Spin-orbit coupling in d2 ordered double perovskites

We construct and analyze a microscopic model for insulating rock-salt ordered double perovskites, with the chemical formula A(2)BB'O-6, where the magnetic ion B' has a 4d(2) or 5d(2) electronic configuration and forms a face-centered cubic lattice. For these B' ions, the combination of the triply degenerate antisymmetric two-electron orbital states and strong spin-orbit coupling forms local quintuplets with an effective spin moment j = 2. Moreover, due to strongly orbital-dependent exchange, the effective spins have substantial biquadratic and bicubic interactions (fourth and sixth order in the spins, respectively). This leads, at the mean-field level, to a rich ground-state phase diagram, which includes seven different phases: a uniform ferromagnetic phase with an ordering wave vector p = 0 and uniform magnetization along the [111] direction, four two-sublattice phases with an ordering wave vector p = 2 pi(001), and two four-sublattice antiferromagnetic phases. Among the two-sublattice phases, there is a quadrupolar ordered phase that preserves time-reversal symmetry. By extending the mean-field theory to finite temperatures, we find 10 different magnetization processes with different magnetic thermal transitions. In particular, we find that thermal fluctuations stabilize the two-sublattice quadrupolar ordered phase in a large portion of the phase diagram. Existing and possible future experiments are discussed in light of these theoretical predictions.