Interlayer superexchange in bilayer chromium trihalides

• DOI: 10.48550/arxiv.2305.00870
• Publication Date: 2023-06-23
• Authors: Kok Wee Song
• Keywords: Condensed Matter - Strongly Correlated Electrons; Condensed Matter - Mesoscale and Nanoscale Physics; Strongly Correlated Electrons (cond-mat.str-el); Mesoscale and Nanoscale Physics (cond-mat.mes-hall); FOS: Physical sciences

8+8 pages, 5 figures, including supplemental materials and minor corrections<br/>We construct a microscopic model based on superexchange theory for a moiré bilayer in chromium trihalides (Cr$X_3$, $X=$Br, I). In particular, we derive analytically the interlayer Heisenberg exchange and the interlayer Dzyaloshinskii-Moriya interaction with arbitrary distances (x) between spins. Importantly, our model takes into account sliding and twisting geometries in the interlayer $X$-$X$ hopping processes. Our approach can directly access the $x$-dependent interlayer exchange without large unit-cell calculations. We argue that deducing interlayer exchange by various sliding bilayers may lead to an incomplete result in a moiré bilayer. Using the \textit{ab initio} tight-binding Hamiltonian, we numerically evaluate the exchange interactions in CrI$_3$. We find that our analytical model agrees with previous comprehensive density functional theory studies. Furthermore, our findings reveal the important role of the correlation effects in the $X$'s $p$ orbitals, which gives rise to a rich interlayer magnetic interaction with remarkable tunability.<br/>