Nonlinear microwave properties of superconducting Nb microstrip resonators

We present measurements of the nonlinear surface impedance ${\mathit{Z}}_{\mathit{S}}$=${\mathit{R}}_{\mathit{S}}$+${\mathit{iX}}_{\mathit{S}}$ of thin-film Nb micro- strip resonators. We demonstrate correlation between material properties of the films and the occurrence of nonlinearity. The nonlinearity is characterized using a dimensionless parameter r=Δ${\mathit{R}}_{\mathit{S}}$(P)/Δ${\mathit{X}}_{\mathit{S}}$(P). We make a short survey of the mechanisms of nonlinear electrodynamics of superconductors and demonstrate that our experimental results are best accounted for by the vortex penetration into the grains.