Microwave measurements of MgB2: implications for applications and order-parameter symmetry

We present measurements of the microwave properties of high-quality thin films of MgB2 deposited by reactive evaporation on both dielectric and metallic substrates. The measurements include those of the surface impedance and the intermodulation distortion (IMD), both as a function of microwave power at temperatures from 1.8 to 35 K. A stripline resonator at 2 GHz is used for the measurements on dielectric substrates and a dielectric resonator at 10.7 GHz is used for the films on metallic substrates. The surface resistance of the MgB2 is lower than that of our sputtered niobium films, and no power dependence was observed up to surface radio-frequency magnetic fields of 400 Oe at 5 K. The temperature dependence of the IMD at low circulating power shows an increase at temperatures T < 10 K that cannot be explained on the basis of s-wave symmetry of the order parameter in both energy gaps. Within the gap-symmetry constraints of the hexagonal crystal symmetry of MgB2, the best fit with our IMD and penetration depth measurements is obtained for the π-gap symmetry given by Δ(φ, T) = Δ0(T)sin(6φ), where φ is the azimuthal angle in the ab plane, and Δ0(T) is a weakly temperature dependent amplitude at low temperatures. This symmetry entails there being six nodal lines.