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Interface magnetic anisotropy in cobalt clusters embedded in a platinum or niobium

matrix.

M. Jamet1, M. Negrier1, V. Dupuis1, J. Tuaillon-Combes1, P. Melinon1, A. Perez1, W. Wernsdorfer2, B. Barbara2,J. Vogel2 and B. Baguenard3

1 Departement de Physique des Materiaux, Universite Claude Bernard-Lyon 1 et CNRS, 69622 Villeurbanne, FRANCE.2 Laboratoire Louis Neel, CNRS, 38042 Grenoble, FRANCE.

3 Laboratoire de Spectrometrie ionique et moleculaire, Universite Claude Bernard Lyon 1 et CNRS, 69622 Villeurbanne,

FRANCE.

(February 1, 2008)

A low concentration of cobalt clusters with a fcc struc-ture and containing almost one thousand atoms are embed-ded in two different metallic matrices: platinum and niobium.Samples have been prepared using a co-deposition technique.Cobalt clusters preformed in the gas phase and matrix atomsare simultaneously deposited on a silicon substrate under Ul-tra High Vacuum (UHV) conditions. This original techniqueallows to prepare nanostructured systems from miscible ele-ments such as Co/Pt and Co/Nb in which clusters keep a purecobalt core surrounded with an alloyed interface. Magneticmeasurements performed using a Vibrating Sample Magne-tometer (VSM) reveal large differences in the magnetic prop-erties of cobalt clusters in Pt and Nb pointing out the keyrole of cluster/matrix interfaces.

PACS numbers: 75.50.Tt, 61.46.+w, 75.30.Gw

I. INTRODUCTION

Magnetic nanostructures are subjects of growing in-terest on account of their potential applications in thefields of high density magnetic recording media and spinelectronics. Indeed, using magnetic clusters (contain-ing from a few hundreds to a few thousand atoms) asmemory bits should highly increase the storage density.However, clusters with a large magnetic anisotropy haveto be used in this case to overcome the superparamag-netic limit1. Cobalt clusters embedded in a platinum ma-trix could be good candidates because Co/Pt multilay-ers display very large perpendicular magnetic anisotropy(PMA)2. Despite the nearly spherical shape of clusters,a large remaining interface magnetic anisotropy is ex-pected. Therefore, this system would allow to increasethe particle blocking temperature up to temperaturescompatible with magnetic recording applications. In thesame time, we are investigating the magnetic propertiesof individual cobalt clusters using a new microSQUIDtechnique3 to rule out any statistical treatment of theexperimental data (taking into account size, shape or de-fects distributions). Note that Co/Nb multilayers arealso used in superconducting spin valve devices4. Forthese reasons, a detailed study of Co clusters embedded

in a superconducting niobium matrix is reported in a pre-vious paper5. Though cobalt clusters have similar struc-tures in Co/Pt and Co/Nb systems (a pure cobalt coreand an alloyed interface), we observe that their magneticproperties are drastically different. In the present paper,we first report a detailed magnetic study of the Co/Ptsystem showing an anomalous dependence of the clus-ter magnetization with temperature and a large interfaceanisotropy. Then, we compare these results with previ-ous ones obtained with the Co/Nb system.

II. SAMPLE PREPARATION ANDSTRUCTURAL CHARACTERIZATION

Cobalt clusters are prepared using a laser vaporizationsource improved according to Milani-de Heer design6.The Ti:sapphire vaporization laser used provides outputenergies up to 300 mJ at 790 nm, for a pulse durationof 3 µs and a 10 Hz repetition rate7. This source pro-duces an intense supersonic cluster beam allowing us togrow films in the Low Energy Cluster Beam Deposition(LECBD) regime. In this case, clusters do not fragmentupon impact on the substrate or in the matrix8. We canprepare nanostructured thin films by random stacking ofincident free clusters on different substrates or films ofcobalt clusters embedded in various matrices (here Ptand Nb) thanks to the co-deposition technique. This lastone consists in two independent beams reaching at thesame time a silicon (100) substrate tilted at 45◦ at roomtemperature: the preformed neutral cluster beam and theatomic beam used for the matrix. Depositions are per-formed in a UHV chamber (p=5×10−10 Torr) to limitcluster and matrix contamination. The matrix is evap-orated using a UHV electron gun evaporator mountedin the deposition chamber. By controlling both evapo-ration rates with quartz balance monitors, we can con-tinuously adjust the cluster concentration in the matrix.Moreover, few neutral cobalt clusters (thickness e < 1monolayer) are deposited on a carbon coated copper gridand subsequently protected by a thin amorphous carbonlayer on top (10 nm) to perform ex-situ High Resolu-tion Transmission Electron Microscopy (HRTEM) obser-vations. Nearly spherical clusters with a fcc structure anda rather sharp size distribution (mean diameterDm ≈ 3.0

