Contrasting magnetic anisotropy in CrCl3 and CrBr3: A first-principles study

We present a first-principles study of the contrasting easy magnetization axes(EMAs) in the layered chromium trihalides CrCl3 and CrBr3, which exhibit in-plane and out-of-plane EMAs, respectively. Using density-functional theory calculations, we show that the EMA is determined by the interplay between spin-orbit coupling-induced magnetocrystalline anisotropy energy (SOC-MAE) and shape magnetic anisotropy energy(shape-MAE) arising from dipole-dipole interactions. While the Cr d orbitals contribute similarly to the SOC-MAE in both compounds, the key difference stems from the halogen p orbitals. In CrCl3, the localized Cl 3p orbitals favor spin-flip SOC interactions, particularly between the (px, py) and (py, pz) channels. These channels contribute with opposite signs-negative and positive, respectively-leading to partial cancellation and a small net SOC-MAE. As a result, the shape-MAE exceeds the SOC-MAE in magnitude, favoring an in-plane EMA. In contrast, CrBr3 features more delocalized Br 4p orbitals, enhanced p-d hybridization, and stronger SOC. This leads to stronger spin-conserving SOC interactions, with dominant contributions from both the (px, py) and (py, pz) channels. In this case, the positive contribution from the (px, py) channel outweighs the smaller negative contribution from the (py, pz) channel, resulting in a sizable net SOC-MAE. The SOC-MAE thus surpasses the shape-MAE and stabilizes an out-of-plane EMA. These findings demonstrate that the contrasting magnetic anisotropies in CrCl3 and CrBr3 originate from differences in the spatial distribution, SOC strength, and hybridization of the halogen p orbitals, highlighting the critical role of orbital anisotropy and spin selection rules in governing magnetic behavior in layered semiconductors.