Impact of gapped spin-orbit excitons on low-energy pseudospin exchange interactions

The quest for exotic quantum magnetic ground states, including the Kitaev spin liquid and quantum spin ices, has led to the discovery of several quantum materials where low-energy pseudospin-$1/2$ doublets arise from the splitting of spin-orbit entangled multiplets with higher degeneracy. Such systems include d-orbital and f-orbital Mott insulators. When the gap between the low-energy pseudospin-$1/2$ levels and the excited levels of the multiplet or ``excitons'' is not large, the effective low-energy exchange interactions between the low-energy pseudospin-$1/2$ moments can acquire significant corrections from coupling to the excitons. We extract these corrections using an extended perturbation theory that takes into account the most relevant higher-order perturbations. Such corrections can impact the exchange matrix for the low-energy pseudospin-$1/2$ levels by renormalizing the strength and the sign of Heisenberg exchange or Ising anisotropies, and potentially even inducing bond-anisotropic couplings such as Kitaev-Γ exchange interactions. We discuss recent experiments on various cobaltate and osmate materials, which hint at the ubiquity and importance of this physics. Our study suggests a distinct direction in the search for exotic spin liquids---quantum pseudospin-1/2 systems with low-energy spin-orbit excitons.