1

nm, dispersion σ = 0.2 − 0.3) are observed. Actually, inorder to minimize their surface energy, clusters mainlyhave a truncated octahedron shape9. A 20 nm-thick filmof randomly stacked cobalt clusters on a silicon substrateis prepared to perform Grazing Incidence Small AngleX-ray Diffraction (GISAXD) measurements at LURE(Laboratoire pour l’Utilisation du Rayonnement Electro-magnetique, Orsay-FRANCE). The diffraction spectrumreported in Fig. 1 clearly confirms that cobalt clustersexhibit a fcc structure with roughly the same mean di-ameter (Dm ≈ 3.9 nm) as the one derived from TEMobservations.In order to investigate the crystallographic structure ofcobalt clusters embedded in Pt and Nb matrices, we pre-pared 500 nm-thick Pt and Nb films containing a 15 %volumic concentration of clusters. We recorded and com-pared the GISAXD signals for two different photon en-ergies: hν =7.7 keV (cobalt K-edge) and hν =7 keVin Co/Nb. For hν =7 keV, we still observe the cobaltfcc (111) peak as in the pure cobalt cluster film (Fig.1). Note that we previously obtained the same result forcobalt clusters embedded in a SiOx matrix10. Unfortu-nately, in the particular case of Co/Pt, the X-ray contrastbetween Co and Pt is so large that we cannot observethe cobalt signal. As a consequence, we will assume thatcobalt clusters keep their fcc structure in Co/Pt as inCo/Nb. Furthermore, previous X-ray absorption mea-surements (Extended X-ray Absorption Fine Structure:EXAFS) were performed at LURE on Co/Pt11 (resp.Co/Nb5) systems. They revealed an alloying effect atthe cluster surface in both Co/Pt and Co/Nb misciblesystems. For magnetic measurements using a VSM ap-paratus, we prepared a 500 nm-thick Pt film containinga 4 % cobalt volume concentration (Co/Pt sample) anda 500 nm-thick Nb film containing a 2 % cobalt volumeconcentration (Co/Nb sample). Very low concentrationsare chosen to rule out any magnetic coupling betweenparticles in the sample.

III. MAGNETIC STUDY OF THE CO/PTSYSTEM

In the following, we note Ms(T) the particle magneti-zation which is temperature dependent. This parameteris important since it gives information on the magneticstate of the particles. The magnetization is proportionnalto the saturation moment of the sample labeled msat(T)through the relation:

msat(T ) = Ms(T )

∫

∞

0

N(πD3/6)f(D) dD ∝Ms(T )(1)

Particles are assumed to be nearly spherical and D isthe diameter, N is the total number of particles in thesample and f(D) is the log-normal magnetic size distri-bution with Dm the mean diameter and σ the dispersion:

f(D) =1

D√

2πσ2exp

(

−(

ln( D

Dm

)

)21

2σ2

)

(2)

Considering the narrow size distribution of clusters asdeduced from TEM observations, we assume that themagnetization does not depend on the particle size in Eq.(1) (ref. 12). Moreover, in the following, we consider non-interacting particles i.e. only the applied magnetic field(Happ) has to be taken into account. Furthermore forcobalt, the exchange length is 7 nm which is larger thanthe mean particle size of 3 nm. Thus, a single domaincluster can be seen as a macrospin with uniform rota-tion of its magnetization. Finally, we will assume a uni-axial magnetic anisotropy within the particles13. If theeasy magnetization directions are randomly distributedand the applied magnetic field is larger than the coercivefield Hc(T), the magnetic moment of the sample can bewritten as1:

m(Happ, T ) = msat(T )

⟨

∫ π

0

dψsinψ

2(3)

∫ π

0 dθ sinθ∫ 2π

0 dφ cosα exp (η cos2θ + ξ cosα)∫ π

0dθ sinθ

∫ 2π

0dφ exp (η cos2θ + ξ cosα)

⟩

Here, we use the spherical coordinates. The two an-gles (θ,φ) give the direction of the particle magnetiza-tion. The easy magnetization direction is fixed alongthe z axis while the magnetic field orientation givenby the angle ψ between Happ and the easy directionis continuously varied from ψ = 0 to ψ = π. cosα =sinψ sinθ sinφ+ cosψ cosθ, η = ∆E/kBT where ∆E isthe energy barrier to cross in order to reverse the parti-cle magnetization, and ξ = µ0Happ(πD

3/6)Ms(T )/kBT .The final expression is then averaged over the magneticsize distribution f(D) according to the formula:

< Γ > =

∫

∞

0D3Γ(D)f(D) dD∫

∞

0D3f(D) dD

(4)

where Γ(D) is a function of the particle diameter.Eq. (3) simplifies in the case ξ >> 1 (high field, lowtemperature)1:

m(Happ, T ) ≈ msat(T )

(

1 −⟨

1

ξ

⟩

−4

15

⟨

η2

ξ2

⟩

+ ...

