- Email: [email protected]
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 embedded in a platinum matrix M. Jameta,*, M. Ne! griera, V. Dupuisa, J. Tuaillon-Combesa, P. Me! linona, A. Pe! reza, W. Wernsdorferb, B. Barbarab, B. Baguenardc a
! ! Departement de Physique des Materiaux, Universite! Claude Bernard Lyon, 43 Boulevard du 11 Novembre 1918, 69622 Villeurbanne, France b ! CNRS, 38042 Grenoble, France Laboratoire Louis Neel, c ! ! Laboratoire de Spectrometrie ionique et moleculaire, Universite! 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 codeposition 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 measurements performed 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 Elsevier Science 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 films and Co/Pt multilayers have been intensively studied because of their very large perpendicular magnetic anisotropy (PMA) [1,2]. Actually such systems are the best candidates for high density magnetic recording media. Magnetic Co–Pt dots made by electron lithography are now 10–20 nm wide but one hundred grains are required for one *Corresponding author. Fax: +33-472-43-15-92. E-mail address: [email protected] (M. Jamet).
memory bit [3]. In order to increase the recording density, even smaller dots will be used as only one memory bit. Cobalt clusters containing almost one thousand atoms (3 nm in diameter) embedded in a platinum matrix could be good candidates. Despite their nearly spherical shape, a large remaining interface magnetic anisotropy is expected to overcome the superparamagnetic limit [4]. In the present paper, we report a detailed magnetic study of a collection of noninteracting Co grains embedded in a Pt matrix (named Co/Pt system). A large local interface anisotropy and an anomalous dependence of the cluster magnetization as a
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
294
M. Jamet et al. / Journal of Magnetism and Magnetic Materials 237 (2001) 293–301
function of temperature have been found. These results are compared with previous ones obtained with the Co/Nb system [5].
2. Sample preparation and structural characterization Cobalt clusters are prepared using a laser vaporization source improved according to Milani de Heer design [6]. The Ti : sapphire vaporization laser used provides output energies up to 300 mJ at 790 nm, for a pulse duration of 3 ms and a 10 Hz repetition rate [7]. This source produces an intense supersonic cluster beam allowing us to grow films in the low energy cluster beam deposition (LECBD) regime. In this case, clusters do not fragment upon impact on the substrate or in the matrix [8]. We can prepare nanostructured thin films by random stacking of incident free clusters on different substrates or films of cobalt clusters embedded in a platinum matrix thanks to the codeposition technique. This last one consists in two independent beams reaching at the same time a silicon (1 0 0) substrate tilted at 451 at room temperature: the preformed neutral Co-cluster beam and the atomic beam used for the matrix. Depositions are performed in a UHV chamber (p ¼ 5 1010 Torr) to limit cluster and matrix
contamination. The matrix element is evaporated using a UHV electron gun evaporator mounted in the deposition chamber. By controlling both evaporation rates with quartz balance monitors, we can continuously adjust the cluster concentration in the matrix. Moreover, few neutral cobalt clusters (thickness eo1 monolayer) are deposited on a carbon coated copper grid and subsequently protected by a thin amorphous carbon layer on top (10 nm) to perform ex-situ High Resolution Transmission Electron Microscopy (HRTEM) observations. Nearly spherical clusters with a FCC structure and a rather sharp size distribution (mean diameter Dm E3:0 nm, dispersion sE0:2) are observed. Actually, in order to minimize their surface energy, clusters mainly have a truncated octahedron shape [9] (Fig. 1(a)). A 20 nm-thick film of randomly stacked cobalt clusters on a silicon substrate is prepared to perform grazing incidence small angle X-ray diffraction (GISAXD) measurements at LURE (Laboratoire pour l’Utilisation du Rayonnement Electromagne! tique, Orsay-FRANCE). The diffraction spectrum reported in Fig. 2 clearly confirms that cobalt clusters exhibit a FCC structure with roughly the same mean diameter (Dm E3:9 nm) as the one derived from TEM observations. Further X-ray absorption measurements (Extended X-ray Absorption Fine 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) 293–301
arb. units
Cofcc (311) Cofcc (220)
Cofcc (111) 2.4
2.8
3.2
3.6
4
4.4
4.8
5.2
5.6
k (Å- 1) Fig. 2. Diffraction pattern (GISAXD) obtained on a 20 nmthick 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.
Co/Pt samples [10] allow us to deduce the cluster structure in more details: a pure FCC cobalt core surrounded with an alloyed interface (corresponding to the interdiffusion of one cobalt atomic monolayer with platinum at the cluster/matrix interface). For magnetic measurements using a VSM (Vibrating Sample Magnetometer) apparatus, we prepared a 500 nm-thick Pt film containing a 4% cobalt-cluster volume concentration. A very low concentration is chosen to rule out any magnetic coupling between particles in the sample.
3. Magnetic study of the Co/Pt system In the following, we achieve a statistical treatment of magnetic measurements to deduce the cluster magnetization (noted Ms ðTÞ), their magnetic size distribution and anisotropy energy barrier. The cluster concentration is low enough to consider noninteracting particles i.e. only the applied magnetic field (Happ ) has to be taken into account. Furthermore for cobalt, the exchange length is 7 nm which is larger than the 3 nm mean particle size. Thus, a single domain cluster can be seen as a macrospin with uniform rotation of its magnetization. Finally, we will assume a uniaxial
295
magnetic anisotropy within the particles.1 In order to derive relevant information from measurements performed on a cluster assembly at any temperature, we have to take further factors into consideration: thermal fluctuations, the random distribution of easy magnetization axes and the magnetic size distribution. For this purpose, we use the following expression for the magnetic moment of the sample [4]: *Z p sin c mðHapp ; TÞ ¼ msat ðTÞ dc 2 0 + R 2p Rp dy sin y df cos a expðE=k TÞ B 0 0 Rp :; ð1Þ R 2p dy sin y 0 df expðE=kB TÞ 0 where msat ðTÞ is the saturation moment of the sample at temperature T: We use the spherical coordinates in which the two angles (y; f) give the direction of the particle magnetization. For a simple description of the random distribution of easy magnetization axes, we set the particle easy axis along the z direction while the magnetic field orientation given by the angle c between Happ and (Oz) is continuously varied from c ¼ 0 to p: E ¼ DE cos2 y þ m0 Happ Ms ðTÞ (pD3 =6) cosb is the magnetic energy of an individual cluster of volume V ¼ pD3 =6 (D is the particle diameter). b is the angle between the particle magnetization and the applied magnetic field and DE corresponds to the anisotropy energy barrier to cross in order to reverse the particle magnetization. In the following we take DE ¼ KDa where K is the anisotropy constant and D the particle diameter: a ¼ 2 means a surface anisotropy and a ¼ 3 a volume anisotropy. Finally, square brackets stand for the average over the log-normal magnetic size distribution f ðDÞ given by: ! 2 1 D 1 f ðDÞ ¼ pffiffiffiffiffiffiffiffiffiffi exp ln ; ð2Þ Dm 2s2 D 2ps2 where Dm is the mean cluster diameter and s the dispersion. 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.
