graphene layer, the G' peak is composed of a single peak [148]. For our

experiment, in the virgin sample the interaction between the layers in 3D graphite makes

the G' peak to be split into G'1 and G'2. When the irradiation time is less than 6 hours,

two peaks can t the spectra, but their strength becomes weak with increasing irradiation

uence. This indicates a slight crystalline damage in the graphene sheet stacking. The

inuence of shear moments caused by the interstitial atoms between the two sheets is less

notable for irradiation times of less than 6 hours. When the irradiation time is over 30 hours,

G'1 and G'2 peaks decease strongly and mix into a single weak peak. This is attributed

to the out-of-plane defects in graphite [156, 152]. With increasing neutron uence, more

interstitial atoms are assumed to diuse into regions between the graphene sheets so that

the distance between the sheets increases strongly enough, such that the graphene sheets

behave like an isolated single graphene sheet. The appearance of the D1 peak at around

1500 cm−1 for sample 150H is another indication for the interstitial atoms between graphene

sheets [157, 152]. At low uence range, the D1 peak is too weak to be tted even for samples

30H. The D1 peak was also observed in ion implanted graphite when the implantation uence

is large enough [152].

This Raman analysis allows us to dene two regimes for the four reported uences. In

the rst regime (3H, 6H and 30H) defects are created in plane without interaction between

neighboring planes. In the second regime (30H and 150H), the latter interaction becomes a

dominant eect and trans-planar defects (interstitial or vacancy) are expected to play a major

role: due to the high defect concentration, newly created defects are expected to combine

with pre-existing defects in the neighboring planes as revealed by the rather saturated value

of ID/IG in the second uence regime. Interestingly, these transplanar defects seem also

contribute to the total magnetization.

7.3.3 X-ray absorption spectroscopy

To further probe the change in the electronic state in graphite after neutron irradiation

from a microscopic point of view, we performed near-edge X-ray absorption ne structure

spectroscopy (NEXAFS, Beamline 6.3.1 at the Advanced Light Source in Berkeley). The

description of the experimental set up can be found in reference [34]. In our experiment, the


1018 1019

1

10

N (1

019

B/c

m3 )

Fluence (/cm2)

M0 at 1.8 K

0.0

0.5

1.0

1.5

ID/IG

ID1/IG I D/I G

(or I

D1/I

G)

Figure 7.6: The intensity ratio between D and G peaks (ID/IG) and the tted paramagneticcenter density (N, at 1.8 K) vs. neutron irradiation uence. The grey bar indicates thesaturation value of ID/IG for ion implanted graphite [153].

incident light was inclined by 45 to the sample surface. The signals were collected in the

total electron yield mode at room temperature. All the spectra are normalized by the input

ux for comparison.

As shown in Fig. 7.7, there are two resonances around 285 eV and 292 eV, respectively.

They correspond to the transitions from 1s core-level electrons to π∗ and σ∗ empty states,

respectively. For samples 3H and 6H with a small neutron uence, there is no signicant

change either in the peak intensity or in the peak shape compared with the virgin sample.

After the irradiation over 30 hours, the intensity of the π∗ peak decreases, which indicates

that the aromatic π system is severely perturbed. At the same time, the π∗ and σ∗ features

are becoming broader. In previous literature, it has been shown that the π∗ and σ∗ resonances

of carbon are much more broadened in proton implanted graphite than our case here [30, 34].

The inset of Fig. 7.7 shows a zoom into the energy range 280284 eV. Compared with

previous results on ion implanted graphite [73], the fundamental dierence of our sample

is the missing of a pre-edge peak at around 282 eV. In ref. [73], a new small, but sizeable

peak in the pre-edge region (281.5 eV to 284.5 eV) [73], has been reported in ion implanted

ferromagnetic graphite. This new peak was attributed to be closely related with defect states

near the Fermi energy level, and it was temporarily assigned to rehybridized C-H bonds.


280 285 290 295 300

280 281 282 283 284

Photon energy (eV)

Virgin 3H 6H 30H 150H

Inte

nsity

(arb

.uni

ts)

Figure 7.7: The NEXAFS spectra of the graphite samples after neutron irradiation fordierent time. Inset: zoom into the energy range 280284 eV.

