Vibronic order and emergent magnetism in cubic $d^1$ double perovskites

The synergistic interplay of different interactions in materials leads to the emergence of novel quantum phenomena. Spin-orbit and vibronic couplings usually counteract each other, however, in cubic $d^1$ double perovskites they coexist and give rise to spin-orbit-lattice entanglement with unquenched dynamic Jahn-Teller effect on the metal sites. The correlation of these entangled states induced by intersite interactions was not assessed so far. Here, we investigate the joint cooperative effect of spin-orbit and vibronic interactions on the formation of the ordered phases in $d^1$ double perovskites. We found that the magnetic ordered states in these systems coexist with a dynamic vibronic order characterized by the ordering of vibronic quadrupole moments on sites. This treatment allows the rationalization of a number of unexplained features of experimentally investigated phases.