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

Abstract

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.

(main text - 7 pages, 3 figures, 1 table; supplementary information - 6 pages, 3 figures, 2 tables, to be published in Physical Review B)