  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.
