Origin of perpendicular magnetic anisotropy in CoxFe3−xO4+δ thin films studied by x-ray magnetic circular and linear dichroisms

We investigate the element-specific spin and orbital states and their roles in magnetic anisotropy in Co-ferrite [${\mathrm{Co}}_x{\mathrm{Fe}}_{3\ensuremath{-}x}{\mathrm{O}}_{4+\ensuremath{\delta}}$ (001)] thin films which exhibit perpendicular magnetic anisotropy (PMA). The origin of PMA in the low-$x$ region ($x\phantom{\rule{4pt}{0ex}}<$ 1) can be mainly explained by the large perpendicular orbital magnetic moments in the ${\mathrm{Co}}²⁺$ ($3{d}⁷$) states detected by x-ray magnetic circular dichroism and x-ray magnetic linear dichroism (XMLD). The XMLD for a PMA film ($x=0.2$) with a square hysteresis curve shows the oblate charge distribution in the ${\mathrm{Co}}²⁺$ site, which is consistent with the change in local nearest-neighbor distance in Co detected by extended x-ray absorption fine structure analysis. Our finding reveals that the microscopic origin of PMA in Co ferrite comes from the enhanced orbital magnetic moments along the out-of-plane [001] direction through in-plane charge distribution by tensile strain, which adds the material functionalities in spinel ferrite thin films from the viewpoint of strain and orbital magnetic moments.