Spin-orbital nature of the high-field magnetic state in theSr4Ru3O10

We perform a spin-polarized neutron-diffraction study to investigate the nature of the high-field magnetic state of the trilayered ${\mathrm{Sr}}₄{\mathrm{Ru}}₃{\mathrm{O}}₁₀$. The analysis indicates that a high field applied within the $ab$ plane leads to an unbalance of the spin and orbital moments with a spatial profile that is strongly tied to the layers where the electrons are located in the unit cell. We provide evidence of a layer dependent magnetic anisotropy with the inner layers having larger spin and orbital magnetic moments than the outer ones and show that such behavior is robust to temperature variation being persistent above the Curie temperature. By means of an effective model that includes the coupling between the spin-orbital degrees of freedom at inequivalent Ru sites we ascribe the origin of the layer anisotropy to the cooperative effects between octahedral distortions, spin orbit, and Coulomb interactions.