Journal of Magnetism and Magnetic Materials 344 (2013) 72–78

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Journal of Magnetism and Magnetic Materials

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Magnetization reversal studies in structurally tailoredcobalt nanowires

Daljit Kaur a, Sujeet Chaudhary a, Dinesh K. Pandya a,n, Rekha Gupta b, R.K. Kotnala b

a Thin Film Laboratory, Department of Physics, Indian Institute of Technology Delhi, Hauz Khas, New Delhi 110016, Indiab National Physical Laboratory, K. S. Krishnan Marg, New Delhi 110012, India

a r t i c l e i n f o

Article history:Received 17 February 2013Received in revised form18 May 2013Available online 1 June 2013

Keywords:Cobalt nanowireMagnetization reversalCurling modeMagnetic anisotropyElectrodepositionStructurally tailored nanowire

53/$ - see front matter & 2013 Elsevier B.V. Ax.doi.org/10.1016/j.jmmm.2013.05.031

esponding author. Tel.: +91 11 26591347; fax:ail address: dkpandya@physics.iitd.ac.in (D.K.

a b s t r a c t

Cobalt nanowires (NWs) having hcp crystal structure are structurally tailored for different preferredorientations (PO) of (0002), ð1010Þ, ð1120Þ and ð1011Þ by varying bath temperature and bathconcentration in commercially available 50 nm pore diameter polycarbonate (PCT) and 20 nm porediameter anodic alumina (AAO) membranes. The magnetization studies show orientation dependentcompetition of magneto-crystalline anisotropy with shape anisotropy. The large effective anisotropy,Keff (along longitudinal direction) of 1.42�106 erg/cc is observed in (0002) PO NWs, which changes sign(−1.50�106 erg/cc) in ð1010Þ PO NWs. The angular dependence of coercivity [HC(θ)] in (0002) orientedCo NWs exhibits a non-monotonic behavior in both the 50 nm and 20 nm samples. The fitting of HC(θ)data reveals that the magnetization reversal mechanism initially takes place by curling and subsequentlychanges to coherent rotation mode after a certain transition angle, which is higher in case of denser NWarray. This increase in transition angle can be attributed to the increased magneto-static interactions inthe AAO membrane array having 103 times higher NW areal-density than that in PCT membrane array.

& 2013 Elsevier B.V. All rights reserved.

1. Introduction

Magnetic nanowires (NWs) have drawn immense interest dueto their application in reprogrammable magnonic crystal devices,magnetic sensors and spintronics application based GMR and TMRdevices [1,2]. Cobalt has the strongest uniaxial magnetocrystallineanisotropy (MCA) along the c-axis of its closed packed hcp unit cellwhose energy (4.5�106 erg/cc) is comparable to the shape aniso-tropy (SA) energy (6�106 erg/cc) of infinitely long cylindrical NW.Magnetization in cobalt NWs has been recently studied because ofits tailoring of the magnetic crystal anisotropy energy in thesenanostructures via growth conditions [3—6]. Different techniquesare used to fabricate NWs. Among these, the electro-depositionprovides a simple and controllable method to deposit NWs withdifferent structural orientations in commercially available anodicalumina (AAO) [3,4] and polycarbonate (PCT) [5,6] membranes.Another important anisotropic contribution in a NW-array ismagneto-static interactions among the NWs which is dependenton the pore density of the membrane. Tailoring of the magneticanisotropy in such a system therefore can play an important role indeveloping various technological applications.

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+91 11 26581114.Pandya).

Magnetization behavior in such oriented cobalt NWs is ofparticular interest since one nanowire could behave as a “singledomain” entity and its magnetization reversal could be similar tothe coherent rotation, i.e., all spins rotating in unison as in singledomain ferromagnetic particles. Apart from this, there are othercomplex magnetization reversal mechanisms that could be opera-tive due to nucleation of a vortex or transverse domain at the endsof the NW. The nucleated domain then propagates along thelength of the NW as the field is swept and results in spin reversal.The reversal mechanism mode could be curling (for vortex domainnucleation) or transverse (for transverse domain nucleation). Theoperative magnetization reversal mechanism is mainly derivedfrom the study of the dependence of nucleation field (which is thefield at which a change in magnetization just starts in a saturatedsingle-domain state) [7] or from the dependence of coercive field(which is the field at which the magnetization changes sign) withthe angle θ between the applied magnetic field (H) and NW-axis.

