Influence of Point-like Disorder on the Guiding of Vortices and the Hall Effect in a Washboard Planar Pinning Potential

TL;DR

This paper develops a Fokker-Planck model to analyze how point-like disorder affects vortex guiding and Hall effect in a washboard pinning potential, revealing nonlinear anisotropic magnetoresistivity and transition behaviors.

Contribution

It introduces a detailed theoretical framework for understanding nonlinear anisotropic magnetoresistivity and Hall effects influenced by point-like disorder in vortex dynamics.

Findings

Gradual decrease of anisotropy with increasing isotropic pinning force

Transition from new to known Hall resistance scaling relations

Hall resistivity can change sign due to pinning competition

Abstract

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 point-like 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 point-like (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 transition from the new scaling relations for anisotropic Hall resistance in the absence of point-like pins to the well-known scaling relations for the point-like disorder is elucidated. This is discussed in terms of a gradual isotropizaton 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.