Key role of orbital exchange in CoO magnetism

Abstract

Co ions in the antiferromagnetic phase of CoO are known to possess a substantial orbital moment, making this material promising for orbitronic applications. However, intersite exchange interactions involving these orbital degrees of freedom remain poorly quantified, and their role in CoO magnetism is unclear. Here, we derive a full low-energy effective Hamiltonian for CoO, including orbital exchange terms, using an ab initio force-theorem approach based on DFT+dynamical mean-field theory. We find sizable orbital interactions, with quadrupolar orbital exchange emerging as the dominant nearest-neighbor term. The collinear antiferromagnetic order obtained from the effective Hamiltonian features magnetic moments tilted away from the pseudocubic <001> direction and an orbital contribution amounting to about one-third of the total moment, in agreement with experimental estimates. We show that the moment tilting originates from the combined effect of orbital and spin-orbital exchange interactions. The same interactions also produce a prominent splitting of the lowest excitation band. By directly modeling the inelastic neutron scattering (INS) intensity, we further show that the characteristic column-like structures previously observed in CoO INS provide a clear fingerprint of orbital exchange. We also discuss possible impact of our findings for further advances in the field of complex collective excitations, their transport properties and applications in the realm of orbitronics.