MAGNETIC PROPERTIESOF NANOSTRUCTURED MATERIALS Monte Carlo Simulation and Experimental Approach for Nanocrystalline Alloys and Core-Shell Nanoparticles

O. CRISANa,b, J.-M. GRENECHEc, Y. LABAYEc, L. BERGERc,A.D. CRISANb M. ANGELAKERISb, J.M. LeBRETONd, N.K. FLEVARISb

aNational Institute for Materials Physics, P.O. Box MG-7, 76900 Bucharest, RomaniabDepartment of Physics, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece cLPEC, UMR 6087 CNRS, Université du Maine, 72085 Le Mans, France dGPM, UMR 6634 CNRS, Université de Rouen, 76801 St. Etienne du Rouvray, France

Corresponding author: O. Crisan, e-mail: ocrisan@yahoo.com

Abstract: The magnetic properties of FINEMET-type nanocrystalline alloys and isolated ferromagnetic AgCo nanoparticles are investigated both experimentally and nu-merically. Theoretical models of spins that simulate ideal nanocrystalline alloys and isolated nanoparticles are considered while their magnetic properties are de-rived from Monte Carlo simulation of low-temperature spin ordering. Interesting features such as magnetic polarization of the matrix due to penetrating fields aris-ing from nanograins and the role played by the crystalline fraction in the overall magnetic behaviour, in the case of nanocrystalline alloys are investigated. For iso-lated nanoparticles it is shown that the competition between surface and bulk ani-sotropy gives rise to surface spin disorder that, together with finite-size effects, is responsible for the experimentally observed lack of saturation of the magnetization in high applied fields. These simulation results are confirmed by experimental data obtained on FINEMET nanocrystalline alloys and isolated ferromagnetic AgCo colloidal nanoparticles.

1. INTRODUCTION

A great deal of interest has been devoted recently to the magnetic properties of nanocrystalline materials from both the experimental [1-8] and the theoretical [9-12] point of view. These nanomaterials have a huge potential in technological applications in many fields. Besides this, they may also be regarded as model systems for studying fundamental issues such as quantum tunneling of magnetization, spin dependent magneto-transport, and so on. Nowadays there are several patented systems based on nanocrystalline alloys, such as FINEMET (or VITROPERM) with the nominal com-position Fe73.5Cu1Nb3Si13.5B9, or NANOPERM (Fe-Nb-Cu-B or Fe-Zr-Cu-B). Usually,

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these materials are obtained by a subsequent annealing of rapidly quenched amorphous ribbons. The microstructure consists thus of ferromagnetic crystalline nanograins dispersed within a weakly ferromagnetic amorphous matrix. Such nanocrystalline alloys have received great attention during recent years mostly because of their outstanding potential as soft ferromagnets or magnetostrictive materials. The so-called FINEMET [1]. Nanocrystalline Fe73.5Cu1Nb3Si13.5B9 ribbons, obtained after subsequent annealing of the amorphous precursor, consist of -Fe(Si) or Fe3Si nanocrystalline grains dispersed into an amorphous residual Fe-Nb-B matrix, and exhibit excellent soft magnetic properties (high permeability, high saturation magnetization, low losses and low magnetostriction). These soft magnetic properties are mostly related to the exchange coupling between nanocrystalline grains through the amorphous matrix if the exchange correlation length does not exceed the nanocrystalline grain size [2]. The annealing parameters, such as temperature/time, atmosphere and/or applied field need to be strictly controlled. Tailoring of desired macroscopic properties for specific applications requires a deep insight in the magnetic features of these nanocrystalline Fe-based ribbons. For this purpose one has to elucidate the correlation between the micro-structural evolution of both the nanocrystalline and amorphous residual phase, and the magnetic behaviour of the ribbons. The key issue for understanding the magnetic macroscopic properties, such as magnetization or susceptibility, would be to investigate the contributions arising both from the nanograins and from the amorphous residual matrix, but also to study the role played by the nanograin surface and the interfacial zone between the nanograins and the matrix. 57Mössbauer spectroscopy studies of FINEMET-type [4] and NANOPERM-type [5-8] nanocrystalline alloys provide evidence for an interfacial zone between the nanograins and the amorphous residual matrix. This interface exhibits a disordered atomic structure and spin-glass-like behaviour and has a chemical composition that differs strongly from those of both the nanograin and the matrix [8]. In addition, contrary to the low-temperature case where both intergranular and nanocrystalline grains behave as strongly coupled ferromagnets, the high temperature magnetic behaviour, i.e. above the Curie temperature of the amor-phous matrix, is strongly dependent on the crystalline volume fraction [13-15].

