Lattice dielectric response of ${\mathrm{CdCu}}_3{\mathrm{Ti}}_4{\mathrm{O}}_{12}$ and ${\mathrm{CaCu}}_3{\mathrm{Ti}}_4{\mathrm{O}}_{12}$ from first principles

Structural, vibrational, and lattice dielectric properties of ${\mathrm{CdCu}}_3{\mathrm{Ti}}_4{\mathrm{O}}_{12}$ are studied using the density-functional theory within the local spin-density approximation, and the results are compared with those computed previously for ${\mathrm{CaCu}}_3{\mathrm{Ti}}_4{\mathrm{O}}_{12}.$ Replacing Ca with Cd is found to leave many calculated quantities largely unaltered, although significant differences do emerge in zone-center optical phonon frequencies and mode effective charges. The computed phonon frequencies of ${\mathrm{CdCu}}_3{\mathrm{Ti}}_4{\mathrm{O}}_{12}$ are found to be in excellent agreement with experiment, and the computed lattice contribution to the intrinsic static dielectric constant $\left(\sim 60\right)$ also agrees exceptionally well with a recent optical absorption experiment. These results provide further support for a picture in which the lattice dielectric response is essentially conventional, suggesting an extrinsic origin for the anomalous low-frequency dielectric response recently observed in both materials.