Surface impedance anisotropy of YBa$_2$Cu$_3$O$_{6.95}$ single crystals: electrodynamic basis of the measurements

Abstract

An electrodynamic technique is developed for determining the components of surface impedance and complex conductivity tensors of HTSC single crystals on the basis of measured quantities of a quality factor and a resonator frequency shift. A simple formula is obtained for a geometrical factor of a crystal in the form of a plate with dimensions $b\gg a>c$ in a microwave magnetic field ${\bf H_{\omega}}\perp ab$. To obtain the c-axis complex conductivity from measurements at ${\bf H_{\omega}}\parallel ab$ we propose a procedure which takes account of sample size effects. With the aid of the technique involved temperature dependences of all impedance and conductivity tensors components of YBa$_2$Cu$_3$O$_{6.95}$ single crystal, grown in BaZrO$_3$ crucible, are determined at a frequency of $f=9.4$ GHz in its normal and superconducting states. All of them proved to be linear at $T<T_c/2$, and their extrapolation to zero temperature gives the values of residual surface resistance $R_{ab}(0)\approx 40$ $\mu\Omega$ and $R_c(0)\approx 0.8$ m$\Omega$ and magnetic field penetration depth $\lambda_{ab}(0)\approx 150$ nm and $\lambda_c(0)\approx 1.55$ $\mu$m.