Validity of perturbative methods to treat the spin–orbit interaction: application to magnetocrystalline anisotropy

Abstract

Abstract A second-order perturbation (2PT) approach to the spin–orbit interaction (SOI) is implemented within a density-functional theory framework. Its performance is examined by applying it to the calculation of the magnetocrystalline anisotropy energies (MAE) of benchmark systems, and its efficiency and accuracy are compared with the popular force theorem method. The case studies are tetragonal FeMe alloys (Me=Co, Cu, Pd, Pt, Au), as well as FeMe (Me=Co, Pt) bilayers with (111) and (100) symmetry, which cover a wide range of SOI strength and electronic band structures. The 2PT approach is found to provide a very accurate description for 3d and 4d metals and, moreover, this methodology is robust enough to predict easy axis switching under doping conditions. In all cases, the details of the bandstructure, including states far from the Fermi level, are responsible for the finally observed MAE value, sometimes overruling the effect of the SOI strength. From a technical point of view, it is confirmed that accuracy in the MAE calculations is subject to the accuracy of the Fermi level determination.