  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.
