Magnetic anisotropy of FePt nanoparticles

ABSTRACT.

Magnetic anisotropy of FePt nanoparticles – We carry out a systematic theoretical investigation of Magneto Crystalline Anisotropy (MCA) of L10 FePt clusters with alternating Fe and Pt planes along the (001) direction. The clusters studied contain 30 – 484 atoms. We calculate the structural relaxation and magnetic moment of each cluster by using ab initio spin-polarized density functional theory (DFT), and the MCA with both the self-consistent direct method and the torque method. We find the two methods give equivalent results for all the structures examined. We find that bipyramidal clusters whose central layer is Pt have higher MCA than their same-sized counterparts whose central layer is Fe. This results from the fact that the Pt atoms in such configurations are coordinated with more Fe atoms than in the latter. By thus participating in more instances of hybridization, they contribute higher orbital moments to the overall MCA of the unit. Our findings suggest that by properly tailoring the structure, one can avoid encapsulating the FePt L10 nanoparticles, as has been proposed earlier to protect a high and stable magnetic anisotropy. Additionally, using a simple model to capture the thermal behavior, we predict that a five-layered nanoparticle with approximately 700 atoms can be expected to be useful in magnetic recording applications at room temperature.

Magnetic anisotropy of FePt nanoparticles

Magnetic anisotropy of FePt nanoparticles

I. Introduction

Understanding the physics of smaller structures can help in exploiting their useful properties. For example, the high surface-to-volume ratio and tailorable surface chemistry of metal nanoparticles have long been relied on in optimizing the activity and specificity of catalysts.

And small metal-particle arrays have been used to build single-electron devices. Recently demand has arisen for magnetic particles with high anisotropic energy necessary for energy-harvesting technologies4 as well as for ultra-high-density recording media.
Satisfaction of this demand requires development of metal thin-film media with smaller particles, more tightly-sized distributions, and optimized compositions. Since the mid-1930s Fe-Pt alloys of L10 phase have been known to exhibit high magnetocrystalline anisotropy. Since among the various ferromagnetic metals and alloys FePt alloys show large perpendicular MCA (on the order of meV/atom) and since, in nanoscale particles, they do not exhibit the superparamagnetism often characteristic of such small clusters, it lends itself to magnetic applications requiring small-grained constructions. FePt alloys also have advantages over rare-earth transition-metal-based compound with high MCA, such as Nd2Fe14B and SmCo5 in that they are very ductile and chemically inert. L10-based thin films and nanoparticles in general would seem to be promising candidates for ultra-high density magnetic storage media owing to their high corrosion resistance and excellent intrinsic magnetic properties. But, in contrast to the fine grain of the L10 FePt systems, other conventional magnetic materials (Fe, Co, Ni and their alloys) would, through thermal fluctuation, within a very short time become superparamagnetic, losing any stored information. And given their high cost, bulk FePt-based permanent magnets can be used only for some especially delicate applications, as in magnetic micro-electromechanical systems (MEMS), and in dentistry as attachment devices for retaining a dental cap in the cavity.

