Interface magnetic anisotropy in cobalt clusters embedded in a platinum matrix

Journal of Magnetism and Magnetic Materials 237 (2001) 293–301

Interface magnetic anisotropy in cobalt clusters embeddedin a platinum matrix

M. Jameta,*, M. N!egriera, V. Dupuisa, J. Tuaillon-Combesa, P. M!elinona,A. P!ereza, W. Wernsdorferb, B. Barbarab, B. Baguenardc

aD !epartement de Physique des Mat !eriaux, Universit !e Claude Bernard Lyon, 43 Boulevard du 11 Novembre 1918,

69622 Villeurbanne, FrancebLaboratoire Louis N !eel, CNRS, 38042 Grenoble, France

cLaboratoire de Spectrom !etrie ionique et mol !eculaire, Universit !e Claude Bernard Lyon 1-CNRS,

69622 Villeurbanne, France

Received 11 June 2001

Abstract

Noninteracting cobalt clusters containing almost one thousand atoms are embedded in a platinum matrix using a co-

deposition technique. This one allows us to prepare nanostructured films from miscible elements such as Co/Pt.Deposited clusters keep a pure cobalt core surrounded with an alloyed CoPt interface. Magnetic measurementsperformed on this cluster assembly reveal a very strong interface anisotropy. Moreover, we find that a simple core-shell

model can account for the observed anomalous temperature dependence of the cluster magnetization. r 2001 ElsevierScience B.V. All rights reserved.

PACS: 75.50.Tt; 75.30.Gw; 75.70.Cn

Keywords: Magnetic nanoclusters; Surface anisotropy; Interface effects

1. Introduction

In the past few years, ordered Co–Pt alloy filmsand Co/Pt multilayers have been intensivelystudied because of their very large perpendicularmagnetic anisotropy (PMA) [1,2]. Actually suchsystems are the best candidates for high densitymagnetic recording media. Magnetic Co–Pt dotsmade by electron lithography are now 10–20 nmwide but one hundred grains are required for one

memory bit [3]. In order to increase the recordingdensity, even smaller dots will be used as only onememory bit. Cobalt clusters containing almost onethousand atoms (3 nm in diameter) embedded in aplatinum matrix could be good candidates. De-spite their nearly spherical shape, a large remain-ing interface magnetic anisotropy is expected toovercome the superparamagnetic limit [4]. In thepresent paper, we report a detailed magnetic studyof a collection of noninteracting Co grainsembedded in a Pt matrix (named Co/Pt system).A large local interface anisotropy and an anom-alous dependence of the cluster magnetization as a

*Corresponding author. Fax: +33-472-43-15-92.

E-mail address: [email protected] (M. Jamet).

0304-8853/01/$ - see front matter r 2001 Elsevier Science B.V. All rights reserved.

PII: S 0 3 0 4 - 8 8 5 3 ( 0 1 ) 0 0 6 9 5 - 3

function of temperature have been found. Theseresults are compared with previous ones obtainedwith the Co/Nb system [5].

2. Sample preparation and structural

characterization

Cobalt clusters are prepared using a laservaporization source improved according to Milanide Heer design [6]. The Ti : sapphire vaporizationlaser used provides output energies up to 300 mJ at790 nm, for a pulse duration of 3 ms and a 10 Hzrepetition rate [7]. This source produces an intensesupersonic cluster beam allowing us to grow filmsin the low energy cluster beam deposition(LECBD) regime. In this case, clusters do notfragment upon impact on the substrate or in thematrix [8]. We can prepare nanostructured thinfilms by random stacking of incident free clusterson different substrates or films of cobalt clustersembedded in a platinum matrix thanks to the co-deposition technique. This last one consists in twoindependent beams reaching at the same time asilicon (1 0 0) substrate tilted at 451 at roomtemperature: the preformed neutral Co-clusterbeam and the atomic beam used for the matrix.Depositions are performed in a UHV chamber(p ¼ 5 � 10�10 Torr) to limit cluster and matrix

