Reciprocal space study of Heisenberg exchange interactions in ferromagnetic metals

TL;DR

This paper introduces a reciprocal space method to analyze exchange interactions in ferromagnetic metals, addressing convergence issues and revealing symmetry breaking in bcc iron at the orbital level.

Contribution

It develops a novel reciprocal space framework for studying exchange interactions, overcoming convergence problems and clarifying magnetic symmetry breaking in metallic ferromagnets.

Findings

On-site magnetic precursors dominate atomic interactions.

Reciprocal space technique improves convergence in metallic systems.

Symmetry breaking in bcc Fe is elucidated at the orbital level.

Abstract

The modern quantum theory of magnetism in solids is getting commonly derived using Green's functions formalism. The popularity draws itself from remarkable opportunities to capture the microscopic landscape of exchange interactions, starting from a tight-binding representation of the electronic structure. Indeed, the conventional method of infinitesimal spin rotations, considered in terms of local force theorem, opens vast prospects of investigations regarding the magnetic environment, as well as pairwise atomic couplings. However, this theoretical concept practically does not devoid of intrinsic inconsistencies. In particular, naturally expected correspondence between single and pairwise infinitesimal spin rotations is being numerically revealed to diverge. In this work, we elaborate this question on the model example and canonical case of bcc iron. Our analytical derivations discovered the principal preference of on-site magnetic precursors if the compositions of individual atomic interactions are in focus. The problem of extremely slow or even absent spatial convergence while considering metallic compounds was solved by suggesting the original technique, based on reciprocal space framework. Using fundamental Fourier transform-inspired interconnection between suggested technique and traditional spatial representation, we shed light on symmetry breaking in bcc Fe on the level of orbitally decomposed total exchange surrounding.