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Rational design of new materials for spintronics: Co2FeZ (Z=Al, Ga, Si, Ge)

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2008 Sci. Technol. Adv. Mater. 9 014102

(http://iopscience.iop.org/1468-6996/9/1/014102)

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Sci. Technol. Adv. Mater.9 (2008) 014102 (13pp) doi:10.1088/1468-6996/9/1/014102

TOPICAL REVIEW

Rational design of new materials forspintronics: Co2FeZ (Z = Al, Ga, Si, Ge)*Benjamin Balke1, Sabine Wurmehl1, Gerhard H Fecher1, Claudia Felser1

and Jürgen Kübler2

1 Institut für Anorganische Chemie und Analytische Chemie, Johannes Gutenberg-Universität Mainz,D-55099 Mainz, Germany2 Institut für Festkörperphysik, Technische Universität Darmstadt, Germany

E-mail: felser@uni-mainz.deandjkubler@fkp.tu-darmstadt.de

Received 3 August 2007Accepted for publication 29 January 2008Published 13 March 2008Online atstacks.iop.org/STAM/9/014102

AbstractSpintronic is a multidisciplinary field and a new research area. New materials must be foundfor satisfying the different types of demands. The search for stable half-metallic ferromagnetsand ferromagnetic semiconductors with Curie temperatures higher than room temperature isstill a challenge for solid state scientists. A general understanding of how structures are relatedto properties is a necessary prerequisite for material design. Computational simulations are animportant tool for a rational design of new materials. The new developments in this new fieldare reported from the point of view of material scientists. The development of magneticHeusler compounds specifically designed as material for spintronic applications has madetremendous progress in the very recent past. Heusler compounds can be made as half-metals,showing a high spin polarization of the conduction electrons of up to 100% in magnetic tunneljunctions. High Curie temperatures were found in Co2-based Heusler compounds with valuesup to 1120 K in Co2FeSi. The latest results at the time of writing are a tunnelling magnetresistance (TMR) device made from the Co2FeAl0.5Si0.5 Heusler compound and working atroom temperature with a (TMR) effect higher than 200%. Good interfaces and a well-orderedcompound are the precondition to realize the predicted half-metallic properties. The seriesCo2FeAl1−xSix is found to exhibit half-metallic ferromagnetism over a broad range, and it isshown that electron doping stabilizes the gap in the minority states forx = 0.5. This might bea reason for the exceptional temperature behaviour of Co2FeAl0.5Si0.5 TMR devices.

Using x-ray diffraction (XRD), it was shown conclusively that Co2FeAl crystallizes inthe B2 structure whereas Co2FeSi crystallizes in theL21 structure. For the compoundsCo2FeGa or Co2FeGe, with Curie temperatures expected higher than 1000 K, the standardXRD technique using laboratory sources cannot be used to easily distinguish between the twostructures. For this reason, the EXAFS technique was used to elucidate the structure of thesetwo compounds. Analysis of the data indicated that both compounds crystallize in theL21

structure which makes these two compounds suitable new candidates as materials in magnetictunnel junctions.

Keywords: Heusler compounds, electronic structure, intermetallics, half-metallic ferromagnets

(Some figures in this article are in colour only in the electronic version.)

∗ Invited paper.

1468-6996/08/014102+13$30.00 1 © 2008 National Institute for Materials Science Printed in the UK

Sci. Technol. Adv. Mater.9 (2008) 014102 Topical Review

1. Introduction

Spintronic is a multidisciplinary field and a new researcharea. New materials must be found that satisfy differenttypes of demands like high spin polarization or highCurie temperature. One important group of materials withsuitable candidates for spintronic applications are the Heuslercompounds [1] as found from reviews about spintronic andhalf-metals in general in the recent past [2–4]. Heusler’scompounds[5] are ternary intermetallics with a 2 : 1 : 1stoichiometry and the chemical formulaX2Y Z. They usuallyconsist of two transition metals (X2, Y) and a main groupelement (Z). They first attracted the interest of the magnetismcommunity when Heusleret al had shown that the compoundCuxMnyAl becomes ferromagnetic in the 2 : 1 : 1 form (x = 2andy = 1), even none of its constituents is ferromagnetic byitself [6]. However, it took three decades before their structurewas explained to be that of an ordered compound with a facecentred cubic structure [7, 8].

The main interest during the first decades after thediscovery of the Heusler compounds was concentrated on Cuand Mn containing compounds. Co2-based compounds weresynthesized and investigated in the 1970s [9]. Kübleret al [10]recognized that the minority spin densities at the Fermi energy(εF) nearly vanish for Co2MnAl and Co2MnSn. The authorsconcluded that this should lead to peculiar transport propertiesin these Heusler compounds because only the majority densitycontributes to the states atεF. At the same time, de Grootet al [11] proposed the concept of the so-called half-metallicferromagnets (HMFs) that are materials predicted to exhibit100% spin polarization atεF. This exceptional property wouldmake the HMF ideal candidates for spin injection devices tobe used in spin electronics [12].

The calculation of the electronic structure plays animportant role in determining the magnetic propertiesof Heusler compounds and, in particular, for predictinghalf-metallic ferromagnetism. Therefore, the band structurecalculations must be performed very carefully. The firstattempt to calculate the band structure of some Co2

based compounds (Co2MnSn, Co2TiSi and Co2TiAl) didnot indicate half-metallic ferromagnetism [13]. Thesecalculations displayed a minimum of the minority density ofstates (DOS) atεF but not a gap. At that time, the calculationswere based on spherical potentials, and the exchange-correlation potential of the local spin density approximation(LSDA) was used in a rather simple form [14–17]. The firstclear indication of half-metallic ferromagnetism in Co2 basedHeusler compounds was reported by Ishidaet al [18, 19] forCo2MnZ and Ru2MnZ (Z = Al, Si, Sn and Sb). Using fullsymmetry potentials, Mohnet al [20] found the magneticground state of Co2TiZ (Z = Al and Sn), but not a half-metallic state. Galanakiset al [21] reported half-metallicbehaviour in variousX2Y Z compounds, but not for the Co2

compounds with Ti or Fe. The results were compatible withthose found for the Mn compounds as calculated by Picozzietal [22] using the generalized gradient approximation (GGA)instead of the pure LSDA. The GGA, as introduced by Perdewet al [23–26], accounts for gradients of the density that are