contamination. The matrix element is evaporatedusing a UHV electron gun evaporator mounted inthe deposition chamber. By controlling bothevaporation rates with quartz balance monitors,we can continuously adjust the cluster concentra-tion in the matrix. Moreover, few neutral cobaltclusters (thickness eo1 monolayer) are depositedon a carbon coated copper grid and subsequentlyprotected by a thin amorphous carbon layer ontop (10 nm) to perform ex-situ High ResolutionTransmission Electron Microscopy (HRTEM)observations. Nearly spherical clusters with aFCC structure and a rather sharp size distribution(mean diameter DmE3:0 nm, dispersion sE0:2)are observed. Actually, in order to minimize theirsurface energy, clusters mainly have a truncatedoctahedron shape [9] (Fig. 1(a)). A 20 nm-thickfilm of randomly stacked cobalt clusters on asilicon substrate is prepared to perform grazingincidence small angle X-ray diffraction (GISAXD)measurements at LURE (Laboratoire pour l’Uti-lisation du Rayonnement Electromagn!etique, Or-say-FRANCE). The diffraction spectrum reportedin Fig. 2 clearly confirms that cobalt clustersexhibit a FCC structure with roughly the samemean diameter (DmE3:9 nm) as the one derivedfrom TEM observations. Further X-ray absorp-tion measurements (Extended X-ray AbsorptionFine Structure: EXAFS) performed at LURE on

Fig. 1. (a) Model of cluster containing 1289 atoms with a truncated octahedron shape. (1 1 1) and (1 0 0) facets allow to minimize the

cluster surface energy. (b) Model of cluster containing 1337 atoms. Dark atoms belonging to the (1 1 1) facet are added to a perfect

truncated octahedron basis of 1289 atoms (light atoms) in order to break the cluster symmetry.

M. Jamet et al. / Journal of Magnetism and Magnetic Materials 237 (2001) 293–301294

Co/Pt samples [10] allow us to deduce the clusterstructure in more details: a pure FCC cobalt coresurrounded with an alloyed interface (correspond-ing to the interdiffusion of one cobalt atomicmonolayer with platinum at the cluster/matrixinterface). For magnetic measurements using aVSM (Vibrating Sample Magnetometer) appara-tus, we prepared a 500 nm-thick Pt film containinga 4% cobalt-cluster volume concentration. A verylow concentration is chosen to rule out anymagnetic coupling between particles in the sample.

3. Magnetic study of the Co/Pt system

In the following, we achieve a statistical treat-ment of magnetic measurements to deduce thecluster magnetization (noted MsðTÞ), their mag-netic size distribution and anisotropy energybarrier. The cluster concentration is low enoughto consider noninteracting particles i.e. only theapplied magnetic field (Happ) has to be taken intoaccount. Furthermore for cobalt, the exchangelength is 7 nm which is larger than the 3 nm meanparticle size. Thus, a single domain cluster can beseen as a macrospin with uniform rotation of itsmagnetization. Finally, we will assume a uniaxial

magnetic anisotropy within the particles.1 In orderto derive relevant information from measurementsperformed on a cluster assembly at any tempera-ture, we have to take further factors intoconsideration: thermal fluctuations, the randomdistribution of easy magnetization axes and themagnetic size distribution. For this purpose, weuse the following expression for the magneticmoment of the sample [4]:

mðHapp;TÞ ¼ msatðTÞ

*Z p

0

dcsin c

2

�

R p0 dy sin y

R 2p0 df cos a expðE=kBTÞR p

0 dy sin yR 2p

0 df expðE=kBTÞ

+:; ð1Þ

where msatðTÞ is the saturation moment of thesample at temperature T : We use the sphericalcoordinates in which the two angles (y;f) give thedirection of the particle magnetization. For asimple description of the random distribution ofeasy magnetization axes, we set the particle easyaxis along the z direction while the magnetic fieldorientation given by the angle c between Happ and(Oz) is continuously varied from c ¼ 0 to p: E ¼DE cos2yþ m0HappMsðTÞ (pD3=6) cosb is themagnetic energy of an individual cluster of volumeV ¼ pD3=6 (D is the particle diameter). b is theangle between the particle magnetization andthe applied magnetic field and DE corresponds tothe anisotropy energy barrier to cross in order toreverse the particle magnetization. In the followingwe take DE ¼ KDa where K is the anisotropyconstant and D the particle diameter: a ¼ 2 meansa surface anisotropy and a ¼ 3 a volume aniso-tropy. Finally, square brackets stand for theaverage over the log-normal magnetic size dis-tribution f ðDÞ given by:

f ðDÞ ¼1

Dffiffiffiffiffiffiffiffiffiffi2ps2

p exp � lnD

Dm

� �� 21

2s2

!; ð2Þ

where Dm is the mean cluster diameter and s thedispersion.

