Oxygen magnetic polarization, nodes in spin density, and zigzag spin order in oxides

Recent studies on ${\mathrm{Ba}}₂{\mathrm{CoO}}₄$ (BCO) and ${\mathrm{SrRuO}}₃$ (SRO) have unveiled a variety of intriguing phenomena, such as magnetic polarization on oxygens, unexpected nodes in the spin density profile along bonds, and unusual zigzag spin patterns in triangular lattices. Here, using simple model calculations supplemented by density functional theory we explain the presence of nodes based on the antibonding character of the dominant singly occupied molecular orbitals along the transition metal (TM) to oxygen bonds. Our simple model also allows us to explain the net polarization on oxygen as originated from the hybridization between atoms and mobility of the electrons with spins opposite to those of the closest TM atoms. Our results are not limited to BCO and SRO, but they are generic and qualitatively predict the net polarization expected on any ligands, according to the spin order of the closest TM atoms and the number of intermediate ligand atoms. Finally, we propose that a robust easy-axis anisotropy would suppress the competing ${120}^{\ensuremath{\circ}}$ antiferromagnetic order to stabilize the zigzag pattern order as ground state in a triangular lattice. Our generic predictions should be applicable to any other compound with characteristics similar to those of BCO and SRO.