Another key issue in understanding the magnetic properties of such systems is related to the surface and finite-size effects. Both effects have a stronger influence on the magnetic properties of the assemblies of nanograins, either isolated or interacting, as the size of nanograins decreases. Several theoretical studies of the magnetic behaviour of oxide nanoparticles have been reported [9-12]. It has been shown that broken exchange bonds at the nanoparticles surface, resulting in lower coordination compared to the bulk, give rise to a surface spin disorder and hence an increased surface anisotropy [9]. This surface spin disorder is particularly important in the case of isolated nanoparticles, which can be described by a core-shell model. It has been reported that in the case of CoRh nanoparticles, strongly enhanced magnetic moments are obtained and the magnetization does not saturate even at pulsed applied fields (of the order of 35 T) [16]. This unusual result can be explained in terms of surface spin disorder imposed by strong surface anisotropy and can be understood by observing the spin configurations in theoretical systems of spins, obtained by Monte Carlo simulation. The influence of the competition between bulk and surface energies resulting in finite-size effects on

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the magnetic behaviour of oxide nanoparticles has also been evidenced [9, 10]. The method of Monte Carlo simulation of low-temperature spin ordering was used for studying the surface and finite-size effects in oxide nanoparticles [11, 12]. Unlike micromagnetic [17, 18] or molecular dynamics calculations [19], the Monte-Carlo simulations (MCS) take into account the atomic structure of the lattice and the short-range nature of the exchange interactions.

The present work is structured in two main parts. In the first one we report the usual observed magnetic behaviour and phase structure in the case of FINEMET-type alloys with an emphasis on the chemical nature of the nanograin – matrix interfaces and the consequently modified magnetic behaviour compared with those of the nanograin core and of the matrix. Monte Carlo simulations of low-temperature spin ordering of a single ferromagnetic grain immersed into a weak ferromagnetic environment, identified with the amorphous matrix, will allow to evidence the two-phase magnetic behaviours, as observed in real systems. Thermodynamic quantities such as susceptibility, magnetiza-tion, energy-per-spin as well as parameters such as the Curie temperature, are investigated as a function of the crystalline fraction and exchange coupling inside the nanograin core, the matrix and at the interfaces. The other part is devoted to the investigation of surface and finite size effects occurring in the magnetic behaviour of the isolated nanoparticles. Spin ordering at low temperatures obtained by Monte Carlo simulation is studied as depending on surface anisotropy and exchange interactions between spins. The theoretical data are then corroborated with experimental magnetic measurements on core-shell-type AgCo nanoparticles obtained by colloidal chemistry.

2. STATE-OF-THE-ART

It has already been mentioned that FINEMET-type nanocrystalline alloys exhibit excellent soft magnetic properties that are related to the exchange coupling between the nanograins [2]. Therefore, a crucial parameter that directly influences the high- and low-temperature magnetic behaviour of the nanocrystalline alloys is considered to be the crystalline volumetric fraction. The crystalline volume fraction, as well as the interfaces between nanocrystalline grains and matrix, significantly influences the magnetic properties of these alloys. It has been shown that this interface features a disordered atomic structure and a spin-glass-like magnetic behaviour [5]. For temperatures above the Curie point of the amorphous matrix, the magnetic behaviour is strongly dependent on the crystalline fraction. A low crystalline fraction leads to the occurrence of high-temperature superparamagnetic (SPM) single-domain grains while for a high crystalline fraction, the paramagnetic intergranular phase is polarized by penetrating fields arising from the nanocrystalline grains [4, 13, 15]. The magnetic polarization of the amorphous matrix and the interfacial regions by the nanocrystalline grains have a significant influ-ence on the macroscopic magnetic behaviour of the nanocrystalline alloys. In the case of Fe-based nanocrystalline alloys, this crystalline fraction can be quite conveniently derived from Mössbauer spectrometry. It is known that such nanocrystalline alloys are often described as two-phase (amorphous + nanocrystalline grains) materials. Nevertheless, one should take into account that the amorphous intergranular phase is