7.4 Discussion

We have investigated the magnetic and structural properties of graphite after neutron irra-

diation. Dierent from ion implantation, neutron irradiation can introduce defects in the

whole graphite sample. The resulting magnetization is very large and allows one to draw a

reliable conclusion free of the inuence of contamination. Our experimental results lead to

two conclusions: (1) only spin 1/2 paramagnetism is induced in graphite by neutron irradi-

ation; and (2) both in-plane vacancies and out-of-plane defects appear after irradiation. In

this discussion, we attempt to correlate the magnetization and defects and to understand

why the magnetic ordering is lacking.

7.4.1 The origin of the paramagnetism

Defect induced magnetism in both graphite and graphene has been intensively investigated

theoretically. Structural defects, in general, can give rise to localized electronic states. It

is well accepted that the in-plane vacancies are the origin of local magnetic moments [35].

Upon removal of one atom, each of the three neighboring atoms has one sp2 dangling bond.

Two of the C atoms can form a pentagon, leaving one bond unsaturated. This remaining

dangling bond is responsible for the magnetic moment. Moreover, the at bands associated

with defects lead to an increase in the density of states at the Fermi level. Lehtinen et

al., used spin-polarized DFT and demonstrated that vacancies in graphite are magnetic [36].

7.4. DISCUSSION 87

Figure 7.8: The top (left) and side (right) view of the two considered trans-planar divacancies:V1

2 (a, c) and V22 (b, d). Black balls are carbon atoms. Bonds between two neighboring atoms

are colored as a function of length: black stands for standard distances [2.70 ± 0.05 Bohrradius (a0)], blue and red stand for short (2.60±0.05 a0) and long (2.80±0.05 a0) distances,respectively.

They also found that hydrogen will strongly adsorb at vacancies in graphite, maintaining the

magnetic moment of the defect. Zhang et al. [37] have conrmed that the local moments

appear near the vacancies and with increasing vacancy accumulation the magnetization

decreases non-monotonically. Using a combination of a mean-eld Hubbard model and rst

principles calculations, Yazyev also conrmed that vacancies in graphite and graphene can

result in net magnetic moments [38], while the preserved stacking order of graphene layers is

shown to be a necessary condition for achieving a nite net magnetic moment of irradiated

graphite. In most calculations, the moment per vacancy is sizeable up to 12 µB [36, 37].

Indeed, by scanning tunneling microscopy experiments, Ugeda et al. have observed a sharp

electronic resonance at the Fermi energy around a single vacancy in graphite, which can be

associated with the formation of local magnetic moments [39].

In our neutron irradiated graphite, we observed a strong correlation between the mag-

netization and vacancies. Figure 7.6 shows the irradiation-uence dependent magnetization

and the values of ID/IG of the Raman spectra. At the low uence regime, the density of

magnetic moments shows an excellent correlation with ID/IG (the density of in-plane va-

cancies): both increase monotonically with the uence. This indicates an agreement with

the theoretical calculation: the vacancy in graphite results in local magnetic moment. In

the next subsection, we discuss the role of out-of-plane defects.

7.4.2 The role of trans-planar defects

As shown in Fig. 7.6, ID/IG reaches its saturation value of around 1.21.4 when the neutron

uence is higher. ID/IG of 1.21.4 is also a threshold of amorphisation in ion irradiated

graphite [153]. Despite the saturation in the density of in-plane vacancies, the density

of local moments still increases with neutron uence as shown in Fig. 7.6. What is the

contribution for these additional local magnetic moments? We consider the role of the

trans-planar defects. As shown in Fig. 7.5, for the largest irradiation uence, D1 peaks

appears, which has been attributed to the trans-planar defects [152]. In order to assess

the experimental ndings described in the above sections, we have investigated the possible

magnetic state for trans-planar defects.


Table 7.1: Formation energy (Ef ) and energy dierence (Espin) between the singlet andtriplet states for the three considered divacancies. The values in bracket are correspondingresults in ref. [158].

Samples Ef (eV) Espin (meV)V2 in-plane 7.55 (8.7) 2

V12 trans-planar 13.85 (14.6) 560

V22 trans-planar 12.77 (13.0) 1

We start our analysis from the seminal work of Telling et al. [158] who rstly propose

the trans-planar divacancy congurations (see Figure 7.8) that breaks the symmetry rules

in graphite. Interestingly, the spin-polarized states for these defects was discussed in the

paper but never assessed. In order to answer this question without any artifacts we have

decided to run additional spin-polarized calculations in a super-cell which is large enough to

avoid elastic eects between neighboring defect images (in-plane). Systems containing 448

atoms per graphene sheets have proven to be reliable to study triangular vacancy clusters

in hexagonal boron nitride sheets [159] and are also used in the present study. Here, two

of these sheets with Bernal stacking were considered. The distance between the two sheets

was xed to 6.45 Bohr radii (a0) for simplifying the treatment of the interlayer. This is

achieved by the freezing of the perpendicular displacements in a band close to the edges

of the super-cell (pink area in Fig. 7.8). This treatment allows for a full relaxation both

in-plane and out-of-plane of the central part of the super-cell where the defect sits. The

PBE exchange and correlation function was chosen as it was found to well reproduce the

in-plane relaxations [160]. The BigDFT [161] code was used to perform DFT calculations

within surface boundary conditions [162].