The chemically ordered FePt L10 structure can be obtained by annealing from the fcc structure of FePt alloy or by deposition on substrate above the L10 ordering temperature. At high temperature an fcc solid solution of Fe-Pt is observed in the A1 phase; below 1573K (and down to 973K) alloys with a nearly equal number of Fe and Pt atoms (35-55% Pt) show order-disorder transition and the L10 ordered phase begins to form.11 Though the L10 phase is typically obtained by heat treatment of A1 phase, it can also be produced by chemical synthesis of nanoparticles. Deposition of alternate Fe and Pt monolayers can reduce the onset temperature of L10 phase. Another way to obtain L10 phase experimentally is by annealing alternating multi-layers of Fe and Pt. Stable FePt L10 nanoparticles have been prepared experimentally both without any covering and with Al encapsulation.
The L10 structure has alternating Fe and Pt planes along the (001) direction, which is also the easy axis of magnetization, abandoning the cubic symmetry of the fcc system. In this type of layered magnetic system the MCA is mainly due to the contribution from the Pt (5d element) having large spin-orbit coupling while the Fe (3d element) provides the exchange splitting of the Pt sub-lattice.19-21 It is well known that in the FePt system, the Pt atoms play an important role in magnetic anisotropy, because the hybridization of Fe orbitals cause spin polarization of Pt atoms, which in turn enhance the MCA owing to the relative strong SOC of the Pt atoms in comparison with that of the Fe atoms.
There have been several theoretical studies on MCA of nanoparticles. Cyrille et al.
calculated the size- and shape-dependent magnetic properties of L10 FePt clusters using a tight-binding approach. In their study the central plane of clusters is always Fe and they do not take into account the atomic relaxation of the clusters. Błonski and Hafner23 undertook ab initio densityfunctional calculations of the magnetic anisotropy of supported nanostructures. FernandezSeivane and Ferrer24 studied the correlation of the magnetic anisotropy with the geometric structure and magnetic ordering of small atomic clusters of sizes up to 7 atoms. Gruner et al. 25
demonstrated that in cuboctahedral nanoparticles the high anisotropy of the layers increases as one moves towards the surface, and the anisotropy can be even enhanced by embedding the material in some suitable other metal (e.g., Au in the case of Pt-terminated structures). Various experimental studies, using X-ray Magnetic Circular Dichroism Spectroscopy (XMCD) or X-ray

Absorption spectra (XAS), have recently confirmed the enhancement of MCA in free or supported clusters.
The earlier theoretical results suggest that in order to preserve the high values of the MCA, one needs to encapsulate the particles. 25 However issues coming from encapsulation such as charge transfer or structural integrity may adversely affect the MCA. In this work, we explore a possibility to tune the MCA by changing system geometry in such a way that the anisotropy mostly comes from the central part of the particle, which may help avoid the necessity of capping.
We carry out a systematic theoretical investigation of the MCA of L10 FePt clusters consisting of alternating Fe and Pt planes along the (001) direction. The clusters studied have 1(2), 2(3), 3(4) and 4(5) layers of Fe(Pt) atoms – both with Pt outer layers and with Fe outer layers – of sizes 30, 38, 71, 79, 114, 132, 140, 230, 386 and 484 atoms, respectively. We also examine the electronic structural and magnetic properties (including the orbital moments) of each atom in each of these configurations.
To calculate the structural relaxation and magnetic moments of the clusters we adopted an ab initio spin-polarized density functional theory (DFT) approach. To calculate the MCA we employed two methods: (i) the direct method where we take the difference in band energy for two orientations of the average magnetic moment and (ii) the torque method.

The latter method is simpler and computationally less demanding. In this work we show its validity even for systems at the nanoscale. We found that the MCA of layered L10 FePt clusters is enhanced over that of both bulk FePt and that of either a pure Fe or Pt cluster of comparable size, all with L10 geometry. Previous investigations attributed this enhancement is due to the hybridization 3d orbital of Fe atom with the 5d orbital of Pt atom. Our calculations indicate that this is so because this hybridization increases both spin and orbital moment of the Pt atoms. And given the large spin-orbit coupling constant of Pt it is this enhanced orbital moment of Pt that is responsible for the higher anisotropy of the system as a whole. We also found that when the central layer of the bipyramidal cluster is Pt, the cluster has higher MCA than a cluster of the same size but with Fe as the central layer, in contrast to the cuboctahedral cases,  in which it is the surface layers that play crucial role in high MCA . This stems from the fact that when Pt atoms comprise the central layer they have more Fe atoms neighboring them, so that hybridization increases, lending them higher orbital moments than are possessed by Pt atoms in other layers. This center-ofsystem ‘concentration’ of the MCA makes it possible to preserve the anisotropy without having to resort to capping of the particles.

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