Plane wave implementation of the magnetic force theorem for magnetic exchange constants: Application to bulk Fe, Co and Ni

TL;DR

This paper introduces a plane wave implementation of the magnetic force theorem to compute exchange constants in magnetic materials, enabling systematic and robust calculations of magnetic interactions in metals like Fe, Co, and Ni.

Contribution

It develops a plane wave-based method to calculate exchange constants from first principles, independent of orbital decomposition, and demonstrates its robustness and accuracy for transition metals.

Findings

Good agreement with previous calculations of spin wave spectra.

Exchange parameters are robust to the definition of magnetic sites.

Method allows systematic convergence with respect to unoccupied bands.

Abstract

We present a plane wave implementation of the magnetic force theorem, which provides a first principles framework for extracting exchange constants parameterizing a classical Heisenberg model description of magnetic materials. It is shown that the full microscopic exchange tensor may be expressed in terms of the static Kohn-Sham susceptibility tensor and the exchange-correlation magnetic field. This formulation allows one to define arbitrary magnetic sites localized to predefined spatial regions, hence rendering the problem of finding Heisenberg parameters independent of any orbital decomposition of the problem. The susceptibility is calculated in a plane wave basis, which allows for systematic convergence with respect to unoccupied bands and spatial representation. We then apply the method to the well-studied problem of calculating adiabatic spin wave spectra for bulk Fe, Co and Ni, finding good agreement with previous calculations. In particular, we utilize the freedom of defining magnetic sites to show that the calculated Heisenberg parameters are robust towards changes in the definition of magnetic sites. This demonstrates that the magnetic sites can be regarded as well-defined and thus asserts the relevance of the Heisenberg model description despite the itinerant nature of the magnetic state.