)

(5)

In a first approximation, we use this expansion lim-ited to the first order as a saturation approach law todetermine msat(T):

m(Happ, T ) ≈ msat(T )

(

1 −a

µ0Happ

)

, (6)

a =kBT exp (−9σ2/2)

(πD3m/6) Ms(T )

2

Since we assume that the magnetization is independenton the applied magnetic field, we certainly give an up-per limit for msat(T). From the magnetization curves re-ported in Fig. 2, we clearly show that the saturation mo-ment is temperature dependent. Thus the magnetizationalso depends on the temperature and its evolution vs. Tis shown in Fig. 3. At very low temperature, the ther-mal fluctuations of the magnetization are negligible andwe obtain a relevant information on the magnetic state ofthe cluster: Ms(0K) ≈Ms(1.5K) = 1600±200 kA.m−1.This value is larger than the cobalt bulk magnetization(M bulk

s = 1430 kA.m−1).When the coercive field Hc(T) is zero, Eq. (3) also sim-plifies in the case ξ << 1 (low field, high temperature),and can be written to the first order14:

m(Happ, T ) ≈ msat(T )

⟨

ξ

3

⟩

(7)

= msat(T )µ0Happ(πD

3m/6)Ms(T )

3kBTexp(13.5 σ2)

and using Eq. (1), we find:

m(Happ, T ) =N(πD3

m/6)2exp(18σ2)

3kB

µ0HappM2s (T )

T (8)

This corresponds exactly to the magnetic moment wemeasure in the Zero Field Cooled (ZFC) protocole whenall the particles are superparamagnetic (the remanentmoment of the sample being equal to zero). Thus, we

deduce: Ms(T ) ∝√

T mZFC(Happ, T )/µ0Happ (ref. 15).

In Fig. 3, we plot√

T mZFC(Happ, T )/µ0Happ for 3 dif-ferent applied magnetic fields. The resulting curves su-perimpose with the one obtained from msat(T) for T>150K in the superparamagnetic regime. In this field range,we notice that the magnetization does not depend onµ0Happ. In the following, the temperature dependenceof the particle magnetization is systematically taken intoaccount. We first estimate the magnetic size distribu-tion from the highest temperature magnetization curves.At T=300 K and T=250 K, anisotropy terms can be ne-glected and a simple Langevin function L(ξ) allows us tofit m(Happ,T) (ref. 5) (Fig. 4):

m(Happ, T )

msat(T )=

∫

∞

0 D3L(ξ)f(D) dD∫

∞

0D3f(D) dD

(9)

We deduce: Dm = 2.7 ± 0.1 nm and σ = 0.35 ± 0.05which roughly corresponds to the size distribution ob-tained from TEM observations. Decreasing the temper-ature, anisotropy terms are no more negligible and haveto be considered to fit the experimental data. To esti-mate them, we perform a detailed analysis of both theremanent moment vs. temperature and the ZFC magne-tization curves using the magnetic size distribution pre-viously found.

From hysteresis loops at low temperature, we deduce theremanent moment mr(T) of the sample. We do not ob-serve a narrowing of the loops at the vicinity of µ0Happ =0 T below 10 K so that we can assume that almost all thecobalt particles are magnetically blocked below this tem-perature. Moreover, we notice that mr(T ) ≈ msat(T )/2which implies a uniaxial magnetic anisotropy within theparticles16. In Fig. 5(a), we plot mr(T )/mr(1.5K) andfit this curve using the following expression5:

mr(T )

mr(1.5K)=

∫

∞

DB(T )D3f(D) dD

∫

∞

DB(1.5K)D3f(D) dD

(10)

where DB(T) is the blocking diameter of the parti-cles at temperature T and µ0Happ = 0 T . One findsDB(T) when the relaxation time of the particle is equalto the measuring time: τ = τ0 exp (∆E/kBT ) = τmes ⇔∆E = kBT ln(τmes/τ0). In our case, τmes = 10 s andthe attempt frequency τ−1

