Fig. 5: Comparison of dynamic and static JT effect on equilibrium ion positions at time-scales longer than t₀.

At very high temperatures, the octahedra are not distorted, and the ground state is four-fold degenerate. In the dynamical JT scenario, the degeneracy is lowered by a contraction of Re - O distances (~ − 1.5 %) on time scales t < t₀, but the equilibrium positions of ions at t > t₀ do not change significantly, with the Re charge distribution remaining spherical (gray circle). At much lower temperatures (T < T_Q), a quadrupolar order sets in, including the ferroic \({{{{\mathcal{T}}}}}_{z}\) (blue - increased charge density, yellow - decreased charge density), which is accompanied by a coherent shift of apical oxygen ions (red arrows), leading to a small c-axis elongation (~ + 0.15 %)²⁷ (green arrows). In the static JT scenario, each octahedron is locally distorted, with an equal distribution of elongations along three principal axes. This implies a random distribution of \({{{{\mathcal{T}}}}}_{z}\) quadrupolar moments and a lack of coherent ordering at low temperatures. The local Ba cage is also distorted, leading to the accumulation of lattice strain.