*Corresponding author. Tel.: #1 847 491 8637; e-mail:mykim@moon.phys.nwu.edu.

Journal of Magnetism and Magnetic Materials 186 (1998) 277—282

Orientational and thickness dependence of interfacialmagnetocrystalline anisotropy in Co/Cu superlattices

Miyoung Kim*, Lieping Zhong, Xindong Wang, A.J. FreemanDepartment of Physics and Astronomy, Northwestern University, Evanston, IL 60208-3112, USA

Received 22 July 1997; received in revised form 20 January 1998

Abstract

The interface magnetocrystalline anisotropy (MCA) of (0 0 1), (1 1 0) and (1 1 1) oriented Co/Cunsuperlattices (n)5)

was investigated by means of the full potential linearized augmented-plane-wave (FLAPW) method. The results showa marked dependence of the interface MCA on both the orientation and the thickness of the Cu layer. For (0 0 1) orientedsuperlattices, the small value of the interface MCA with one Cu layer increases significantly as more Cu layers are added.In contrast, the interface MCA of (1 1 0) and (1 1 1) oriented superlattices are not sensitive to the number of Cu layers.The interface MCA is large and positive in the (0 0 1) orientation for n"3 and 5 and slightly positive in the (1 1 1)orientation for n"2 and 5, corresponding to a perpendicular easy axis while the (1 1 0) oriented superlattices showin-plane easy axis. ( 1998 Elsevier Science B.V. All rights reserved.

Keywords: Superlattices; Anisotropy — magnetocrystalline; Anisotropy — interface

1. Introduction

The underlying mechanism of perpendicular in-terface magnetocrystalline anisotropy (MCA) is aninteresting scientific problem which has great tech-nical importance. The most well-known examplesof perpendicular MCA arising from the interfacebetween magnetic and non-magnetic films aremultilayers and superlattices of Co/X whereX"Cu, Ag, Pd, Pt and Ni which have been pro-ved, by both experiment and theory [1], to have

perpendicular MCA when the thickness of Co isone or two layers. However, the experimental re-sults show that the MCA is very sensitive to thestructure and quality of the interface which areinfluenced by various factors such as the elementswhich are grown, their thickness, lattice spacing,and even the growth technique used or the prepara-tion conditions employed. Among these factors,one of the recent interesting issues is the depend-ence of the interface MCA on the growth orienta-tion. Owing to the advanced technique of seededepitaxy by MBE, which enables the orientation ofthe sample to be controlled and also permits in situstructural characterization at all stages of filmgrowth, experiments on the orientation dependence

0304-8853/98/$19.00 ( 1998 Elsevier Science B.V. All rights reserved.PII: S 0 3 0 4 - 8 8 5 3 ( 9 8 ) 0 0 0 9 4 - 8

of the interface MCA have been spurred. Engelet al. [2] have reported anisotropy for MBE grownCo/Pd superlattices along three high-symmetryaxes, (0 0 1), (1 1 0) and (1 1 1). Surprisingly theyfound that the interface anisotropy is the same,independent of the growth orientation. But this re-sult is not universally observed for other interfacesystems: for the Co/Pt superlattice [3] andNi/Co/Ni sandwiches [4], the interface MCA hasbeen observed to be dependent on the orientation ofthe samples. For Co/Cu multilayers, relativelysmall but orientationally dependent interface MCAhas been reported by Hillebrands et al. [5].

Stimulated by the experiments, various explana-tions for the origin of the interface MCA have beenput forward. First-principle calculations within theframework of the local-spin-density approximation(LSDA) have played a leading role to explain theabrupt change in magnetic anisotropy in reduceddimension relative to the electronic structure. Re-cently, the structural dependence of MCA of Cooverlayer on Cu (1 1 1) substrate was calculated bythe full-potential linearized augmented-plane-wave(FLAPW) approach and explained by the hybrid-ization of the Co and Cu d bands [6]. Since thehybridization strength may be strongly affected bythe different geometry arising from different ori-entations, it is natural to expect different behaviorof interface magnetic properties for different ori-entations. Another explanation invokes the effect ofsymmetry breaking due to spin—orbit coupling(SOC), namely that low-symmetry interfaces suchas (1 1 0) will exhibit a very different interface an-isotropy compared to (1 1 1) oriented interfaceswhich show the lifting of the two-fold degeneracy bySOC [7]. It is interesting that the layer Korringa—Kohn—Rostoker (LKKR) calculation found an ori-entation independent MCA for Co/Pd and orienta-tion dependent MCA for Co/Pt superlattices [8].