2 .4 2 .8 3 .2 3 .6 4 4 .4 4 .8 5 .2 5 .6

k (Å- 1)

arb.

uni

ts

Cofcc

(111)

Cofcc

(220)

Cofcc

(311)

Fig. 2. Diffraction pattern (GISAXD) obtained on a 20 nm-

thick film of randomly stacked cobalt clusters (crosses). All the

ðh k lÞ identified peaks correspond to the cobalt FCC structure

with the bulk lattice parameter.

1 This assertion is justified in the next sections. A biaxial

magnetic anisotropy should be a more general case. But the

main difference only comes from the reversal path: the

magnetization preferentially rotates perpendicularly to the hard

magnetization axis in the case of a biaxial anisotropy.

M. Jamet et al. / Journal of Magnetism and Magnetic Materials 237 (2001) 293–301 295

We are first interested in the particle magnetiza-tion MsðTÞ and its temperature dependence. Thisparameter is important since it gives informationon the magnetic state of the particles. It isproportional to the saturation moment of thesample through the relation:

msatðTÞ ¼ MsðTÞZ

N

0

NðpD3=6Þf ðDÞ dDpMsðTÞ;

ð3Þ

where N is the total number of particles in thesample. Considering the narrow size distributionof clusters as deduced from TEM observations, weassumed in Eq. (3) that the magnetization isindependent on the particle size [11]. We use theexpansion of Eq. (1) in high fields as a saturationapproach law to determine msatðTÞ [4]. We limitthis expansion to the first order:

mðHapp;TÞEmsatðTÞ 1 �a

m0Happ

� �;

a ¼kBT expð�9s2=2ÞðpD3

m=6ÞMsðTÞ: ð4Þ

From the magnetization curves reportedin Fig. 3, we clearly show that the saturationmoment is temperature dependent. Thus the

magnetization also depends on the temperatureand its evolution vs. T is shown in Fig. 4. At verylow temperature, Ms can be extrapolated to:Msð0 KÞEMsð1:5 KÞ ¼ 16007200 kA m�1: Thisvalue is larger than the cobalt bulk magnetization(Mbulk

s ¼ 1430 kA m�1). As a comparison, wemention that: Msð0 KÞE500750 kA m�1 for theCo/Nb system [5].

Another way to estimate MsðTÞ consists in usingthe expansion of Eq. (1) in low fields. This can bewritten to the first order as [12]:

mðHapp;TÞEmsatðTÞm0HappðpD3

m=6ÞMsðTÞ3kBT

� expð13:5s2Þ ð5Þ

and using Eq. (3), we find:

mðHapp;TÞENðpD3

m=6Þ2 expð18s2Þ3kB

m0HappM2s ðTÞ

T:

ð6Þ

This corresponds to the magnetic momentwe measure in the Zero Field Cooled (ZFC)protocole when all the particles are super-paramagnetic (the remanent moment of thesample being equal to zero). Thus, we deduce:

-2

-1

0

1

2

3

4

5

0 3µ0Η (Τ)

m (

10-4

mA

.m2 ) 1.5 K

300 K

1 2 4 5

Fig. 3. Magnetization curves obtained for isolated cobalt

clusters embedded in a platinum matrix (Co/Pt sample). Dots:

experimental data, solid lines: saturation approach simulated

using Eq. (4). At T ¼ 1:5 K, in the ferromagnetic regime, the

saturation moment is much higher than the one at T ¼ 300 K,

in the superparamagnetic regime showing the large dependence

of the magnetization on temperature.

0

500

1000

1500

2000

2500

3000

0 40 80 120 160 200 240 280 320

Ms (

kA.m

-1)

T (K)

as-prepared sample

annealed sample

Fig. 4. Experimental magnetization of the as-prepared and

annealed Co/Pt sample (full circles) estimated using Eq. (4) as a

saturation approach law. In the annealed sample, the Curie

temperature is approximately 150 K and Ms(0K) is much

larger than in the as-prepared sample. We also plotffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiTmZFCðHapp;TÞ=m0Happ

pfor three different applied magnetic

fields: m0Happ ¼ 10 mT; 12.5 and 15 mT (full squares). Note that

for T > 150 K, the three curves superimpose with the magne-

tization curve obtained from the saturation approach.


MsðTÞpffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiTmZFCðHapp;TÞ=m0Happ

p(Ref. [14]). In

Fig. 4, we plotffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiTmZFCðHapp;TÞ=m0Happ

pfor 3

different applied magnetic fields. The resultingcurves superimpose with the one obtained frommsatðTÞ for T > 150 K in the superparamagneticregime. In the following, the temperature depen-dence of the particle magnetization is system-atically taken into account.

