A Low-Temperature Specific Heat Study of the Giant Dielectric Constant Materials

Low-temperature specific-heat study has been performed on the insulating giant dielectric constant material CaCu$_{3}$Ti$_{4}$O$_{12}$ and two related compounds, Bi$_{2/3}$Cu$_{3}$Ti$_{4}$O$_{12}$ and La$_{0.5}$Na$_{0.5}$Cu$_{3}$Ti$_{4}$O$_{12}$, from 0.6 to 10 K. From analyzing the specific heat data at very low-temperature range, 0.6 to 1.5 K, and moderately low-temperature range, 1.5 to 5 K, in addition to the expected Debye terms, we noticed significant contributions originated from the linear and Einstein terms, which we attributed as the manifestation of low-lying elementary excitations due to lattice vibrations occurred at the grain boundaries and induced by local defects. Together with the findings on electronic and mechanical properties, a phenomenological model is proposed to explain the high dielectric constant behaviors at both low and high frequency regions.