Interplay between multipolar spin interactions, Jahn-Teller effect, and electronic correlation in a J eff = 3 2 insulator

In this work we study the complex entanglement between spin interactions, electron correlation and Janh-Teller structural instabilities in the 5d 1 J ef f = 3 2 spin-orbit coupled double perovskite Ba2NaOsO6 using first principles approaches. By combining non-collinear magnetic calculations with multipolar pseudospin Hamiltonian analysis and many-body techniques we elucidate the origin of the observed quadrupolar canted antifferomagnetic. We show that the non-collinear magnetic order originates from Jahn-Teller distortions due to the cooperation of Heisenberg exchange, quadrupolar spin-spin terms and both dipolar and multipolar Dzyaloshinskii-Moriya interactions. We find a strong competition between ferromagnetic and antiferromagnetic canted and collinear quadrupolar magnetic phases: the transition from one magnetic order to another can be controlled by the strength of the electronic correlation (U) and by the degree of Jahn-Teller distortions.