296
M. Jamet et al. / Journal of Magnetism and Magnetic Materials 237 (2001) 293–301
We are first interested in the particle magnetization Ms ðTÞ and its temperature dependence. This parameter is important since it gives information on the magnetic state of the particles. It is proportional to the saturation moment of the sample through the relation: Z N msat ðTÞ ¼ Ms ðTÞ NðpD3 =6Þf ðDÞ dDpMs ðTÞ; 0
ð3Þ where N is the total number of particles in the sample. Considering the narrow size distribution of clusters as deduced from TEM observations, we assumed in Eq. (3) that the magnetization is independent on the particle size [11]. We use the expansion of Eq. (1) in high fields as a saturation approach law to determine msat ðTÞ [4]. We limit this expansion to the first order: a mðHapp ; TÞEmsat ðTÞ 1 ; m0 Happ a¼
kB T expð9s2 =2Þ : ðpD3m =6ÞMs ðTÞ
ð4Þ
From the magnetization curves reported in Fig. 3, we clearly show that the saturation moment is temperature dependent. Thus the
magnetization also depends on the temperature and its evolution vs. T is shown in Fig. 4. At very low temperature, Ms can be extrapolated to: Ms ð0 KÞEMs ð1:5 KÞ ¼ 16007200 kA m1 : This value is larger than the cobalt bulk magnetization (Msbulk ¼ 1430 kA m1). As a comparison, we mention that: Ms ð0 KÞE500750 kA m1 for the Co/Nb system [5]. Another way to estimate Ms ðTÞ consists in using the expansion of Eq. (1) in low fields. This can be written to the first order as [12]: m0 Happ ðpD3m =6ÞMs ðTÞ 3kB T 2 expð13:5s Þ
mðHapp ; TÞE msat ðTÞ
ð5Þ
and using Eq. (3), we find: mðHapp ; TÞE
NðpD3m =6Þ2 expð18s2 Þ m0 Happ Ms2 ðTÞ : 3kB T ð6Þ
This corresponds to the magnetic moment we measure in the Zero Field Cooled (ZFC) protocole when all the particles are superparamagnetic (the remanent moment of the sample being equal to zero). Thus, we deduce: 3000
M s (kA.m-1)
4
m (10-4 mA.m2)
annealed sample
2500
5 1.5 K
3 2
300 K
2000 1500
as-prepared sample
1000
1 500
0
0
-1
0
-2 0
1
2
3
µ0Η (Τ)
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.
40
80 120 160 200 240 280 320
T (K) 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 plot pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi TmZFC ðHapp ; TÞ=m0 Happ for three different applied magnetic fields: m0 Happ ¼ 10 mT; 12.5 and 15 mT (full squares). Note that for T > 150 K, the three curves superimpose with the magnetization curve obtained from the saturation approach.
297
M. Jamet et al. / Journal of Magnetism and Magnetic Materials 237 (2001) 293–301
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi In Ms ðTÞp TmZFCp ðHffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi app ; TÞ=m0 Happ (Ref. [14]). ffi Fig. 4, we plot TmZFC ðHapp ; TÞ=m0 Happ for 3 different applied magnetic fields. The resulting curves superimpose with the one obtained from msat ðTÞ for T > 150 K in the superparamagnetic regime. In the following, the temperature dependence of the particle magnetization is systematically taken into account. We estimate the magnetic size distribution from the highest temperature magnetization curves. At T ¼ 300 and 250 K, anisotropy terms can be neglected and Eq. (1) becomes [5]: RN 3 D LðxÞf ðDÞ dD mðHapp ; TÞ ; ¼ 0RN 3 msat ðTÞ 0 D f ðDÞ dD
Decreasing the temperature, anisotropy terms are no more negligible and have to be considered to fit the experimental data. To estimate them, let us perform a detailed analysis of both the remanent moment vs. temperature and the ZFC magnetization curves using the magnetic size distribution previously found. From hysteresis loops at low temperature, we deduce the remanent moment mr ðTÞ of the sample. For To10 K, we find mr ðTÞEmsat ðTÞ=2 which confirms a uniaxial magnetic anisotropy within the particles [13] and shows that cobalt particles are magnetically blocked below this temperature. In Fig. 6(a), we plot
ð7Þ
m Happ ðpD3 =6ÞMs ðTÞ ; x¼ 0 kB T
where LðxÞ is a simple Langevin function. We fit experimental curves in Fig. 5 using this equation and we find: Dm ¼ 2:770:1 nm and s ¼ 0:3570:05: Therefore the cluster magnetic size is smaller than the one derived from TEM observations. This diffrence is related to the diffused cluster/matrix interface and is discussed in the next section.
m (T)/m (1.5K) r r
1 (a)
0.8 0.6 0.4 0.2 0
0
50
100
150
200
250
300
T (K) 5
1
250 K 300 K
0.6 0.4
4
m (10-5mA.m2)
m/m
sat
0.8
(b)
3 2 15 mT 12.5 mT 10 mT 7.5 mT 5 mT 2.5 mT
1 0.2
0 0
0 0
0.4
0.8
1.2
1.6
µ 0Η (Τ) Fig. 5. Experimental magnetization curves in the superparamagnetic 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:
50
100
150
200
250
300
350
T (K) Fig. 6. (a) Experimental temperature dependence of the remanent moment (full circles) in the Co/Pt sample. The corresponding 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).
