General spin models from noncollinear spin density functional theory and spin-cluster expansion

TL;DR

This paper introduces a data-efficient method combining spin-cluster expansion with noncollinear DFT to accurately model complex spin interactions, enabling predictive simulations of magnetic materials at reduced computational cost.

Contribution

The authors develop a novel framework fitting spin-cluster expansion models to magnetic torques from noncollinear DFT, improving efficiency and accuracy in constructing classical spin Hamiltonians.

Findings

Successfully modeled exchange interactions in chiral magnets.

Predicted spin textures and periods consistent with experimental data.

Demonstrated systematic improvement with higher-order interaction inclusion.

Abstract

We present a data-efficient framework for constructing general classical spin Hamiltonians by combining the spin-cluster expansion (SCE) with fully self-consistent noncollinear spin density functional theory (DFT). The key idea is to fit the SCE model to magnetic torques rather than to total energies. Because torques are site-resolved vectors, each spin configuration provides many informative regression targets, improving conditioning and substantially reducing the number of required DFT calculations, especially for large supercells. Applied to the B20-type chiral magnets ${\rm Mn}_{1-x}{\rm Fe}_{x}{\rm Ge}$ and ${\rm Fe}_{1-y}{\rm Co}_{y}{\rm Ge}$, the resulting SCE models determine full pairwise exchange tensors -- including isotropic exchange, symmetric anisotropic exchange, and the Dzyaloshinskii--Moriya interaction -- and predict the helical spin period via a micromagnetic mapping. The composition trends and the divergence of the period at the chirality sign-change point are well reproduced, in agreement with experiment. Moreover, the systematic nature of SCE enables controlled assessment of interaction order: as the training spin configurations become more disordered, the lowest-order model loses torque accuracy, whereas including higher-order interactions restores predictive power. These advances enable near-DFT-accurate spin models for finite-temperature magnetism and complex spin textures at modest computational cost, providing an extensible route to quantitative first-principles parameterization and predictive materials design. An open-source implementation is available as a Julia package, \textit{Magesty.jl}.