We present a first-principles study of the contrasting easy magnetization axes (EMAs) in the layered chromium trihalides ${\mathrm{CrCl}}_3$ and ${\mathrm{CrBr}}_3$, 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 ${\mathrm{CrCl}}_3$, the localized Cl $3p$ orbitals favor spin-flip SOC interactions, particularly between the $(p_x,p_y)$ and $(p_y,p_z)$ 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, ${\mathrm{CrBr}}_3$ features more delocalized Br $4p$ orbitals, enhanced $p\text{−}d$ hybridization, and stronger SOC. This leads to stronger spin-conserving SOC interactions, with dominant contributions from both the $(p_x,p_y)$ and $(p_y,p_z)$ channels. In this case, the positive contribution from the $(p_x,p_y)$ channel outweighs the smaller negative contribution from the $(p_y,p_z)$ 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 ${\mathrm{CrCl}}_3$ and ${\mathrm{CrBr}}_3$ 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.

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• Magnetic anisotropy
• Magnetism