Intertwined orbital and magnetic order in 5d¹ and 5d² Double Perovskite Mott Insulators

In this talk I summarize our work on understanding the unusual properties of Mott-insulating double perovskites A₂BB'O₆ where the B' sites are 5d magnetic ions with either 1 or 2 electrons in t_2g orbitals and the B sites are non-magnetic. Our theory is motivated by several experimental puzzles, including: (i) Why do almost all cubic 5d¹ materials exhibit ferromagnetic (FM) order, rare in Mott insulators, while all the 5d² materials have antiferromagnetic (AFM) ground states? (ii) Why is only partial (log 2) entropy recovered above the magnetic transition, rather than the expected log 4 for j = 3/2, in cubic 5d¹ materials? (iii) Why do the cubic 5d¹ materials exhibit a high temperature magnetic susceptibility that deviates from a Curie-Weiss form? We derive and analyze low-energy effective Hamiltonians for these systems that include spin-orbit coupling, superexchange, inter-site Coulomb interactions and Hund’s coupling. We predict that novel orbital order sets in at a high temperature T_o and strongly constrains the non-collinear magnetic order that appears at a much lower T_c. Our results allow us to understand all the puzzles noted above and make predictions for new experiments. This research was done in collaboration with W. Zhang, C. Svoboda, P. M. Woodward and N. Trivedi.