DFT calculations of magnetocrystalline anisotropy energy with fixed spin moment

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, $m_s$] calculated with different exchange-correlation potentials overlap with the MAE($m_s$) curve determined from the FR-FSM method ($m_s$ 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(FSM) analysis allows the optimal alloying additions to be determined in order to improve the MAE value. Concluding, the framework we describe for MAE versus FSM calculations can be a useful tool in the design of new permanent magnets.