Microwave Surface Resistance of Type-II Superconductors in the Vortex State

We have measured the microwave surface resistance of various Nb-Ta and Pb-In superconducting alloys using a derivative technique to determine its rate of change with field near $H_{c2\mathrm{}}$. Previous dc measurements of this slope have generally been interpreted to show agreement with the Caroli-Maki theory, which Thompson has found to be incomplete. Our measurements show a region of constant slope somewhat below $H_{c2\mathrm{}}$ with a magnitude in agreement with the dc results, but also show that the slope increases rapidly to approach the Thompson values in the limit $H\to H_{c2\mathrm{}}$. Theoretical arguments are presented indicating why the two theories can have different regions of validity.