Anatomy of magnetic anisotropy induced by Rashba spin-orbit interactions

TL;DR

This paper develops a simplified tight-binding model to understand interfacial magnetic anisotropy in heavy-metal/ferromagnetic-metal bilayers, revealing how Fermi-sea and Fermi-surface contributions influence magnetic orientation stability.

Contribution

It introduces a new approach to calculate magnetic anisotropy energy using quasiparticle spin-susceptibility and interprets anisotropy as a competition between Fermi-sea and Fermi-surface effects.

Findings

Perpendicular anisotropy occurs when spin magnetization density exceeds a specific threshold.

Magnetic anisotropy results from a balance between Fermi-sea and Fermi-surface contributions.

The model aligns with first-principles calculations for certain film/substrate systems.

Abstract

Magnetic anisotropy controls the orientational stability and switching properties of magnetic states, and therefore plays a central role in spintronics. First-principles density-functional-theory calculations are able, in most cases, to provide a satisfactory description of bulk and interface contributions to the magnetic anisotropy of particular film/substrate combinations. In this paper we focus on achieving a simplified understanding of some trends in interfacial magnetic anisotropy based on a simple tight-binding model for quasiparticle states in a heavy-metal/ferromagnetic-metal bilayer film. We explain how to calculate the magnetic anisotropy energy of this model from the quasiparticle spin-susceptibility, compare with more conventional approaches using either a perturbative treatment of spin-orbit interactions or a direct calculation of the dependence of the energy on the orientation of the magnetization, and show that the magnetic anisotropy can be interpreted as a competition between a Fermi-sea term favoring perpendicular anisotropy and a Fermi-surface term favoring in-plane anisotropy. Based on this finding, we conclude that perpendicular magnetic anisotropy should be expected in an itinerant electron thin film when the spin magnetization density is larger than the product of the band exchange splitting and the Fermi level density-of-states of the magnetic state.