Temperature dependence of low-frequency phonon behavior in gadolinium gallium garnet and yttrium aluminum garnet

The temperature dependence of the dielectric properties and phonon behavior of gadolinium gallium garnet (GGG) and yttrium aluminum garnet (YAG) single crystals were analyzed by terahertz time-domain spectroscopy (THz-TDS), Fourier transform infrared spectroscopy (FT-IR), and density-functional-theory (DFT) calculations. A custom air-plasma-based THz-TDS system was calibrated using the well-studied MgO single crystal, and the results in the low-frequency range were validated by a commercial high-resolution FT-IR system. Consequently, the THz-TDS and FT-IR measurement results for GGG and YAG were in good agreement. Due to the high absorption in the phonon response range, only the TO1 and TO4 phonons of GGG and the TO1 phonon of YAG were observed. A manual phase adjustment was introduced in analyzing GGG in order to calculate reliable values of dielectric constants. The Lorentz oscillator model was employed to identify the phonon modes. With increasing temperature, the phonon frequencies slightly shift to lower frequencies, the damping parameters generally increase, and the oscillator strengths stay constant. The theoretical calculations, based on DFT and a shell model, in which the thermal expansion of the crystals was considered, explain the temperature-dependent phonon frequency shift and are in good agreement with the experimental results. Finally, the phonon behavior was evaluated using the Grüneisen parameter and compared with the experimental data. The results show that thermal expansion contributes significantly to phonon frequency shift, and the minor contribution from phonon anharmonicity increases with increasing temperature.