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Isotropic orbital magnetic moments in magnetically anisotropic SrRuO3 films

Epitaxially strained SrRuO3 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) SrRuO3 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 M2,3-edge and O K-edge soft X-ray absorption spectroscopy and X-ray 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 SrRuO3 films; i.e., the orbital magnetic moments have a negligibly small contribution to the magnetic anisotropy. This result contradicts Bruno 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.