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Motivated by the experiments on the rare-earth double perovskites, we proposea generalized Kitaev-Heisenberg model to describe the generic interactionbetween the spin-orbit-entangled Kramers' doublets of the rare-earth moments.We carry out a systematic analysis of the mean-field phase diagram of this newmodel. In the phase diagram, there exist large regions with a continuous U(1)or O(3) degeneracy. Since no symmetry of the model protects such a continuousdegeneracy, we predict that the quantum fluctuation lifts the continuousdegeneracy and favors various magnetic orders in the phase diagram. From thisorder by quantum disorder mechanism, we further predict that the magneticexcitations of the resulting ordered phases are characterized by nearly gaplesspseudo-Goldstone modes. We find that there exist Weyl magnon excitations forcertain magnetic orders. We expect our prediction to inspire further study ofKitaev physics, the order by quantum disorder phenomenon and topological spinwave modes in the rare-earth magnets and the systems alike.

Kitaev materials beyond iridates: order by quantum disorder and Weyl magnons in rare-earth double perovskites