In this communication, we present the study of magneticbehavior in structurally tailored cobalt NWs of (0002), ð1010Þ,ð1120Þ and ð1011Þ preferred orientations (PO) in two differentmembranes viz., 50 nm dia polycarbonate and 20 nm dia anodicalumina. We have used the angular dependence of coercivity HC(θ)to study the magnetization reversal mechanism in the two sets ofNWs having different areal-densities, AAO membrane having 103

times higher density than PCT. The results are explained inconformity with competition of different anisotropy contributions.

D. Kaur et al. / Journal of Magnetism and Magnetic Materials 344 (2013) 72–78 73

2. Experimental

Two types of commercially available porous membranes, namely(1) polycarbonate membrane with nominal pore diameter of 50 nmand a pore density of 109 cm—2 and (2) anodic alumina membranewith 20 nm pore diameter and pore density of 1012 cm—2 werecoated with 200 nm gold on one side that serves as cathode forelectro-deposition in the pores. Different crystallographic orienta-tions of cobalt NWs were obtained by using two different bathtemperatures of 50 1C and 60 1C and two different concentrations ofelectrolytic bath with compositions: 25 mM CoSO4 �7H2O & 0.1 MH3BO3 and 500 mM CoSO4 �7H2O & 0.4 M H3BO3. The bath pH wasmaintained at 4.5 by either by adding few drops of H2SO4 or NaOH.The electro-deposition is carried out at a constant potential of−1.0 V in a three electrode cell using computer controlled Potentio-stat (Model CHI-1100A). The cell consists of a standard calomel (Hg/HgCl2/KCl) reference electrode and a 2 cm�1.5 cm Pt sheet as thecounter electrode. Deposition was done for the predetermined timeto obtain a wire length of about 1200 nm. The structural measure-ments of the synthesized nanowires were subsequently done byusing Philips X’Pert PRO X-ray diffractometer (40 mA, 45 kV) withCu-Kα radiation (λ¼1.5406 Å) in Bragg—Brentano geometry. The X-ray diffractograms were recorded on the NWs embedded inmembrane itself. The scanning electron microscope (SEM) imagesof the nanowires were obtained by a ZEISS EVO-50 microscope. Onselected samples high-resolution transmission electron microscope(HRTEM) images are acquired using JEOL JEM 2100F microscopeequipped with a field emission gun operated at 200 kV. Threesamples of the Co NWs deposited in 50 nm PCT and two samples ofCo NWs deposited in 20 nm AAO of different PO of hcp-Co wereselected for the study. Magnetization measurements were thendone with vibrating sample magnetometer (VSM).

3. Results and discussion

3.1. Structural characterization

Fig. 1(a) and (b) shows the X-ray diffraction (XRD) patterns offive samples with NWs embedded in the membrane itself. Since thenanowire axis is perpendicular to the plane of the membrane, theobserved peaks in the diffractograms would come from the cobaltplanes lying parallel to the membrane plane. Fig. 1(a) shows XRDpatterns of three NW samples namely PCT-S1, PCT-S2 and PCT-S3deposited in 50 nm PCT under different conditions. The sample PCT-S1 (shown in red), was deposited from 25 mM cobalt bath at atemperature of 60 1C which shows the highest intensity peak at

Fig. 1. XRD patterns of cobalt nanowires samples (a) PCT-S1, PCT-S2 and PCT-S3 depositThe peaks labeled with ‘*’ are due to the Au under-layer. (For interpretation of the referearticle.)