298
M. Jamet et al. / Journal of Magnetism and Magnetic Materials 237 (2001) 293–301
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
2.0 0.3
2.5 mT
5 mT
7.5 mT
10 mT
12.5 mT
15 mT
150 K
200 K
2.3 0.2
1.9 0.3
1.9 0.3
1.9 0.3
1.9 0.3
1.9 0.3
2.0 (fixed) 0.3
2.0 (fixed) 0.3
mr ðTÞ=mr ð1:5 KÞ and fit this curve using the following expression [5]: RN 3 mr ðTÞ D ðTÞ D f ðDÞ dD ¼ RNB ; ð8Þ 3 mr ð1:5 KÞ DB ð1:5 KÞ D f ðDÞ dD where DB ðTÞ is the blocking diameter of the particles at temperature T for m0 Happ ¼ 0 T. One finds DB ðTÞ when the relaxation time of the particle is equal to the measuring time t ¼ t0 expðDE=kB TÞ ¼ tmes then DE ¼ kB Tlnðtmes =t0 Þ ¼ KDB ðTÞa (in our case, tmes ¼ 10 s and the attempt frequency t1 is 0 typically 109–1012 Hz). To fit the mr ðTÞ=mr ð1:5KÞ ratio, we consider the anisotropy constant K and the exponent a as free parameters. The best fitting values are given in Table 1, they correspond to an interface anisotropy with aE2: We also fit the ZFC magnetization curves for different applied magnetic fields using (Fig. 6(b)) [5]: R DB ðHapp ;TÞ 3 D ðx=3Þf ðDÞ dD mZFC ðHapp ; TÞ RN ; ¼ 0 3 msat ðTÞ 0 D f ðDÞ dD x¼
m0 Happ ðpD3 =6ÞMs ðTÞ : kB T
Magnetization curves
ð9Þ
Here, we neglect the blocked particle susceptibility. The blocking diameter DB ðHapp ; TÞ now depends on the applied magnetic field, and the anisotropy energy barrier is written: DE ¼ K ðHapp ÞDa where the anisotropy constant KðHapp Þ which may depend on the applied magnetic field and the exponent a are free parameters. The results
1 (a) 0.8
m/msat
a K (mJ/m2)
ZFC magnetization curves
0.6 0.4 0.2
150 K
0 0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1 (b) 0.8
m/msat
Remanent moment
0.6 0.4 0.2
200 K
0 0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
µ0Η (Τ) 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).
M. Jamet et al. / Journal of Magnetism and Magnetic Materials 237 (2001) 293–301
are given in Table 1 for 6 different magnetic fields. They show that the anisotropy constant is actually independent on the magnetic field and confirm an interface anisotropy within the particles: aE2: Finally, for intermediate temperatures: T ¼ 200 and 150 K, we cannot fit the magnetization curves using a simple Langevin function as shown in Fig. 7 but we have to take the anisotropy term into account [15] (i.e. DE ¼ KDa ). Thus by assuming an interface anisotropy (i.e. a ¼ 2) we solve numerically Eq. (1) in order to deduce the anisotropy constant K given in Table 1. Fig. 7 shows the very good agreement between the theoretical and experimental curves. From all these results we can assert that interface is responsible for the large uniaxial magnetic anisotropy in cobalt clusters embedded in a platinum matrix. In comparison, if we assume an interface anisotropy in the Co/Nb system we find [5]: KS ¼ 0:0570:008 mJ/m2 which is almost one order of magnitude smaller than in Co/Pt.
4. Discussion Cobalt and platinum elements are miscible which may promote interdiffusion at the cluster/ matrix interface. Indeed, previous structural studies [10] showed that one cobalt atomic layer diffuses inside the Pt matrix. In this discussion we show that a simple core-shell model with a pure cobalt core surrounded with a disordered CoxPt1x alloyed shell can originally account for the magnetic properties of cobalt clusters embedded in platinum. We can write the cluster magnetization as Ms ðTÞ ¼ xMscore ðTÞ þ ð1 xÞMsshell ðTÞ;
ð10Þ
where x is the fraction of cobalt atoms in the core with Mscore ðTÞ ¼ Msbulk ðTÞ 1 ðMs ð0 KÞ ¼ 1430 kA m Þ; and (1 x) the fraction of cobalt atoms in the alloyed interface shell. For the following calculations we consider the cluster model reported in Fig. 1(a) which contains 1289 atoms. For Co/Pt, one atomic layer is expected to diffuse inside the matrix giving x ¼ 0:63: Thus one finds: Ms ð0 KÞ ¼ 0:63 1430 þ 0:37Msshell ð0 KÞ ¼ 1600 kA m1 which provides: Msshell ð0 KÞE
299
1900 kA m1 : This magnetization enhancement of cobalt is much smaller than that in CoPt alloys (3325 kA m1). This may be due to dimensional effects as mentioned by Canedy et al. [16]. However, the magnetization increase at low temperature indicates that the Curie temperature of the interface (TC ) is quite small (the Curie temperature in the core is assumed to be much higher than 300 K). This low value in CoPt disordered alloys is also pointed out by Weller et al. [17] or Devolder [18]. For this reason we find a reduced cluster magnetic size compared with the one derived from TEM observations at T ¼ 250 and 300 K (see previous section). We further annealed this sample during 10 min at T¼ 4501C under a vacuum of 107 Torr to promote cobalt-platinum interdifusion at the cluster surface. In Fig. 4, we plot the sample magnetization vs. T using the saturation approach law given by Eq. (4). It shows the transition from a superparamagnetic state to a paramagnetic state. At 2 K, the large magnetization Ms ¼ 2720 kA m1 now approaches the CoPt alloy value. It implies that almost all the cluster atoms have diffused inside the platinum matrix to form small alloyed ‘‘clusters’’. The low Curie temperature: TC E150 K confirms that there is no more pure cobalt core in the sample (x ¼ 0). Moreover, magnetization curves measured down to 2 K show no remanent moment so that the alloyed ‘‘cluster’’ anisotropy is negligible as expected for disordered CoPt alloys [18]. In the case of Co/Nb previously reported [5], two atomic layers are expected to diffuse inside the matrix, thus: x ¼ 0:36: If we assume that the CoNb disordered alloy is magnetically dead [5] one finds the sample magnetization: Ms ðTÞ ¼ xMsbulk ðTÞE0:36 1430 ¼ 515 kA m1 which is in good agreement with our experimental data. Finally, experimental magnetization values in Co/ Pt or Co/Nb can be well interpreted on the basis of a simple core-shell model. In Co/Pt, we unambiguously find the existence of an interface anisotropy and it is actually impossible to fit the experimental data by only considering a volume anisotropy within the clusters. Interface anisotropy originates from the combination of the large spin-orbit coupling in Pt
