Efficient technique for ab-initio calculation of magnetocrystalline anisotropy energy

Ab-initio calculation of magnetocrystalline anisotropy energy (MCAE) often requires a strict convergence criterion and a dense k-point mesh to sample the Brillouin zone, making its convergence problematic and time-consuming. The force theorem for MCAE states that MCAE can be calculated by the band energy difference between two magnetization directions at a fixed potential. The maximally localized Wannier function can be utilized to construct a compact Hilbert space of low-lying electron states and interpolate band eigenvalues with high precession. We combine the force theorem and the Wannier interpolation of eigenvalues together to improve the efficiency of MCAE calculations with no loss of accuracy. We use a Fe chain, a Fe monolayer and a FeNi alloy as examples and demonstrate that the Wannier interpolation method for MCAE is able to reduce the computational cost significantly and remain accurate simultaneously, compared with a direct ab-initio calculation on a very dense k-point mesh. This efficient Wannier interpolation approach makes it possible for large-scale and high-throughput MCAE calculations, which could benefit the design of spintronics devices.