44.51 that corresponds to the (0002) hcp-Co peak. Though it hassmall contribution from Au under-layer peak at 44.21 but its strongintensity at 44.51 is assigned to come mainly from cobalt depositedin the membrane after taking into account the intensity of the otherweak fcc-Au peaks at 64.51 and 77.51 due to the gold under-layer.The (0002) PO growth suggests that c-axes of the unit cells invarious grains are parallel to NW-axis. Sample PCT-S2 was depos-ited from 25 mM cobalt bath at 50 1C and its XRD (shown in blue)shows the dominant presence of ð1120Þ and ð1010Þ peaks of hcp-Coalong with weak Au peaks. This observation of ð1120Þ and ð1010ÞPO growth thus suggests that the c-axes of the unit cells in thevarious grains are perpendicular to NW-axis. The two different setof planes along which the PO growth occurs in this case means arelative rotation of hexagonal-prism unit cells about the c-axis. Onthe other hand the sample PCT-S3 (shown in black) deposited fromconcentrated 500 mM cobalt bath at 60 1C shows the high intensitypeak at 47.51 that corresponds to the ð1011Þ hcp-Co peak. The otherweak peaks at 44.21, 64.51 and 77.51 correspond to the fcc-Au peaks.It may be noted that fcc (200) peak of Au occurs at 44.21 and hcp-Co(0002) peak occurs at 44.51. The inset of Fig. 1(a) presenting theexpanded view near 2θ-range of 44—451 reveals that the observeddiffraction peak in case of PCT-S1 is due to Co and that in case ofPCT-S3 is due to Au. Thus all the nanowire samples possess welldefined PO character. This has been confirmed by detailed HRTEMstudy of samples PCT-S1 and PCT-S2 reported previously [6], inwhich deposition-mechanism controlled PO effects were concluded.HRTEM study of PCT-S3 sample is presented later in Fig. 4.

Fig. 1(b) shows X-ray diffractograms of two samples namelyAAO-S1 and AAO-S2 deposited in 20 nm AAO membranes. SampleAAO-S1 (shown in red) is deposited from 500 mM cobalt bath at60 1C which shows the prominent peak at 44.51 that correspondsto the (0002) hcp-Co planes along with the presence of weakfcc-Au peaks due to under-layer. Thus samples PCT-S1 and AAO-S1possess the same preferred orientation. The sample AAO-S2(shown in blue) deposited from 500 mM cobalt bath at 50 1Cshows ð1010Þ and ð1120Þ PO growth, like the sample PCT-S2.

Fig. 2 (a) and (b) respectively shows the SEM images of Conanowires of sample PCT-S1 after dissolving the PC membrane indichloromethane and sample AAO-S1after dissolving AAO mem-brane in 0.1 M NaOH solution. The length and diameter of observedNWs are 1.2 mm and ∼80 nm in PCT-S1 and 1.6 mm and ∼25 nm inAAO-S1. Fig. 3(a) and 4(a) shows the TEM images of the NW samplesAAO-S2 and PCT-S3. HRTEM images of the AAO-S2 NW taken at twodifferent locations of the same NW are shown in Fig. 3(b) and (c).The white arrow in these HRTEM images indicates the NW-axis. Thelattice spacing of the planes seen in these images is 0.24 nm, whichis twice that of the lattice spacing of the ð1120Þ planes, i.e. 0.12 nm,and thus clearly establishes the PO growth of ð1120Þ planes

ed in 50 nm PCT membrane and (b) AAO-S1 and AAO-S2 in 20 nm AAO membrane.nces to color in this figure legend, the reader is referred to the web version of this

Fig. 2. The SEM images of (a) 80 nm Co NWs obtained from PCT-S1 after dissolving out the PC membrane using CH2Cl2 and (b) 25 nm Co NWs obtained from AAO-S1 afterdissolving out AAO membrane using 0.1 M NaOH.

Fig. 3. (a) Low resolution TEM image of sample AAO-S2, (b) and (c) high-resolution TEM images showing the ð1120Þ plane growth in two different locations on the same NW.White arrows indicate the direction of NW-axis.

