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

Recent DFT calculations for Ba2CoO4 (BCO) and neutron scattering experiments for SrRuO3 (SRO) have shown that oxygen develops a magnetic polarization. Moreover, DFT calculations for these compounds also unveiled unexpected nodes in the spin density, both along Co-O and Ru-O. For BCO, the overall antiferromagnetic state in its triangular lattice contains unusual zigzag spin patterns. Here, using simple model calculations supplemented by DFT we explain and extend these results. We predict that ligands that in principle should be spinless, such as O$^{2-}$, will develop a net polarization when they act as electronic bridges between transition metal (TM) spins ferromagnetically ordered, regardless of the number of intermediate ligand atoms. The reason is the hybridization between atoms and mobility of the electrons with spins opposite to those of the closest TM atoms. Moreover, for bonds with TMs antiferromagnetically ordered, counterintuitively our calculations show that oxygens should also have a net magnetization for the super-super-exchange cases TM-O-O-TM while for only one oxygen, as in Cu-O-Cu, the O-polarization should cancel. Our simple model also allows us to explain the presence of nodes based on the antibonding character of the dominant singly occupied molecular orbitals along the TM-O bonds. Finally, the zigzag pattern order becomes the ground state mainly due to the influence of the Hubbard $U$, that creates the moments, in combination with a robust easy-axis anisotropy that suppresses the competing 120$^{\circ}$ degree antiferromagnetic order of a triangular lattice. Our predictions are generic and should be applicable to any other compound with characteristics similar to those of BCO and SRO.