Spin-orbit coupling in $d^{2}$ ordered double perovskites

TL;DR

This paper develops a microscopic model for 4d$^2$ and 5d$^2$ double perovskites, revealing complex magnetic phases and the stabilizing role of thermal fluctuations, with implications for experimental observations.

Contribution

It introduces a detailed theoretical framework capturing spin-orbit coupling effects and orbital-dependent exchange in double perovskites, predicting diverse magnetic phases and thermal behaviors.

Findings

Seven distinct ground state magnetic phases identified.

Thermal fluctuations stabilize quadrupolar order.

Ten different magnetization processes at finite temperature.

Abstract

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 (fcc) 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 wavevector ${\bf p} = {\bf 0}$ and uniform magnetization along $[111]$ direction, four two-sublattice phases with an ordering wavevector ${\bf p} = 2\pi(001)$ and two four-sublattice antiferromagnetic phases. Amongst the two-sublattice phases there is a quadrupolar ordered phase which preserves time reversal symmetry. Extending the mean field theory to finite temperatures, we find ten 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 phase diagram. Existing and possible future experiments are discussed in light of these theoretical predictions.