The interplay of spin-orbit coupling and vibronic coupling on the heavy $d^1$ site of cubic double perovskites is investigated by ab initio calculations. The stabilization energy of spin-orbital-lattice entangled states is found to be comparable to or larger than the exchange interactions, suggesting the presence of Jahn-Teller dynamics in the systems. In ${\mathrm{Ba}}_2{\mathrm{YMoO}}_6$, the pseudo-Jahn-Teller coupling enhances the mixing of the ground and excited spin-orbit multiplet states, which results in strong temperature dependence of effective magnetic moments. The entanglement of the spin and lattice degrees of freedom induces a strong magnetoelastic response. This multiferroic effect is at the origin of the recently reported breaking of local point symmetry accompanying the development of magnetic ordering in ${\mathrm{Ba}}_2{\mathrm{NaOsO}}_6$.

• Received 19 March 2018

DOI:https://doi.org/10.1103/PhysRevB.98.075138