0 is typically 109-1012 Hz. Tofit the ratio mr(T )/mr(1.5K), we take ∆E = K Dα

where K and α are free parameters. The best fitting val-ues are given in Table I, they correspond to an interfaceanisotropy with α ≈ 2. We also fit the ZFC magneti-zation curves for different applied magnetic fields using(Fig. 5(b)):

mZFC(Happ, T )

msat(T )=

∫ DB(Happ,T )

0D3(ξ/3)f(D) dD

∫

∞

0D3f(D) dD (11)

Here, we neglect the blocked particle susceptibility.The blocking diameter DB(Happ,T) now depends on theapplied magnetic field, and the anisotropy energy barrieris written: ∆E = K(Happ) D

α where the anisotropy con-stant K(Happ) which may depend on the applied mag-netic field and the exponent α are free parameters. Theresults are given in Table I for six different magneticfields. They show that the anisotropy constant is ac-tually independent on the magnetic field and confirm aninterface anisotropy within the particles: α ≈ 2.At intermediate temperatures: T=200 K and T=150 K,we cannot fit the magnetization curves using a simpleLangevin function as shown in Fig. 6. Indeed to achievethis, one has to use Eq. (3) to take the anisotropy terminto account17 (i.e. ∆E = K Dα). Thus we assume aninterface anisotropy as previously suggested and solve nu-merically Eq. (3) in order to deduce the anisotropy con-stant. Fig. 6 shows theoretical and experimental curves,and the resulting anisotropy constants are given in Ta-ble I. From all these results we can assert that interfaceis responsible for the large uniaxial magnetic anisotropyin cobalt clusters embedded in a platinum matrix. Notethat it was not necessary to take the temperature depen-dence of the anisotropy constant into account to fit theexperimental data. It is now interesting to compare thissystem with Co/Nb.

3

IV. COMPARISON WITH THE CO/NB SYSTEM

Here, we summarize briefly the main results we ob-tained on the Co/Nb sample in a previous paper5. Mag-netization measurements are performed at temperatureshigher than 8 K because of the superconducting behaviorof niobium films for T<7 K. As in the case of Co/Pt,we use Eq. (6) as a saturation approach law to de-termine msat(T) and subsequently Eq. (1) to deducethe cobalt magnetization Ms(T) in the sample (Fig. 7).

In the same figure, we plot√

T mZFC(Happ, T )/µ0Happ

for 3 different applied magnetic fields and T<150 K(above this temperature the magnetic signal reachesthe magnetometer resolution). We find the magnetiza-tion: Ms = 500 ± 50 kA.m−1 which shows nearly nodependence on the temperature. The same magneticmeasurements performed with a second sample contain-ing a 3 % volume concentration of cobalt clusters give:Ms = 510 ± 60 kA.m−1. Finally, complementary X-rayMagnetic Circular Dichroism (XMCD) was performedat the ESRF (European Synchrotron Radiation Facility,Grenoble-FRANCE). The absorption signal was recordedunder a 3 Tesla magnetic field at T=5 K, and we mea-sured the total electron yield in the photon energy rangewhich spans the L2 and L3 absorption lines of cobalt.Using the sum rules18, we can estimate the mean atomicmagnetic moment of cobalt atoms: µat = 0.5 ± 0.05 µB

which corresponds to Ms = 430 ± 50 kA.m−1. Thisvalue is in good agreement with the previous ones. More-over, the orbital to spin moment ratio is enhanced com-pared with the bulk value19 as expected in small parti-cles: mL/mS ≈ 0.2. However, one has to notice thatthis technique probes the first 3 nm of the sample whereslight oxidation might be possible.We note Dmag

m and σmag (resp. DTEMm and σTEM )

the mean cluster diameter and the dispersion of themagnetic (resp. TEM) size distribution. If we as-sume that: σmag = σTEM , one can write: Ms =M bulk

s (Dmagm /DTEM

m )3. By taking Ms = 500 ±50 kA.m−1 and DTEM

m = 3.0 ± 0.1 nm, we find Dmagm =

2.1± 0.2 nm. This is in rather good agreement with themagnetic size: Dm = 2.1±0.1 nm, σ = 0.35±0.05 whichfits really well the magnetization curves at T=300 K andT=200 K using the bulk magnetization (Fig. 8). Wefirst notice a large difference between the magnetic meandiameter in Co/Pt (2.7 nm) and the one in Co/Nb (2.1nm). In the case of Co/Nb, we conclude that at leasttwo cobalt atomic monolayers are magnetically dead atthe cluster surface (Fig. 9(a) and 9(b)) while in Co/Pt,the alloying effect is limited since we roughly find thesame diameter as the one derived from TEM observa-tions. In ref. 5 concerned with Co/Nb, we only con-sidered a volume anisotropy KV within cobalt clustersand found: KV = 2.0 ± 0.3.105 J/m3. In the presentwork, we assume that cobalt clusters exhibit an inter-face anisotropy in Co/Nb to allow a comparison withCo/Pt. In this case, the anisotropy energy barrier is writ-

ten: ∆E = KSD2. We use Eq. (10) to fit the evolution

of the remanent moment vs. temperature (Fig. 10(a))and Eq. (11) to fit the ZFC magnetization curves (Fig.10(b)). In both cases, we find: KS = 0.05±0.008mJ/m2

which is almost one order of magnitude smaller than inCo/Pt.