Figure 1. Slater–Pauling curve for 3d transition metals and theiralloys. Experimental values forselectedCo2-based Heuslercompounds are given for comparison. (Note: theA1−x Bx alloys aregiven as AB in the legend, for short.)

absent in the pure LSDA parameterization of the exchange-correlation functional [14–17]. Using spherical potentialsand the GGA, a half-metallic state could not be verifiedfor Co2FeAl [27, 28]. A half-metallic ferromagnetic groundstate was also found for the complete series Co2Cr1−xFexAl,when the full symmetry potentials were used along with theGGA in the calculations [29]. This clearly indicates that oneprincipally needs both the full symmetry potentials and theGGA to find the correct electronic structure and ground statefor the Heusler compounds. In some cases it is sufficient touse LSDA with spherical potentials. Parts of the results shownin section8 and the work of Kübleret al [10] are calculatedusing this method.

2. Theory and motivation

For both scientific and technological reasons it is useful todefine the electron spin polarization at the Fermi energy ofa material, although it is difficult to measure [30]. The spinpolarization atεF is given by:

P =ρ↑(εF) − ρ↓(εF)

ρ↑(εF) +ρ↓(εF), (1)

whereρ↑(εF) andρ↓(εF) are the spin projected DOS at theεF.The arrows↑ and ↓ assign states of opposite spin that aremajority and minority states, respectively.P vanishes forparamagnetic or in anti-ferromagnetic materials even belowthe magnetic transition temperature. However, it has a finitevalue in ferromagnetic or ferrimagnetic materials below theCurie temperature. The electrons atεF are fully spin polarized(P = 100%) when eitherρ↑(εF) or ρ↓(εF) equals zero. Inthe present work, the classification scheme for half-metals asproposed by Coeyet al is used [1, 12].

The Slater–Pauling curve [31, 32] is a simple way tostudy for ferromagnetic alloys the interrelation between thevalence electron concentration and the magnetic moments(see figure1). It is well known that Heusler compounds

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based on Co2 follow the Slater–Pauling rule for predictingtheir total spin magnetic moment [21, 33, 34] that scaleslinearly with the number of valence electrons. The Co2- basedcompounds are found on the so calledlocalizedpart of theSlater–Pauling curve [33, 34] where the magnetic momentincreases with an increasing number of valence electrons. Inthis part of the curve one has predominantly materials withbcc or bcc-derived structures. Like iron, for the example,the electronic structure of these alloys exhibits a minimumin the minority DOS and the Fermi energy is pinned inthis minimum. The minimum in the minority spin densityconstrains the number of occupied electrons in the minoritybands to be approximately three such that the number ofmajority electrons increases proportional to the total numberof electrons and so does the magnetic moment as a directconsequence (for more details see for example: [33, 34]).

Half-metallic ferromagnets, like the Co2 based Heuslercompounds exhibit not only a minimum but a real gap in theminority DOS and the Fermi energy is pinned inside of thatgap. From this point of view, the Slater–Pauling rule is strictlyfulfilled with

mHMF = nV − 6, (2)

for the mean magnetic moment per atom (mHMF). nV isthe mean number of valence electrons per atom found byaveraging over all atoms and 6 is two times the mean numberof occupied minority states. The advantage of this equationis that it neither depends on the number of atoms in thecompound nor relies on integer site occupancies.

For ordered compounds with different kinds of atoms itmight be more convenient to work with all atoms of the unitcell. In the case of four atoms per unit cell, as in Heuslercompounds, one has to subtract 24 (6 multiplied by thenumber of atoms) from the accumulated number of valenceelectrons in the unit cellNV (s, d electrons for the transitionmetals ands, p electrons for the main group element) to findthe magnetic moment per unit cell (m):

m = NV − 24. (3)

with NV denoting the accumulated number of valenceelectrons in the unit cell containing four atoms. In the case ofHeusler compounds, the number 24 arises from the number ofcompletely occupied minority bands that has to be 12 in thehalf-metallic state. In particular, these are ones (a1g), threep (t1u), and eightd bands [35, 36]. The latter consist of twotriply degenerate bands witht2g symmetry and one witheg

symmetry (note that the given assignments of the irreduciblerepresentations are only valid at the0-point and neglect thespin of the electrons.).

A similar rule was first noted by Kübler [35] for C1b

compounds with three atoms per unit cell (mC1b = NV − 18).In both cases the magnetic moment per unit cell becomesstrictly integer (in multiples of Bohr magnetonsµB) for typeI or II half-metals, what may be seen as an advantage of thevalence electron rule(equation (3)) compared to the originalSlater–Paulingapproach (equation (2)) even so it suggeststhe existence of different laws. It is worthwhile to note that

Figure 2. Curie-temperatures of X2YZ Heusler compounds. Theline is found from a linear fit of the measuredTC for Co2-basedcompounds (red cross). The elemental metals Fe, Co and Ni aregiven for comparison (left panel). Calculated versus measured Curietemperatures for Co2-based compounds. The calculation done withGGA are denoted with a plus sign (right panel).

equation (3) leads only for ternary 2 : 1 : 1 compounds tointeger magnetic moments but not for quarternary derivativeslike X2Y1−xYx Z or X2Y Z1−xZx as reported in [37] or [38],respectively. In those cases, one observes from (3) non-integervalues of the magnetic moment even in the half-metallic casedue to the non-integer site occupancy.

The Slater–Pauling curve is shown in figure1.Experimental values of the magnetic moments in selectedCo2-based Heusler compounds are compared to 3d transitionmetals and their alloys. This comparison is only possible ifthe Slater–Pauling rule in the formulation of (2) is used. Theitinerant part of the curve is included for clarity about thebehaviour of the Heusler compounds in comparison to otherferromagnetic alloys. For a detailed discussion of that partsee [1, 33, 34].