300
M. Jamet et al. / Journal of Magnetism and Magnetic Materials 237 (2001) 293–301
with the natural anisotropy directions induced by the surface [2]. Further surface strains induced by the surrounding Pt atoms may contribute to this interface anisotropy. Let us assume a volume anisotropy within the cobalt clusters. That leads to an anisotropy constant KV given by the relation: DE ¼ KV Vm ¼ KS Sm where Vm and Sm are the mean cluster volume and surface respectively. Using the mean diameter Dm obtained in Section 3, one finds: KV ¼ 6KS =Dm E7 105 J/m3. For an infinite cobalt cylinder, shape anisotropy is equal to D0 Ms2 =4E6:4 105 J/m3 if we use the bulk magnetization [19]. This is even smaller than the above KV value, thus shape anisotropy cannot account for the experimental one. Furthermore, cubic magnetocrystalline 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 the experimental value. In conclusion the assumption of a volume anisotropy seems not physically obvious. In order to compare our surface anisotropy with previous works, we can estimate the corresponding anisotropy energy per cobalt atom at the cluster surface. For that purpose, we use the cluster model in Fig. 1(b). Indeed, for a perfect truncated octahedron as the one given in Fig. 1(a), symmetries cancel surface anisotropy and we add one (1 1 1) facet to break this symmetry. We note K at the atomic anisotropy energy. Summing over all the cluster surface atoms, one finds the anisotropy energy in the whole particle: E ¼ 15K at cos2 y; where y is the angle between the magnetization and the [1 1 1] direction. Dividing by the cluster surface, we can deduce K at from the experimental anisotropy: K at E3 meV/at. This is one order of magnitude larger than the experimental values given in Refs. [2,22,23] ranging between 0.1 and 0.3 meV/at for 1–2 cobalt monolayers in Co/Pt multilayers.
5. Conclusion We have shown that the anisotropy energy barrier DE of cobalt clusters embedded in a platinum matrix is proportional to the particle
surface (i.e. D2 ) which implies an interface anisotropy. Moreover, taking into account the nearly spherical shape of the particles, we found that this interface anisotropy is locally one order of magnitude larger than the one reported in Co/Pt multilayers. The mean cluster blocking temperature now reaches 100 K compared with 10 K in Co/ Nb. Since interface anisotropy is proportional to the particle deformation, one possible experimental issue to increase this blocking temperature could be the use of slightly elongated particles. Moreover, we have seen that in miscible systems such as Co/Pt we have two contributions in the particle magnetization: one from the pure cobalt core and a second one from the alloyed interface at the cluster surface (shell). We are now investigating the magnetic properties of CoPt ordered alloy clusters for potential magneto-optical recording.
References [1] C. Menechini, M. Maret, V. Parasote, M.C. Cadeville, J.L. Hazemann, R. Cortes, S. Colonna, Europhys. Journal B 7 (1999) 347. [2] N. Nakajima, T. Koide, T. Shidara, H. Miyauchi, H. Fukutani, A. Fujimori, K. Iio, T. Katayama, Phys. Rev. Lett. 81 (1998) 5229. [3] D.A. Thomson, J.S. Best, IBM J. Res. Develop. 44 (2000) 311. [4] J.L. Dormann, D. Fiorani, E. Tronc, Advances in Chemical Physics, Vol. XCVIII, I. Prigogine and Stuart Rice, p. 288, 1997. [5] M. Jamet, V. Dupuis, P. M!elinon, G. Guiraud, A. P!erez, W. Wernsdorfer, A. Traverse, B. Baguenard, Phys. Rev. B 62 (2000) 493. [6] P. Milani, W.A. de Heer, Rev. Sci. Instrum. 61 (1990) 1835. [7] M. Pellarin, E. Cottancin, J. Lerm!e, J.L. Vialle, J.P. Wolf, M. Broyer, V. Paillard, V. Dupuis, A. P!erez, J.P. P!erez, J. Tuaillon, P. M!elinon, Chem. Phys. Lett. 224 (1994) 338. [8] A. P!erez, P. M!elinon, V. Dupuis, P. Jensen, B. Pr!evel, M. Broyer, M. Pellarin, J.L. Vialle, B. Palpant, J. Phys. D 30 (1997) 709. [9] J. Buttet, J.P. Borel, Helvetica Phys. Acta 56 (1983) 541. [10] M. N!egrier, J. Tuaillon, V. Dupuis, P. M!elinon, A. P!erez, A. Traverse, Phil. Mag. A (2001), in press. [11] I.M.L. Billas, A. Chatelain, W.A. de Heer, Science 265 (1994) 1682. [12] K. Muller, F. Thurley, Int. J. Mag. 5 (1973) 203. [13] H. Pfeiffer, Phys. Stat. Sol. A 118 (1990) 295. [14] G. Xiao, C.L. Chien, J. Appl. Phys. 61 (1987) 3308.
M. Jamet et al. / Journal of Magnetism and Magnetic Materials 237 (2001) 293–301 [15] M. Hanson, C. Johansson, S. Morup, J. Phys.: Condens. Matter 5 (1993) 725. [16] C.L. Canedy, X.W. Li, G. Xiao, Phys. Rev. B 62 (2000) 508. [17] D. Weller, H. Br.andle, G. Gorman, C.-J. Lin, H. Notarys, Appl. Phys. Lett. 61 (1992) 2726. [18] T. Devolder, Phys. Rev. B 62 (2000) 5794. [19] A. Aharoni, Introduction to the Theory of Ferromagnetism, Oxford Science Publications, Oxford, 1996, p. 115.
301
[20] C.H. Lee, H. He, F.J. Lamelas, W. Vavra, C. Uher, R. Clarke, Phys. Rev. B 42 (1990) 1066. [21] J.P. Chen, C.M. Sorensen, K.J. Klabunde, G.C. Hadjipanayis, J. Appl. Phys. 76 (1994) 6676. [22] B. Hillebrands, J.R. Dutcher, Phys. Rev. B 47 (1993) 6126. [23] C.-J. Lin, G.L. Gorman, C.H. Lee, R.F.C. Farrow, E.E. Marinero, H.V. Do, H. Notarys, C.J. Chien, J. Magn. Magn. Mater. 93 (1991) 194.
