Electron theory of perpendicular magnetic anisotropy of Co-ferrite thin films

We develop an electron theory for the t2g electrons of Co2+ ions to clarify the perpendicular magnetic anisotropy (PMA) mechanism of Co-ferrite thin films by considering the spin-orbit interaction (SOI) and crystal-field (CF) potentials induced by the local symmetry around the Co ions and the global tetragonal symmetry of the film. Uniaxial and in-plane MA constants Ku and K1 at 0 K, respectively, are calculated for various values of SOI and CF. We show that reasonable parameter values explain the observed PMA and that the orbital moment for the in-plane magnetization reduces to nearly half of that of the out-of-plane magnetization.