Inspecting the magnetic data of the known Heuslercompounds in more detail (see data and referencesin [39, 40]), one finds a very interesting aspect. A lineardependence is obtained approximately for Co2-based Heuslercompounds when plotting the Curie temperature (TC) of theknown, 3d metal based Heusler compounds as function oftheir magnetic moment (see figure2, left panel). According tothis plot,TC is highest for those half-metallic compounds thatexhibit a large magnetic moment, or equivalently for thosewith a high valence electron concentration as derived fromthe Slater–Pauling rule.TC is estimated to be above 1000 Kfor compounds with 6µB by an extrapolation from the lineardependence.

Recently, Kübler [41] developed anab initio estimatefor calculating the Curie temperature of an itinerant-electronferromagnet in the spherical approximation using the LDAscheme. With this approach, Kübleret al [42] calculatedthe Curie temperatures of Co2-based Heusler compounds.Figure 2 (right panel) compares the calculated Curietemperatures with the measured ones for several Co2-basedcompounds. A very good agreement between calculation andexperiment is obvious. A Curie temperature of 1185 K was

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Sci. Technol. Adv. Mater.9 (2008) 014102 Topical Review

calculated for Co2FeSi that fits quite well the experimentalvalue of 1100 K [43].

From this finding one expects Co2FeZ (with Z = Al, Ga,Si or Ge) compounds to have a large magnetic moment andhigh Curie temperatures that makes these compounds suitablecandidates for spintronic applications.

3. Crystal structure

Besides the high Curie temperature the crystallographic orderof the sample is highly important for the use of thesecompounds in any kind of spintronic application.

Generally, theX2Y Z Heusler compounds crystallize inthe cubicL21 structure (space group no 225:F m3̄m), theprototype is AlCu2Mn. The structure was first explained byHeusler [7] as well as Bradley and Rodgers [8]. In general,the X and Y atoms are transition metals andZ is a maingroup element. In some cases,Y is replaced by a rare earthelement. TheX atoms are placed on the Wyckoff position 8c( 1

4, 14, 1

4). TheY and Z atoms are located on 4a (0, 0, 0) and4b ( 1

2, 12, 1

2) positions, respectively. The cubicL21 structureconsists of four interpenetratingfccsub-lattices, two of whichare equally occupied byX. The two X-site fcc sub-latticescombine to form a simple cubic sub-lattice. TheY and Zatoms occupy alternatingly the centre of the simple cubic sub-lattice resulting in a CsCl-type super structure. This resultsin Oh symmetry for the 4a and 4b positions, whereas the 8cposition hasTd symmetry.

The cubic X2Y Z compounds are not only found withthe AlCu2Mn type structure but also with the CuHg2Ti typestructure (note that the classification of the cubicX2Y Zcompounds with those two structures is sometimes notuniquely given inPearson’s Handbook[44]). The CuHg2Titype structure exhibitsTd symmetry (space group no 216:F 4̄3m). In that structure theX2 atoms occupy the nonequivalent 4a, 4c Wyckoff positions at(0, 0, 0) and( 1

4, 14, 1

4).The Y and Z are located on 4b( 1

2, 12, 1

2) and 4d( 34, 3

4, 34)

positions, respectively. All four positions adoptTd symmetryand there is no position withOh symmetry. This structure issimilar to theXY Z compounds withC1b structure, but withthe vacancy filled by an additionalX atom. This structure isfrequently observed if the nuclear charge of theY element islarger than the one of theX element from the same period, thatis Z(Y) > Z(X) for two 3d transition metals. The structuremay also appear in compounds with transition metals fromdifferent periods. However, the two structures may be hardlydistinguishable by XRD and much care has to be taken inthe structural analysis, as both have the generalf cc-likesymmetry.

The reviewing articles of Neumann and Ziebeck [39, 40]summarize a possible disorder in Heusler (X2Y Z) and C1b

(XY Z) compounds. A detailed description of the disorder inL21 andC1b compounds with half and quarter occupancies ofthe sites is given by Bacon and Plant [45]. The simplest typesof disorder are theB2 and theA2 structure. In theB2 structurethe Y and Z atoms are mixing which results in a CsCl-likestructure (see figure3, middle) while in theA2 structure allthe atoms are mixing resulting in a complete alloyed structure

Figure 3. The ordered L21 Heusler structure (left) and the simplesttypes of disorder: The B2 (middle) and the A2 (right) structure.Note that all positions are shifted by( 1

4, 14, 1

4) with respect to thestandardF m3̄m cell to make the CsCl superstructure visible.

(see figure3, right). Almost all properties of the compoundreact very sensitive to any kind of disorder even if there isonly a small amount ofB2-type disorder.

For example, Wurmehlet al calculated the magneticmoments for different kinds of disorder of Co2FeAl andreported a value of 5.46µB for the A2 structure [46]. Theincrease of the magnetic moment in the disorderedA2structure emerges mainly from an increase of the magneticmoment of the Co atoms. At the same time the orbital momentis enhanced. The latter effect can be attributed to the loss ofthe local cubic environment in the disordered structure. It isworthwhile to note that the structural disorder destroys thehalf-metallic character and results in a dramatic decrease ofthe spin polarization [27].

4. Co2FeSi

From the findings above that one expects for Co2FeZ (withZ = Al, Ga, Si or Ge) compounds to have a large magneticmoment and high Curie temperatures Co2FeSi was revisitedas a practical test for the findings above [43, 47].

4.1. Theory

As starting point, self consistent first principle calculationswere performed using the linearized muffin tin orbital(LMTO) method [48], as this method is very fast. Usingthe experimental lattice parameter (aexp = 5.64 Å), the resultspredicted Co2FeSi to be a regular ferromagnet with a magneticmoment of 5.08µB per formula unit. The latter value is muchtoo small compared to the experimental one of 6µB.

More detailed calculations were performed to check ifthe low value of the moment is the result of a particularmethod or the parameterization of the energy functional.The Korringa–Kohn–Rostocker method as provided by Akaiand Dederichs [49] was chosen as this program allowscalculations in the muffin tin (MT) and the atomic sphere(ASA) approximations. Additionally, it provides the coherentpotential approximation (CPA) to be used for disorderedsystems. This method was used to estimate the influence ofdisorder on the magnetic structure.