Interface magnetic anisotropy in cobalt clusters embedded in a platinum matrix M. Jameta,*, M. Ne! griera, V. Dupuisa, J. Tuaillon-Combesa, P. Me! linona, A. Pe! reza, W. Wernsdorferb, B. Barbarab, B. Baguenardc a
! ! Departement de Physique des Materiaux, Universite! Claude Bernard Lyon, 43 Boulevard du 11 Novembre 1918, 69622 Villeurbanne, France b ! CNRS, 38042 Grenoble, France Laboratoire Louis Neel, c ! ! Laboratoire de Spectrometrie ionique et moleculaire, Universite! 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 codeposition 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 measurements performed 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 Elsevier Science 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 films and Co/Pt multilayers have been intensively studied because of their very large perpendicular magnetic anisotropy (PMA) [1,2]. Actually such systems are the best candidates for high density magnetic recording media. Magnetic Co–Pt dots made by electron lithography are now 10–20 nm wide but one hundred grains are required for one *Corresponding author. Fax: +33-472-43-15-92. E-mail address: [email protected] (M. Jamet).
memory bit [3]. In order to increase the recording density, even smaller dots will be used as only one memory bit. Cobalt clusters containing almost one thousand atoms (3 nm in diameter) embedded in a platinum matrix could be good candidates. Despite their nearly spherical shape, a large remaining interface magnetic anisotropy is expected to overcome the superparamagnetic limit [4]. In the present paper, we report a detailed magnetic study of a collection of noninteracting Co grains embedded in a Pt matrix (named Co/Pt system). A large local interface anisotropy and an anomalous dependence of the cluster magnetization as a
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
294
M. Jamet et al. / Journal of Magnetism and Magnetic Materials 237 (2001) 293–301
function of temperature have been found. These results are compared with previous ones obtained with the Co/Nb system [5].
2. Sample preparation and structural characterization Cobalt clusters are prepared using a laser vaporization source improved according to Milani de Heer design [6]. The Ti : sapphire vaporization laser used provides output energies up to 300 mJ at 790 nm, for a pulse duration of 3 ms and a 10 Hz repetition rate [7]. This source produces an intense supersonic cluster beam allowing us to grow films in the low energy cluster beam deposition (LECBD) regime. In this case, clusters do not fragment upon impact on the substrate or in the matrix [8]. We can prepare nanostructured thin films by random stacking of incident free clusters on different substrates or films of cobalt clusters embedded in a platinum matrix thanks to the codeposition technique. This last one consists in two independent beams reaching at the same time a silicon (1 0 0) substrate tilted at 451 at room temperature: the preformed neutral Co-cluster beam and the atomic beam used for the matrix. Depositions are performed in a UHV chamber (p ¼ 5 1010 Torr) to limit cluster and matrix
contamination. The matrix element is evaporated using a UHV electron gun evaporator mounted in the deposition chamber. By controlling both evaporation rates with quartz balance monitors, we can continuously adjust the cluster concentration in the matrix. Moreover, few neutral cobalt clusters (thickness eo1 monolayer) are deposited on a carbon coated copper grid and subsequently protected by a thin amorphous carbon layer on top (10 nm) to perform ex-situ High Resolution Transmission Electron Microscopy (HRTEM) observations. Nearly spherical clusters with a FCC structure and a rather sharp size distribution (mean diameter Dm E3:0 nm, dispersion sE0:2) are observed. Actually, in order to minimize their surface energy, clusters mainly have a truncated octahedron shape [9] (Fig. 1(a)). A 20 nm-thick film of randomly stacked cobalt clusters on a silicon substrate is prepared to perform grazing incidence small angle X-ray diffraction (GISAXD) measurements at LURE (Laboratoire pour l’Utilisation du Rayonnement Electromagne! tique, Orsay-FRANCE). The diffraction spectrum reported in Fig. 2 clearly confirms that cobalt clusters exhibit a FCC structure with roughly the same mean diameter (Dm E3:9 nm) as the one derived from TEM observations. Further X-ray absorption measurements (Extended X-ray Absorption Fine 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) 293–301
arb. units
Cofcc (311) Cofcc (220)
Cofcc (111) 2.4
2.8
3.2
3.6
4
4.4
4.8
5.2
5.6
k (Å- 1) Fig. 2. Diffraction pattern (GISAXD) obtained on a 20 nmthick 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.
Co/Pt samples [10] allow us to deduce the cluster structure in more details: a pure FCC cobalt core surrounded with an alloyed interface (corresponding to the interdiffusion of one cobalt atomic monolayer with platinum at the cluster/matrix interface). For magnetic measurements using a VSM (Vibrating Sample Magnetometer) apparatus, we prepared a 500 nm-thick Pt film containing a 4% cobalt-cluster volume concentration. A very low concentration is chosen to rule out any magnetic coupling between particles in the sample.
3. Magnetic study of the Co/Pt system In the following, we achieve a statistical treatment of magnetic measurements to deduce the cluster magnetization (noted Ms ðTÞ), their magnetic size distribution and anisotropy energy barrier. The cluster concentration is low enough to consider noninteracting particles i.e. only the applied magnetic field (Happ ) has to be taken into account. Furthermore for cobalt, the exchange length is 7 nm which is larger than the 3 nm mean particle size. Thus, a single domain cluster can be seen as a macrospin with uniform rotation of its magnetization. Finally, we will assume a uniaxial
295
magnetic anisotropy within the particles.1 In order to derive relevant information from measurements performed on a cluster assembly at any temperature, we have to take further factors into consideration: thermal fluctuations, the random distribution of easy magnetization axes and the magnetic size distribution. For this purpose, we use the following expression for the magnetic moment of the sample [4]: *Z p sin c mðHapp ; TÞ ¼ msat ðTÞ dc 2 0 + R 2p Rp dy sin y df cos a expðE=k TÞ B 0 0 Rp :; ð1Þ R 2p dy sin y 0 df expðE=kB TÞ 0 where msat ðTÞ is the saturation moment of the sample at temperature T: We use the spherical coordinates in which the two angles (y; f) give the direction of the particle magnetization. For a simple description of the random distribution of easy magnetization axes, we set the particle easy axis along the z direction while the magnetic field orientation given by the angle c between Happ and (Oz) is continuously varied from c ¼ 0 to p: E ¼ DE cos2 y þ m0 Happ Ms ðTÞ (pD3 =6) cosb is the magnetic energy of an individual cluster of volume V ¼ pD3 =6 (D is the particle diameter). b is the angle between the particle magnetization and the applied magnetic field and DE corresponds to the anisotropy energy barrier to cross in order to reverse the particle magnetization. In the following we take DE ¼ KDa where K is the anisotropy constant and D the particle diameter: a ¼ 2 means a surface anisotropy and a ¼ 3 a volume anisotropy. Finally, square brackets stand for the average over the log-normal magnetic size distribution f ðDÞ given by: ! 2 1 D 1 f ðDÞ ¼ pffiffiffiffiffiffiffiffiffiffi exp ln ; ð2Þ Dm 2s2 D 2ps2 where Dm is the mean cluster diameter and s the dispersion. 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.
