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 has not been 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 magnetically ordered states in these systems coexist with a dynamic vibronic order characterized by the ordering of vibronic quadrupole moments on sites. This treatment allows for the rationalization of a number of unexplained features of experimentally investigated phases.

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• Elastic forces
• Exchange interaction
• Frustrated magnetism
• Jahn-Teller effect
• Magnetic order
• Orbital order
• Phase diagrams
• Spin-orbit coupling
• Mott insulators
• Perovskites
• Transition metals