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chemically and structurally heterogeneous, originating from the atomic diffusion mechanisms which have occurred during the transformation from the crystalline into the nanocrystalline state. For this purpose since both the local atomic density and the coordination in the boundary regions are different from those of bulk crystalline and amorphous phases. It seems that a third Mössbauer component corresponding to Fe sites located at the grain surfaces and/or in the interphase boundaries has to be considered. For NANOPERM-type alloys, besides the magnetic sextet for the nanocrystalline phase (in that case -Fe) and the low-field hyperfine field distribution for the amorphous phase, a third contribution corresponding to the interfacial regions between nanograins and amorphous matrix [5] was introduced to fit the Mössbauer spectra. In the case of FINEMET-type alloys, due to the complexity of the hyperfine structure of the crystalline component and to the high spectral overlapping of the different contribution, this third component cannot be accurately estimated, even though evidence for distinct magnetic behaviour of the interfacial regions compared with the nanograins and the amorphous matrix has been provided [5-8]. To come to the point, for FINEMET alloys the contribution of the magnetically disordered crystalline interface would be included in the contribution due to nanocrystalline grains.

The nanograin exchange field penetration into the matrix is still an open issue [20-22]. 57Fe Mössbauer spectrometry data [7] and thermomagnetic data [23] obtained on two-phase nanocrystalline alloys provided evidence for exchange coupling between the grains even above the Curie temperature of the matrix. This exchange field penetration has been also observed and modeled by several authors using random anisotropy concept [14], molecular field approach [21, 22] and assuming an exponential decay of exchange interactions through the amorphous matrix [15, 24]. Nevertheless, all these approaches are based on experimental features (either Mössbauer or magnetic measurements) performed on the integrality of the samples. By using Monte Carlo simulation, one can directly obtain the magnetic behaviour of outer shells of the nanocrystalline grain or of the interfacial regions (2-3 successive atomic layers covering the nanocrystalline grain) and their behaviour could be correlated with the evolution of physical parameters hardly tunable in real materials, such as the matrix-nanograin exchange coupling, or surface anisotropy. For this reason and many more, Monte Carlo simulation (MCS) seems to be a suitable approach to predict magnetic features of real materials, even by using simple assumptions, idealized systems of small sizes. The overall magnetic response of the systems submitted to extreme conditions that eventually cannot be achieved in laboratories, i.e. high magnetic fields or huge surface anisotropies, may be obtained via MCS.

The magnetic properties of nanostructured materials in general, and of the nano-particles in particular are, as it has already been underlined, strongly altered comparing to the bulk. This altering may occur in different ways and may lead to unexpected new phenomena related to technological applications. Besides their enhanced interest in catalysis, nanoelectronics [25], biomedical applications [26] or magnetic recording media [27, 28], magnetic nanostructures obtained by self-organization of nanoparticles onto substrates can be used as model systems for studying fundamental aspects arising from nanoscopic scaling of different magnetic features. Two main effects that originate from the spatial confinement in nanostructured materials, i.e. surface and finite size

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effects, have been previously considered in order to explain anomalous magnetic behaviour of nanomaterials. It has been found [29] strong variation of perpendicular magnetic anisotropy and increased orbital magnetic moments for small SPM Co clusters on Au(111) surface, this being attributed to finite size effects which directly influence the 3d electronic structure. For iron nanoparticles [30] it has been established that the surface spins are noncollinear and ferromagnetically coupled to the core. Interesting fundamental issues such as enhanced exchange bias in Fe/FeRh bilayers [31] and at Fe/oxide interfaces [32] have been also corroborated with the spin flop coupling of the interfacial spins and with the surface spin-glass-like state, respectively. Evidence of surface spin disorder and finite size effects has been found in ferrite and metallic oxide nanoparticles [33-35] and the influence of surface spins on the overall magnetic behav-iour has been modelled [9] considering enhanced surface anisotropy due to broken exchange bonds at the surface. Also, in the case of maghemite nanoparticles, both ex-perimental and simulation studies [11, 12, 36] have proved that highly disordered surface layers dominate the magnetic properties for small sizes of nanoparticles. Colloidal Co [37] and CoRh [16] nanoparticles have been shown to exhibit greatly enhanced magnetic moments comparing to the bulk, and their magnetization does not saturate even at applied pulsed field as high as 35 T. This anomalous behaviour could also be associated with the surface spin disorder and finite size effects.

