We investigate the element-specific spin and orbital states and their roles in magnetic anisotropy in Co-ferrite [${\mathrm{Co}}_x{\mathrm{Fe}}_{3-x}{\mathrm{O}}_{4+\delta }$ (001)] thin films which exhibit perpendicular magnetic anisotropy (PMA). The origin of PMA in the low-$x$ region ($x<$ 1) can be mainly explained by the large perpendicular orbital magnetic moments in the ${\mathrm{Co}}^{2+}$ ($3d^7$) 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.

• Received 15 January 2022
• Revised 19 March 2022
• Accepted 28 March 2022

DOI:https://doi.org/10.1103/PhysRevB.105.134416