Phonon anomalies in Cu halides

A great number of the observed phonon anomalies in the zinc-blende phase of Cu-halide crystals are explained by means of a dynamical model. It is assumed that a Cu ion populates four equivalent off-center sites or its ideal position. The off-center ${\mathrm{Cu}}^{+}$ population is temperature and pressure dependent. With regard to phonons, this system is described as having a two-mode behavior of the optical vibrations at $\overrightarrow{\mathrm{k}}\approx 0$; one is due to ${\mathrm{Cu}}^{+}$ at the ideal positions and the other is due to ${\mathrm{Cu}}^{+}$ at the off-center tunneling states. The latter has basically also a $T_2$ symmetry, but a shorter correlation length. This explains the appearance, width, and polarization properties of the "extra" lines observed in Raman and infrared, as well as their irregular intensity temperature and pressure dependence. Consequently, the polariton dispersion and the resonant Raman data in CuCl can readily be understood. This model also explains the anomalous intensity $\overrightarrow{\mathrm{k}}$ and $T$ dependence of the inelastic-neutron-scattering in CuCl. The trend in the phonon characteristics, observed in Cu halides and which is an integral part of this model, follows the same course deduced from the intensity temperature dependence of Bragg x-ray and neutron scattering data.