Temperature and frequency dependences of the dielectric properties of ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{6+\mathit{x}}$ (x≊0)

The real (ε’) and imaginary (ε’ ’) parts of the dielectric constant of dense tetragonal ceramic (91–93% of theoretical density) ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{6+\mathit{x}}$ samples with x=0.04 and 0.06 were investigated as functions of temperature (4–300 K) and frequency (${10}^2$–${10}^6$ Hz). At 4K the dielectric loss is very small (tan δ<0.005) and ε’=14.7±0.3, independent of frequency. This value of ε’ represents the intrinsic value of the static dielectric constant of the material, i.e., the combined electronic and lattice contributions to ε’. Both ε’ and ε’ ’ exhibit small increases with increasing temperature at low temperatures—behavior characteristic of normal dielectrics; however, on further heating strong increases and frequency dispersions develop. Above ∼160 K, the ε’(T) and ε’ ’(T) responses are nearly exponential. These temperature and frequency effects are interpreted in terms of dipolar polarization associated with the hopping motion of localized charge carriers. Consistent with this view, the observed frequency dependence of the conductivity is found to obey a power law of the form σ(ω)=A${\mathrm{\omega }}^{\mathit{s}}$, where s is a temperature-dependent constant (<1) and ω is the angular frequency. The results can be well represented by Pike’s classical hopping model which yields explicitly the ${\mathrm{\omega }}^{\mathit{s}}$ behavior, the temperature dependence of s, and the energy barrier to the hopping process.