An attempt to give evidence of the influence of such surface and finite size effects on the magnetic behaviour of isolated nanoparticles will consist in investigating the low-temperature spin configurations for a single ferromagnetic nanoparticle via Monte Carlo simulation. These results will be consequently corroborated with experimental data on colloidal AgCo magnetic nanoparticles.

3. CASE OF NANOCRYSTALLINE FINEMET ALLOYS

3.1. Framework of the simulation

The model considered for Monte Carlo simulation consists of a spherical nanograin embedded in a matrix of cubic shape. This cubic box contains 153 sites on a simple cubic lattice, i.e. each i site has six nearest neighbours. To each cubic lattice site, a classical spin Si that interacts with its j nearest-neighbours via an exchange cou-pling constant Jij will be assigned. Contained in the box, a sphere of radius R (in units of interatomic distance) is defined. The sites belonging to the sphere (nanograin) and to the matrix, are denoted as A and B sites, respectively. Moreover, two non-equivalent atomic layers at the nanograin surface are defined: the first one consists of A sites having at least one first-nearest-neighbour of B type and denoted AB, and the other consists of B sites having at least one first-nearest-neighbour of A type, denoted BA. These two atomic shells represent the nanograin surface and the matrix-nanograin interface, respectively, featuring magnetic behaviour different from that of the bulk (AA and BB regions). Taking into account the broken symmetry (lower coordination) for the sites in the surface that leads to a distribution of magnetization over the whole system, one has to consider JAA JBB JAB (for reasons of symmetry JAB = JBA).The macroscopic thermodynamic properties, such as the temperature dependence of magnetization, specific heat and magnetic susceptibility for our system, are obtained

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from a Heisenberg-type hamiltonian which contains several terms corresponding to different energy contributions: exchange, anisotropy, magnetostatic and dipolar. In the present study, only the first two prevailing energy contributions are considered: the hamiltonian defined at a given site i thus reads as:

VjSiSViVjiji nSKySKSSJH 2

,2

,)ˆ()ˆ( (1)

V is the nearest-neighbourhood of site i, Jij are the exchange coupling constants, Si, Sj

the spins corresponding to the i and j sites, Ki the site dependent anisotropy constant (Ki = KS for AB sites and Ki = KV elsewhere), y and n denote the directions chosen for the anisotropy (uniaxial for the bulk and normal for the surface). The grain had different radii, ranging from 4 (N 268 sites) to 7 (N 1436 sites), leading to an atomic crystalline fraction of 7 and 40%, respectively. We associate the same spin value S = 1 to each site in both regions. The ferromagnetic exchange coupling constants (only over the nearest-neighbours) considered for calculations equal JAA = 3 (inside the nanograin) and JBB = 1/2 (inside the matrix), a choice consistent with two phases exhibiting significantly different Curie temperatures.

Figure 1. Simulated total magnetization vs. T for 153 cubic box, for JAB = 2 and different nanograin radius

Figure 2. Simulated total magnetization vs. T for 153 cubic box, for nanograin radius R = 6 and different matrix-nano-grain exchange coupling JAB

The high ratio JAA /JBB allows thus to separate clearly the two phases because the magnetic behaviour is worth to be discussed for temperatures ranged between the two Curie temperatures. The exchange coupling constant between the nanograin and the matrix JAB ranges from 0.01 to 50. The calculations were performed using periodic boundary conditions. Moreover, the anisotropy is considered uniaxial along the y-axisand equal for all sites: KV = 0.3 while surface anisotropy was considered radial to the surface and equal to KS = 3.0. By neglecting the dipolar term, each computation needs less CPU time. This gain allows thus a greater number of Monte Carlo steps (2 105 steps per spin and per temperature) to be taken, in order to obtain better statistics and a better estimate of magnetic parameters such as Curie temperatures. Figure 1 shows the temperature dependence of total magnetization (normalized) of the 153 site cubic box, with different values of nanograin radius (different crystalline fractions), for JAB (exchange coupling between the matrix and the nanograin) equal 2.