The two trans-planar divacancies V22 and V1

2 are considered together with the in-plane

divacancy V2 as a reference. The formation energy of the defect is calculated using the

chemical potential of carbon in the pristine bilayer system. Singlet and triplet states are

obtained by running spin averaged and spin polarized calculations, respectively. The results

are summarized in table 7.1. The formation energy of the three defects increases in-line with

the initial report of Telling et al. [158]. However, important dierences arise, underlying the

role of the in-plane relaxations that were blocked in the previously used 64 atoms box [158].

Indeed, while the estimated error of about 0.4 eV [158] holds for the trans-planar vacancies,

the dierence is much more bigger for V2. As a consequence, the energy dierence between

the two trans-planar divacancies remains in the order of 1.5 eV.

In Table 7.1 we also report the singlet to triplet formation energy for each defect. In line

with the report of a double bond [158] for the inter-planar C-C bond (see bond length scale

in gure 7.8), the V22 divacancy is in a singlet state. This situation is dierent for the V1

2

divacancy: the inter-planar C-C bond is longer and more twisted, thus preventing further

hybridization between the two carbon atoms. As a consequence, the triplet state is stabilized

by more than 500 meV with respect to the singlet state. According to Telling et al., the

existence of triplet states gives a solid explanation for the observed spin 1/2 paramagnetism.

7.4. DISCUSSION 89

7.4.3 Why is the magnetic interaction missing?

As shown in Fig. 7.2 and Fig. 7.6, the paramagnetism in graphite can be strongly enhanced

by irradiation induced defects. After irradiation even to the largest uence, the samples are

not fully amorphous and ID/IG of around 1.2 corresponds to a planar grain size of 3.5 nm

[153]. Why is the magnetic interaction between the generated paramagnetic centers then

missing? To answer this question, we rst need to estimate the density of defects, i.e. the

average distance between adjacent local moments.

Assuming the defects are homogeneously distributed in the sample matrix, we estimate

the average distances (r) between local moments in our irradiated graphite samples. This

value amounts to 2.2 nm for the sample with the largest neutron uence. The nearest

average distance between two spins is around 16a (a = 0.14 nm is the C-C bond length).

Therefore, the direct coupling between the localized spins at the vacancies is nearly negligible.

Alternatively, the Ruderman-Kittel-Kasuya-Yosida (RKKY) coupling is suggested to appear

in defective graphite and graphene [163]. This coupling might be ferromagnetic at a nite

temperature when kF r 1. If assuming a Fermi energy of 20 meV in graphite [115],

the inverse of the Fermi wave vector 1/kF ∼ 30 nm. To have ferromagnetic ordering, the

distance between two spins r should be 30 nm which corresponds to a spin density of

3.7×1018 cm−3. In principle, all samples fulll this criteria. All these moments may tend to

be ferromagnetically coupled via the RKKY coupling, although the Curie temperature can

be very low [115]. However, we do not observe any magnetic ordering down to 1.8 K even

for sample 150H. It is not practical to further increase the defect density, since the stacking

order of graphenes plane must be preserved [38, 117]. Our sample with the highest neutron

uence is already at the verge of amorphization. A larger irradiation uence will perturb

the graphene lattice too much and destroy the necessary band structure and carrier density.

Both published theory and experimental results suggest a crucial role of hydrogen or ni-

trogen chemisorption in enhancing the spin density and in establishing the magnetic coupling

[36, 37, 38, 115, 34]. All these moments from chemisorption will tend to be ferromagnetically

coupled, enhancing the Curie temperature by the RKKY coupling. Recently, by careful an-

gular dependent NEXAFS, He et al. observed a new small peak in the pre-edge region (281.5

eV to 284.5 eV) [117]. This new peak has been interpreted to be closely related with the

defect states near the Fermi energy level and it is assigned to the formation of C-H bonds

[34]. Ohldag et al. also observed an X-ray magnetic circular dichroism (XMCD) signal in the

pre-edge region of the C K-edge. However, as shown in Fig. 7.7, our present ndings do not

exhibit any new peak in the pre-edge of the C K-edge. Meanwhile, it is not expected that

hydrogen or nitrogen can be absorbed and homogenously distributed in neutron irradiated

bulk graphite. This may explain why the ferromagnetic coupling is missing. Without the

help of the hybridization induced by the chemisorption, the defects generated by irradiation

could not form enough unoccupied states near the Fermi level, so that the Stoner criterion

is not met with and no ferromagnetic order is induced.


