Heisenberg models with minimal number of parameters for two-dimensional magnetic crystals

TL;DR

This paper introduces a minimal-parameter anisotropic Heisenberg model for 2D magnetic materials, validated on monolayer CrI3, reducing complexity while aligning with ab-initio calculations.

Contribution

It develops a symmetry-invariant tensor approach to minimize parameters in the Heisenberg model for 2D magnets, including higher-order corrections, and tests it on CrI3.

Findings

Reduced parameter model accurately describes monolayer CrI3.

Symmetry invariants effectively simplify anisotropic tensor modeling.

Model aligns with ab-initio calculations using least squares fitting.

Abstract

In this work we investigated adequacy of the Heisenberg model application to novel two-dimensional magnetic materials, on an example of monolayer CrI3. We introduced the concept of the mean tensor invariant under symmetry operations of the magnetic structure, which allows the number of parameters of the anisotropic tensor Heisenberg model to be significantly reduced, while maintaining the compliance with the results of ab-initio calculations. We derived the expressions for fourth-order corrections to Heisenberg Hamiltonian and to Dzyaloshinskii-Moriya interaction in the form of quartic symmetry invariants with minimal number of parameters. We tested the physical adequacy of such approach in the case of monolayer CrI3, utilizing an alternative to four-states energy mapping -- the all-parameters least square fit.