V. DISCUSSION AND CONCLUSION

Cobalt-platinum and cobalt-niobium elements are mis-cible which may promote interdiffusions at the clus-ter/matrix interfaces. Indeed, previous structuralstudies11,5 showed that one (resp. two) cobalt atomiclayer diffuses inside the Pt (resp. Nb) matrix. In thisdiscussion we show that a simple core-shell model with apure cobalt core surrounded with a disordered CoxPt1−x

or CoxNb1−x alloyed shell can originally account for themagnetic properties of cobalt clusters embedded in bothPt and Nb matrices. A comparable model has alreadybeen suggested by Canedy et al.

20 in Co/Pt superlat-tices. We can write the cluster magnetization as:

Ms(T ) = xM cores (T ) + (1 − x)M shell

s (T )(12)

where x is the fraction of cobalt atoms in the corewith M core

s (T ) = M bulks (T ) (Ms(0K) = 1430 kA.m−1),

and (1 − x) the fraction of cobalt atoms in the alloyedinterface shell. For the following calculations we con-sider the cluster model reported in Fig. 9(a) and 9(b)which contains 1289 atoms. For Co/Pt, one atomiclayer is expected to diffuse inside the matrix givingx = 0.63. Thus one finds: Ms(0K) = 0.63 × 1430 +0.37 × M shell

s (0K) = 1600 kA.m−1 which provides:M shell

s (0K) ≈ 1900 kA.m−1. This magnetization en-hancement of cobalt is much smaller than that in CoPtalloys (3325 kA.m−1) (ref. 20). This may be due to di-mensional effects as mentioned by Canedy et al.

20. How-ever, the temperature dependence of the magnetizationindicates that the Curie temperature of the interface (TC)is quite small (the Curie temperature in the core is as-sumed to be much higher than 300 K). Besides, above thistemperature the sample magnetization reaches: Ms(T ) =xM bulk

s (T ) ≈ 0.63 × 1430 = 901 kA.m−1. Experimen-tally, that gives: 200 < TC < 250 K (Fig. 3). The lowCurie temperature of CoPt disordered alloys has alreadybeen pointed out by Weller et al.

21 or Devolder22.We further annealed this sample during 10 minutes atT=450◦C under a vacuum of 10−7 Torr. In Fig. 3, weplot the sample magnetization vs. T using the satura-tion approach law given by Eq. (6). At 2 K, the largemagnetization Ms = 2720 kA.m−1 now approaches theCoPt alloy value. It implies that almost all the clus-ter atoms have diffused inside the platinum matrix toform small alloyed ”clusters”. The low Curie tempera-ture: TC ≈ 150 K confirms that there is no more pure

4

cobalt core in the sample (x = 0). Moreover, magneti-zation curves measured down to 2 K show no remanentmoment so that the alloyed ”cluster” anisotropy is neg-ligible as expected for disordered CoPt alloys22.For Co/Nb, two atomic layers are expected to diffuseinside the matrix thus: x = 0.36. If we assume thatthe CoNb disordered alloy is magnetically dead5, onefinds the sample magnetization: Ms(T ) = xM bulk

s (T ) ≈0.36 × 1430 = 515 kA.m−1, which is in good agreementwith the experimental data (Fig. 7). Finally, experimen-tal magnetization values in Co/Pt and Co/Nb samplescan be well interpreted on the basis of a simple core-shellmodel.In Co/Pt, we unambiguously find the existence of aninterface anisotropy and it is actually impossible to fitthe experimental data by only considering a volumeanisotropy within the clusters. Interface anisotropy orig-inates from the combination of the large spin-orbit cou-pling in Pt with the natural anisotropy directions inducedby the surface2. Further surface strains induced by thesurrounding Pt atoms may contribute to this interfaceanisotropy.Let us assume a volume anisotropy within the cobalt clus-ters. That leads to an anisotropy constant KV givenby the relation: KV Vm = KSSm where Vm and Sm arethe mean cluster volume and surface respectively. Us-ing the mean diameter Dm obtained in section III, onefinds: KV = 6KS/Dm ≈ 7.105 J/m3. For an infinitecobalt cylinder, shape anisotropy is equal to µ0M