296
M. Jamet et al. / Journal of Magnetism and Magnetic Materials 237 (2001) 293–301
We are first interested in the particle magnetization Ms ðTÞ and its temperature dependence. This parameter is important since it gives information on the magnetic state of the particles. It is proportional to the saturation moment of the sample through the relation: Z N msat ðTÞ ¼ Ms ðTÞ NðpD3 =6Þf ðDÞ dDpMs ðTÞ; 0
ð3Þ where N is the total number of particles in the sample. Considering the narrow size distribution of clusters as deduced from TEM observations, we assumed in Eq. (3) that the magnetization is independent on the particle size [11]. We use the expansion of Eq. (1) in high fields as a saturation approach law to determine msat ðTÞ [4]. We limit this expansion to the first order: a mðHapp ; TÞEmsat ðTÞ 1 ; m0 Happ a¼
kB T expð9s2 =2Þ : ðpD3m =6ÞMs ðTÞ
ð4Þ
From the magnetization curves reported in Fig. 3, we clearly show that the saturation moment is temperature dependent. Thus the
magnetization also depends on the temperature and its evolution vs. T is shown in Fig. 4. At very low temperature, Ms can be extrapolated to: Ms ð0 KÞEMs ð1:5 KÞ ¼ 16007200 kA m1 : This value is larger than the cobalt bulk magnetization (Msbulk ¼ 1430 kA m1). As a comparison, we mention that: Ms ð0 KÞE500750 kA m1 for the Co/Nb system [5]. Another way to estimate Ms ðTÞ consists in using the expansion of Eq. (1) in low fields. This can be written to the first order as [12]: m0 Happ ðpD3m =6ÞMs ðTÞ 3kB T 2 expð13:5s Þ
mðHapp ; TÞE msat ðTÞ
ð5Þ
and using Eq. (3), we find: mðHapp ; TÞE
NðpD3m =6Þ2 expð18s2 Þ m0 Happ Ms2 ðTÞ : 3kB T ð6Þ
This corresponds to the magnetic moment we measure in the Zero Field Cooled (ZFC) protocole when all the particles are superparamagnetic (the remanent moment of the sample being equal to zero). Thus, we deduce: 3000
M s (kA.m-1)
4
m (10-4 mA.m2)
annealed sample
2500
5 1.5 K
3 2
300 K
2000 1500
as-prepared sample
1000
1 500
0
0
-1
0
-2 0
1
2
3
µ0Η (Τ)
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.
40
80 120 160 200 240 280 320
T (K) 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 plot pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi TmZFC ðHapp ; TÞ=m0 Happ for three different applied magnetic fields: m0 Happ ¼ 10 mT; 12.5 and 15 mT (full squares). Note that for T > 150 K, the three curves superimpose with the magnetization curve obtained from the saturation approach.
297
M. Jamet et al. / Journal of Magnetism and Magnetic Materials 237 (2001) 293–301
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi In Ms ðTÞp TmZFCp ðHffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi app ; TÞ=m0 Happ (Ref. [14]). ffi Fig. 4, we plot TmZFC ðHapp ; TÞ=m0 Happ for 3 different applied magnetic fields. The resulting curves superimpose with the one obtained from msat ðTÞ for T > 150 K in the superparamagnetic regime. In the following, the temperature dependence of the particle magnetization is systematically taken into account. We estimate the magnetic size distribution from the highest temperature magnetization curves. At T ¼ 300 and 250 K, anisotropy terms can be neglected and Eq. (1) becomes [5]: RN 3 D LðxÞf ðDÞ dD mðHapp ; TÞ ; ¼ 0RN 3 msat ðTÞ 0 D f ðDÞ dD
Decreasing the temperature, anisotropy terms are no more negligible and have to be considered to fit the experimental data. To estimate them, let us perform a detailed analysis of both the remanent moment vs. temperature and the ZFC magnetization curves using the magnetic size distribution previously found. From hysteresis loops at low temperature, we deduce the remanent moment mr ðTÞ of the sample. For To10 K, we find mr ðTÞEmsat ðTÞ=2 which confirms a uniaxial magnetic anisotropy within the particles [13] and shows that cobalt particles are magnetically blocked below this temperature. In Fig. 6(a), we plot
ð7Þ
m Happ ðpD3 =6ÞMs ðTÞ ; x¼ 0 kB T
where LðxÞ is a simple Langevin function. We fit experimental curves in Fig. 5 using this equation and we find: Dm ¼ 2:770:1 nm and s ¼ 0:3570:05: Therefore the cluster magnetic size is smaller than the one derived from TEM observations. This diffrence is related to the diffused cluster/matrix interface and is discussed in the next section.
m (T)/m (1.5K) r r
1 (a)
0.8 0.6 0.4 0.2 0
0
50
100
150
200
250
300
T (K) 5
1
250 K 300 K
0.6 0.4
4
m (10-5mA.m2)
m/m
sat
0.8
(b)
3 2 15 mT 12.5 mT 10 mT 7.5 mT 5 mT 2.5 mT
1 0.2
0 0
0 0
0.4
0.8
1.2
1.6
µ 0Η (Τ) Fig. 5. Experimental magnetization curves in the superparamagnetic 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:
50
100
150
200
250
300
350
T (K) Fig. 6. (a) Experimental temperature dependence of the remanent moment (full circles) in the Co/Pt sample. The corresponding 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).
