Quantifying temperature-induced magnetic disorder effects on the anisotropy of MnBi

MnBi is remarkable for having a magnetocrystalline anisotropy (MCA) that increases with temperature. This unusual behavior has been attributed to the thermal expansion of lattice and, more recently, an anisotropic vibrational free energy. However, effect magnetic fluctuations on MCA not yet quantified. Here, first-principles density-functional theory calculations based disordered local moment picture (DFT-DLM) are used calculate in presence disorder. The obtained from torque, calculated as function magnetization angle and temperature $T$. At fixed ionic positions, decays monotonically increasing DFT-DLM torques provide access individual constants ${\ensuremath{\kappa}}_{l}$ (which parametrize relation between energy angle), their dependence order parameter $m$. lowest constant ${\ensuremath{\kappa}}_{2}$ follows single-ion-like at low $T$ but ${m}^{4}$ increases, while higher-order deviate strongly single-ion predictions. Zero-$T$ show spin reorientation transition can be triggered by removing 0.1 electrons, resulting $c$-axis once 0.25 electrons have removed. zero-temperature cross-validated using alternative implementation DFT wave functions, plane waves, pseudopotentials.