D. Kaur et al. / Journal of Magnetism and Magnetic Materials 344 (2013) 72–7874

perpendicular to the NW axis which is in agreement with XRD data,i.e. c-axis of the grains lies perpendicular to the NW-axis. In theHRTEM images recorded at two different locations on a NW of thesample PCT-S3 shown in Fig. 4 (b) and (c), the growth of ð1011Þplanes having lattice spacing of 0.19 nm can be seen to be occurringprominently both along as well as perpendicular to the NW-axis(Fig. 4(c)). In addition, in some regions ð1011Þ planes are rotated by∼301, as seen in the HRTEM image of Fig. 4(b). Therefore, the HRTEManalysis of the PCT-S3 sample reveals a lack of well defined POcharacter in these NWs.

3.2. Magnetic characterization

Fig. 5(a)—(c) shows the M—H loops recorded on the samplesPCT-S1, PCT-S2 and PCT-S3, respectively with magnetic fieldapplied parallel (longitudinal) and perpendicular (transverse) tothe NW-axis. Generally, there are three main anisotropy contribu-tions that are observed in a NW-array, namely (1) the shape

anisotropy (SA), which tries to align the magnetization parallel tothe NW-axis, (2) the magneto-crystalline anisotropy (MCA)energy, which in case of hcp cobalt favours the magnetizationalong the its c-axis, and (3) the magneto-static interaction energyamong the NWs, which is dependent on the pore density of themembrane and tries to align the magnetization perpendicular tothe NW-axis. Considering the competition of SA with MCA, the(0002) PO in PCT-S1 will result in adding MCA energy to the SAenergy along the NW-axis and NWs thus will have large effectiveanisotropy energy along the longitudinal direction as indeedobserved from the M—H loop in Fig. 5(a). As expected the NWsare easily saturated in longitudinal direction with higher coercivitythan that in transverse direction. In sample PCT-S2, whose PO isalong ð1010Þ and ð1120Þ;(meaning that c-axis is radially orientedin these NWs) the MCA energy would compete with SA energy andtry to make the transverse direction as easy-axis of magnetization.This is consistent with the large reduction in HC along both appliedfield directions, compared to PCT-S1, as seen in Fig. 5(b).

Fig. 4. (a) Low resolution TEM image of sample PCT-S3, (b) and (c) high-resolution TEM images showing the ð1011Þ plane growth in two different locations on the same NW.White arrows indicate the direction of NW-axis.

Fig. 5. Hysteresis loops recorded with field applied parallel (-■-) and perpendicular ( ) to the NW axis in 50 nm Co nanowire samples; (a) PCT-S1 with (0002) PO,(b) PCT-S2 with ð1010Þ PO and (c) PCT-S3 with ð1011Þ PO.

D. Kaur et al. / Journal of Magnetism and Magnetic Materials 344 (2013) 72–78 75

Further, we observe almost the same M—H behavior in thesample PCT-S2 till 2 kOe along both the directions, after which themagnetization in the longitudinal direction shows a tendency

toward saturation beyond a field of 3 kOe compared to themagnetization in the transverse direction that continues toincrease up to the maximum applied field of 8 kOe. This behavior

D. Kaur et al. / Journal of Magnetism and Magnetic Materials 344 (2013) 72–7876

of late saturation of M could be ascribed to the different initialdomain state formed in the nanowire with ð1010Þ orientation incomparison to that with (0002) orientation [8].

In case of (0002) oriented NWs, the MCA and SA are both alongthe NW-axis. The initial magnetization M would lie along thewire-axis which may result in longitudinal single domain state(LSD) or a multi-domain state (MD) with most of the domains inlongitudinal direction. So when the field is applied in longitudinaldirection, magnetization of the sample is easily saturated onincreasing the applied field. As the field is swept back fromsaturated state at 8 kOe, the magnetization remains aligned inlongitudinal direction even at a field of 2.5 kOe after which thedomain nucleation starts and magnetization rapidly decreaseswith a remnant M of 0.4 MS. However in transverse direction, asthe field is swept back from 8 kOe, the magnetization M startsdecreasing gradually because the spins start rotating from hard-direction to easy-direction and very low remnant value of 0.1 MS isobserved. On the other hand, in case of ð1010Þ oriented NWs, theMCA is perpendicular to the NW-axis and SA is along the NW-axis.MCA tries to orient initial magnetization perpendicular to thelength of the wire while SA tries to orient it along the wire length.For these NWs with ð1010Þ orientation, the ground state couldcomprise of non-uniform multi-domain states containing domainwalls [8] such as (i) the transverse single domain (TSD) state withM perpendicular to the NW-axis, (ii) an open stripe (OS) domainstructure and (iii) a stripe domain structure with flux closuredomains (FCS), depending on the wire diameter, which has beenobserved in Co NWs earlier [8,9]. In this case, when the appliedfield in longitudinal direction is swept back from saturated state at8 kOe, the magnetization M steadily decreases as it is the hard-direction for MCA. Similarly the magnetization M decreasessteadily in the transverse direction also when the field is sweptback from the maximum applied field of 8 kOe except thatmagnetization M has a higher value at higher fields (as alsoreported previously [10]) and it has tendency to saturate slowlythan in the longitudinal direction. The above mentioned initialstates are expected to have perpendicular domains along theNW-axis that do not move and hence sort of block the nucleateddomain from propagating during magnetization reversal [11].Hence a slower rise to saturation in transverse case is expected,which is indeed observed in Fig. 5(b).

