Magnetocrystalline Anisotropy Energy of Transition Metal Thin Films: A Non-perturbative Theory

TL;DR

This paper presents a non-perturbative, semi-empirical analysis of magnetocrystalline anisotropy energy in Fe and Ni thin films, emphasizing the role of band degeneracies and spin-orbit coupling, with results aligning well with experiments.

Contribution

It introduces a non-perturbative approach to calculate anisotropy energy, including s-bands and hybridization, and applies it to multilayer systems with detailed temperature and structural analysis.

Findings

Degeneracies near the Fermi level significantly influence E(anis)

E(anis) scales with the square of the SOC constant

Calculated anisotropy energies agree well with experimental data

Abstract

The magnetocrystalline anisotropy energy E(anis) of free-standing monolayers and thin films of Fe and Ni is determined using two different semi-empirical schemes. Within a tight-binding calculation for the 3d bands alone, we analyze in detail the relation between bandstructure and E(anis), treating spin-orbit coupling non-pertubatively. We find important contributions to E(anis) due to the lifting of band degeneracies near the Fermi level by SOC. The important role of degeneracies is supported by the calculation of the electron temperature dependence of the magnetocrystalline anisotropy energy, which decreases with the temperature increasing on a scale of several hundred K. In general, E(anis) scales with the square of the SOC constant. Including 4s bands and s-d hybridization, the combined interpolation scheme yields anisotropy energies that quantitatively agree well with experiments for Fe and Ni monolayers on Cu(001). Finally, the anisotropy energy is calculated for systems of up to 14 layers. Even after including s-bands and for multilayers, the importance of degeneracies persists. Considering a fixed fct-Fe structure, we find a reorientation of the magnetization from perpendicular to in-plane at about 4 layers. For Ni, we find the correct in-plane easy-axis for the monolayer. However, since the anisotropy energy remains nearly constant, we do not find the experimentally observed reorientation.