Interatomic exchange interactions in non-collinear magnets

TL;DR

This paper derives ab initio exchange parameters for non-collinear magnets, revealing anisotropic-like terms and their impact on effective spin Hamiltonians, with practical calculations matching neutron scattering data.

Contribution

It introduces a general exchange formula accounting for anisotropic terms in non-collinear systems, impacting the modeling of magnetic interactions.

Findings

Anisotropic-like exchange term exists even without spin-orbit coupling.

Biquadratic effective spin Hamiltonian is necessary for collinear configurations.

Calculated magnon spectra agree with neutron scattering experiments.

Abstract

We derive ab inito exchange parameters for general non-collinear magnetic configurations, in terms of a multiple scattering formalism. We show that the general exchange formula has an anisotropic-like term even in the absence of spin-orbit coupling, and that this term is large, for instance for collinear configuration in bcc Fe, whereas for fcc Ni it is quite small. We demonstrate that keeping this term leads to that one should consider a biquadratic effective spin Hamiltonian even in case of collinear arrangement. In non-collinear systems this term results in new tensor elements, that are important for exchange interactions at finite temperatures but they have less importance at low temperature. To illustrate our results in practice, we calculate for bcc Fe magnon spectra obtained from configuration dependent exchange parameters, where the configurations are determined by finite temperature effects. Our theory results in the same quantitative results as the finite temperature neutron scattering experiments.