Microwave surface impedance of MgB₂ thin film

The microwave surface impedance Z_s = R_s + jωμ₀λ was measured with dielectric resonator techniques for two c-axis-oriented MgB₂ thin films. The temperature dependence of the penetration depth λ measured with a sapphire resonator at 17.93 GHz can be well fitted from 5 K close to T_c by the standard BCS integral expression assuming the reduced energy gap Δ(0)/kT_c to be as low as 1.13 and 1.03 for the two samples. From these fits the penetration depth at zero temperatures was determined to be 102 nm and 107 nm, respectively. The results clearly indicate the s-wave nature of the order parameter. The temperature dependence of surface resistance R_s, measured with a rutile dielectric resonator, shows an exponential behaviour below about T_c/2 with a reduced energy gap being consistent with the one determined from the λ data. The R_s value at 4.2 K was found to be as low as 19 μΩ at 7.2 GHz, which is comparable with that of a high-quality high-temperature thin film of YBa₂Cu₃O₇. A higher-order mode at 17.9 GHz was employed to determine the frequency f dependence of R_s ∝ f^n(T). Our results revealed a decrease of n with increasing temperature ranging from n = 2 below 8 K to n = 1 from 13 to 34 K.