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

Abstract

We present measurements of the microwave properties of high-quality thin films ofMgB2 deposited by reactive evaporation on both dielectric and metallic substrates. Themeasurements 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 striplineresonator at 2 GHz is used for the measurements on dielectric substrates and a dielectricresonator at 10.7 GHz is used for the films on metallic substrates. The surface resistance of theMgB2 is lower than that of our sputtered niobium films, and no power dependence was observedup to surface radio-frequency magnetic fields of 400 Oe at 5 K. The temperaturedependence of the IMD at low circulating power shows an increase at temperaturesT < 10 K that cannot be explained on the basis of s-wave symmetry of the order parameter in bothenergy gaps. Within the gap-symmetry constraints of the hexagonal crystal symmetry ofMgB2, the best fit with our IMD and penetration depth measurements is obtained for theπ-gap symmetrygiven by Δ(ϕ, T) = Δ0(T)sin(6ϕ), whereϕ is the azimuthalangle in the ab plane, and Δ0(T) is a weakly temperature dependent amplitude at low temperatures. This symmetry entailsthere being six nodal lines.