Microwave Losses in Strontium Titanate above the Phase Transition

Abstract

The microwave losses in both pure and doped SrTi${\mathrm{O}}_{3}$ have been investigated as a function of frequency and temperature. It is found that the loss tangent is proportional to frequency in the range 3-36 kMc/sec. Above the phase transition at 112\ifmmode^\circ\else\textdegree\fi{}K, the temperature dependence of the loss tangent is well represented by $tan\ensuremath{\delta}={(T\ensuremath{-}{T}_{c})}^{\ensuremath{-}1}(\ensuremath{\alpha}+\ensuremath{\beta}T+\ensuremath{\gamma}{T}^{2})$, where the Curie temperature, ${T}_{c}=37\ifmmode^\circ\else\textdegree\fi{}$K. The parameter $\ensuremath{\alpha}$ is shown to be determined by lattice imperfections and vanishes for pure single-crystalline material. The parameters $\ensuremath{\beta}$ and $\ensuremath{\gamma}$, which are related to third-and fourth-order anharmonic terms in the interionic potential, are shown to be intrinsic properties of the perfect lattice and are unaffected by imperfections.