Analysis of the measurements of anisotropic a.c. vortex resistivity in tilted magnetic fields

Measurements of the high-frequency complex resistivity in superconductors are a tool often used to obtain the vortex parameters, such as the vortex viscosity, the pinning constant and the depinning frequency. In anisotropic superconductors, the extraction of these quantities from the measurements faces new difficulties due to the tensor nature of the electromagnetic problem. The problem is specifically intricate when the magnetic field is tilted with respect to the crystallographic axes. Partial solutions exist in the free-flux-flow (no pinning) and Campbell (pinning dominated) regimes. In this paper we develop a full tensor model for the vortex motion complex resistivity, including flux-flow, pinning, and creep. We give explicit expressions for the tensors involved. We obtain that, despite the complexity of the physics, some parameters remain scalar in nature. We show that under specific circumstances the directly measured quantities do not reflect the true vortex parameters, and we give procedures to derive the true vortex parameters from measurements taken with arbitrary field orientations. Finally, we discuss the applicability of the angular scaling properties to the measured and transformed vortex parameters and we exploit these properties as a tool to unveil the existence of directional pinning.