7.5 Conclusion

As a conclusion, neutron irradiation introduces only spin 1/2 paramagnetism in graphite over

a broad uence range. There is no indication of bulk ferromagnetism induced by defects.

Using Raman and XAS spectroscopies, we investigated the structure evolution during the

whole irradiation process. The creation of trans-planar vacancies (without dangling bonds)

reduces the concentration of single in-plane vacancies. By correlating the magnetic and

structural properties, we conclude that both in-plane vacancies and trans-planar defects can

form local magnetic moments. The paramagnetism scales up with increasing the amount of

defects, however, magnetic order unlikely can occur in a bulk form in defective graphite.

Chapter 8

Summary and outlook

8.1 Summary

In this thesis, defect-induced ferromagnetism in ion implanted and neutron irradiated SiC

has been systematically investigated. We have tried to establish the relation between the de-

fects and ferromagnetism and to understand the mechanism of the observed ferromagnetism.

The structure changes of 6H-SiC are measured by XRD and RBS. The XRD θ-2θ scans

at SiC (000 12) shows that the normal strain is roughly proportional to the uence. Its

corresponding reciprocal spacing mapping (RSM) reveals a streak in the vertical and no

obvious broadening in the horizontal direction. These experiments indicate that defects are

point defects or small defect clusters. We nd that the defect-induced ferromagnetism only

exists in a narrow uence range. The initial introduction of structural disorder leads to

pronounced magnetization. Further increasing disorder induces the amorphization of the

host SiC crystal and therefore decreases the saturation magnetization. Approching to full

amorphization, the saturation magnetization nearly drops to zero.

By a careful measurement and analyzing the magnetic properties of Ne implanted SiC,

we have found a multi-phase nature of the observed ferromagnetism. Three magnetic phases

(paramagnetic,superparamagnetic and ferromagnetic phases) can be identied by numerical

tting. For superparamagnetism, the blocking temperature is slightly above 50 K, and the

average size of each superparamagnetic cluster contains 8.1×104 µB. For the ferromagnetic

contribution, the tted Curie temperatures are all around 760 K for dierent samples. Based

on these experiments, we can envision the following pictures:

• Defects in SiC are inhomogenously distributed,

• Isolated, uncoupled defects contribute to the paramagnetism,

• Coupled defects result in the superparamagnetic and ferromagnetic components.

Moreover, the ferromagnetic SiC samples exhibit a pronounced magnetic anisotropy with

the easy axis along the SiC(0001) basal plane. By comparing with the model and experimen-

tal data in literature, we tentatively attribute the magnetic properties to the inhomogenous

91

92 CHAPTER 8. SUMMARY AND OUTLOOK

distribution of defects in SiC and the preferential clustering along the basal plane.

To understand the defect-induced ferromagnetism in SiC, we carried out X-ray absorp-

tion spectroscopies at both the silicon and carbon K-edges and rst-principles calculations.

We observed no spin-polarized states close to the Fermi level occur at silicon atoms. In sharp

contrast to the silicon K-edge, a clear XMCD signal appears at the carbon K-edge. These

experimental observations are in a nice agrement with rst-principles calculation. Therefore,

the p electrons of the nearest-neighbor carbon atoms of VSiVC are mainly responsible for

the observed ferromagnetism.

Neutron irradiated SiC and graphite is another meaningful attempt to modify the mag-

netic properties in the bulk samples. A broad neutron uence range is applied for both SiC

and graphite, which should modify the material from slight damage to approaching amor-

phous. Besides a weak ferromagnetic contribution in SiC or in graphite, we observe a strong

paramagnetism, scaling up with the neutron uence. However, no ferromagnetic order is

detected between the induced magnetic centers as revealed by sensitive magnetometry down

to 1.8 K. The ferromagnetic contribution in SiC is induced by neutron irradiation and only

occurs in a narrow uence window or after annealing. On the other hand, a weak ferromag-

netic contribution already appears in the non-irradiated graphite and remains unchanged

upon neutron irradiation. Nevertheless, it seems non-realistic to make the bulk specimens

ferromagnetic by introducing defects. Instead, it seems that defect-induced ferromagnetism

rather locally appears in particular regions, like surface/interface/grain boundaries.