The M—H behavior of the sample PCT-S3 (Fig. 5(c)) displaysvery weak anisotropy as inferred from the nearly similar square-ness and the same coercivities observed in the longitudinal andtransverse directions. This is consistent with the absence of welldefined PO character in these NWs (c.f. Fig. 4(b) and (c)), whichsupports the observed nearly isotropic magnetization behavior inFig. 5(c). In order to quantify the anisotropic nature of the NWs,the following expression is used for estimating the effectiveanisotropy constant, Keff given as [12]

Kef f ¼1v

Z mtot

0H==dm−

Z mtot

0H⊥dm

� �ð1Þ

where v is the volume of all the deposited NWs in the membrane,mtot is the total moment at maximum applied fields that areapplied parallel (H//) and perpendicular (H⊥) to the NW-axis. Thevalue of Keff is largest 1.42�106 erg/cc in PCT-S1 and it decreasesto 0.22�106 erg/cc in sample PCT-S3. On the other hand, the Keff

value changes sign and becomes −1.50�106 erg/cc in ð1010Þ POPCT-S2 sample indicating higher anisotropy in transverse direc-tion. It can be seen that the value of Keff is least in the sample PCT-S3 compared to the other NWs samples with well defined PO.

Fig. 6(a) and (b) shows the M—H loops recorded on the 20 nmdia NW sample AAO-S1 and AAO-S2, respectively with magneticfield applied parallel (longitudinal) and perpendicular (transverse)to the NW-axis. The AAO-S1 sample having PO of (0002) with

planes transverse to NW-axis exhibited the expected anisotropicbehavior with the NWs becoming easily saturated in longitudinaldirection and possessing larger coercivity than that found alongthe transverse direction. While in sample AAO-S2 having ð1010ÞPO, the magnetization M(H) behavior is qualitatively identical inboth the directions till 2.15 kOe and above that field it becomeslarger for the transverse direction. In addition, the saturation isalso delayed than that in longitudinal direction. This magneticbehavior of samples AAO-S1 and AAO-S2, when compared to thesame PO samples PCT-S1 and PCT-S2 respectively, is almost similarexcept that there is relatively larger decrease in coercivities andsquareness of the M—H loops in 20 nm NWs. This could be theoutcome of dipolar interactions among the NWs in the array onaccount of higher areal-density of NWs in AAO membrane. The Keff

has a value of 0.76�104 erg/cc in AAO-S1 where both MCA and SAare along NW-axis. The Keff changes sign to —6.42�104 erg/cc inAAO-S2 sample where MCA is now ⊥ NW-axis. A much highervalue of anisotropic energy in transverse direction is the outcomeof the additional magneto-static energy in the transverse directionon account of larger NW areal-density in AAO membrane. Thelower value of Keff, particularly in case of AAO-S1, cannot beregarded as absolute due to limited access of applied field(8 kOe) compared to that required for complete saturation.

