Interplay between multipolar spin interactions, Jahn-Teller effect, and electronic correlation in a Jeff= 32 insulator

In this work, we study the complex entanglement between spin interactions, electron correlation, and Janh-Teller structural instabilities in the 5d1Jeff=32 spin-orbit coupled double perovskite Ba2NaOsO6 using first principles approaches. By combining noncollinear 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 noncollinear 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.