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Magnetic Properties of Hard Magnetic FePt Prepared by Cold Deformation Nguyen H. Hai, Nora M. Dempsey, and Dominique Givord

Abstract—The second-order anisotropy constant, 1 ( ), in tetragonal L10 FePt is deduced from the analysis of the magnetization versus field curves, between 4.2 K and 700 K. 1 ( ) varies approximately as expected for local moments in the classical limit. The temperature dependence of the coercive field ( ) is discussed with reference to the so-called micromagnetic and global models. The observed behavior suggests that coercivity is governed by passage-expansion or de-pinning. Dipolar interactions are shown to increase the coercive field, rather than reduce it, which is usually the case. Index Terms—Coercivity models, dipolar interactions, hard magnetic FePt, magnetocrystalline anisotropy.

I. INTRODUCTION

T

HE phase of the Fe–Pt system, which is equi-atomic, chemically ordered and of face-centered-tetragonal crystal structure, is a hard magnetic material [1]. The spontaneous magT at 4.2 K and it netization of the phase reaches has a Curie temperature of the order of 750 K [1]. The Pt 5d electrons, polarized by interactions with Fe, are the source of a MJm at very large magnetocrystalline anisotropy ( 300 K) [2], [3]. While the intrinsic magnetic properties of FePt are comparable to those of today’s high-performance rare-earth transition metal (TM) magnets (Nd Fe B or SmCo based), its resistance to corrosion is greatly superior. Coercivities of around 0.5 T have been reported for bulk FePt samples [4] while higher values (1–2 T) were obtained in thin film samples [3], [5], [6]. The recent surge in interest in this material is due to its potential use as a magnetic recording medium or as a permanent magnet for micro-system applications [7], [8]. We have recently developed a novel technique to prepare hard magnetic foils of FePt with foil thickness 100 m (for details of sample preparation and characterization, see [9]). In this paper, we analyze coercivity, the essential property of hard materials, in these FePt foils. Such an analysis requires a knowledge of the intrinsic magnetic properties of the material. The , is extracted in the entire value of the anisotropy constant temperature range studied. The temperature dependence of coercivity is then analyzed within the framework of the global and Manuscript received January 13, 2003. This work was carried out within the framework of the European project for the development of high-temperature magnets “HITEMAG” (G5RD-2000-00213) which is supported by the Commission of the European Union. N. H. Hai is with the Laboratoire Louis Néel,CNRS, Grenoble 38042, France, on leave from Cryogenic Laboratory, Vietnam National University, 334 Nguyentrai, Hanoi, Vietnam (e-mail: [email protected]). N. M. Dempsey and D. Givord are with the Laboratoire Louis Néel, CNRS, Grenoble 38042, France (e-mail: [email protected]; [email protected]). Digital Object Identifier 10.1109/TMAG.2003.815762

micromagnetic models. Qualitative conclusions are drawn on the reversal mechanisms involved. II. DETERMINATION OF

IN

FePt

Due to the unavailability of FePt single crystals, an analysis of the high field magnetization measurements, adapted to the polycrystalline nature of our samples, was used to extract the (see [10]). Let us consider an aranisotropy constant bitrary crystallite, the c-axis of which makes the angle ( ) with the direction of the applied magnetic field, . , may be exThe crystallite energy at the temperature , pressed as (1) where the first term represents the Zeeman energy and the is the second term represents the anisotropy energy. is the angle between the spontaneous magnetization and magnetization and the -axis. For a given , was obtained by minimizing (1) with respect to . The total sample magnetization was then obtained by summing over all possible values (2) is the crystallite In this relation, magnetization projected along the applied field. The distribution , , function of crystallite orientations with respect to , the distribution function of crystallite orienis linked to tations with respect to the crystallites’ main orientation, ( is the angle between and ) through (3) where

is the angle over which the integration is performed and

where is the full-width at half maximum of the Gaussian distribution function. In the in-plane (IP) configuration, the angles , , and are linked by , and in the per. pendicular-to-plane (PP) configuration, At each temperature, the IP and PP magnetization variations were fitted simultaneously. The only free parameters were the and the temperaturesecond-order anisotropy constant independent parameter [for each probed value of , may be extracted from the value of the remanent magnetiza]. was obtained. This value represents tion

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HAI et al.: MAGNETIC PROPERTIES OF HARD MAGNETIC FePt PREPARED BY COLD DEFORMATION

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whether the fact that the observed temperature dependence of follows that predicted for local moments is fortuitous or it has a more fundamental physical origin. III. TEMPERATURE DEPENDENCE OF THE COERCIVE FIELD

K

Fig. 1. Comparison of values determined from simultaneous fitting of IP and PP magnetization curves (open circles) with the function (m ) = I^ [L (m )] (solid line) (see text). Top right inset: Experimental and fitted magnetization versus applied field, from which K values are deduced. Bottom left inset: Temperature dependence of the anisotropy field  H (T ) and of the coercive field  H (T ) in L1 FePt foils.