Obviously, analyses of the change of electronicstructure due to the change of orientation anddetermining the influence of this change on theinterface MCA will give an opportunity to under-stand the origin of MCA. In this paper, we use theFLAPW method to investigate the orientation andstructural dependence of the interface MCA forCo/Cu

n(0 0 1) superlattices where n"1, 3 and 5,

for (1 1 0) superlattices where n"1 and 3, and for

(1 1 1) superlattices where n"2 and 5. After a briefsummary of the methodology for calculating theMCA is given in Section 2, results including themagnetic moments, the MCA versus band fillingand hybridization effects on the interface MCA arepresented and discussed in Section 3, and someconclusions are given in Section 4.

2. Methodology and computational details

The Co/Cun

superlattices (SL) are constructedfrom the magnetic Co monolayers separated byn layers of nonmagnetic FCC Cu with the Culattice constant (a"6.83 a.u.), without includingrelaxation. The number of Cu layers are deter-mined by considering the symmetry of each ori-entation. For the (1 1 1) orientation, the atoms arestacked in a close-packed sequence, ABCABC, soas to have inversion symmetry. The Kohn—Shamequations were solved self-consistently in LSDAusing the FLAPW method without any shape ap-proximation to the wave functions, charge densityand potential. We use the von Barth—Hedin ex-change-correlation potential and treat core statesfully relativistically and valence states semi-relativ-istically. Within the muffin-tin (MT) spheres(rC6"r

C0"2.3 a.u.), lattice harmonics with angular-

momentum l up to 8 are used to expand the chargedensity, potential and wave functions. Integrationsover k space are substituted by summations over40, 64, and 36 special k points in the 1

16th, 1

8th and

112

th irreducible 3D BZ for (0 0 1), (1 1 0) and (1 1 1)orientations, respectively. Self-consistent conver-gence is assumed when the average root meansquare distance between the input and outputcharge and spin densities is less than 2]10~4 and0.5]10~4e/(a.u.)3, respectively.

The SOC Hamiltonian matrix elements are cal-culated by integrating the derivative of the spheri-cal potential over the muffin-tin regions in boththe Co and Cu atoms, and the contributions fromthe interstitial regions are neglected. The z direc-tion is set along the layer normal, and the x and ydirections are in the layer plane. The interfaceMCA *E4-, defined by the difference in the totalenergy of the magnetic moment oriented in-plane and oriented perpendicular to the surface, is

278 M. Kim et al. / Journal of Magnetism and Magnetic Materials 186 (1998) 277—282

Table 1Interface MCA, *E4-, in meV (and in mJ/m2 in parenthesis) and Co magnetic moment, M, in k

B

Orientation System M *E4- Experiment (2K4) [5]

(0 0 1) Co ML 2.06 !1.25 (!3.07)Co/Cu

11.67 0.02 (0.05)

Co/Cu3

1.65 0.31 (0.76)Co/Cu

51.63 0.46 (1.13)

(0.30)(1 1 0) Co ML 2.20 !1.80 (!3.14)

Co/Cu1

1.67 !0.01 (!0.02)Co/Cu

31.52 !0.08 (!0.14)

(in plane)(1 1 1) Co ML 1.83 !0.85 (!2.41)

Co/Cu2

1.52 0.06 (0.17)Co/Cu

51.58 0.10 (0.28)

(0.26)

determined by calculating the torque at h"45°,which gives the physical MCA values accurately[9]. The / is fixed along the direction of the near-est-neighbor atom in x—y plane for all systems. Wesimplify the calculations by adopting the self-con-sistent scalar relativistic charge/spin density, wherethe occupied states are determined by tracking thewave function as in the previous state-tracking ap-proach (STA) treatment [10]. The combination ofSTA and torque methods has been proved to be theeffective way to determine MCA in our test calcu-lations. The total contribution to the interfaceMCA is integrated over the k-points in an increasedirreducible BZ, which corresponds to around 8000in the full 3D BZ. We chose the number of k-pointswhich suppresses the MCA fluctuation within$0.05 meV for the small system in each orienta-tion, and adopted those k-points for larger systems.

3. Results and Discussion

The calculated interface MCA and magnetic mo-ments are given in Table 1. For comparison, wealso show the result for free Co monolayers (ML) ineach orientation calculated using the FLAPWmethod. The calculated MCA can be simply relatedto the spin—orbit coupling between the occupiedand the empty valence states. In the simple Co MLcase, the lifting of two-fold degeneracies is found toplay an important role in determining the interface

MCA for (0 0 1) and (1 1 1) orientations [7]. There-fore, a low-symmetry orientation such as (1 1 0),which has no degeneracies, is expected to showa very different interface MCA. As shown inTable 1, strongly enhanced magnetic moments anda strong in-plane easy axis are found in all orienta-tions for Co ML. As expected, the interface MCAexhibits appreciable orientational dependence, thatis, the low symmetry interface (1 1 0) has a pro-nounced negative MCA which is almost twice aslarge as the value of the (1 1 1) oriented ML.

