Archetypal Soft-Mode-Driven Antipolar Transition in Francisite Cu_{3}Bi(SeO_{3})_{2}O_{2}Cl

Model materials are precious test cases for elementary theories and provide building blocks for the understanding of more complex cases. Here, we describe the lattice dynamics of the structural phase transition in francisite Cu_{3}Bi(SeO_{3})_{2}O_{2}Cl at 115 K and show that it provides a rare archetype of a transition driven by a soft antipolar phonon mode. In the high-symmetry phase at high temperatures, the soft mode is found at (0,0,0.5) at the Brillouin zone boundary and is measured by inelastic x-ray scattering and thermal diffuse scattering. In the low-symmetry phase, this soft-mode is folded back onto the center of the Brillouin zone as a result of the doubling of the unit cell, and appears as a fully symmetric mode that can be tracked by Raman spectroscopy. On both sides of the transition, the mode energy squared follows a linear behavior over a large temperature range. First-principles calculations reveal that, surprisingly, the flat phonon band calculated for the high-symmetry phase seems incompatible with the displacive character found experimentally. We discuss this unusual behavior in the context of an ideal Kittel model of an antiferroelectric transition.