The calculations were started with the most commonparameterizations of the exchange-correlation functional asgiven by Moruzzi, Janak and Williams (MJW) [50], vonBarth and Hedin (vBH) [16], and Vosco, Wilk, and Nussair(VWN) [17]. The GGA was used in the form given by

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Sci. Technol. Adv. Mater.9 (2008) 014102 Topical Review

Perdewet al [51]. To include non-local effects, the VWNparameterization with additions by Perdewet al [23, 52] wasused (PYVWN). The so-called exact exchange is supposed togive the correct values for the gap in semiconductors usinglocal density approximation. Here it was used in the formgiven by Engel and Vosko (EV) [53].

The calculated total magnetic moments range from≈4.9µB to ≈5.7µB, thus they are throughout too lowcompared to the experiment. They include, however, the valueof 5.27µB found in [21] by means of the full potential KKRmethod.

In the next step, the full potential linear augmented planewave (FLAPW) method as provided by Wien2k [54] was usedto exclude that the observed deviations are due to the sphericalapproximation for the potential (MT or ASA) as used in theabove KKR methods.

First, the exchange-correlation energy functional beingparameterized within the GGA was used. It turned out,however, that the magnetic moment of Co2FeSi is still toosmall compared to the experimental value. Comparing theresult for Co2FeSi, the magnetic moments found by thedifferent calculational schemes are very similar, implying thatCo and Fe atoms are aligned parallel independent of themethod used. The small, induced moment at the Si atom isaligned anti-parallel to that at the transition metal sites. Asfor KKR, the use of the EV parameterization of the energyfunctional did not improve the magnetic moment, the resultwas only 5.72µB.

In contrast to the LMTO or KKR methods (sphericalpotentials), the FLAPW (full symmetry potential) calculationsrevealed a very small gap in the minority states, but beinglocated below the Fermi energy. The fact that the Fermi energycuts the minority bands above the gap causes the magneticmoment to be too low and not integer, as would be expectedfor a HMF.

A structural refinement was performed to check if theexperimental lattice parameter minimizes the total energy. Thedependence of the energy with lattice parametera revealedthat the minimum occurs at the experimentally observedlattice parameteraexp. From the lattice parameter-dependentcalculations it is seen that the experimentally found magneticmoment appears at larger values ofa. At the same time thesize of the gap increased. Inspecting the band structure, onefinds that the Fermi energy is inside of the gap for latticeparameters being enlarged by about 2.4–4%.

The magnetic moment is integer (6µB) in the regionwereεF falls into the gap, that is the region of half-metallicferromagnetism. The reason for the integer value is clear:the number of filled minority states is integer and thus themagnetic moment, too (see equations (2) and (3)).

Usually, Heusler compounds are attributed to exhibitlocalized moments. In that case, electron–electron correlationmay play an important rule. The LDA +U scheme [55] wasused for calculation of the electronic structure to find outwhether the inclusion of correlation resolves the discrepancybetween the theoretical and measured magnetic moment. InWien2k, the effective Coulomb-exchange interaction (Ueff =

U − J, where U and J are the Coulomb and exchange

Figure 4. LDA + U band structure and DOS of Co2FeSi. Thecalculation was performed by Wien2k using the experimental latticeparameter.

parameter) is used. The use ofUeff neglects multipole terms inthe expansion of the Coulomb interaction. The self interactioncorrection (SIC) scheme was used to account for double-counting corrections. It turned out that values ofUeff from 2.5to 5.0 eV for Co and simultaneously 2.4 to 4.8 eV for Fe resultin a magnetic moment of 6µB and a gap in the minority states.

Figure 4 shows the band structure and DOS calculatedusing the LDA +U method. The effective Coulomb-exchangeparameters were set to Ueff, Co= 4.8 eV and Ueff, Fe=

4.5 eV at the Co and Fe sites, respectively. These values arecomparable to those found in [56] for bcc Fe (4.5 eV) andf cc Ni (5 eV).

The minority DOS (figure4) exhibits a clear gap aroundεF, confirming the half-metallic character of the material. Thehigh density belowεF is dominated byd-states being locatedat Co and Fe sites. Inspecting the majority DOS one finds asmall DOS nearεF. This density is mainly derived from stateslocated at Co and Si sites.

It is found that in average three minority states per atomare occupied (2n↓ = 6) as required by the Slater–Paulingrule for the range of increasing magnetic moments with anincreasing number of valence electrons. It is worthwhile tonote that the same is true for the other Heusler compoundsshown in figure1 exhibiting half-metallic ferromagnetism.However, the electrons are distributed in a different wayacross theX, Y andZ sites.

4.2. Experiments

The correctL21 structure of the Co2FeSi compound (preparedby arc-melting in an argon atmosphere) was verified byXRD. The lattice constant was determined to be 5.64 Å. Adisorder between Co and Fe atoms (DO3 type disorder) canbe excluded from the Rietveld refinement of the XRD data,as well as from neutron scattering data. A small (<10%)disorder between Fe and Si atoms (B2 type disorder) can notbe excluded by either of these methods, particularly due tothe low intensities of the (111) and (200) diffraction peaks inXRD.

For further site specific structural information, extendedx-ray absorption fine structure (EXAFS) measurements werecarried out. A powder sample, as used for XRD, wasinvestigated in transmission mode. The best fitting of theFourier transform modulus consider theL21 structure. It was

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Sci. Technol. Adv. Mater.9 (2008) 014102 Topical Review

Figure 5. Site resolved magnetic properties of Co2FeSi. Shown arethe XAS and XMCD (IMCD) spectra taken at theL2,3 absorptionedges of Fe (a) and Co (b) after subtracting a constant background.

not possible to fit the experimental data to a structural modelincluding DO3 type disorder, as expected. Thus, the EXAFSmeasurements corroborate the XRD results even at the shortrange order for both Co and Fe.

Low temperature magnetometry was performed by meansof SQUID to proof the estimated saturation moment. Themeasured magnetic moment in saturation is(5.97± 0.05)µB

at 5 K corresponding to 1.49µB per atom. An extrapolation to6µB per unit cell at 0 K fits perfectly to the one estimated fromthe Slater–Pauling rule. The measurement of the magneticmoment reveals, as expected for a HMF, an integer withinthe experimental uncertainty. Regarding the result of themeasurement (an integer) and thevalence electron rule, it allsums up to an evidence for half-metallic ferromagnetism inCo2FeSi.