2s /4 ≈

6.4.105 J/m3 if we use the bulk magnetization23. Thisis even smaller than the above KV value thus shapeanisotropy cannot account for the experimental one. Fur-thermore, cubic magnetocrystalline anisotropy reportedin ref. 24 (1.2.105 J/m3) or in ref. 25 (2.7.105 J/m3) arealso too small to account for the experimental value. Inconclusion the assumption of a volume anisotropy seemsnot physically obvious.In order to compare our surface anisotropy with previ-ous works, we can estimate the corresponding anisotropyenergy per cobalt atom at the cluster surface. For thispurpose, we use the cluster model in Fig. 9(c). Indeed,for a perfect truncated octahedron as the one given inFig. 9(a) and 9(b), symmetries cancel surface anisotropyand we add one (111) facet to break this symmetry. WenoteKat the atomic anisotropy energy. Summing over allthe cluster surface atoms, one finds the anisotropy energyin the whole particle: E = −15Katcos2(θ) where θ is theangle between the magnetization and the [111] direction.Dividing by the cluster surface, we can deduce Kat fromthe experimental anisotropy: Kat ≈ 3 meV/at. This isone order of magnitude larger than the experimental val-ues given in ref. 2, 26, 27 ranging between 0.1 and 0.3meV/at for 1-2 cobalt monolayers in Co/Pt multilayers.However, comparisons with Co/Pt multilayers are quitedifficult because this is more a two-dimensional problemwhereas clusters involve a three-dimensional treatment.Concerning Co/Nb, we believe that interface anisotropyis so small that it becomes possible to fit the magne-

tization curves using a volume anisotropy. But recentworks performed on single cobalt clusters3 embedded ina niobium matrix show that interface still rules magneticanisotropy in this system.Otherexperimental issues to increase magnetic anisotropy innanosized particles and consequently the correspondingblocking temperature could be tested in the near future:using another matrix element to increase spin-orbit cou-pling at the cluster surface, preparing slightly elongatedparticles since interface anisotropy is proportional to thedeformation...

VI. AKNOWLEDGEMENTS

The authors would like to thank Professor C. BINNSfrom the Department of Physics and Astronomy-University of Leceister-UK, for his help during theXMCD measurements on the ID12B line at the ESRF.

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Chemical Physics (I. Prigogine and Stuart Rice, p. 288,1997) Vol. XCVIII.

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3 M. Jamet, W. Wernsdorfer, C. Thirion, D. Mailly, V.Dupuis, P. Melinon, and A. Perez, cond-mat/0012029.

4 A. Buzdin, A. Vedyayev, and N. Ryzhanova, Europhys.Lett. 48, 686 (1999).

5 M. Jamet, V. Dupuis, P. Melinon, G. Guiraud, A. Perez,W. Wernsdorfer, A. Traverse, and B. Baguenard, Phys.Rev. B 62, 493 (2000).

6 P. Milani and W. A. de Heer, Rev. Sci. Instrum. 61, 1835(1990).

7 M. Pellarin, E. Cottancin, J. Lerme, J. L. Vialle, J. P. Wolf,M. Broyer, V. Paillard, V. Dupuis, A. Perez, J. P. Perez,J. Tuaillon, and P. Melinon, Chem. Phys. Lett. 224, 338(1994).

8 A. Perez, P. Melinon, V. Dupuis, P. Jensen, B. Prevel, M.Broyer, M. Pellarin, J. L. Vialle, and B. Palpant, J. Phys.D 30, 709 (1997).

9 J. Buttet, and J. P. Borel, Helvetica Physica Acta 56, 541(1983).

10 J. Tuaillon, Ph. D. Thesis, Villeurbanne, France, 1995.11 M. Negrier, J. Tuaillon, V. Dupuis, P. Melinon, A. Perez,

and A. Traverse (unpublished).12 I. M. L. Billas, A. Chatelain, and W. A. de Heer, Science

265, 1682 (1994).13 This assertion is justified in the next sections. A biaxial

magnetic anisotropy should be a more general case. Butthe main difference only comes from the reversal path: the

5

magnetization preferentially rotates perpendicularly to thehard magnetization axis in the case of a biaxial anisotropy.

14 K. Muller, and F. Thurley, Int. J. Mag. 5, 203 (1973).15 G. Xiao, and C. L. Chien, J. Appl. Phys. 61, 3308 (1987).16 H. Pfeiffer, Phys. Stat. Sol. (a) 118, 295 (1990).17 M. Hanson, C. Johansson, and S. Morup, J. Phys.:Condens.

