Neutron-scattering study on phase transitions of CsPbCl3

Abstract

Neutron-scattering experiments have elucidated the mechanism of the successive phase transitions of CsPb${\mathrm{Cl}}_{3}$ at 47, 42, and 37\ifmmode^\circ\else\textdegree\fi{}C. These phase transitions are basically associated with the condensation of rotational modes of Pb${\mathrm{Cl}}_{6}$ octahedra around the three principal axes. The phase transition at 47\ifmmode^\circ\else\textdegree\fi{}C is caused by the condensation of the nondegenerate ${M}_{3}$ phonon mode at the zone boundary along the [110] direction of the cubic lattice. The axis of rotation of the Pb${\mathrm{Cl}}_{6}$ octahedra is along the [001] axis. The second phase transition at 42\ifmmode^\circ\else\textdegree\fi{}C is associated with the condensation of one of doubly degenerate modes ${Z}_{5}^{x}$ and ${Z}_{5}^{y}$ at the zone boundary along the [001] direction of the tetragonal lattice, which are derived from the triply degenerate ${R}_{25}$ mode in the cubic phase. The direction of the rotation axis is along the [100] axis when we assign ${Z}_{5}^{x}$ as the condensing mode. The third phase transition at 37\ifmmode^\circ\else\textdegree\fi{}C is caused by the condensation of the remaining ${Z}_{5}^{y}$ mode. The crystal systems and the space groups of three low-temperature phases were determined from the eigenvectors of the condensing modes as tetragonal ${D}_{4h}^{5}$, orthorhombic ${D}_{2h}^{17}$, and monoclinic ${C}_{2h}^{2}$ in the sequence of decreasing temperature. These are consistent with the previous experimental results on nuclear-quadrupole-resonance spectra of ${\mathrm{Cl}}^{\ensuremath{-}}$ ion. A phenomenological theory has been developed to explain these successive phase transitions caused by the condensation of the ${M}_{3}$ and ${R}_{25}$ zone-boundary phonons. The observed phase-transition schemes can be qualitatively explained by a suitable choice of the parameters in the free-energy expansion with respect to order parameters.