Title:Magnetocrystalline Anisotropy of Fe-based $L1_0$ Alloys: Validity of Approximate Methods to Treat the Spin-Orbit Interaction

Abstract:First-principles calculations are used to gauge different levels of approximation to calculate the magnetocrystalline anisotropy energies (MAE) of five $L1_0$ FeMe alloys (Me=Co, Cu, Pd, Pt, Au). We find that a second-order perturbation (2PT) treatment of the spin-orbit interaction (SOI) breaks down for the alloys containing heavier ions, while it provides a very accurate description of the MAE behaviour of FeCo, FeCu, and FePd. Moreover, the robustness of the 2PT approximation is such that in these cases it accounts for the MAE of highly-non-neutral alloys and, thus, it can be used to predict their performance when dopants are present or when they are subject to applied gate bias, which are typical conditions in working magnetoelectric devices. We also observe that switching of the easy axis direction can be induced in some of these alloys by addition or removal of, at least, one electron per cell. In all cases, the details of the bandstructure are responsible for the finally observed MAE value and, therefore, suggest a limited predicting power of models based on the expected orbital moment values and bandwidths. Finally, we have confirmed the importance of various calculation parameters to obtain converged MAE values, in particular, those related to the accuracy of the Fermi level determination.