We estimate the magnetic size distribution fromthe highest temperature magnetization curves. AtT ¼ 300 and 250 K, anisotropy terms can beneglected and Eq. (1) becomes [5]:

mðHapp;TÞmsatðTÞ

¼

RN

0 D3LðxÞf ðDÞ dDRN

0 D3f ðDÞ dD;

x ¼m0HappðpD3=6ÞMsðTÞ

kBT;

ð7Þ

where LðxÞ is a simple Langevin function. We fitexperimental curves in Fig. 5 using this equationand we find: Dm ¼ 2:770:1 nm and s ¼0:3570:05: Therefore the cluster magnetic size issmaller than the one derived from TEM observa-tions. This diffrence is related to the diffusedcluster/matrix interface and is discussed in the nextsection.

Decreasing the temperature, anisotropyterms are no more negligible and have to beconsidered to fit the experimental data. Toestimate them, let us perform a detailed analysisof both the remanent moment vs. temperatureand the ZFC magnetization curves using themagnetic size distribution previously found.From hysteresis loops at low temperature,we deduce the remanent moment mrðTÞ of thesample. For To10 K, we find mrðTÞEmsatðTÞ=2which confirms a uniaxial magnetic aniso-tropy within the particles [13] and showsthat cobalt particles are magnetically blockedbelow this temperature. In Fig. 6(a), we plot

0

0.2

0.4

0.6

0.8

1

0 0.4 0.8 1.2 1.6

m/m

sat

250 K

300 K

µ0Η (Τ)

Fig. 5. Experimental magnetization curves in the superpara-

magnetic regime (T ¼ 250 K: full squares, T ¼ 300 K: full

circles) for the Co/Pt sample. These curves are easily fitted using

a simple Langevin function (solid lines) which gives a magnetic

diameter for cobalt clusters equal to Dm ¼ 2:770:1 nm and a

dispersion: s ¼ 0:3570:05:

0

0.2

0.4

0.6

0.8

1

0 50 100 150 200 250 300

mr(T

)/m

r(1.5

K)

T (K)

0

1

2

3

4

5

0 50 100 150 200 250 300 350T (K)

m (

10-5

mA

.m2 )

15 mT12.5 mT10 mT

5 mT7.5 mT

2.5 mT

(a)

(b)

Fig. 6. (a) Experimental temperature dependence of the rema-

nent moment (full circles) in the Co/Pt sample. The correspond-

ing fitting curve (solid line) gives a and K in the anisotropy

energy barrier (see Table 1): DE ¼ KDa: (b) Experimental zero

field cooled (ZFC) magnetization curves given for 6 different

applied magnetic fields. The fitting curves (solid lines)

allow us to deduce a and K in the anisotropy energy barrier

(see Table 1).


mrðTÞ=mrð1:5 KÞ and fit this curve using thefollowing expression [5]:

mrðTÞmrð1:5 KÞ

¼

RN

DBðTÞ D3f ðDÞ dDR

N

DBð1:5 KÞ D3f ðDÞ dD

; ð8Þ

where DBðTÞ is the blocking diameter of theparticles at temperature T for m0Happ ¼ 0 T.One finds DBðTÞ when the relaxation time ofthe particle is equal to the measuringtime t ¼ t0 expðDE=kBTÞ ¼ tmes then DE ¼kBT lnðtmes=t0Þ ¼ KDBðTÞa (in our case,tmes ¼ 10 s and the attempt frequency t�1

0 istypically 109–1012 Hz). To fit the mrðTÞ=mrð1:5KÞratio, we consider the anisotropy constant K andthe exponent a as free parameters. The best fittingvalues are given in Table 1, they correspond to aninterface anisotropy with aE2:

We also fit the ZFC magnetization curves fordifferent applied magnetic fields using (Fig. 6(b))[5]:

mZFCðHapp;TÞmsatðTÞ

¼

RDBðHapp;TÞ0 D3ðx=3Þf ðDÞ dDR

N

0 D3f ðDÞ dD;

x ¼m0HappðpD3=6ÞMsðTÞ

kBT:

ð9Þ

Here, we neglect the blocked particle suscept-ibility. The blocking diameter DBðHapp;TÞ nowdepends on the applied magnetic field, and theanisotropy energy barrier is written: DE ¼ K �ðHappÞDa where the anisotropy constant KðHappÞwhich may depend on the applied magnetic fieldand the exponent a are free parameters. The results

