Influence of pointlike disorder on the guiding of vortices and the Hall effect in a washboard planar pinning potential
Explicit current-dependent expressions for anisotropic longitudinal and transverse nonlinear magnetoresistivities are represented and analyzed on the basis of a Fokker-Planck approach for two-dimensional single-vortex dynamics in a washboard pinning potential in the presence of pointlike disorder. Graphical analysis of the resistive responses is presented both in the current-angle coordinates and in the rotating current scheme. The model describes nonlinear anisotropy effects caused by the competition of pointlike (isotropic) and anisotropic pinning. Nonlinear guiding effects are discussed, and the critical current anisotropy is analyzed. Gradually increasing the magnitude of isotropic pinning force this theory predicts a gradual decrease of the anisotropy of the magnetoresistivities. The physics of the transition from the new scaling relations for anisotropic Hall resistance in the absence of pointlike pins to the well-known scaling relations for the pointlike disorder is elucidated. This is discussed in terms of a gradual isotropization of the guided vortex motion, which is responsible for the existence in a washboard pinning potential of new (with respect to magnetic field reversal) Hall voltages. It is shown that whereas the Hall conductivity is not changed by pinning, the Hall resistivity can change its sign in some current-angle range due to presence of the competition between $i$ and $a$ pins.