Matter 5, 725 (1993).18 B. T. Thole, P. Carra, F. K. Sette, and G. Van Der Laan,

Phys. Rev. Lett. 68, 1943 (1992).19 D. A. Eastham, and I. W. Kirkman, J. Phys.: Condens.

Matter 12, 525 (2000).20 C. L. Canedy, X. W. Li, and G. Xiao, Phys. Rev. B 62,

508 (2000).21 D. Weller, H. Brandle, G. Gorman, C.-J. Lin, and H. No-

tarys, Appl. Phys. Lett. 61, 2726 (1992).22 T. Devolder, Phys. Rev. B 62, 5794 (2000).23 A. Aharoni, Introduction to the Theory of Ferromagnetism

(Oxford Science Publications, p. 115, 1996).24 C. H. Lee, Hui He, F. J. Lamelas, W. Vavra, C. Uher, and

Roy Clarke, Phys. Rev. B 42, 1066 (1990).25 J. P. Chen, C. M. Sorensen, K. J. Klabunde, and G. C.

Hadjipanayis, J. Appl. Phys. 76, 6676 (1994).26 B. Hillebrands, and J. R. Dutcher, Phys. Rev. B 47, 6126

(1993).27 C.-J. Lin, G. L. Gorman, C. H. Lee, R. F. C. Farrow, E. E.

Marinero, H. V. Do, H. Notarys, and C. J. Chien, J. Magn.Magn. Mater. 93, 194 (1991).

FIG. 1. (a) Diffraction pattern (GISAXD) obtained on a 20nm-thick film of randomly stacked cobalt clusters (crosses).Supported clusters clearly exhibit a fcc structure. (b) XRDspectra obtained on a 500 nm-thick niobium film containing a15 % volume concentration of cobalt clusters for two differentphoton energies: hν =7.7 keV (cobalt K-edge) (solid line)and hν =7 keV (empty circles). Even embedded in a niobiummatrix cobalt clusters still exhibit a fcc structure.

FIG. 2. Magnetization curves obtained for isolated cobaltclusters embedded in a platinum matrix (Co/Pt sample).Dots: experimental data, solid lines: approach to saturationsimulated using Eq. (6). At T=1.5 K, in the ferromagneticregime, the saturation moment is much higher than the oneat T=300 K, in the superparamagnetic regime showing thelarge dependence of the magnetization on temperature.

FIG. 3. Experimental magnetization of the as-preparedand annealed Co/Pt sample estimated using Eq. (6) as a sat-uration approach law (full circles). In the as-prepared sam-ple, a core-shell cluster model with a pure cobalt core andan alloyed CoxPt1−x interface well accounts for the tempera-ture dependence of the sample magnetization. We can deducethe interface Curie temperature: 200<TC <250 K. In the an-nealed sample, the Curie temperature is approximately 150 Kand Ms(0K) is much larger than in the as-prepared sample.

We also plot√

T mZF C(Happ, T )/µ0Happ which is propor-tional to Ms in the superparamagnetic regime for three dif-ferent applied magnetic fields: µ0Happ =10 mT; 12.5 mT and15 mT (full squares). The three curves superimpose with themagnetization curve obtained from the saturation approachfor T>150 K.

FIG. 4. Experimental magnetization curves in the super-paramagnetic regime (T=250 K: full squares, T=300 K: fullcircles) for the Co/Pt sample. These curves are easily fittedusing a simple Langevin function (solid lines) which gives themagnetic size distribution of cobalt clusters: Dm=2.7±0.1 nmand σ=0.35±0.05.

FIG. 5. (a) Experimental temperature dependence of theremanent moment (full circles) in the Co/Pt sample. Thecorresponding fitting curve (solid line) gives α and K in theanisotropy energy barrier (see Table I): ∆E = KDα. (b)Experimental Zero Field Cooled (ZFC) magnetization curvesgiven for 6 different applied magnetic fields. The fitting curves(solid lines) allow us to deduce α and K in the anisotropyenergy barrier (see Table I).

FIG. 6. (a) Experimental magnetization curve at T=150K (full squares) obtained for the Co/Pt sample. A simpleLangevin function (dashed line) does not allow to fit the ex-perimental data since the cluster anisotropy is no more neg-ligible. Assuming an interface anisotropy, we can fit m/msat

(solid line) and deduce the anisotropy constant K (see TableI). (b) Experimental magnetization curve at T=200 K (fullsquares). A simple Langevin function (dashed line) does notallow to fit the experimental data since the cluster anisotropyis no more negligible. Assuming an interface anisotropy, wecan fit m/msat (solid line) and deduce the anisotropy constantK (see Table I).

