Wide range dielectric and infrared spectroscopy of (Nb+In) co-doped rutile ceramics

The dielectric response of ceramics of co-doped rutile $\mathrm{T}{\mathrm{i}}_{1\text{\ensuremath{-}}x}{(\mathrm{N}{\mathrm{b}}_{0.5}\mathrm{I}{\mathrm{n}}_{0.5})}_{x}{\mathrm{O}}_{2}$ has been measured via a combination of impedance, high-frequency coaxial, terahertz transmission, and infrared reflectivity spectroscopies spanning 15 decades of frequency between 0.1 Hz and 240 THz. It is argued that the colossal dielectric permittivity reported by Hu et al. [Hu et al., Nat. Mater. 12, 821 (2013)] has the same explanation as in the original colossal permittivity material $\mathrm{CaC}{\mathrm{u}}_{3}\mathrm{Ti}{\mathrm{O}}_{4}{\mathrm{O}}_{12}$ (CCTO), namely, a combination of the internal barrier layer capacitor (IBLC) and the surface barrier layer capacitor (SBLC) effects. The IBLC effect is caused by a microstructure consisting of insulating grain boundaries (thickness \ensuremath{\sim}1 nm and conductivity of $\ensuremath{\sim}{10}^{\ensuremath{-}6}\phantom{\rule{0.16em}{0ex}}\mathrm{S}/\mathrm{cm})$ surrounding interior regions of bulk conductivity approximately equal to ${10}^{\ensuremath{-}1}\phantom{\rule{0.16em}{0ex}}\mathrm{S}/\mathrm{cm}$. The SBLC effect is the result of a depletion layer adjacent to the contacts approximately 100 nm thick with conductivity of $5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}7}\phantom{\rule{0.16em}{0ex}}\mathrm{S}/\mathrm{cm}$. The SBLC and IBLC effects give rise to dielectric relaxations in low-frequency and radiofrequency regions, respectively. The temperature dependence of both relaxation rates measured down to 20 K is thermally activated. No separate absorption process has been observed that could be linked to giant defect dipoles. Infrared spectroscopy has revealed four weak defect-related modes at frequencies close to the Raman mode frequencies of rutile, activated in the infrared through a symmetry-breaking process. Co-doping produces a significant loss in the partial spectral weight between 75 and $350\phantom{\rule{0.16em}{0ex}}\mathrm{c}{\mathrm{m}}^{\ensuremath{-}1}$ associated with the lowest transverse optical mode, which softens on cooling. The loss in its spectral weight corresponds to the gain in near-infrared spectral weight, previously assigned to small polaron absorption.