8.2 Outlook:

Although the defect-induced ferromagnetism is reproducible in SiC, and the magnetic proper-

ties and the structure evolution with increasing ion/neutron uence haven been investigated,

there are still several questions unsolved:

(1) How can one locally identify the ferromagnetic regions in SiC?

From our investigation of ion implanted and neutron irradiated SiC, there are evidences

that the ferromagnetic coupling is not homogenously occurring in the sample. The ferro-

magnetism distributes non-homogeneously regarding its lateral distribution or depth dis-

tribution. The question remains how to locally address the ferromagnetism. We propose

a careful magnetic eld microscopy investigation to scan over the surface. For the depth

distribution, physical or chemical etching could be used to control the aected depth. And,

together with step by step magnetization measurement, one probably can identify the depth

prole of the magnetization. Such an investigation may allow us to identify if the ferromag-

netism is mainly at the surface, near the RP or near the end of the ion range.

(2) What is the role of free carriers in magnetic SiC?

Magnetotransport can directly determine the free carrier concentration, mobility and the

8.2. OUTLOOK: 93

amount of spin-polarized charge carriers. From the appearance of an anomalous Hall eect

and magnetoresistance, one can conrm the coupling between free carriers and magnetic

moments. In the future experiment, this kind of measurements should be performed. For

this experiment, we have to use doped SiC. However, we also bear in mind the conductivity

change after irradiation.

(3) What is the magnetic state of a single defect in SiC?

By scanning tunneling microscopy experiments, Ugeda et al. have observed a sharp elec-

tronic resonance at the Fermi energy around a single vacancy in graphite, which can be

associated with the formation of local magnetic moments [39]. In the future, such an exper-

iment for SiC should be feasible.

(4) What is the thermal stability of defect-induced ferromagnetism in SiC?

The thermal stability is the key factor for potential application because some defects will

recombine or even disappear at room temperature. Sometimes the neutralization occurring

at room temperature will also lead to the loss of the ferromagnetism. Moreover, it will lead to

a better understanding of the thermal dynamics of the defects especially in the paramagnetic

regime. The annealing eect will also help us to correlate the spin-polarization with the

specic point/extended defects.

94 CHAPTER 8. SUMMARY AND OUTLOOK

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Appendix A

Publications

A.1 Paper published or accepted

1. Yutian Wang, Lin Li, S. Prucnal, Xuliang Chen, Wei Tong, Zhaorong Yang, F.

Munnik, K. Potzger, W. Skorupa, S. Gemming, M. Helm, Shengqiang Zhou, Dis-

entangling defect-induced ferromagnetism in SiC, Phys. Rev. B., 89, 014417

(2014).

2. Yutian Wang, Xuliang Chen, Lin Li, A. Shalimov, Wei Tong, S. Prucnal, F. Munnik,

Zhaorong Yang, W. Skorupa, M. Helm, Shengqiang Zhou, Structural and magnetic

properties of irradiated SiC. J. Appl. Phys., 115, 17C104 (2014).

3. Kun Gao, S. Prucnal, R. Huebner, C. Baehtz, I. Skorupa, Yutian Wang, W. Skorupa,

M. Helm, Shengqiang Zhou, Ge1−xSnx alloys synthesized by ion implantation

and pulsed laser melting. Appl. Phys. Lett., 105, 042107 (2014).

4. Qingfang Luan, Yuechen Jia, Yutian Wang, S. Akhmadaliev, Shengqiang Zhou,

Vázquez de Aldana, R. Javier, Yang Tan, Feng Chen, Optical ridge waveguides

in 4H-SiC single crystal produced by combination of carbon ion irradiation

and femtosecond laser ablation. Optical Materials Express, 4, 1167 (2014).

5. Shengqiang Zhou, Yutian Wang, Zenan Jiang, E. Weschke, M. Helm, Ferromag-

netic InMnAs on InAs Prepared by Ion Implantation and Pulsed Laser

Annealing. Appl. Phys. Express., 5, 093007 (2012).

6. Shengqiang Zhou, Wenxu Zhang, A. Shalimov,Yutian Wang, Zhisuo Huang, D. Bürger,

A. Mücklich, Wanli Zhang, H. Schmidt, M .Helm,Magnetic Mn5Ge3 nanocrystals

embedded in crystalline Ge: a magnet/semiconductor hybrid synthesized by

ion implantation, Nanoscale. Res. Lett., 7, 528, (2012).

