Microwave response of thin niobium films under perpendicular static magnetic fields

The microwave response of high quality niobium films in a perpendicular static magnetic field has been investigated. The complex frequency shift was measured up to the upper critical fields. The data have been analyzed by the effective conductivity model for the type-II superconductors in the mixed state. This model is found to yield consistent results for the coherence lengths in high-$\ensuremath{\kappa}$ superconducting samples, and can be used with high-temperature superconductors even at temperatures much below ${T}_{c}$. It is shown that for samples with high values of depinning frequency, one should measure both components of the complex frequency shift in order to determine the flow resistivity. The thick Nb film $(160\phantom{\rule{0.3em}{0ex}}\mathrm{nm})$ has low resistivity at $10\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, comparable to the best single crystals, and low $\ensuremath{\kappa}$ value. In contrast, the thinnest $(10\phantom{\rule{0.3em}{0ex}}\mathrm{nm})$ film has $\ensuremath{\kappa}\ensuremath{\approx}9.5$ and exhibits a high depinning frequency $(\ensuremath{\approx}20\phantom{\rule{0.3em}{0ex}}\mathrm{GHz})$. The upper critical field determined from microwave measurements is related to the radius of nonoverlaping vortices, and appears to be larger than the one determined by the transition to the normal state.