298
M. Jamet et al. / Journal of Magnetism and Magnetic Materials 237 (2001) 293–301
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
2.0 0.3
2.5 mT
5 mT
7.5 mT
10 mT
12.5 mT
15 mT
150 K
200 K
2.3 0.2
1.9 0.3
1.9 0.3
1.9 0.3
1.9 0.3
1.9 0.3
2.0 (fixed) 0.3
2.0 (fixed) 0.3
mr ðTÞ=mr ð1:5 KÞ and fit this curve using the following expression [5]: RN 3 mr ðTÞ D ðTÞ D f ðDÞ dD ¼ RNB ; ð8Þ 3 mr ð1:5 KÞ DB ð1:5 KÞ D f ðDÞ dD where DB ðTÞ is the blocking diameter of the particles at temperature T for m0 Happ ¼ 0 T. One finds DB ðTÞ when the relaxation time of the particle is equal to the measuring time t ¼ t0 expðDE=kB TÞ ¼ tmes then DE ¼ kB Tlnðtmes =t0 Þ ¼ KDB ðTÞa (in our case, tmes ¼ 10 s and the attempt frequency t1 is 0 typically 109–1012 Hz). To fit the mr ðTÞ=mr ð1:5KÞ ratio, we consider the anisotropy constant K and the exponent a as free parameters. The best fitting values are given in Table 1, they correspond to an interface anisotropy with aE2: We also fit the ZFC magnetization curves for different applied magnetic fields using (Fig. 6(b)) [5]: R DB ðHapp ;TÞ 3 D ðx=3Þf ðDÞ dD mZFC ðHapp ; TÞ RN ; ¼ 0 3 msat ðTÞ 0 D f ðDÞ dD x¼
m0 Happ ðpD3 =6ÞMs ðTÞ : kB T
Magnetization curves
ð9Þ
Here, we neglect the blocked particle susceptibility. The blocking diameter DB ðHapp ; TÞ now depends on the applied magnetic field, and the anisotropy energy barrier is written: DE ¼ K ðHapp ÞDa where the anisotropy constant KðHapp Þ which may depend on the applied magnetic field and the exponent a are free parameters. The results
1 (a) 0.8
m/msat
a K (mJ/m2)
ZFC magnetization curves
0.6 0.4 0.2
150 K
0 0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1 (b) 0.8
m/msat
Remanent moment
0.6 0.4 0.2
200 K
0 0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
µ0Η (Τ) 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).
M. Jamet et al. / Journal of Magnetism and Magnetic Materials 237 (2001) 293–301
are given in Table 1 for 6 different magnetic fields. They show that the anisotropy constant is actually independent on the magnetic field and confirm an interface anisotropy within the particles: aE2: Finally, for intermediate temperatures: T ¼ 200 and 150 K, we cannot fit the magnetization curves using a simple Langevin function as shown in Fig. 7 but we have to take the anisotropy term into account [15] (i.e. DE ¼ KDa ). Thus by assuming an interface anisotropy (i.e. a ¼ 2) we solve numerically Eq. (1) in order to deduce the anisotropy constant K given in Table 1. Fig. 7 shows the very good agreement between the theoretical and experimental curves. From all these results we can assert that interface is responsible for the large uniaxial magnetic anisotropy in cobalt clusters embedded in a platinum matrix. In comparison, if we assume an interface anisotropy in the Co/Nb system we find [5]: KS ¼ 0:0570:008 mJ/m2 which is almost one order of magnitude smaller than in Co/Pt.
4. Discussion Cobalt and platinum elements are miscible which may promote interdiffusion at the cluster/ matrix interface. Indeed, previous structural studies [10] showed that one cobalt atomic layer diffuses inside the Pt matrix. In this discussion we show that a simple core-shell model with a pure cobalt core surrounded with a disordered CoxPt1x alloyed shell can originally account for the magnetic properties of cobalt clusters embedded in platinum. We can write the cluster magnetization as Ms ðTÞ ¼ xMscore ðTÞ þ ð1 xÞMsshell ðTÞ;
ð10Þ
where x is the fraction of cobalt atoms in the core with Mscore ðTÞ ¼ Msbulk ðTÞ 1 ðMs ð0 KÞ ¼ 1430 kA m Þ; and (1 x) the fraction of cobalt atoms in the alloyed interface shell. For the following calculations we consider the cluster model reported in Fig. 1(a) which contains 1289 atoms. For Co/Pt, one atomic layer is expected to diffuse inside the matrix giving x ¼ 0:63: Thus one finds: Ms ð0 KÞ ¼ 0:63 1430 þ 0:37Msshell ð0 KÞ ¼ 1600 kA m1 which provides: Msshell ð0 KÞE
299
1900 kA m1 : This magnetization enhancement of cobalt is much smaller than that in CoPt alloys (3325 kA m1). This may be due to dimensional effects as mentioned by Canedy et al. [16]. However, the magnetization increase at low temperature indicates that the Curie temperature of the interface (TC ) is quite small (the Curie temperature in the core is assumed to be much higher than 300 K). This low value in CoPt disordered alloys is also pointed out by Weller et al. [17] or Devolder [18]. For this reason we find a reduced cluster magnetic size compared with the one derived from TEM observations at T ¼ 250 and 300 K (see previous section). We further annealed this sample during 10 min at T¼ 4501C under a vacuum of 107 Torr to promote cobalt-platinum interdifusion at the cluster surface. In Fig. 4, we plot the sample magnetization vs. T using the saturation approach law given by Eq. (4). It shows the transition from a superparamagnetic state to a paramagnetic state. At 2 K, the large magnetization Ms ¼ 2720 kA m1 now approaches the CoPt alloy value. It implies that almost all the cluster atoms have diffused inside the platinum matrix to form small alloyed ‘‘clusters’’. The low Curie temperature: TC E150 K confirms that there is no more pure cobalt core in the sample (x ¼ 0). Moreover, magnetization curves measured down to 2 K show no remanent moment so that the alloyed ‘‘cluster’’ anisotropy is negligible as expected for disordered CoPt alloys [18]. In the case of Co/Nb previously reported [5], two atomic layers are expected to diffuse inside the matrix, thus: x ¼ 0:36: If we assume that the CoNb disordered alloy is magnetically dead [5] one finds the sample magnetization: Ms ðTÞ ¼ xMsbulk ðTÞE0:36 1430 ¼ 515 kA m1 which is in good agreement with our experimental data. Finally, experimental magnetization values in Co/ Pt or Co/Nb can be well interpreted on the basis of a simple core-shell model. In Co/Pt, we unambiguously find the existence of an interface anisotropy and it is actually impossible to fit the experimental data by only considering a volume anisotropy within the clusters. Interface anisotropy originates from the combination of the large spin-orbit coupling in Pt