A.2 Paper submitted or in preparation

1. Yutian Wang, M. Helm, P. Pochet, C. A. Jenkins, E. Arenholz, G. Bukalis, S. Gem-

ming, and Shengqiang Zhou, Revisiting defect-induced magnetism in graphite

through neutron irradiation. Phys. Res. B. to be submitted (2014).

109

110 APPENDIX A. PUBLICATIONS

2. Yutian Wang, Yu Liu, Gang Wang, W. Anwand, C. A. Jenkins, E. Arenholz, F.

Munnik, O. D. Gordan, G. Salvan, Dietrich R. T. Zahn, Xiaolong Chen, S. Gemming,

M. Helm, Shengqiang Zhou, Carbon p Electron Ferromagnetism in SiC Single

Crystal. Scientic Reports, submitted (2014).

3. Yutian Wang, Yu Liu, E. Wendler, Gang Wang, Xuliang Chen, Wei Tong, Zhaorong

Yang, F. Munnik, G. Bukalis, Xiaolong Chen, S. Gemming, M. Helm, Shengqiang

Zhou, Why is defect induced ferromagnetism weak. in preparation (2014).

4. P. Satyarthi, S. Ghosh, P. Kumar, D. Kanjilal, E. Weschke, Yutian Wang, S. Zhou,

D. Bürger, I. Skorupa, H. Schmidt, L. Gregoratti, P. Srivastava, Irradiation induced

tunable spontaneous magnetization in Zn0.95Co0.05O epitaxial lms. Phys.

Res. B. to be submitted (2014).

5. Ye Yuan, M. Khalid, Chuangui Wu, Wenxu Zhang, Yutian Wang, E. Weschke ,

Kun Gao, C. Baehtz, W. Skorupa, M. Helm, Shengqiang Zhou. High Curie tem-

perature and perpendicular magnetic anisotropy in homoepitaxial InMnAs

lms. Appl. Phys. Lett. to be submitted (2014).

Appendix B

Curriculum vitae

B.1 Personal data

Name: Yutian Wang

Birthday: 29 Mar. 1984

Birth place: Shannxi, China

Family status: single

B.2 Education

Sep. 2000 - Jul. 2003 No. 6 High school of Xi'an, China

Sep. 2003 - Jul. 2007 Bachelor degree in Science Hefei University of Technology, China

Sep. 2007 - Jul. 2010 Master degree in Science

South China Normal University, China

Thesis: First-principles study of Mg-doped in GaN nanowires

Oct. 2010 - Aug. 2011 PhD student

Free university of Berlin

Topic: Near-eld optical microscopy in liquid environment for the

application to medical problems

Oct. 2011 - Dec. 2014 PhD student

Helmholtz-Zentrum Dresden-Rossendorf Dresden-Rossendorf

TU-Dresden, Germany

Topic: Defect-induced ferromagnetism in SiC

B.3 Short-term advanced school

Oct. 2012 6th International Mittelwihr School on Magnetism and Synchrotron Radiation

Mittel, France

111

112 APPENDIX B. CURRICULUM VITAE

Erklärung

Hiermit versichere ich, daÿich die vorliegende Arbeit ohne unzulässige Hilfe Dritter und

ohne Benutzung anderer als der angegebenen Hilfsmittel angefertigt habe; die aus fremden

Quellen direkt oder indirekt übernommenen Gedanken sind als solche kenntlich gemacht.

Die Arbeit wurde bisher weder im Inland noch im Ausland in gleicher oder ähnlicher Form

einer anderen Prüfungsbehörde vorgelegt.

Diese Dissertation wurde angefertigt im

Helmholtz-Zentrum Dresden-Rossendorf

Institut für Ionenstrahlphysik und Materialforschung

Postfach 51 01 19

01314 Dresden

Die wissenschaftliche Betreuung der Arbeit erfolgte durch Prof. Dr. Manfred Helm.

Ich versichere, an keiner Institution, auch nicht im Ausland, jemals den Antrag auf Erünung

eines Promotionsverfahrens gestellt zu haben.

Ich erkenne die Promotionsordnung der Fakultät Mathematik und Naturwissenschaften der

Technischen Universität Dresden vom 23.10.2011 sowie deren Änderung vom 10.10.2014 an.

Dresden, 30.01.2015

Yutian Wang

113

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