Effect of a dc magnetic field on the microwave losses in MgB₂ thin films

The microwave surface impedance (Z_s=R_s+iX_s) of in situ MgB₂ thin films was measured as a function of temperature and parallel dc magnetic field at several frequencies between 5.7 and 18.5 GHz using a dielectric resonator technique. The results are consistent with the expectations for a classical type-II superconductor and, consequently, quite different from those of the high-T_c cuprates. The films cooled in zero field revealed a clear indication of the lower critical field B_c1, with a small hysteresis around B⩽B_c1. In higher fields (B>B_c1), the losses followed the Coffey-Clem and Brandt model, including the frequency dependences, whereas high-T_c Y-Ba-Cu-O films did not show a reasonable agreement with this model. Both the relatively high values of ΔX_s∕ΔR_s ratio and their frequency dependence indicate a weak effect of flux creep on the measured microwave loss in MgB₂ films. The temperature dependence of ΔX_s∕ΔR_s ratio can be described by a microscopic pinning model for BCS superconductors.