Table 1

a Exponent and magnetic anisotropy constant K deduced from three different experimental measurements performed on the Co/Pt

sample: remanent moment vs. temperature (Fig 6(a)), ZFC magnetization curves (Fig. 6(b)) and magnetization curves at intermediate

temperatures (Fig. 7). They give the anisotropy energy barrier: DE ¼ KDa to cross in order to reverse the magnetization of a cobalt

cluster with a diameter D

Remanent moment ZFC magnetization curves Magnetization curves

2.5 mT 5 mT 7.5 mT 10 mT 12.5 mT 15 mT 150 K 200 K

a 2.0 2.3 1.9 1.9 1.9 1.9 1.9 2.0 (fixed) 2.0 (fixed)

K (mJ/m�2) 0.3 0.2 0.3 0.3 0.3 0.3 0.3 0.3 0.3

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

m/m

sat

150 K

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

m/m

sat

µ0Η (Τ)

200 K

(a)

(b)

Fig. 7. Experimental magnetization curves at (a) T ¼ 150 K

and (b) T ¼ 200 K (full squares) obtained for the Co/Pt sample.

A simple Langevin function (dashed lines) does not allow to fit

the experimental data since the cluster anisotropy is no more

negligible. Assuming an interface anisotropy (a ¼ 2), we can fit

m=msat (solid lines) and deduce the anisotropy constant K (see

Table 1).


are given in Table 1 for 6 different magnetic fields.They show that the anisotropy constant is actuallyindependent on the magnetic field and confirm aninterface anisotropy within the particles: aE2:

Finally, for intermediate temperatures: T ¼ 200and 150 K, we cannot fit the magnetization curvesusing a simple Langevin function as shown inFig. 7 but we have to take the anisotropy term intoaccount [15] (i.e. DE ¼ KDa). Thus by assumingan interface anisotropy (i.e. a ¼ 2) we solvenumerically Eq. (1) in order to deduce the aniso-tropy constant K given in Table 1. Fig. 7 shows thevery good agreement between the theoretical andexperimental curves. From all these results we canassert that interface is responsible for the largeuniaxial magnetic anisotropy in cobalt clustersembedded in a platinum matrix. In comparison, ifwe assume an interface anisotropy in the Co/Nbsystem we find [5]: KS ¼ 0:0570:008 mJ/m2 whichis almost one order of magnitude smaller than inCo/Pt.

4. Discussion

Cobalt and platinum elements are misciblewhich may promote interdiffusion at the cluster/matrix interface. Indeed, previous structural stu-dies [10] showed that one cobalt atomic layerdiffuses inside the Pt matrix. In this discussion weshow that a simple core-shell model with a purecobalt core surrounded with a disorderedCoxPt1�x alloyed shell can originally account forthe magnetic properties of cobalt clusters em-bedded in platinum. We can write the clustermagnetization as

MsðTÞ ¼ xMcores ðTÞ þ ð1 � xÞMshell

s ðTÞ; ð10Þ

where x is the fraction of cobalt atomsin the core with Mcore

s ðTÞ ¼ Mbulks ðTÞ

ðMsð0 KÞ ¼ 1430 kA m�1Þ; and (1 � x) the fractionof cobalt atoms in the alloyed interface shell. Forthe following calculations we consider the clustermodel reported in Fig. 1(a) which contains 1289atoms. For Co/Pt, one atomic layer is expectedto diffuse inside the matrix giving x ¼ 0:63: Thusone finds: Msð0 KÞ ¼ 0:63 � 1430 þ 0:37�Mshell

s

ð0 KÞ ¼ 1600 kA m�1 which provides: Mshells ð0 KÞE

1900 kA m�1: This magnetization enhancement ofcobalt is much smaller than that in CoPt alloys(3325 kA m�1). This may be due to dimensionaleffects as mentioned by Canedy et al. [16].However, the magnetization increase at lowtemperature indicates that the Curie temperatureof the interface (TC) is quite small (the Curietemperature in the core is assumed to be muchhigher than 300 K). This low value in CoPtdisordered alloys is also pointed out by Welleret al. [17] or Devolder [18]. For this reason we finda reduced cluster magnetic size compared with theone derived from TEM observations at T ¼ 250and 300 K (see previous section).