K

weak PP texture, in qualitative agreement with X-ray diffraction spectra [9]. The fitted magnetization variations at 300 K are shown in the inset of Fig. 1. The high field difference between the experimental data and the fit may be tentatively attributed to higher order anisotropy terms neglected in our analysis. obtained reaches 11 MJ/m at 4.2 K and it decreases monotonously as increases (Fig. 1). The room-temperature value of the anisotropy is in satisfactory agreement with literature values [2], [3]. [and In a system of local moments, ], is expected to be a function of the reduced . In the classical limit, Callen spontaneous magnetization, and Callen [11] have shown that where is the reciprocal Langevin function. For each value, derived from the Callen and Callen law, may be has the selected associated to the temperature at which , thus value. Renormalizing the data to the 0 K value, deduced, follows closely the experimentally deduced (Fig. 1). Note that the analysis is not strongly affected when the Langevin function is replaced by a Brillouin function. The temperature dependence of the anisotropy found in FePt follows the behavior expected for a system of local moments. The same result was found earlier in FePd and CoPt alloys [12]. It was related to band structure calculations which show that the source of the TM moment is a narrow peak in the TM downward spin electron states. In this discussion, it is implicitly assumed that magnetism is carried by TM atoms only. This may be questioned in FePt where magnetism is dominated by Fe but Pt is the source of anisotropy. Quantiatively, the anisotropy is represented by the variation in the term LS when the moments are rotated from the easy to the hard axis. From band strucamounts to 0.20 for ture calculations [13], the product , ) and 0.015 for Pt ( , Fe ( ). The ratio between the spin-orbit coupling parameters of Fe and Pt is, however, of the order of 12 and, thus, the LS terms are expected to have similar values for both Fe and Pt atoms. Under such circumstances, we were not able to conclude

The temperature dependence of the coercive field is in the bottom left compared to that of the anisotropy field inset of Fig. 1. The coercive field decreases monotonously from 0.95 T at 4.2 K to 0.37 T at 600 K. The temperature dependence is similar to that of . However, it must be noted of varies less with temperature than the anisotropy field that , while the opposite has been observed in other high-performance magnets in which coercivity is due to magnetocrystalline anisotropy. In FePt, as in other hard materials, the coercive field is , the value expected for an ideal system much smaller than [14], and this may be ascribed to the presence of structural defects which are the source of local anisotropy reduction. It is then usual to discuss coercivity within the framework of two alternative models: the so-called micromagnetic [15] and global models [14], [16]. In the micromagnetic model, the coercive field is expressed as (4) In this relation, the first term represents the coercive field re) resulting from defects and the second term deduction ( scribes interactions, , assumed to be of dipolar origin, with being a phenomenological parameter. Within the global model [14], [16], it is considered that magnetization reversal occurs by thermal activation over the coercive energy barrier. The value of the coercive field is a function of the domain wall energy within the activation volume, , and of the size of the activation volume, deduced from magnetic after-effect measurements. The coercive field corrected for ( , where thermal activation effects is the magnetic viscosity coefficient) is usually expressed as (5) in which the phenomenological parameter includes geometrical factors and links the domain wall energy barrier in the activation volume, , to the main phase domain wall energy . In the particular case where the anisotropy may be described in terms of a second-order term only, an alternative expression is derived from (5) [16] (6) is a phewhere is the hard phase exchange constant and nomenological parameter. was plotted as a function of [Fig. 2(a)], of [Fig. 2(b)], and of [Fig. 2(c)]. From the approximate linear variations observed, , , and are the values values, deduced from the curves in Fig. 2, deduced. The are between 0.26 (5) and 0.42 (5).

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REFERENCES

Fig. 2. Coercivity analysis within the framework of (a) the micromagnetic model and (b), (c) the global model (for the difference between (b) and (c) see text).

Possible reversal mechanisms in hard systems, as described in [14], are true nucleation, passage-expansion of the nucleated domain wall into the main hard phase, and de-pinning from defects in the bulk of the hard phase. As shown in [16], the fact that all models apply implies that coercivity is governed by passage-expansion or depinning. The values obtained are significantly smaller than in other optimally processed hard materials (NdFeB, Ferrites, Sm–Co) [16]. This suggests that higher coercive field values could be reached by optimizing further the preparation procedure of the FePt foils. is posiIn usual hard magnetic systems, the parameter tive which implies that the dipolar interactions are a source of coercivity reduction [14]. In the present case, the negative values result directly from the weaker temperature dependence with respect to [see (4)–(6)]. A significant reducof and even negative values have also been tion in (positive) obtained in NdFeB magnets made from ribbons [14]. In these systems as for in the FePt foils, the microstructure is formed of intimately connected submicrometer size grains. It could be that dipolar interactions do not have the usual sign in these specific microstructures. Alternatively, residual exchange interactions may be superimposed on dipolar interactions.

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