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All the curves exhibit a two-phase behaviour, typical for nanocrystalline soft magnetic alloys. The two contributions that show distinct behaviour could unambiguously be attributed to the matrix and the nanograin, respectively. The effect of increasing the crystalline fraction is obvious in the magnetization curves, i.e. higher magnetization values above the Curie temperature of the matrix (hereafter denoted TC

M) up to the Curie temperature of the nanograin (hereafter denoted TC

N). It is worthwhile noticing that the magnetization apparently does not vanish at temperatures above TC

N. This is an illustration of the size effects acting on the magnetic state of the system. When one deals with finite-sized magnetic objects, the magnetic correlation established through exchange coupling between reversal spins does not completely disappear even at temperatures above TC

N, where thermally activated magnetic fluctuations should prevent the local alignment of the spins. For the nanograin radius R = 6 (Fig. 2) the magnetization curve with JAB = 0.01 shows a very sharp transition between the matrix and the nanograin contributions, typical of a system with completely decoupled mag-netic phases. With increasing JAB, the transition between the two contributions becomes more and more smooth and one can observe that the exchange coupling in the surface influences the matrix and the nanograin differently.

Figure 3. Simulated magnetization of the nanograin surface AB (top) and of the matrix-nanograin interface BA (bot-tom) for different nanograin radius and JAB = 2

Figure 4. Magnetization vs. T for as-cast (open circles) and annealed (open squares) FINEMET sample [42]. Con-tinuous line: nanograin contribution. Dashed line: matrix contribution

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In Fig. 3 the normalized magnetization vs. temperature curves obtained for the nanograin surface shell (AB) and the matrix-nanograin interface (BA) for different nanograins radius, for JAB = 2, are shown. Increase of TC (compared with the cor-responding values in case of almost decoupled system, i.e. JAB = 0.01) with the crystal-line fraction is observed for both regions. This indicates a magnetic polarization of the matrix by exchange coupling in the matrix-nanocrystalline grain interface. The observed small fluctuations around TC are due to the finite-size effects, important in such systems. An interesting behaviour here is exhibiting by MBA dependence. MBA not only vanishes far above TC

M of the matrix (see Fig. 1) – in fact, it vanishes at TCN, just as the nano-

crystalline grain core and surface contribution, providing thus an increase of its TC of more than 300% – but also the dependence is far from the expected ferromagnetic profile, exhibiting a rather paramagnetic-like behaviour instead. Evidences about paramagnetic behaviour of the interface in various nanocrystalline (either FINEMET or NANOPERM type) alloys have been reported by several authors [22, 23] and explained by boron enrichment of the interface during annealing [22]. As in our simulation, no difference is assumed between atoms in nanocrystalline grain, matrix or interface. This suggests that the high degree of magnetic disorder (apparent paramagnetism) of the shell considered as matrix-nanocrystalline grain interface, in real materials, could also be due to the difference in exchange coupling values of its neighbourhood (weak for the matrix and strong for the nanocrystalline grain) and also to the competition between enhanced surface anisotropy and exchange coupling inside the nanocrystalline grain.

3.2. Experimental results

The magnetic behaviour of the FINEMET samples, as-cast and annealed, has been investigated by thermomagnetic measurements. The specific magnetization vs. tem-perature for both the as-cast sample (open circles) and for the sample annealed at 510 C(open squares) is presented in Figure 4. It is well established that the specific magnetization of a single-phase ferromagnet decreases with temperature according to the following Heisenberg-type dependence: CTTT 10 (2) where (0) is the

specific magnetization at zero temperature, TC the Curie temperature and the critical exponent (typically = 0.36 for Heisenberg ferromagnets). The thermomagnetic curve of the as-quenched sample shows weak ferromagnetic features, typical of the topologi-cally disordered Fe-rich amorphous ribbons, i.e. a decrease of the magnetization towards zero at a temperature value TC corresponding to the Curie point of the amorphous precursor of about 390 C. The sample shows zero magnetization up to about 475 C. Then the magnetization starts to increase. This is due to the onset of crystal-lization at 475 C. When the sample begins to crystallize and the number of progres-sively formed magnetically ordered nanocrystallites increases with the temperature, the nanocrystals net magnetization overcomes the thermally induced spin reversal and the total specific magnetization of the sample increases up to a value corresponding to the end of primary crystallization, point from which the nucleation process has finished ( 550ºC from the DSC curves for same samples [38, 39]). At higher temperatures, it can be assumed that the magnetization of the as-cast sample vanishes. The specific

