Entangled spin orbital order in 5d¹ and 5d² Double Pervoskite Mott Insulators

We theoretically investigate the unusual properties of Mott-insulating double perovskites A2BB'O6 where the magnetic B' ions have 1 or 2 electrons in the 5d shell and the B sites are non-magnetic. We derive a low-energy effective Hamiltonian that includes spin-orbit coupling, super-exchange, inter-site Coulomb interactions and Hund’s coupling, and analyze it within mean field theory. We show that orbital order sets in at a high temperature To and strongly constrains the non-collinear magnetic order that appears at a much lower Tc.Our results give insight into several experimental puzzles. The prediction of orbital ordering well above Tc explains the puzzle of the missing entropy above the magnetic transition. Orbital order is also responsible for the deviations of the high temperature magnetic susceptibility from a Curie-Weiss form. Finally, we show why cubic 5d1 materials most often exhibit canted ferromagnetism, which is rare in Mott insulators, while the 5d2 and distorted 5d1 materials are all antiferromagnetically ordered.