We further annealed this sample during 10 minat T¼ 4501C under a vacuum of 10�7 Torr topromote cobalt-platinum interdifusion at thecluster surface. In Fig. 4, we plot the samplemagnetization vs. T using the saturation app-roach law given by Eq. (4). It shows the transitionfrom a superparamagnetic state to a paramag-netic state. At 2 K, the large magnetizationMs ¼ 2720 kA m�1 now approaches the CoPt alloyvalue. It implies that almost all the cluster atomshave diffused inside the platinum matrix to formsmall alloyed ‘‘clusters’’. The low Curie tempera-ture: TCE150 K confirms that there is no morepure cobalt core in the sample (x ¼ 0). Moreover,magnetization curves measured down to 2 K showno remanent moment so that the alloyed ‘‘cluster’’anisotropy is negligible as expected for disorderedCoPt alloys [18].

In the case of Co/Nb previously reported [5],two atomic layers are expected to diffuse insidethe matrix, thus: x ¼ 0:36: If we assume that theCoNb disordered alloy is magnetically dead [5]one finds the sample magnetization: MsðTÞ ¼xMbulk

s ðTÞE0:36 � 1430 ¼ 515 kA m�1 which isin good agreement with our experimental data.Finally, experimental magnetization values in Co/Pt or Co/Nb can be well interpreted on the basis ofa simple core-shell model.

In Co/Pt, we unambiguously find the existenceof an interface anisotropy and it is actuallyimpossible to fit the experimental data by onlyconsidering a volume anisotropy within theclusters. Interface anisotropy originates from thecombination of the large spin-orbit coupling in Pt


with the natural anisotropy directions induced bythe surface [2]. Further surface strains induced bythe surrounding Pt atoms may contribute to thisinterface anisotropy.

Let us assume a volume anisotropy within thecobalt clusters. That leads to an anisotropyconstant KV given by the relation: DE ¼ KVVm ¼KSSm where Vm and Sm are the mean clustervolume and surface respectively. Using the meandiameter Dm obtained in Section 3, one finds:KV ¼ 6KS=DmE7 � 105 J/m3. For an infinite co-balt cylinder, shape anisotropy is equal toD0M

2s =4E6:4 � 105 J/m3 if we use the bulk mag-

netization [19]. This is even smaller than the aboveKV value, thus shape anisotropy cannot accountfor the experimental one. Furthermore, cubicmagnetocrystalline anisotropy reported in Ref.[20] (1.2� 105 J/m3) or in Ref. [21] (2.7� 105 J/m3) are also too small to account for theexperimental value. In conclusion the assumptionof a volume anisotropy seems not physicallyobvious.

In order to compare our surface anisotropy withprevious works, we can estimate the correspondinganisotropy energy per cobalt atom at the clustersurface. For that purpose, we use the cluster modelin Fig. 1(b). Indeed, for a perfect truncatedoctahedron as the one given in Fig. 1(a), symme-tries cancel surface anisotropy and we add one(1 1 1) facet to break this symmetry. We note Kat

the atomic anisotropy energy. Summing over allthe cluster surface atoms, one finds the anisotropyenergy in the whole particle: E ¼ �15Katcos2y;where y is the angle between the magnetizationand the [1 1 1] direction. Dividing by the clustersurface, we can deduce Kat from the experimentalanisotropy: KatE3 meV/at. This is one order ofmagnitude larger than the experimental valuesgiven in Refs. [2,22,23] ranging between 0.1 and0.3 meV/at for 1–2 cobalt monolayers in Co/Ptmultilayers.

5. Conclusion

We have shown that the anisotropy energybarrier DE of cobalt clusters embedded in aplatinum matrix is proportional to the particle

surface (i.e. D2) which implies an interfaceanisotropy. Moreover, taking into account thenearly spherical shape of the particles, we foundthat this interface anisotropy is locally one orderof magnitude larger than the one reported in Co/Ptmultilayers. The mean cluster blocking tempera-ture now reaches 100 K compared with 10 K in Co/Nb. Since interface anisotropy is proportional tothe particle deformation, one possible experimen-tal issue to increase this blocking temperaturecould be the use of slightly elongated particles.Moreover, we have seen that in miscible systemssuch as Co/Pt we have two contributions in theparticle magnetization: one from the pure cobaltcore and a second one from the alloyed interface atthe cluster surface (shell). We are now investigat-ing the magnetic properties of CoPt ordered alloyclusters for potential magneto-optical recording.

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Interface magnetic anisotropy in cobalt clusters embedded in a platinum matrix

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