Extrinsic Mechanisms for the Giant Dielectric Constant in CaCu$_{3}$Ti$_{4}$O$_{12}$: A Low-Temperature Specific-Heat Study

Low-temperature specific-heat study has been performed on the insulating giant dielectric constant material CaCu$_{3}$Ti$_{4}$O$_{12}$. Analyzing the specific heat data in the very low-temperature range (0.6 to 1.5 K) and moderately low-temperature range (1.5 to 5 K), we noticed significant contributions originated from the linear and Einstein terms, we attributed as the low-lying elementary excitations due to lattice vibrations occurred at the grain boundaries and induced by local defects. These findings correlate well with the core-shell model deduced from the earlier experiments, and offer explanation to the extrinsic mechanisms of the giant dielectric constants at both low (DC to 10$^{5}$ Hz) and high frequency (10$^{6}$ to 10$^{9 }$Hz) regions.