Isotropic orbital magnetic moments in magnetically anisotropic SrRuO3 films

Epitaxially strained ${\mathrm{SrRuO}}₃$ films have been a model system for understanding the magnetic anisotropy in metallic oxides. In this paper, we investigate the anisotropy of the Ru $4d$ and O $2p$ electronic structure and magnetic properties using high-quality epitaxially strained (compressive and tensile) ${\mathrm{SrRuO}}₃$ films grown by machine-learning-assisted molecular beam epitaxy. The element-specific magnetic properties and the hybridization between the Ru $4d$ and O $2p$ orbitals were characterized by Ru ${M}_2,3$-edge and O $K$-edge soft x-ray absorption spectroscopy and magnetic circular dichroism measurements. The magnetization curves for the Ru $4d$ and O $2p$ magnetic moments are identical, irrespective of the strain type, indicating the strong magnetic coupling between the Ru and O ions. The electronic structure and the orbital magnetic moment relative to the spin magnetic moment are isotropic despite the perpendicular and in-plane magnetic anisotropy in the compressive-strained and tensile-strained ${\mathrm{SrRuO}}₃$ films; i.e., the orbital magnetic moments make a negligibly small contribution to the magnetic anisotropy. This result contradicts Bruno's model, where magnetic anisotropy arises from the difference in the orbital magnetic moment between the perpendicular and in-plane directions. Contributions of strain-induced electric quadrupole moments to the magnetic anisotropy are discussed, too.