Magnetic Properties of Nanostructured Materials 261

magnetization vs. temperature curve for the nanocrystalline sample annealed at 510 Cexhibits typical ferromagnetic features – a decrease due to the thermally induced spin disorder in the sample – with an inflection point, characteristic of a two-phase behaviour, with well separated Curie temperatures, which is usually the case in nano-crystalline alloys. The decrease of magnetization with increasing temperature is slower than in the case of the as-cast amorphous sample and the magnetization values are higher for the nanocrystalline sample than for the amorphous precursor, for any given temperature. It is well established [40, 41] that below the observed inflection point the curve comprises the magnetization contribution of the amorphous residual matrix together with the nanocrystalline grains contribution. It should nevertheless be men-tioned that in this temperature range the nanocrystals, being ferromagnetically coupled strongly than in the amorphous, have a less important contribution to the magnetization decrease than the amorphous. Above the inflection point, the amorphous contribution to the magnetization vanishes and only the nanocrystals contribute to the net magnetiza-tion of the sample. By separating the low temperature profile (contribution of the amorphous phase) from the high temperature profile (contribution of only the nanocrystalline grains) and numerically fitting them using Eq. (2), one can roughly estimate the Curie temperatures of the amorphous as well as of the nanocrystalline phase. The fittings are shown in Fig. 4 by solid line (nanocrystalline contribution) and a dashed line (amorphous part), respectively. The amorphous contribution has been obtained by the subtraction of a nanocrystalline contribution (solid line) from the experimental data, for temperatures below the inflection point. The numerical fitting results show that the Curie temperature of the -Fe(Si) nanocrystalline grains is about 590 C, while the Curie temperature of the residual amorphous is about 440 C. If one compares this value with that obtained for the amorphous precursor (390 C), with iron content obviously higher than the amorphous residual matrix, the Curie temperature increases at about 12% [42]. This increase is a further indication of the magnetic polarization of the amorphous residual matrix by penetrating fields arising from nanocrystalline grains. It is expected to be even larger if one compares the amorphous residual matrix with an amorphous as-quenched alloy of identical composition. Some authors [15, 24] have reported an increase of TC by up to 100 K for the amorphous residual matrix compared to the amorphous as-cast samples with identical composition, in the case of Fe-Zr-B-Cu and Fe-Nb-B-Cu (NANOPERM) alloys. However, unlike the NANOPERM alloy, in the case of FINEMET nanocrystalline alloys, the exact composition of the amorphous residual matrix and the heterogeneous behaviour are difficult to be estimated from Mössbauer data, mainly due to the lack of estimation of the interfacial region.

4. CASE OF ISOLATED AGCO NANOPARTICLES

4.1. Framework of the simulation

The isolated ferromagnetic nanosphere was modelled as a sphere with radius R = 15 and containing N = 14328 atoms in a cubic symmetry with a surface-to-volume ratio of 0.16. The same hamiltonian as in Eq. (1) is used to obtain the equilibrium spin configuration. The exchange coupling in the nanograin core (AA region) is taken the same as in the nanograin surface (AB region): JAA = JAB = 1000, KV = 20

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while KS is ranging between 20 and 2000. The spin configuration calculated in the demagnetized state exhibits distinct features as the surface anisotropy increases. For KS/KV = 10 the surface spins tend to be radially oriented, a tendency which is propa-gated (via exchange coupling) inside the core where it competes with the uniaxial orientation along Oz imposed by the bulk anisotropy. This competition gives rise to a “throttled” spin configuration that has the surface spins oriented inward for upper hemi-sphere and outward for the lower hemisphere [43]. The surface spin reversal that occurs at the equator takes place over several interatomic distances. For KS/KV = 60 the surface spin reversal takes place only over one interatomic distance by creating vortex-type re-versal centers (Fig. 5). The calculated spin configuration in the case of isolated ferro-magnetic nanoparticles shows the occurrence of different equilibrium orientation for surface spins than for the core spins, essentially due to the increased surface anisotropy. This surface spin disorder may be responsible for the peculiar magnetic behaviour observed in the low-dimensional systems, and, in particular, for the enhanced magnetic moments and the lack of saturation of the magnetization in high applied fields.

