Characteristic features of the temperature dependence of the surface impedance in polycrystalline MgB$_2$ samples

Abstract

The real $R_s(T)$ and imaginary $X_s(T)$ parts of the surface impedance $Z_s(T)=R_s(T)+iX_s(T)$ in polycrystalline MgB$_2$ samples of different density with the critical temperature $T_c\approx 38$ K are measured at the frequency of 9.4 GHz and in the temperature range $5\le T<200$ K. The normal skin-effect condition $R_s(T)=X_s(T)$ at $T\ge T_c$ holds only for the samples of the highest density with roughness sizes not more than 0.1 $\mu$m. For such samples extrapolation $T\to 0$ of the linear at $T<T_c/2$ temperature dependences $\lambda_L(T)=X_s(T)/\omega\mu_0$ and $R_s(T)$ results in values of the London penetration depth $\lambda_L(0)\approx 600$ \AA and residual surface resistance $R_{res}\approx 0.8$ m$\Omega$. In the entire temperature range the dependences $R_s(T)$ and $X_s(T)$ are well described by the modified two-fluid model.