X-ray magnetic circular dichroism (XMCD) in photoabsorption (XAS) was measured to investigate the site specificmagnetic properties. The XAS and XMCD spectra takenat the L2,3 absorption edges of Fe and Co are shown infigure 5. The feature seen at 3 eV below theL3 absorptionedge of Co is related to theL21 structure and points atthe high structural order of the sample (it vanishes forB2like disorder). The magnetic moments per atom derived froma sum rule analysis [57, 58] are (2.6± 0.1)µB for Fe and(1.2± 0.1)µB for Co, at T = 300 K andµ0H = 0.4 T. Theerror arises mainly from the unknown number of holes in the3d shell and the disregard of the magnetic dipole term in thesum rule analysis. A pronounced enhancement of the orbitalmagnetic moments (ml ) (as in Co2Cr1−xFexAl [ 59]) or a fielddependence ofml [60] was not observed for Co2FeSi.

To proof the estimated Curie temperature high temper-ature magnetization of Co2FeSi was measured by means ofVSM. The ferromagnetic Curie temperature is found to beTC = (1100± 20) K. This value fits very well the linear be-haviour shown in figure2 for Co2-based Heusler compounds.The highest known Curie temperature is reported for elemen-tal Co to be 1388 K [61]. Only few materials exhibit aTC

above 1000 K, for example the Fe–Co binary alloys. With avalue of ≈1100K, Co2FeSi has a higher Curie temperature

than Fe and the highest of all HMF and Heusler compoundsbeing measured up to now.

5. The role of correlation in the Heusler compoundsCo2MnSi and Co2FeSi

Besides Co2FeSi the Heusler alloy Co2MnSi has attractedparticular interest because it is predicted to have a largeminority spin band gap of 0.4 eV and, at 985 K, has oneof the highest Curie temperature, among the known Heuslercompounds [62, 63]. Structural and magnetic propertiesof Co2MnSi have been reported for films and singlecrystals [64–70]. In accordance with theoretical predictions,bulk Co2MnSi has been stabilized in theL21 structure with amagnetization of 5µB per formula unit. From TMR data withone electrode consisting of a Co2MnSi film Schmalhorstetal [71, 72] implied a spin polarization of 61% at the barrierinterface. Although the desired spin polarization of 100% wasnot reached, the experimental value of the spin polarisationis larger than the maximum 55% effective spin polarizationof a variety of 3d-transition metal alloys in combinationwith Al2O3 barriers [73]. However, the spin polarization ofphotoelectrons emerging from single crystalline Co2MnSifilms grown on GaAs by pulsed laser deposition indicate aquite low spin polarization at the Fermi level of only 12% atthe free surface [69]. Wanget al [68, 69] assumed that partialchemical disorder was responsible for this discrepancy withthe theoretical predictions.

In order to explain this quite low spin polarization ofCo2MnSi and the assumption that on-site correlation will alsoplay an important role in the Co2MnSi compound if it plays animportant role in the Co2FeSi compound Kandpalet al [74]presented a comprehensive investigation of the equilibriumstructural, electronic and magnetic properties of Co2FeSi andcompared it to the properties of Co2MnSi.

The correct magnetic moment at the experimental valueof the lattice parameter was only found if the +U functionalwas used. Using the LDA +U scheme improves the totalmagnetic moment considerably. It was found that the gap inthe minority DOS stays up to aUeff = 2.3 eV for Mn, and aUeff = 2.5 eV for Co. For larger values ofUeff, which meansstronger correlation, the system loses its HMF characterbecauseεF is shifted outside the minority gap.

In the following, theUeff values will be denoted byUx,where the subscriptx stands for the values (in %) relative tothe atomic values (neutral atoms). The atomic values for theneutral atoms are 22.71, 24.13 and 25.53 eV for Mn, Fe andCo, respectively (see e.g. figure5 in [74]).

It was found for Co2MnSi that even a moderatecorrelation will destroy the gap. IfU10 is applied, then thespin polarization atεF is 75%, a value that is compatible to theapproximately 55% found in [67]. This indicates that on-sitecorrelation might be one more reason why no complete spinpolarization was found in this compound (for others, see [75]).

The dependence of the behaviour of the Co2FeSi minoritygap and the Co2MnSi minority gap on the effective Coulombexchange parameter was examined and compared. The

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Sci. Technol. Adv. Mater.9 (2008) 014102 Topical Review

Figure 6. Dependence of the minority gap on the effectiveCoulomb exchange parameter. The extremal energies of the gapinvolving states for Co2MnSi (a) and Co2FeSi (b) are shown. Theshaded areas indicate the region of half-metallic ferromagnetism.Lines are drawn for clarity. The atomic values for the neutral atomsare 22.71, 24.13 and 25.53 eV for Mn, Fe and Co, respectively.

extremal energies of the gap enveloping bands are shown forboth compounds in figure6.

In both compounds, the size of the gap increases withincreasingUeff. From figure6(a), it is found that Co2MnSistays in an HMF state up to approximatelyU8, which is therange of the integer magnetic moment. Larger values shiftεF

outside the gap. In Co2FeSi (figure6(b)), the minority gapincludesεF from approximatelyU8 to U20. This means thatthe integer value of the magnetic moment is related to theminority gap in both compounds and is therefore a directconsequence of the HMF state.

In both compounds, the gap is completely destroyed atvery large values ofUeff (> 8 eV). The effect of the Coulombexchange interaction on single atoms (Co, Mn or Fe) on theminority band gap was also investigated. As expected, it wasfound that the minority gap is destroyed in both materials ifUeff is added to only one of the 3d elements.

