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.
Highlights
In a model system of interacting magnetic moments various contributions can be identified that lead to the observation of the magnetic anisotropy, i.e. the existence of a preferential magnetization direction in the system
All the approaches provide the same behaviour in the magnetocrystalline anisotropy (MCA) of each alloy, albeit there are some quantitative differences in the corresponding magnetocrystalline anisotropy energy (MAE) values, which will be discussed below
We find larger MAE values for FeCo and FeCu than for FePd and FeAu in spite of xPd,Au being larger than xCo,Cu
Summary
In a model system of interacting magnetic moments various contributions can be identified that lead to the observation of the magnetic anisotropy, i.e. the existence of a preferential magnetization direction in the system These terms are the classical dipole–dipole interaction, resulting in the so-called shape anisotropy, and quantum-mechanical ones with origin in the electronic spin–orbit interaction (SOI). The use of external magnetic fields for this purpose is evolving towards voltage control of spintronic devices [5, 6] and spin transfer torques induced by spin-polarized currents [7] These advances motivate efficient, robust and accurate modelling of the physics of the MCA for different materials/interfaces under external stimuli, such as external fields or strain
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