Large magnetocrystalline anisotropic energy and its impact on magnetostrictions of L10-FePt

Abstract The origin of the anisotropic magnetocrystalline energy (MCAE) guided by the spin-orbit coupling (SOC) in the L1$_0$-FePt alloy was analyzed. The correlation of MCAE with the calculated magnetoelastic constants in the crystalline versus polycrystal hypotheses were determined by means of first-principles theoretical calculations using density functional theory (DFT). More specifically, a systematic analysis of the large MCAE and calculation of magnetostriction coefficients are done by means of plane-wave DFT calculations and post-processing of eigen-values (orbital energies) and eigen-functions (orbital occupancies) which is corroborated from available directional anisotropy energies. Our numerical analysis includes the convolution of the projected wave-function (density of states) of each orbitals of the Fe and Pt sub-lattices into their orbital energies, which in principle should be valid for any such solid alloys regardless of the strength of MCAE. In the hierarchy of the anisotropic magnetostriction calculations of ordered L1$_0$-FePt resulted a significant magnetostrictive ($\lambda$) performance by an order of $\lambda\sim 10^{-4}-10^{-3}$ in most of the crystallographic directions, which is in accordance to the known experiment data. However, the polycrystalline model based on the uniform stress approximation, it leads to a decline of an order or two in the overall magnetostrictive behaviour ($ \lambda\sim 10^{-5}$). This indeed leaving us with an explanation of showing lower magnetostriction for polycrystalline thin-films as similar to the known experimental data, thus validating the robustness of the current theoretical proposition of analyzing MCAE.