Orbital order drives magnetic order in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mn>5</mml:mn><mml:msup><mml:mi>d</mml:mi><mml:mn>1</mml:mn></mml:msup></mml:mrow></mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mn>5</mml:mn><mml:msup><mml:mi>d</mml:mi><mml:mn>2</mml:mn></mml:msup></mml:mrow></mml:math> double perovskite Mott insulators
Christopher Svoboda, Wenjuan Zhang, Mohit Randeria, Nandini Trivedi
Abstract
We derive spin-orbital Hamiltonians for cubic double perovskite ${A}_{2}M{M}^{\ensuremath{'}}{\mathrm{O}}_{6}$ Mott insulators with $5{d}^{1}$ or $5{d}^{2}$ magnetic ${M}^{\ensuremath{'}}$ ions and nonmagnetic $M$ ions. We find that with strong spin-orbit coupling, exchange and intersite Coulomb repulsion lead to orbital order at a temperature ${T}_{o}$ higher than the magnetic ${T}_{c}$. Orbital order produces a $T$-dependent moment below ${T}_{o}$ and stabilizes canted ferromagnetic (FM) and noncollinear antiferromagnetic (AFM) states below ${T}_{c}$. We explain many experimental puzzles including loss of entropy above ${T}_{c}$, deviations from a Curie-Weiss susceptibility, a negative Curie-Weiss intercept for FM systems, and why FM order is common in cubic $5{d}^{1}$ materials but all $5{d}^{2}$ systems are AFM.