The gap in the minority states stays only within a certainrange of the effective Coulomb exchange interaction. Outsideof that limit, the Fermi energy no longer falls inside thegap, and the material loses its HMF character. It is also

obvious that the same mechanism that leads to the half-metallic ferromagnetism in Co2FeSi serves to destroy it inCo2MnSi. The worst case for both materials would appear ifUeff is approximately 7, . . . , 8% of the atomic values. That isthe case where the LDA +U still predicts values very closeto the measured magnetic moments but which is also theborderline for the loss of the HMF character. This indicatesthat nearly integer magnetic moments alone do not verify thehalf-metallic ferromagnetism and that it may be necessary tosearch for alternative materials.

Details of the HubbardU for all 3d-elements in Heuslercompounds are published in [74] and [76]. Some additionaldetails about the values ofU for Co, Mn, Fe are given in [37].

6. Co2Mn1−xFexSi

Co2MnSi and Co2FeSi are unstable HMF as a consequenceof the fact that on-site correlation may destroy the half-metallic properties. Therefore, Balkeet al [37] focused on theinvestigation of mixed compounds Co2Mn1−xFexSi to searchfor a stable half-metallic character.

6.1. Theory

After inspecting and comparing the electronic structureof Co2MnSi and Co2FeSi in more detail, some particularchanges are found. The most striking effect, however, isthe shift of the Fermi energy from the top of the minorityvalence band to the bottom of the minority conduction band.These particular positions of the minority gap with respectto the Fermi energy make both systems rather unstable withrespect to their electronic and magnetic properties. Any smallchange of a physically relevant quantity may serve to destroythe HMF character by shifting the Fermi energy completelyoutside of the minority gap. As long as the shift is assumedto be small, the magnetic moment may still be similar tothe one expected from a Slater–Pauling behaviour, even so,the minority gap is destroyed. For this reason, the magneticmoment may not provide evidence for a half-metallic state. Itis to be expected immediately that the situation improves inthe mixed compounds containing both Mn and Fe.

Band structure calculations using the LDA +U schemewere performed to prove this prediction (for more calculationdetails see [37]). The minority DOS is shifted with respectto the Fermi energy such thatεF moves from the top of theminority valence bands at lowx to the bottom of the minorityconduction bands at highx (see figure7). In general, it canbe concluded that the additional electrons affect both majorityand minority states.

The largest gap in the minority states is found forCo2MnSi. The size of the gap decreases with increasing Fecontentx. At the same time, the position of the Fermi energyis moved from the top of the valence band to the bottom of theconduction band. It is also seen that the compounds withx = 0and 1 are on the borderline to half-metallic ferromagnetism,as the Fermi energy just touches the top of the valence bandor the bottom of the conduction band. In both cases, a slightchange ofUeff in the calculation is able to shiftεF outside ofthe gap in the minority states.

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Figure 7. Dependence of the minority gap on the Fe concentration.The extremal energies of the gap involving states are shown. Theshaded areas indicate the region of half-metallic ferromagnetism.Lines are drawn for clarity.

For intermediate Fe concentration, the Fermi energyfalls close to the middle of the gap in the minority states(see also figure7). This situation makes the magnetic andelectronic properties of the compound very stable againstexternal influences that will not be able to change the numberof minority electrons. This applies both to the parameters inthe theoretical calculations as well as the actual experimentalsituation. From this observation it can be concluded thatCo2Mn1/2Fe1/2Si exhibits a very stable half-metallic characterin this series of compounds. Indeed, this is also true for allconcentration close tox = 0.5.

6.2. Experiments

The substitutional series of the quaternary Heusler compoundCo2Mn1−xFexSi was synthesized and investigated experimen-tally [37]. All samples of the substitutional series exhibitthe L21 structure independent of the Fe concentrationx.Mößbauer measurements show only a negligible paramag-netic contribution confirming the high degree of order overthe whole substitutional series. In agreement with the expec-tation from the Slater–Pauling curve, the magnetic momentincreases linearly withx from 5 to 6µB (see figure8).

Photo emission spectroscopy is the method of choice tostudy the occupied electronic structure of materials. But, lowkinetic energies result in a low electron mean free pathλ.It is only 5.2 Å at kinetic energies of 100 eV (calculatedfor Co2FeSi using the TPP2M equations [77]). Using lowenergies, only a depth of less than one cubic Heusler cell willcontribute to the observed intensity. The situation becomesmuch better at high energies. In the hard x-ray region ofabout 8 keV one will reach a high bulk sensitivity withan escape depth being larger than 115 Å (correspondingto 20 cubic cells). High energy photo emission (at about15 keV excitation energy) was first performed as early as1989 [78] using a 57Co Mößbauerγ -source for excitation,however, with very low resolution only. Nowadays, high

Figure 8. Concentration dependence of the magnetic moment inCo2Mn1−xFexSi. All measurements were performed atT = 5 K.

Figure 9. Valence density of Co2Mn1−xFexSi (x = 0, 1/2, 1).(a)–(c) Compare the calculated total DOS with photoelectronspectra excited byhν = 7.939 keV. The calculated DOS isconvoluted by a Fermi–Dirac distribution usingT = 20 K.(e)–(g) Show high resolution spectra close to the Fermi energy.The range of the calculated minority gap is marked by areas.

energy excitation and analysis of the electrons become easilyfeasible due to the development of high intense sources(insertion devices at synchrotron facilities) and multi-channelelectron detection. Thus, high resolution—hard x-ray photoemission spectroscopy (HAXPES) was recently introducedby several groups [79–84] as a bulk sensitive probe of theelectronic structure in complex materials. Balkeet al[37] usedHAXPES athν ≈ 8 keV to study the DOS of Co2Mn1−xFexSiwith x = 0, 1/2, 1.

Overall, the measured photoelectron spectra agree wellwith the calculated DOS and principally verify the use of theLDA + U scheme (see figure9).

Most interesting is the behaviour of the calculated DOSand the measured spectra close toεF as this might give anadvice about the gap in the minority states. The majorityband structure contributes only few states to the density atεF emerging from strongly dispersing bands. This region of

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low density is enclosed by a high DOS arising from flat bandsat the upper and lower limits of the minority band gap. Theonset of the minority valence band is clearly seen in the totalDOS as well as the low majority density at the Fermi energy.The same behaviour is observed in the measured valenceband spectra. From the spectra, it can be estimated that theFermi energy is in all three cases about 0.5 eV above theminority valence band. This gives strong evidence that allcompounds of the Co2Mn1−xFexSi series exhibit really half-metallic ferromagnetism.

