Higher-order exchange interactions in two-dimensional magnets

TL;DR

This paper reveals that higher-order biquadratic exchange interactions significantly influence the magnetic properties of 2D layered magnets, affecting anisotropies, spin excitations, and thermal stability, and provides a comprehensive theoretical framework.

Contribution

It introduces a universal higher-order exchange theory incorporating biquadratic and antisymmetric interactions for 2D magnets, explaining several experimental observations.

Findings

Higher-order exchange interactions affect magnetic anisotropies and spin-wave gaps.

Inclusion of biquadratic and Dzyaloshinskii-Moriya interactions explains experimental anomalies.

Enhanced thermal stability of 2D magnetic layers due to higher-order couplings.

Abstract

Magnetism in recently discovered van der Waals materials has opened new avenues in the study of fundamental spin interactions in truly two-dimensions. A paramount question is what effect higher-order interactions beyond bilinear Heisenberg exchange have on the magnetic properties of few-atom thick compounds. Here we demonstrate that biquadratic exchange interactions, which is the simplest and most natural form of non-Heisenberg coupling, assume a key role in the magnetic properties of layered magnets. Using a combination of nonperturbative analytical techniques, non-collinear first-principles methods and classical Monte Carlo calculations that incorporate higher-order exchange, we show that several quantities including magnetic anisotropies, spin-wave gaps and topological spin-excitations are intrinsically renormalized leading to further thermal stability of the layers. We develop a spin Hamiltonian that also contains antisymmetric exchanges (e.g. Dzyaloshinskii-Moriya interactions) to successfully rationalize numerous observations currently under debate, such as the non-Ising character of several compounds despite a strong magnetic anisotropy, peculiarities of the magnon spectrum of 2D magnets, and the discrepancy between measured and calculated Curie temperatures. Our results lay the foundation of a universal higher-order exchange theory for novel 2D magnetic design strategies.