Temperature Dependent Magnetic Anisotropy in Metallic Magnets from an Ab Initio Electronic Structure Theory: $L{1}_0$-Ordered FePt

Using a first-principles, relativistic electronic structure theory of finite temperature metallic magnetism, we investigate the variation of magnetic anisotropy $K$ with magnetization $M$ in metallic ferromagnets. We apply the theory to the high uniaxial $K$ material, $L{1}_0$-ordered FePt, and find its magnetic easy axis perpendicular to the $\mathrm{F}\mathrm{e}/\mathrm{P}\mathrm{t}$ layers for all $M$ and $K$ to be proportional to $M^2$ for a broad range of values of $M$. For small $M$, near the Curie temperature, the calculations pick out the easy axis for the onset of magnetic order. Our ab initio results for this important magnetic material agree well with recent experimental measurements, whereas the single-ion anisotropy model fails to give the correct qualitative behavior.

Figure 1

The magnetization of FePt versus $T$. The filled squares refer to a magnetization along $(0,0,1)$ and the open circles along $(1,0,0)$. $T_c$ is at 935 K with the easy axis, $(0,0,1)$. The full line shows the mean field approximation to a classical Heisenberg model for comparison. In the inset, near $T_c$, the lower intercept shows what $T_c$ would be with the system constrained to become magnetically ordered along $(1,0,0)$.

Figure 2

The magnetic anisotropy of FePt as a function of the square of magnetization. The filled circles show the calculations from the ab initio theory, the full line $K_0[M(T)/M(0){]}^2$, and the dashed line the single-ion model function $K_0⟨g_2(\widehat{e}){⟩}_T/⟨g_2(\widehat{e}){⟩}_0$ with $K_0=-1.835\mathrm{m}\mathrm{e}\mathrm{V}$.