The angular dependence of coercivity, HC and squareness isperformed for the (0002) preferentially oriented samples of bothseries to gain deeper insight into the associated magnetizationreversal mechanism as a function of porosity as well as diameter.Fig. 7(a) shows the angular dependence of HC (in black) and theloop-squareness (in blue) in (0002) PO 50 nm PCT-S1 sample.We observe that the angular dependence of HC has a non-monotonic behavior. There is an increase in coercivity from592 Oe at 01 to 630 Oe at 451 and then HC decreases sharply to550 Oe at 751 after which it remains more or less unchanged till901 (HC(901)¼552 Oe). This behavior is generally reported to beencountered in array of nanotubes (NTs) [13,14] due to differentalignment of moments and enhanced surface-effects owing to thegeometry of NTs. However, we are aware of a few reports [15,16]wherein this kind of non-monotonic angular dependence ofcoercivity is observed in the NW-array and is ascribed to beoriginating due to the dominant magneto-static interactionsamong the NWs in the array. The observed non-monotonicbehavior in our PCT-S1NWs suggests that curling is the magneti-zation reversal mechanism at lower angles which gets changed tocoherent reversal mode at larger angles indicated by the decreaseof HC value above a certain transition angle, θT. This kind of angulardependent behavior of coercivity was hypothesized as curlingmechanism by Aharoni et al. [17] for a prolate spheroid andexplaining that above θT, reversal by coherent rotation becomesdominant.

This angular dependence behavior of HC (increase followedby decrease) reveals that the curling magnetization reversalmechanism is prevalent till 451 in PCT-S1, which is the transitionangle after which coherent rotation reversal take place. Also, weobserved nearly similar coercivities at 751 and 901 but a largedecrease in squareness from 751 to 901 in 50 nm PCT-S1 nanowires.Fig. 7(b) shows the angular dependence of HC (in black) and loop-squareness (in blue) in (0002) PO 20 nm AAO-S1 sample showingangular dependence behavior similar to PCT-S1, except that thesharp decrease of coercivity now starts just below 601. Thisrelatively higher transition angle in AAO-S1 could possibly beattributed to the larger magneto-static interactions in the denselypacked NWs in AAO membrane, which do not allow the spins toreverse easily even at angles greater than 451. Escrig et al. [18] havestudied the behavior of angular dependence of coercivity as afunction of radius in Ni NWs and found that transition angleincreases with increase in diameter. In the present work, the

Fig. 6. Hysteresis loops recorded with field applied parallel (-■-) and perpendicular ( ) to the NW axis in 20 nm Co nanowire samples; (a) AAO-S1 with (0002) PO and(b) AAO-S2 with ð1010Þ PO.

Fig. 7. Variation of coercivity (HC) (closed - □ - symbol) and squareness (Mr/Ms) (open - □ - symbol) as a function of angle (θ) between the applied field direction and NW-axis, in (a) PCT-S1 with (0002) PO and (b) AAO-S1 with (0002) PO.

D. Kaur et al. / Journal of Magnetism and Magnetic Materials 344 (2013) 72–78 77

opposite observation is however noticed. In our opinion, themagneto-static interactions in 20 nm AAO membrane are moredominant in deciding the magnetization reversal mechanism inthese dense NWs.

We have attempted to fit our HC(θ) data using the equation forcurling reversal given by [17]:

Hcurlingc ðθÞ ¼−HnðθÞ ¼

ð2Nz−ðk=S2ÞÞð2Nx−ðk=S2ÞÞffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffið2Nz−ðk=S2ÞÞ2 sin 2θ þ ð2Nx−ðk=S2ÞÞ2 cos 2θ

q Hk ð2Þ

where Nz and Nx are the demagnetizing factors along andperpendicular to the NW-axis, 0 and 0.5 in SI units respectively,k is the geometrical parameter whose value for infinite cylinder istaken as 1.08, S is the reduced radius given by R/Ro, Ro being thethreshold radius above which the curling takes place. HereRo ¼ 2√A=Ms, where A is the exchange energy constant and MS issaturation magnetization. In Eq. (2), Hk is the effective anisotropyfield arising by competition of shape anisotropy, magneto-crystalline anisotropy and dipolar interactions from neighboringNWs. We have also used the equation for coherent rotation in aninfinite cylinder as given by [15,19—21]:

