Efficient calculation of magnetocrystalline anisotropy energy using symmetry-adapted Wannier functions

Magnetocrystalline anisotropy, a crucial factor in magnetic properties and applications like magnetoresistive random-access memory, often requires extensive $k$-point mesh in first-principles calculations. In this study, we develop a Wannier orbital tight-binding model incorporating crystal and spin symmetries and utilize time-reversal symmetry to divide magnetization components. This model enables efficient computation of magnetocrystalline anisotropy. Applying this method to $\mathrm{L}{1}_0$ $\mathrm{F}\mathrm{e}\mathrm{P}\mathrm{t}$ and $\mathrm{F}\mathrm{e}\mathrm{N}\mathrm{i}$, we calculate the dependence of the anisotropic energy on $k$-point mesh size, chemical potential, spin-orbit interaction, and magnetization direction. The results validate the practicality of the models to the energy order of $10[\mu \mathrm{e}\mathrm{V}\mathrm{/}f\mathrm{.}u\mathrm{.}]$.