Interplay between lattice distortion and spin-orbit coupling in double perovskites

We develop anisotropic pseudo-spin antiferromagnetic Heisenberg models for monoclinically distorted double perovskites. We focus on these A₂BB^'O₆ materials that have magnetic moments on the $4d$ or $5d$ transition metal B^' ions, which form a face-centered cubic lattice. In these models, we consider local z-axis distortion of B^'-O octahedra, affecting relative occupancy of t2g orbitals, along with geometric effects of the monoclinic distortion and spin-orbit coupling. The resulting pseudo-spin-$1/2$ models are solved in the saddle-point limit of the Sp(N) generalization of the Heisenberg model. The spin S in the SU(2) case generalizes as a parameter κ controlling quantum fluctuation in the Sp(N) case. We consider two different models that may be appropriate for these systems. In particular, using Heisenberg exchange parameters for La₂LiMoO₆ from a spin-dimer calculation, we conclude that this pseudo-spin-$1/2$ system may order, but will be very close to a disordered spin liquid state.