First-principles study of the structure and lattice dielectric response of ${\mathrm{CaCu}}_3{\mathrm{Ti}}_4{\mathrm{O}}_{12}$

Structural and electronic properties of ${\mathrm{CaCu}}_3{\mathrm{Ti}}_4{\mathrm{O}}_{12}$ are calculated using density-functional theory within the local spin-density approximation. After an analysis of structural stability, zone-center optical phonon frequencies are evaluated using the frozen-phonon method and mode effective charges are determined from computed Berry-phase polarizations. Excellent agreement between calculated and measured phonon frequencies is obtained. The calculated mode effective charges are in poorer agreement with experiment, although they are of the correct order of magnitude and the lattice contribution to the static dielectric constant is calculated to be $\sim 40.$ On the basis of these results, various mechanisms are considered for the enormous dielectric response reported in recent experiments. No direct evidence is found for intrinsic lattice or electronic mechanisms, suggesting that increased attention should be given to extrinsic effects.