DFT Calculations of Magnetocrystalline Anisotropy Energy With Fixed Spin Moment

Abstract

The development of new-generation permanent magnets is based on experimental efforts and innovative theoretical tools for modeling magnetic properties. Magnetocrystalline anisotropy energy (MAE)—one of the main intrinsic properties of permanent magnets—can be calculated using density functional theory (DFT). However, MAEs determined with different exchange-correlation potentials can vary widely. We show how these seemingly contradictory results can be reconciled using the fully relativistic fixed spin moment (FR-FSM) method. This is because the equilibrium pairs [MAE, $\boldsymbol{m_s}$ ] calculated with different exchange-correlation potentials overlap with the MAE ( $\boldsymbol{m_s}$ ) curve determined from the FR-FSM method ( $\boldsymbol{m_s}$ denotes the spin magnetic moment). The FR-FSM method also enables the hypothetical maximum MAE value for a given material to be estimated. In the case of magnetic alloys, MAE fixed spin moment (FSM) analysis allows the optimal alloying additions to be determined in order to improve the MAE value. The high independence of the MAE ( $\boldsymbol{m_s}$ ) works well for exchange-correlation functionals, such as local density approximation (LDA) and generalized gradient approximation (GGA). However, it is not a universal measure and varies with changes in the value of the U parameter when using LDA+U or GGA+U functionals. Concluding, the framework we describe for MAE $\textit{versus}$ FSM calculations can be a useful tool in the design of new permanent magnets.