Hcoherentc θð Þ ¼ HcðθÞ ¼−HnðθÞ ¼−2ðK1−K2Þ

ffiffiffiffiffiffiffiffiffiffiffiffiffi1−t2þt4

p� �μ0Msð1þt2Þ ; 0≤θ≤π=4

HcðθÞ ¼Hnðπ=4Þ−HnðθÞ; π=4≤θ≤π=2

8<:

9=; ð3Þ

where t¼tan1/3(θ), K1 and K2 are the shape anisotropy and themagneto-crystalline anisotropy constants, MS is the saturationmagnetization whose value is taken to be fixed at 1400 emu/cc(close to MS of bulk Co) for fitting in both cases.

The Ro for bulk cobalt comes out to be 12 nm. We fixed the valueof S as 4 in 50 nm dia sample PCT-S1 and 1.6 in 20 nm dia sampleAAO-S1. The free parameters in the curling mode Nx, Nz and Hk canbe obtained from the fitting of the experimental HC(θ) data [22]. The

complete fitting of curling and coherent reversal modes using Eqs.(2) and (3) are shown in Fig. 8 (a) for 50 nm dia NW sample PCT-S1and in Fig. 8(b) for 20 nm dia NW sample AAO-S1. The HC-increasingpart of the HC(θ) fits well with the curling mode reversal for PCT-S1with fitting parameters: Nx¼0.45, Nz¼0.09 and Hk¼2146 Oe; whilefor AAO-S1 fitting parameters are: Nx¼0.40, Nz¼0.22 andHk¼455 Oe. The higher value of Hk suggests that effective aniso-tropy along NW-axis is higher in 50 nm NWs. This is indeedconsistent when we compare the magnetization behavior of thetwo samples (see Figs. 5(a) and 6(a)). The value of Nz is quite higherin AAO-S1 than the expected value. This suggests that shapeanisotropy energy in the array of AAO-S1 nanowires is quitedifferent from that expected for an infinitely long cylinder. Further-more, in the coherent rotation regime, the value of the fittedparameters K1 and K2 are found to be 5.98�105 erg/cc and5.35�105 erg/cc for PCT-S1 and 6.02�105 erg/cc and 5.55�105

erg/cc for AAO-S1. The values of K1 and K2 in both these samples areone order less than the values expected for an infinitely longcylinder. It can be seen that in PCT-S1, the coherent mode is notfitted properly at higher angle of 901 probably due to the presenceof defects and wire inhomogeneities [23] which lead to an other-wise higher values of HC. From the foregoing, it seems that alongwith the dipolar contributions from the neighboring wires, thedefects also decrease the anisotropies of the NWs and thus lowerthan expected squareness and coercivities are observed.

4. Conclusions

The magnetic properties are effectively tailored by varyingcrystal anisotropy of hcp-Co nanowires via bath temperature andbath concentration using the process of electro-deposition. The

Fig. 8. Data points for angular variation of HC in samples (a) PCT-S1 and (b) AAO-S1; with fittings for curling and coherent reversal modes using Eqs. (2) and (3).

D. Kaur et al. / Journal of Magnetism and Magnetic Materials 344 (2013) 72–7878

non-monotonic variation of the angular dependence of coercivityin (0002) oriented NWs suggests a strong contribution frommagneto-static interactions among the NWs which leads totransition in reversal mode from curling to coherent rotation athigher angle of ∼601 in highly dense 20 nm NW array and ∼451 inlower density 50 nm NW array. The fitting of the angular depen-dence of coercivity suggests that at lower angles, the magnetiza-tion reversal takes place by curling and by coherent rotationmechanism at higher angles. For the ð1010Þ oriented NWs themagnetization reversal has low squareness even for the long-itudinal applied field direction and weak tendency for saturation,though with lesser effective anisotropy in denser NW array due toincreased magneto-static interactions. Presence of ð1011Þ planesoriented both parallel and perpendicular to NW-axis in the sameNW explains to absence of anisotropy in ð1011Þ PO nanowires.

Acknowledgments

One of the authors Daljit Kaur acknowledges CSIR for the SRFfellowship.

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