Superexchange and spin-orbit coupling in monolayer and bilayer chromium trihalides

TL;DR

This paper develops a microscopic model to analyze superexchange interactions and spin-orbit effects in chromium trihalides, revealing the role of hole-pair excitations and competing exchange mechanisms in monolayer and bilayer structures.

Contribution

It introduces a detailed microscopic model highlighting the importance of hole-pair excitations and spin-orbit coupling in chromium trihalides, advancing understanding of their magnetic interactions.

Findings

Inter-layer antiferromagnetic exchange mediated by hole-pair excitations.

Weak intra-layer ferromagnetic exchange due to competing virtual hopping processes.

Spin-orbit coupling influences Dzyaloshinskii-Moriya interactions in these materials.

Abstract

We build a microscopic model to study the intra- and inter-layer superexchange due to electrons hopping in chromium trihalides ($\mathrm{CrX}_3$, X= Cl, Br, and I). In evaluating the superexchange, we identify the relevant intermediate excitations in the hopping. In our study, we find that the intermediate hole-pairs excitations in the $p$-orbitals on X ion play a crucial role in mediating various types of exchange interactions. In particular, the inter-layer antiferromagnetic exchange may be realized by the hole-pair-mediated superexchange. Interestingly, we also find that these virtual hopping processes compete with each other leading to weak intra-layer ferromagnetic exchange. In addition, we also study the spin-orbit coupling effects on the superexchange and investigate the Dzyaloshinskii-Moriya interaction. Finally, we extract the microscopic model parameters from density functional theory for analyzing the exchange interactions in a monolayer $\mathrm{CrI}_3$.