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

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 ${\mathrm{CrI}}_3$.

arXiv comment18 pages, 4 figures, minor corrections with more references added

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Cited by in corpus (4)

• Moiré-driven multiferroic order in twisted CrCl${}_3$, CrBr${}_3$ and CrI${}_3$ bilayers
• Delving into the anisotropic interlayer exchange in bilayer CrI${}_3$
• Interlayer superexchange in bilayer chromium trihalides
• Orbital mixing and strong Hund's coupling stabilize spin order in van der Waals ferromagnet CrI3