Anharmonicity in the Silver and Thallium Halides: Low-Frequency Dielectric Response

The isobaric temperature dependence of the low-frequency (1-100 kHz) dielectric response of AgCl, AgBr, TlCl, and TlBr for the range 2-290 K and the isothermal pressure dependence of the dielectric response for pressures up to 11 kbar in the range 77-290 K are reported. These measurements are used to determine the thermal strain and low-frequency anharmonic self-energy for the $q\approx 0$ transverse-optic mode for these materials. The results reveal that the anharmonic self-energy contribution arising through the quartic anharmonicity is dominant for all four materials at low temperatures. At higher temperatures the quartic anharmonicity continues to provide the dominant contributions for the thallium halides, but for the silver halides the cubic anharmonicity has a stronger temperature dependence and provides the dominant anharmonic self-energy contribution. The quartic self-energy contributions for the thallium halides are sufficiently large that they dominate the thermal-strain self-energy contributions at all temperatures, thus causing the dielectric response for these materials to behave like ferroelectrics in their paraelectric state. No marked difference between the low-frequency and far-infrared anharmonic self-energies is found.