Transferable mechanism of perpendicular magnetic anisotropy switching by hole doping in V$X_2$ ($X$=Te, Se, S) monolayers
The ability to tune and switch magnetic anisotropy to a perpendicular orientation is a key challenge for implementing 2D magnets in spintronic devices. H-phase vanadium dichalcogenides V$X_2$ ($X$=Te, Se, S) are promising ferromagnetic semiconductors with large magnetic anisotropy energy (MAE). Recent work has shown that hole doping can switch their easy axis to out-of-plane, though the microscopic origin of this perpendicular magnetic anisotropy (PMA) remains unclear. Using density-functional-theory calculations, we demonstrate that the PMA enhancement arises from first-order spin-orbit coupling (SOC) acting on topmost degenerate valence states with nonzero orbital angular momentum projection ($m_l\ne 0$). In this case, the $\hat{L}_z\hat{S}_z$ term dominates for perpendicular magnetization, while in-plane orientations involve only weaker, second-order SOC contributions. The increased valence bandwidth leads to depletion of higher-energy states upon hole doping, stabilizing PMA. From this mechanism, we identify two transferable design principles for enhancing MAE under weak hole doping: (i) orbital degeneracy at the valence-band edge protected by point-group symmetry and (ii) finite SOC in the degenerate manifold. Notably, we identify multiple magnetic semiconductors that meet these criteria and display enhanced MAE under hole doping. Furthermore, we show that band engineering can strategically place these degenerate orbitals at the valence band edge, significantly boosting PMA when hole-doped. We also examine trends in VTe$_2$, VSe$_2$, and VS$_2$ to determine the influence of crystal-field splitting, exchange interaction, and orbital hybridization on the valence band edges. These results provide both a fundamental understanding of PMA switching upon hole doping and a transferable strategy for tuning magnetic anisotropy, essential for designing high-performance spintronic materials.