Role of the heavy nonmagnetic Cd cation in magnetic anisotropy of d0 ferromagnetic monolayer TiCdO4.

In d0 ferromagnets, where magnetism arises from spin-polarized p orbitals of light anions, magnetocrystalline anisotropy energy (MAE) is generally weak due to limited spin-orbit coupling (SOC) in the magnetic states. In this work, we investigate the magnetic anisotropy in the two-dimensional d0 ferromagnetic multiferroic monolayer TiCdO4 using first-principles calculations, revealing a novel mechanism for the emergence of MAE. We demonstrate that the heavy nonmagnetic cation Cd, despite its 4d states being well below the Fermi level, plays a crucial role in mediating SOC effects. The hybridization between Cd d states and O 2p orbitals near the Fermi level enhances SOC between Cd and O, thereby contributing to the MAE. Notably, this hybridization induces substantial SOC from Cd to the O p orbitals, which drives the MAE in this d0 ferromagnet. Furthermore, we reveal that the ferroelectric phase transition from the centrosymmetric metallic P2/m phase to the polar insulating P1 phase strengthens a specific Cd-O bond due to a reduced bond length, leading to an increased contribution to the MAE from a particular oxygen site. These findings provide novel theoretical insights into magnetic anisotropy in d0 ferromagnetic multiferroics, demonstrating how the interplay between heavy nonmagnetic cations and oxygen p orbitals can induce significant MAE through orbital hybridization. Our results suggest a new pathway for controlling MAE in d0 systems by tuning cation-anion interactions, advancing the design of multiferroic materials.