Spin and orbital exchange interactions from Dynamical Mean Field Theory

TL;DR

This paper develops a method to derive magnetic interaction parameters from strongly correlated electronic systems using Dynamical Mean Field Theory, enabling detailed spin model mappings including anisotropic and Dzyaloshinskii-Moriya interactions.

Contribution

It introduces a set of equations linking Green's functions and self-energies to magnetic interactions, facilitating computational modeling of complex spin interactions in correlated materials.

Findings

Formulated equations for magnetic interactions from Green's functions.

Mapped electronic systems to spin models with anisotropic interactions.

Provided formulas compatible with DMFT algorithms.

Abstract

We derive a set of equations expressing the parameters of the magnetic interactions characterizing a strongly correlated electronic system in terms of single-electron Green's functions and self-energies. This allows to establish a mapping between the initial electronic system and a spin model including up to quadratic interactions between the effective spins, with a general interaction (exchange) tensor that accounts for anisotropic exchange, Dzyaloshinskii-Moriya interaction and other symmetric terms such as dipole-dipole interaction. We present the formulas in a format that can be used for computations via Dynamical Mean Field Theory algorithms.