Effects of p-d orbital mixings on magnetocrystalline anisotropy for D_3d-symmetric ferromagnetic semiconducting monolayers

Understanding magnetic anisotropy based on electronic properties is vital for theoretical and applied research on ferromagnetic semiconductors. Here, for several representative D_3d-symmetric ferromagnetic semiconducting monolayers, we investigate the effects of mixings between d-orbitals of central magnetic atoms and p-orbitals of ligands on magnetocrystalline anisotropy energy (MAE). For high-spin materials, the weakening of p-d mixing increases the electron occupation of spin-up bonding d-orbitals at the expense of the electron occupation in the corresponding spin-down orbitals, In contrast, the weakening of p-d mixing decreases the electron occupation of the spin-up antibonding d-orbitals and enhances the electron occupation in the corresponding spin-down orbitals. The weakening mixings also result in an overall shift of the spin-down band toward a higher energy with respect to the spin-up band. These changes are just the opposite in a low-spin material. More interestingly, we find that the transition point between the bonding and the antibonding spin-up bands plays a significant role in tuning the MAE. Its shift with strain is almost linearly related to the p-d bond strength and significantly affects both the electron occupation of occupied spin-up antibonding d-bands and the band shift of unoccupied spin-up d-bands. Furthermore, the correlation of these mixing-related changes in electronic structures with the MAE is qualitatively and quantitatively analyzed. Our findings can deepen the understanding of the correlation between MAE and p-d orbital mixings and provide theoretical guidance for modulating the MAE.