Disentangling orbital and spin exchange interactions for Co$^{2+}$ on a rocksalt lattice

Neutron spectroscopy was applied to study the magnetic interactions of orbitally degenerate Co$^{2+}$ on a host MgO rocksalt lattice where no long range spin or orbital order exists. The paramagnetic nature of the substituted monoxide Co$_{0.03}$Mg$_{0.97}$O allows for the disentanglement of spin-exchange and spin-orbit interactions. By considering the prevalent excitations from Co$^{2+}$ spin pairs, we extract 7 exchange constants out to the fourth coordination shell. An antiferromagnetic next nearest neighbor 180$^{\circ}$ exchange interaction is dominant, however dual ferromagnetic and antiferromagnetic interactions are observed for pairings with other pathways. These interactions can be understood in terms of a combination of orbital degeneracy in the $t_{2g}$ channel and the Goodenough-Kanamori-Anderson (GKA) rules. Our work suggests that such a hierarchy of exchange interactions exists in transition metal-based oxides with a $t_{2g}$ orbital degeneracy.