For clarity about the gap, spin resolved photo emissionspectroscopy at high energies would be highly desirable.However, this will make another step of improvement of theinstrumentation necessary, for both photon sources as wellas electron energy and spin analyzers. In particular, the spindetection will need a factor of at least three to four orders ofmagnitude more intensity for a single energy channel at thesame resolution as used here for the intensity spectra.

True bulk sensitive, high energy photo emission beardedout the inclusion of electron–electron correlation in thecalculation of the electronic structure and gave an indirectadvise on the gap in the minority states. Both, valenceband spectra and hyperfine fields indicate an increase of theeffective Coulomb exchange parameters with increasing Feconcentration.

From both the experimental and computational resultsit is concluded that a compound with an intermediate Feconcentration of about 50% should be most stable and bestsuited for spintronic applications.

7. Co2FeAl1−xSix

The end members of this series Co2Mn1−xFexSi (x = 0and 1) have been used for fabrication of magnetic tunneljunctions [85–87]. The TMR ratios of 159% (with AlOxbarrier at 2 K [70]) or 195% (with MgO barrier at 4.2 K [88])in the Mn compound at low temperature compared to about70% (for both barrier materials) at room temperature (41%in the Fe compound) suggest that still an improvement withrespect to the temperature stability of the TMR is necessary.

In Co2Mn1−xFexSi the transition metal carrying thelocalized moment is exchanged. This might lead tounexpected effects on the magnetic properties if the samplesare not completely homogeneous. The situation is different inthe iso-electronic series Co2FeAl1−xSix where the main groupelement is substituted. Tezukaet al [89, 90] reported aboutTMR junctions build from Co2FeAl0.5Si0.5. The junctionsexhibited TMR ratios of 76% at 300 K and 106% at 5 K for theB2 structure while the junctions withL21 structure showed 51and 78% at 300 and 5 K, respectively. The TMR ratio is 175%at 300 K for optimized junctions withL21 structure [90]. Thisvalue is pronouncedly larger than the ones found for pureCo2FeAl or Co2FeSi electrodes.

7.1. Theory

The electronic structure of the substitutional series ofthe quaternary Heusler compounds Co2FeAl1−xSix was

Figure 10. Spin resolved DOS of Co2FeAl1−xSix. The panels(a, . . . , e) show—from top to button—the DOS with increasingamount of Si forx = 0, 0.25, 0.5, 0.75 and 1. The DOS is calculatedusing LDA+U .

investigated by means of FLAPW band structure calculationsusing the LDA and LDA+U approximations [38]. It wasfound that the Co2FeAl1−xSix series of compounds exhibitshalf-metallic ferromagnetism if using the LDA+U scheme.Moderate Coulomb-interaction parameters of less than 2 eVwere used. For the two end-members, Co2FeAl and Co2FeSi,the Fermi energy is close to the band edges of the minoritystates. The high densities at those band edges make thehalf-metallic character of both compounds rather unstableat finite temperatures above 0 K. This might be one reasonexplaining the low TMR ratio found in those compounds atroom temperature.

Figure 10 shows the spin resolved DOS ofCo2FeAl1−xSix for x = 0, 0.25, 0.5, 0.75 and 1. Forx ≈ 0.5,the calculations predict that the Fermi energy is located in themiddle of the gap of the minority states. This behaviour willmake Co2FeAl0.5Si0.5 stable against temperature variations asdiscussed in the introduction.

7.2. Experiments

Experiments were started to verify over what range ofcompositions the series Co2FeAl1−xSix crystallizes in the

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Figure 11. Order–disorder phase transitions in Co2FeAl1−xSix.Shown is the composition dependence of the phase transitiontemperature. The length of the vertical bars corresponds to theexperimental hysteresis.

requiredL21 structure and to find the most stable HMF in thisseries [91]. TheL21 structure is essentially required for a highspin polarization resulting in high magneto-resistive effects.

It was found that the samples exhibiting theL21 structurefor x > 0.4 and theB2 structure forx < 0.4. Differentialscanning calorimetry (DSC) was used to find the hightemperature phase transitions in the substitutional series.Figure 11 displays the dependence of the order–disordertransition temperature as a function of the Si concentrationx.Overall, figure11 demonstrates that the structural transitiontemperature of theL21 to the B2 phaseT B2↔L21

t decreasesalmost linearly with increasing Si content at least forx > 0.4.The results from both, XRD and DSC, demonstrate the betterstructural stability of the compounds with high Si content.This is expected from the stronger hybridization between Coand Si in these compounds [38].

From the combination of experimental (better order forhigh Si content) and theoretical findings (robust gap atx ≈ 0.5± 0.25) it is concluded that a compound with anintermediate Si concentration close tox = 0.5 . . . 0.7 wouldbe best suited for spintronic applications. It was shown thatthe variation of the main group element in Heusler compoundsis a strong tool in order to tune their physical properties.

8. Co2FeGa and Co2FeGe

Studies of the Co2FeZ compounds with Ga or Ge on theZ position are mostly reported for bulk samples rather thanfor thin films. Bulk Co2FeSi has been reported by Niculescuet al [92] and was investigated in detail by Wurmehlet al[43, 47]. Co2FeGa and Co2FeGe have been reported byBushow et al [93] to exist in the L21 structure. In manycases, when the main group element is from the same periodof the periodic system as the transition metals, x-ray orNeutron diffraction does not provide enough information to

Figure 12. LDA + U band structure and DOS of Co2FeGa. Thecalculation was performed by Wien2k using the experimental latticeparameter.

Figure 13. LDA + U band structure and DOS of Co2FeGe. Thecalculation was performed by Wien2k using the experimental latticeparameter.

determine the correct structure unambiguously. The correctL21 structure, however, is a necessary requirement for a highspin polarization of the materials as base for a high TMRratio [1]. Therefore, additional methods are needed to explorethe correct structure. Particularly, EXAFS and Mößbauerspectroscopy can provide additional information about theshort range order of the structure [94].