Upon contact with 1 or 2 nonmagnetic Cu layers,the interface MCA undergoes a remarkable change:it switches to positive in (0 0 1) and (1 1 1) orienta-tions and reduces to a small value in the (1 1 0)orientation. As we add additional Cu layers, theinterface MCA is influenced and shows differentbehavior for each orientation. In the (0 0 1) orienta-tion, the addition of the next-nearest Cu increasesthe interface MCA significantly from 0.02 meVfor Co/Cu

1to 0.31 meV for Co/Cu

3, which means

strong perpendicular interface MCA. But in the(1 1 1) orientation, the additional Cu layer doesnot have much influence and thus both Co/Cu

2and Co/Cu

5have almost the same slightly positive

interface MCA values. The superlattices (SL) in the(1 1 0) orientation have negative values indepen-dent of the number of Cu layers and thus showin-plane preference.

These results showing an orientational de-pendence are consistent with the Brillouin light

M. Kim et al. / Journal of Magnetism and Magnetic Materials 186 (1998) 277—282 279

Fig. 1. Band filling dependence of the MCA *E4-(in meV) for(0 0 1) oriented SL; Co/Cu

1(open circles), Co/Cu

3(filled circles)

and Co/Cu5

(triangles).

scattering experiment for Co/Cu multilayers whichreports a positive interface MCA for (0 0 1) and(1 1 1) and a negative value for the (1 1 0) orienta-tion, as shown in Table 1 [5]. In the (1 1 1) orienta-tion, the interface MCA is in close agreement withexperiment, but in the (0 0 1) orientation it is largerthan the experimental value. Since the demagneti-zation energies in this system are small [11], one ofthe most probable factors causing this difference isthe effect of imperfect growth of SL in the experi-ments. The interdiffusion and the alloy formationat the interface may result in a reduction in theinterface MCA; this was shown to have a largeinfluence in Co/Pd and Co/Pt SLs [8]. The exclu-sion of strain effects in our calculation may beanother reason for the difference. Describing thestrain effect by an assumed model structure, Daal-derop et al. [7] obtained 0.2 meV for both Co/Cu

2and Co/Cu

5(1 1 1) multilayers using the linearized

muffin-tin orbital (LMTO) method in the atomicsphere approximation (ASA) and MacLaren et al.[8] reported 0.08 meV for Co/Cu1 and 0.49 meVfor both Co/Cu

2and Co/Cu

3in (0 0 1) using the

LKKR method with a spherical muffin-tin poten-tial. Both sets of results are still far from experi-ment. Also, recent research on the orbitalpolarization correction indicates a possible way toobtain better agreement with MCA experiments forcertain systems, which is not considered in any ofthese calculations [12].

The Co magnetic moments are given in Table 1.The pronounced exchange splitting of Co MLs bysurface effects is largely reduced by the Cu layers.As a result, the magnetic moments of Co for SL areclose to those of the overlayer or sandwich (1.60 k

Bfor Co/Cu

5in the (1 1 1) multilayer [6] and 1.67 k

Bfor Cu

2/Co/Cu

2in the (0 0 1) sandwich [13]). But

the increase of the number of Cu layers does notmuch influence the Co magnetic moments. Theinfluence of the magnetic Co layer is expected toinduce magnetic moments on the nonmagnetic Cuatoms: indeed the induced magnetic moments arevery small (0.08 k

Band 0.04 k

Bfor the interface Cu

of Co/Cu1

and Co/Cu3

and 0.00 kB

for the nextnearest-neighbor Cu of Co/Cu

3in (0 0 1)). The

small magnetic interaction between Co and Culayers is because the Cu d bands lie much lowerthan the Fermi energy where the Co spin down

d bands are localized. Nevertheless, this small inter-action between Co and Cu results in the significantchange of interface MCA shown in Table 1.

