Frequency and magnetic-field dependence of the dielectric constant and conductivity ofLa2CuO4+y

Abstract

Detailed measurements are reported of the conductivity and dielectric constant at frequencies up to 20 MHz for single crystals of ${\mathrm{La}}_2$ ${\mathrm{CuO}}_{4+\mathit{y}}$, with y varied in the range 0.001–0.01. The hole concentration is determined for each y by Hall measurements. The conductivity shows a power-law dependence on frequency (${\mathrm{\omega }}^{\mathit{s}}$), which is typical of thermally assisted tunneling between localized states. The exponent s<1 decreases with increasing temperature and increasing oxygen content. The dielectric constant decreases with increasing frequency at low frequency with the power law ${\mathrm{\omega }}^{\mathit{s}\mathrm{-}1}$, showing that it is dominated by the same hopping mechanism. At high frequency the dielectric constant saturates and, for the electric field parallel to the ${\mathrm{CuO}}_2$ layers, the saturation value increases with oxygen content. From the polarizability at low acceptor concentration the radius of the bound hole is found to be ∼8 Å, a value that is consistent with a simple hydrogenic model of the impurity state. The small binding energy of the hole to the impurity, 35 meV as determined from Hall measurements, together with this radius of 8 Å, requires that the mass of the hole be fairly small, ∼2${\mathit{m}}_{\mathit{e}}$. The growth of the localization length with hole density is almost purely two dimensional, implying that there is no true insulator-to-metal transition, but rather a crossover from strong to weak localization. From studies of the magnetic-field dependence of the frequency-dependent conductivity and dielectric constant one finds new evidence for the strong coupling of the excess holes to the antiferromagnetically ordered Cu spins.