Correspondence between microwave and submillimeter absorptivity in epitaxial thin films of ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_7$

We have measured the low-temperature loss in six epitaxial ab-plane films of the high-${\mathit{T}}_{\mathit{c}}$ superconductor ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_7$ over a factor of 2000 in frequency. Submillimeter measurements from 25 to 700 ${\mathrm{cm}}^{\mathrm{-}1}$ were made at 2 K by a direct absorption technique in which the film acts as the absorbing element in a composite bolometric detector. Microwave measurements near 10 GHz (0.3 ${\mathrm{cm}}^{\mathrm{-}1}$) were made on five of the same films by resonance techniques at 4 K. The ∼0.4-μm-thick films were grown epitaxially on ${\mathrm{SrTiO}}_3$, ${\mathrm{LaAlO}}_3$, and MgO by off-axis sputtering and laser deposition. The absorptivities measured for all films studied are qualitatively similar, increasing smoothly with frequency, with no gaplike features below the well-known absorption edge at 450 ${\mathrm{cm}}^{\mathrm{-}1}$. A successful three-parameter fit is obtained for all of our films. This fit can be interpreted either in terms of a weakly coupled grain model or a homogeneous two-fluid model with residual normal conductivity. The fitting parameters correspond to a grain-penetration depth ${\lambda }_{\mathit{g}}$ equal to the muon-spin-relaxation value of 140 nm, and to reasonable grain properties. They also give carrier densities in reasonable agreement with optically determined plasma frequencies and conductivities in agreement with a Kramers-Kronig analysis of the absorptivity data.