In order to examine the influence of Cu layers onthe MCA, we plot *E4- against the change in thenumber of valence electrons, by changing the bandfilling through varying the highest occupied energyaround E

Ffor (0 0 1) oriented SLs which exhibit the

most significant Cu thickness dependence in Fig. 1.The change in the number of valence electrons, *Z,are given relative to the physical value, i.e., it equalszero when the number of valence electrons are 20,42 and 64 for Co/Cu

1, Co/Cu

3and Co/Cu

5, respec-

tively. The change of *Z from !2 to 2 (electrons)is mostly caused by the change in the occupation ofthe Co d states lying around E

F. For the Co/Cu

1(0 0 1) SL, the positive anisotropy dominates thebeginning part of filling the spin-down Co d bands,i.e. *Z&!2 to 0. For *Z'0, the negative bumpdevelops near the half-occupation of spin-down Cod bands. This is an appreciable change compared tothat of an isolated Co ML in which the negativebump appears earlier (*Z&!1) [13]. This meansthat the presence of the Cu layer leads to a positivecontribution in this region. For Co/Cu

3, this

positive contribution occurs up to *Z"!1&1and thus results in the large positive MCA valueat *Z"0. However, Co/Cu

5shows similar

behavior to that of Co/Cu3: differences with

280 M. Kim et al. / Journal of Magnetism and Magnetic Materials 186 (1998) 277—282

Fig. 2. Projected density of states (DOS) for Co and Cu spin-down d states for (0 0 1) oriented SL; solid line for Co/Cu

1and

dashed line for Co/Cu3; Cu1 stands for the nearest Cu atom.

Also the DOS of the Co (0 0 1) free-standing monolayer is shownin the inset of upper panel.

Co/Cu1

are supposed to be due to the next nearestCu layers.

The role of non-magnetic Cu layers on the MCAhas been described in the effective ligand inter-action model (ELIM) [13]: (i) the energy separationbetween Co and substrate d bands and (ii) thestrength of the interfacial hybridization arethought to play the key roles in determining theMCA energy. The DOS plot in Fig. 2 reflectsclearly the effect of additional Cu layers in terms ofhybridization. There, we plot the layer projectedDOS for minority d bands for Co/Cu

1(solid line)

and Co/Cu3(dashed line) in the (0 0 1) orientation

which shows the most significant change in MCAdue to the additional Cu layer. For comparison, wealso give the DOS of the Co (0 0 1) free-standingML as an inset into the upper panel in Fig. 2. ForCo/Cu

1, the bandwidth of the Co d band, 2.8 eV, is

not much broadened from the value in Co (001)ML [13]. The Cu d bands lie lower in energy: theaverage distance between the Co and Cu d bands is2.1 eV. The bottom peak of the Co d bandsof Co/Cu

1are enhanced compared to that of

Co (0 0 1) ML due to the interaction of the Co

atoms with the neighboring Cu atoms. As a resultthe large negative MCA of Co ML switches to aslightly positive value for Co/Cu

1(cf. Table 1).

As expected, adding more Cu layers influencesthe energy bands of the Co and Cu atoms: ForCo/Cu

3, the DOS of the nearest Cu atom (Cu1)

near the top of the d bands is clearly enhanced, ascan be seen by inspecting the energy region around!2 eV in the second panel. The next-nearest Cuatom acts to broaden and push up the Cu1 d bandsinto the higher energy region. Since the Cu1d bands move up closer to the Co d bands, there isgreater hybridization between these bands. As aresult of the increased hybridization, the interfaceMCA of Cu/Cu

3is largely enhanced despite a slight

upward shift of the bottom of the Co d band. This isconsistent with the energy band analysis of Co/Cuoverlayers given previously [6] where the Cud states, lying higher in energy than their bulkcounterpart, cause strong interaction and hybrid-ization with the bonding Co bands.

4. Conclusion

We calculated the interface MCA using theFLAPW method for Co/Cu

nsuperlattices with dif-

ferent number of Cu layers in different orientations.The interface MCA was found to be strongly de-pendent both on the orientation and the thicknessof the Cu layer. In agreement with experiment, theeasy axis for (0 0 1) and (1 1 1) oriented Co/Cusuperlattices is perpendicular, whereas for Co/Cu(1 1 0) it is in-plane. In the (0 0 1) orientation, theinterface MCA is enhanced significantly as thenumber of Cu layer increases so that Co/Cu

3(0.31 meV) and Co/Cu

5(0.46 meV) show strong

perpendicular interface anisotropy, which is ex-plained by the distance between Co and Cu d bandsand thus their hybridization. This structural de-pendence of the interface MCA is not found clearlyfor (1 1 0) and (1 1 1) superlattices.

Acknowledgements

Work supported by the Office of Naval Research(Grant No.N00014-94-1-0030) and by grants

M. Kim et al. / Journal of Magnetism and Magnetic Materials 186 (1998) 277—282 281

of computer time at the Pittsburgh Supercom-puting Center supported by the NSF Divisionof Advanced Scientific Computing and the ArcticRegion Supercomputing Center. One of us (A.J.Freeman) thanks S.D. Bader for handling the edi-torial aspects of this manuscript, including theanonymous refereeing.

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