In this work, we study the complex entanglement between spin interactions, electron correlation, and Janh-Teller structural instabilities in the ${5d}^1{J}_{\mathrm{eff}}=\frac{3}{2}$ spin-orbit coupled double perovskite ${\mathrm{Ba}}_2{\mathrm{NaOsO}}_6$ 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.

• Received 28 May 2020
• Revised 4 February 2021
• Accepted 19 February 2021

DOI:https://doi.org/10.1103/PhysRevB.103.104401