  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.
