Structural order-by-disorder in framework materials

Systems which do not order at absolute zero due to a large ground state degeneracy can generate new correlations through thermal or quantum fluctuations and attain long-range order. Here, the internal energy of different ground states is the same, but their free energy can differ because the fluctuations around them give a different entropic weighting to each ground state. This is known as order-by-disorder (ObD) and has proven useful in understanding a wide variety of observed ordering phenomena in magnetic systems such as spin ices and frustrated anti-ferromagnets^. Outside magnetism, however, the ramifications of ObD physics remain largely unexplored. In this talk, we propose an ObD mechanism is at play in the observed structural transitions in a class of framework materials (MF₃ metal triflourides), which display soft manifold lattice dynamics with an inability to go through a symmetry breaking distortion, providing the required ground state degeneracy analogous to that of frustrated magnetism.