8.1. Theory

The half-metallic ferromagnetism manifests itself in a bandgap in one of the spin densities and the Fermi energy is insideof the gap. However, there exist also cases where such a gapexists in the calculations but the Fermi energy may fall outsideof that gap. Both compounds Co2FeGa and Co2FeGe show agap along0 − X that is in the1-direction of the paramagneticstate. The1-direction is perpendicular to the Co2 (100)-planes. As was shown earlier [29], just the1-direction playsthe important role for understanding of the HMF character andmagnetic properties of Heusler compounds. This fact was alsopointed out by Ö̂güt and Rabe [95].

Co2FeGe shows the properties of the Type I half-metalswhereεF is located inside of the gap of the minority bandstructure, even it is very close to a Type III half-metal. As adirect consequence, the minority densityρ↓(εF) at the Fermienergy vanishes and the spin polarization is 100%. On theother hand, Co2FeGa is a Type III half-metal, which meansthat the compound exhibits a band gap in the minority statesbut with εF outside of the gap. In this class of compoundsthe minority band gap does not includeεF. For a detailed

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Figure 14. EXAFS at the Fe K-edges (left panel) and Co K-edges (right panel) of Co2FeZ with Z=Al, Si, Ga, Ge. EXAFS oscillationsextracted from the x-ray absorption measurements at the Fe K-edge (a) and Co K-edge (c). (b) and (d) Corresponding Fourier transforms(symbols) and best fitting results (grey line). The imaginary part of the Fourier transform is displayed for the Co2FeGe compound (opencircles).

investigation and discussion about the calculated electronicand magnetic properties of the half-metallic, transition metalbased Heusler compounds see [76]. Figures 12 and 13show the LDA+U band structure and DOS of Co2FeGa andCo2FeGe, respectively.

As already mentioned above, Kübler [41] developed anab initio estimate for calculating the Curie temperature of anitinerant-electron ferromagnet in the spherical approximationusing the LDA scheme. With this approach the Curietemperatures for Co2FeGa and Co2FeGe were calculated.Depending on the approximation—LSDA or full-potentialGGA—the calculations result in Curie temperatures between1252 and 1369 K for Co2FeGa. For Co2FeGe the range isbetween 972 and 1141 K.

8.2. Experiments

Using XRD, it was shown conclusively that Co2FeAlcrystallizes in theB2 structure whereas Co2FeSi crystallizesin theL21 structure. For the compounds Co2FeGa or Co2FeGethe XRD technique cannot be used to easily distinguishbetween the two structures. For this reason, the EXAFStechnique was used to elucidate the structure of these twocompounds [96].

The EXAFS measurements have been performed at theXAFS1 beamline of the LNLS (Brazilian Synchrotron LightLaboratory). The spectra have been collected at the Fe(7112 eV) and Co (7709 eV) K-edges at room temperaturein the transmission mode using three ionization chambers.The EXAFS signals at the Fe and Co (figure14 (a) and (c))K-edges display the characteristic pattern of a cubic structure.At both edges, the EXAFS signals for the alloys containingthe lighter Z elements (Al and Si) are more attenuated dueto lower back scattering amplitudes of these elements, ifcompared to the Ga and Ge ones. The fitting of the Fouriertransforms are displayed in part (b) and (d) of figure14.The imaginary part is displayed for the Co2FeGe in order toexemplarily demonstrate the typical fine quality of the fittingsachieved.

Taking the results from the Fe- and the Co-K-edgestogether, EXAFS gives a clear indication for theL21 structurein the compounds with Z= Ga and Ge which makes these twocompounds suitable new candidates as materials in magnetictunnel junctions.

This results demonstrate that EXAFS of Heuslercompounds is a suitable method for structural investigations.It is particularly useful if XRD gives ambiguous results aboutthe correct structure. It is expected that EXAFS may also help

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for a better understanding of the structure of thin films in orderto improve the quality of TMR—junctions.

9. Summary and conclusions

This review reported about the design of materials forspintronics. For the search of new materials for spintronicapplications one should focus one Heusler compounds withCurie temperature at least around 1000 K or even higher.Additionally, the compounds should exhibit the requiredL21

structure to show half-metallicity. It has been shown that thecombination of synthesis and electronic structure calculationsis a powerful tool to pick out suitable materials. It wasshown that the variation of the main group element in Heuslercompounds is a strong tool in order to tune their physicalproperties. The HAXPES results of the Co2Mn1−xFexSi seriesgave strong evidence that all compounds of the series exhibitreally half-metallic ferromagnetism. For clarity about the gap,spin resolved photo emission spectroscopy at high energieswould be highly desirable. Due to the high bulk sensitivityspin polarized high resolution HAXPES will be a powerfuland necessary tool to investigate different materials fortunnelling barriers and spacer layers to optimize the structure,configuration and composition of magnetic tunnel junctionsand GMR devices to achieve sophisticated properties andresults.

Acknowledgments

We thank K Kobayashi, E Ikenaga, J-J Kim and S Ueda(all Spring-8, Japan) for support with the photo emissionexperiments at Spring-8; G Azevedo and F F Ferreira (bothLNLS, Campinas) for their great help with the EXAFS andXRD experiments; F Schäfers and the staff of BESSY (Berlin)for help during the beamtimes; M C M Alves and J Morais(both from UFRGS, Porto Alegre, Brazil) for their supportduring lots of LNLS beamtimes and discussions; Y Hwu(Academia Sinica, Taipei, Taiwan) and H-J Lin (NSRRC,Hsinchu, Taiwan) for help with the XMCD experiments. Weare very grateful to P Blaha (Wien2k) and H Ebert (Munich-SPRKKR) and their groups for development and providingthe computer codes. Further we thank our colleagues inMainz who provided samples and characterized the materials:J Barth, L Basit, S Berinskat, Ch Blum, F Caspar, AGloskovskii, V Jung, H C Kandpal, V Ksenofontov, S Ouardi,G Schönhense, H Spiering, U Stumm and J Winterlik. Thiswork is financially supported by the Deutsche ForschungsGemeinschaft (projects P1 and P7 in research group FG 559),BMBF (05KS7UMI) and DAAD (D06/33952).

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