Machine learning assisted derivation of effective low energy models for metallic magnets

TL;DR

This paper introduces a machine learning protocol to derive effective low-energy spin models from a Kondo Lattice Model, accurately capturing phase diagrams and magnetic excitations with reduced computational cost.

Contribution

It presents a novel ML-assisted method to extract multi-spin interactions from the Kondo Lattice Model, enabling efficient analysis of complex magnetic phases.

Findings

Effective spin model reproduces original phase diagram.

Identifies four-spin interactions responsible for skyrmion phases.

Accurately predicts magnon dispersion in polarized phase.

Abstract

We consider the problem of extracting an effective low-energy spin model from a Kondo Lattice Model (KLM) with classical localized moments. The non-analytic dependence of the effective spin-spin interactions on the Kondo exchange $J$ excludes the possibility of using perturbation theory beyond the second order Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction at zero temperature. Here we introduce a Machine Learning (ML) assisted protocol to extract effective two- and four-spin interactions by integrating out the conduction electrons of the original KLM. The resulting effective spin model reproduces the phase diagram obtained with the original KLM as a function of magnetic field and easy-axis anisotropy and reveals the effective four-spin interactions that are responsible for the field induced skyrmion crystal phase. Moreover, this minimal spin model enables an efficient computation of static and dynamical properties with a much lower numerical cost relative to the original KLM. A comparison of the dynamical spin structure factor in the fully polarized phase computed with the effective model and the original KLM reveals a good agreement for the magnon dispersion despite the fact that this information was not included in the training data set.