FIG. 7. Experimental dependence of the magnetization vs.temperature using Eq. (6) as a saturation approach law (fullcircles) obtained for the Co/Nb sample. Note that the magne-tization is nearly independent on temperature in this system.We also plot

√

T mZF C(Happ, T )/µ0Happ which is propor-tional to Ms(T) in the superparamagnetic regime for threedifferent applied magnetic fields: µ0Happ=10 mT; 15 mT and20 mT (full squares). The different curves superimpose forT>50 K in the superparamagnetic regime..

6

FIG. 8. Experimental magnetization curves in the super-paramagnetic regime (T=200 K: full squares, T=300 K: fullcircles) for the Co/Nb sample. These curves are easily fittedusing a simple Langevin function (solid lines) which gives themagnetic size distribution of the clusters: Dm=2.1±0.1 nmand σ=0.35±0.05.

FIG. 9. (a) Model of cluster containing 1289 atoms with atruncated octahedron shape. (111) and (100) facets allow tominimize the cluster surface energy. (b) View along a [110]direction of the cobalt cluster. From the comparison of themagnetic size distribution with the TEM one, it seems thatat least 2 atomic monolayers are magnetically dead at thecluster surface in Co/Nb. (c) Model of cluster containing1337 atoms. Dark atoms belonging to the (111) facet areadded to a perfect truncated octahedron basis of 1289 atoms(light atoms) in order to break the cluster symmetry.

FIG. 10. (a) Experimental temperature dependence of theremanent moment in the Co/Nb sample (full circles). Assum-ing an interface anisotropy, the resulting fitting curve (solidline) gives the anisotropy constant KS. (b) Experimental ZeroField Cooled (ZFC) magnetization curves obtained for 6 dif-ferent applied magnetic fields. The fitting curves (solid lines)allow us to deduce KS.

TABLE I. α exponent and magnetic anisotropy constantK deduced from three different experimental measurementsperformed on the Co/Pt sample: remanent moment vs. tem-perature, Zero Field Cooled (ZFC) magnetization curves andmagnetization curves at intermediate temperatures (see text).They give the anisotropy energy barrier: ∆E = KDα to crossin order to reverse the magnetization of a cobalt cluster witha diameter D.

7

2.4 2.8 3.2 3.6 4 4.4 4.8 5.2 5.6

arb.

uni

ts

k (A- 1)

Nb (220)

Co(311)

Cof c c

(111)

Co(220)

Nb (200)

Nb (211)

Nbbcc

(110)

(a)

(b)

Fig. 1.

jamet et al.

-2

-1

0

1

2

3

4

5

0 1 2 3 4 5µ0Η (Τ)

m (

10-4

mA

.m2 ) 1.5 K

300 K

Fig. 2.

jamet et al.

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. 3.

jamet et al.

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. 4.

jamet et al.

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

Fig. 5.

jamet et al.

(a)

(b)

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)

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

Fig. 6.

jamet et al.

(a)

(b)

200

250

300

350

400

450

500

550

600

0 40 80 120 160 200 240 280

saturation approach

Ms (

kA.m

-1)

T (K)

ZFC, 10 mTZFC, 15 mT

ZFC, 20 mT

Fig. 7.

jamet et al.

0

0.2

0.4

0.6

0.8

0 0.5 1 1.5

m/m

sat

µ0Η (Τ)

200 K

300 K

Fig. 8.

jamet et al.

Fig. 9(a).

jamet et al.

1289 atoms

(a)

[001]

[111]

0.35 nm

0.4 nm

Fig. 9(b).

jamet et al.

(b)

[001]

[100]

[010]

Fig. 9(c).

jamet et al.

(c)

1337 atoms

0

0.2

0.4

0.6

0.8

1

1.2

10 20 30 40 50

mr(T

)/m

r(5.3

K)

µ0Η (Τ)

0

0.05

0.1

0.15

0.2

0.25

0 50 100 150

m/m

sat

T (K)

20 mT15 mT10 mT7.5 mT5 mT2 mT

Fig. 10.

jamet et al.

(a)

(b)

remanent ZFC magnetization urves magnetization urvesmoment 2.5 mT 5 mT 7.5 mT 10 mT 12.5 mT 15 mT T=150 K T=200 K� 2.0 2.3 1.9 1.9 1.9 1.9 1.9 2.0 (�xed) 2.0 (�xed)K (mJ.m�2) 0.3 0.2 0.3 0.3 0.3 0.3 0.3 0.3 0.3Table Ijamet et al.