Lattice dynamics effects on the magnetocrystalline anisotropy energy: application to MnBi

TL;DR

This study uses first-principles calculations to analyze how lattice vibrations influence the magnetocrystalline anisotropy energy in MnBi, revealing significant vibrational contributions that align well with experimental data.

Contribution

It introduces a fully relativistic first-principles approach to quantify phonon effects on MAE in MnBi, highlighting their importance in magnetic property predictions.

Findings

Vibrational free energy differences depend on magnetization orientation.

Phonon contributions significantly affect the MAE constant.

Results agree with experimental spin-reorientation transition temperatures.

Abstract

Using a first-principles fully relativistic scheme based on ultrasoft pseudopotentials and density functional perturbation theory, we study the magnetocrystalline anisotropy free energy of the ferromagnetic binary compound MnBi. We find that differences in the phonon dispersions due to the different orientations of the magnetization (in-plane and perpendicular to the plane) give a difference between the vibrational free energies of the high-temperature and low-temperature phases. This vibrational contribution to the magnetocrystalline anisotropy energy (MAE) constant, $K_u$, is non-negligible. When the energy contribution to the MAE is calculated by the PBEsol exchange and correlation functional, the addition of the phonon contribution allows to get a $T = 0$ K $K_u$ and a spin-reorientation transition temperature in reasonable agreement with experiments.