Theory of rf magnetic permeability of type-II superconductors in slab geometry with an oblique applied static magnetic field

A self-consistent theory of dynamic vortex response in the linear regime is extended to describe (a) the rf complex magnetic permeability μ̃ suitable for slab geometry and (b) the complicating effect of an oblique applied static magnetic field. The resulting theory, which is expected to be valid over a broad range of static-field magnitude and of frequency, for temperatures from absolute zero through the transition temperature, and for all angles of applied static field with respect to the superconductor surface and microwave field, includes in a unified manner vortex pinning, flux flow, and flux creep by using the complex dynamic vortex mobility. In particular, we show how μ̃ depends upon the magnitude and direction of the internal magnetic induction ${\mathbf{B}}_0$ generated by a uniform array of vortices in the superconductor, and we give the corresponding numerical results.