4.2. Experiment and discussions

The AgCo nanoparticles have been obtained via colloidal chemistry techniques [44]. Their composition shown by energy dispersive spectroscopy (EDS) has been found to be Ag30Co70. Their morphology and structure have been studied by XRD and HRTEM [45]. The nanoparticles are deposited onto Si(100) substrates and self-organize into quasi-regular arrays. The structure of a single nanoparticle is determined to be of fcc-Ag core with incomplete hcp-Co shells. The magnetism of this system is essentially determined by the Co spins in surface states. From this point of view, the surface spin orientation is crucial for determining the overall magnetic properties of the system. Hys-teresis loop of Ag30Co70 / Si(100) has been recorded using a SQUID device at 293 K in applied field up to 5.5 T, parallel to the sample plane and is shown on a reduced

Figure 5. Spin configuration in the central plane of R = 15 nanoparticle, obtained by MCS [43]

Figure 6. Hysteresis loop for Ag30Co70

nanoparticles at 293 K [46]. Inset: full cycle up to 5.5 T

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scale in Fig. 6. A very interesting result is the fact that the magnetization (inset of Fig. 6) exhibits no saturation up to 5.5 Tesla and the increase of magnetization for applied fields above 0.3 T looks quite similar to paramagnetic-like materials. This anomalous magnetic behaviour resembles the previously reported investigations on CoRh nanoparticles [16] and could be attributed both to the unusual multiphase poly-crystalline structure of nanoparticles favoring noncollinear arrangement of magnetic moments and to the highly disordered magnetic surface layer, as we have seen in the simulated spin configuration (Fig. 5). The shape of the M(H) curve suggests that the sample exhibits at least two different magnetic components: one is ferromagnetic and gives a sharp increase at very weak applied fields (up to ~ 1500 Oe) and the other is paramagnetic at 293 K and gives a continuous increase of magnetization at higher applied fields.

The surface spin disorder arising from the competition between the surface and the bulk anisotropy may constitute one of the reasons for the experimentally observed lack of saturation for the magnetization and the peculiar behaviour of the M(H) curve in the case of isolated AgCo nanoparticles.

5. CONCLUSIONS AND PROSPECTS

Using a simple model consisting of systems of spins in a cubic symmetry and a Hamiltonian composed of exchange coupling and surface and bulk anisotropy terms, thermomagnetic data are obtained by Monte Carlo simulation of low-temperature spin ordering. In the case of a single ferromagnetic nanograin immersed in a weakly ferromagnetic matrix (assimilated to the nanocrystalline alloys), the magnetic behaviour is investigated as a function of the crystalline fraction and exchange coupling between nanograin and matrix. The peculiar behaviour of the interfaces between nanograin and matrix, i.e. the very strong increase of the Curie temperature of the interfacial layer as observed both theoretically and experimentally, is proven to be due to the polarization of the matrix via penetrating fields arising from the nanograins. The simulated thermomagnetic curves are corroborated with the experimentally obtained phase structure and magnetic data to give a coherent image of the different behaviour of both nanograin surface and interface between matrix and nanograin. The equilibrium spin configuration of an isolated nanoparticle with cubic symmetry is obtained by Monte Carlo simulation and is shown to be extremely sensitive to the competition between surface and bulk anisotropy. This competition yields a particular, so-called “throttled”, low-temperature spin ordering, where surface spins reversal takes place via vortex-type pinning centers. This surface spin disorder is shown to be responsible for the lack of saturation of magnetization at applied high magnetic fields (5.5 T) and peculiar multiphase magnetic behaviour, experimentally observed in AgCo nanoparticles. Further simulation studies implying the use of supplementary (dipolar) terms in the hamiltonian and detailed magnetic and structural data are necessary to clarify the influence of the finite-size and surface effects and to understand the issues regarding interfacial states and matrix polarization by pinning fields, on the magnetic features of nanocrystalline alloys and nanoparticles.

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ACKNOWLEDGEMENTS

The financial support for the postdoc fellowship of O. Crisan from Region Pays de Loire, at the Universite du Maine, Le Mans, France, is gratefully acknowledged. Part of this work has been performed under the EU funded RTN no. HPRN-CT-1999-00150. The simulations were made using Lotus, a 95 processors Beowulf class parallel computational facility: http://weblotus.univ-lemans.fr/w3lotus

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