Microwave Absorption in Cubic Strontium Titanate

An analysis of the temperature dependence of the microwave loss in SrTi${\mathrm{O}}_3$ is presented using the linear chain model of a ferroelectric as a basis for discussion. It is shown that a plausible explanation of the temperature dependence of the microwave loss tangent above liquid air temperature is possible if one considers the loss to be due to the damping of a virtual excitation out in the wing of a fundamental lattice absorption. The fundamental lattice absorption is associated with a low-frequency "ferroelectric" transverse optical mode of the material. The microwave loss tangent can be expressed by $tan\delta ={(T-T_C)}^{-1\mathrm{}}(A+BT+D{T}^2)$. The parameter $A$ is a measure of the damping due to the presence of imperfections in the lattice. The parameters $B$ and $D$ are shown to arise from damping due to three- and four-phonon processes whose origin is attributed to the anharmonic interactions of the lattice.