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Clarifying the underlying mechanisms that govern ordering transitions incondensed matter systems is crucial for comprehending emergent properties andphenomena. While transitions are often classified as electronically driven orlattice-driven, we present a departure from this conventional paradigm in thecase of the double perovskite Ba$_2$MgReO$_6$. Leveraging resonant andnon-resonant elastic x-ray scattering techniques, we unveil the simultaneousordering of structural distortions and charge quadrupoles at a criticaltemperature of $T_\mathrm{q}$$\sim$33 K. Using a variety of complementaryfirst-principles-based computational techniques, we demonstrate that whileelectronic interactions drive the ordering at $T_\mathrm{q}$, it is ultimatelythe lattice that dictates the specific ground state that emerges. Our findingshighlight the crucial interplay between electronic and lattice degrees offreedom, providing a unified framework to understand and predict unconventionalemergent phenomena in quantum materials.

Spectroscopic signatures and origin of a hidden order in Ba$_2$MgReO$_6$