300
M. Jamet et al. / Journal of Magnetism and Magnetic Materials 237 (2001) 293–301
with the natural anisotropy directions induced by the surface [2]. Further surface strains induced by the surrounding Pt atoms may contribute to this interface anisotropy. Let us assume a volume anisotropy within the cobalt clusters. That leads to an anisotropy constant KV given by the relation: DE ¼ KV Vm ¼ KS Sm where Vm and Sm are the mean cluster volume and surface respectively. Using the mean diameter Dm obtained in Section 3, one finds: KV ¼ 6KS =Dm E7 105 J/m3. For an infinite cobalt cylinder, shape anisotropy is equal to D0 Ms2 =4E6:4 105 J/m3 if we use the bulk magnetization [19]. This is even smaller than the above KV value, thus shape anisotropy cannot account for the experimental one. Furthermore, cubic magnetocrystalline 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 the experimental value. In conclusion the assumption of a volume anisotropy seems not physically obvious. In order to compare our surface anisotropy with previous works, we can estimate the corresponding anisotropy energy per cobalt atom at the cluster surface. For that purpose, we use the cluster model in Fig. 1(b). Indeed, for a perfect truncated octahedron as the one given in Fig. 1(a), symmetries cancel surface anisotropy and we add one (1 1 1) facet to break this symmetry. We note K at the atomic anisotropy energy. Summing over all the cluster surface atoms, one finds the anisotropy energy in the whole particle: E ¼ 15K at cos2 y; where y is the angle between the magnetization and the [1 1 1] direction. Dividing by the cluster surface, we can deduce K at from the experimental anisotropy: K at E3 meV/at. This is one order of magnitude larger than the experimental values given in Refs. [2,22,23] ranging between 0.1 and 0.3 meV/at for 1–2 cobalt monolayers in Co/Pt multilayers.
5. Conclusion We have shown that the anisotropy energy barrier DE of cobalt clusters embedded in a platinum matrix is proportional to the particle
surface (i.e. D2 ) which implies an interface anisotropy. Moreover, taking into account the nearly spherical shape of the particles, we found that this interface anisotropy is locally one order of magnitude larger than the one reported in Co/Pt multilayers. The mean cluster blocking temperature now reaches 100 K compared with 10 K in Co/ Nb. Since interface anisotropy is proportional to the particle deformation, one possible experimental issue to increase this blocking temperature could be the use of slightly elongated particles. Moreover, we have seen that in miscible systems such as Co/Pt we have two contributions in the particle magnetization: one from the pure cobalt core and a second one from the alloyed interface at the cluster surface (shell). We are now investigating the magnetic properties of CoPt ordered alloy clusters for potential magneto-optical recording.
References [1] C. Menechini, M. Maret, V. Parasote, M.C. Cadeville, J.L. Hazemann, R. Cortes, S. Colonna, Europhys. Journal B 7 (1999) 347. [2] N. Nakajima, T. Koide, T. Shidara, H. Miyauchi, H. Fukutani, A. Fujimori, K. Iio, T. Katayama, Phys. Rev. Lett. 81 (1998) 5229. [3] D.A. Thomson, J.S. Best, IBM J. Res. Develop. 44 (2000) 311. [4] J.L. Dormann, D. Fiorani, E. Tronc, Advances in Chemical Physics, Vol. XCVIII, I. Prigogine and Stuart Rice, p. 288, 1997. [5] M. Jamet, V. Dupuis, P. M!elinon, G. Guiraud, A. P!erez, W. Wernsdorfer, A. Traverse, B. Baguenard, Phys. Rev. B 62 (2000) 493. [6] P. Milani, W.A. de Heer, Rev. Sci. Instrum. 61 (1990) 1835. [7] M. Pellarin, E. Cottancin, J. Lerm!e, J.L. Vialle, J.P. Wolf, M. Broyer, V. Paillard, V. Dupuis, A. P!erez, J.P. P!erez, J. Tuaillon, P. M!elinon, Chem. Phys. Lett. 224 (1994) 338. [8] A. P!erez, P. M!elinon, V. Dupuis, P. Jensen, B. Pr!evel, M. Broyer, M. Pellarin, J.L. Vialle, B. Palpant, J. Phys. D 30 (1997) 709. [9] J. Buttet, J.P. Borel, Helvetica Phys. Acta 56 (1983) 541. [10] M. N!egrier, J. Tuaillon, V. Dupuis, P. M!elinon, A. P!erez, A. Traverse, Phil. Mag. A (2001), in press. [11] I.M.L. Billas, A. Chatelain, W.A. de Heer, Science 265 (1994) 1682. [12] K. Muller, F. Thurley, Int. J. Mag. 5 (1973) 203. [13] H. Pfeiffer, Phys. Stat. Sol. A 118 (1990) 295. [14] G. Xiao, C.L. Chien, J. Appl. Phys. 61 (1987) 3308.
M. Jamet et al. / Journal of Magnetism and Magnetic Materials 237 (2001) 293–301 [15] M. Hanson, C. Johansson, S. Morup, J. Phys.: Condens. Matter 5 (1993) 725. [16] C.L. Canedy, X.W. Li, G. Xiao, Phys. Rev. B 62 (2000) 508. [17] D. Weller, H. Br.andle, G. Gorman, C.-J. Lin, H. Notarys, Appl. Phys. Lett. 61 (1992) 2726. [18] T. Devolder, Phys. Rev. B 62 (2000) 5794. [19] A. Aharoni, Introduction to the Theory of Ferromagnetism, Oxford Science Publications, Oxford, 1996, p. 115.
301
[20] C.H. Lee, H. He, F.J. Lamelas, W. Vavra, C. Uher, R. Clarke, Phys. Rev. B 42 (1990) 1066. [21] J.P. Chen, C.M. Sorensen, K.J. Klabunde, G.C. Hadjipanayis, J. Appl. Phys. 76 (1994) 6676. [22] B. Hillebrands, J.R. Dutcher, Phys. Rev. B 47 (1993) 6126. [23] C.-J. Lin, G.L. Gorman, C.H. Lee, R.F.C. Farrow, E.E. Marinero, H.V. Do, H. Notarys, C.J. Chien, J. Magn. Magn. Mater. 93 (1991) 194.