Nonlinear dynamics of vortices pinned to unidirectional twins

Abstract

The nonlinear resistive properties of superconductors in the mixed state in the presence of a system of unidirectional planar defects (twins) have been investigated theoretically within the framework of the two-dimensional stochastic model of anisotropic pinning based on the Fokker-Planck equations with a concrete form of the pinning potential. These equations allow one to obtain an exact analytical solution of the problem. Formulas are obtained for experimentally observable even and odd (relative to reversal of the direction of the external magnetic field) nonlinear longitudinal and transverse magnetoresistivities ρ ^±_‖,⊥ ( j,t,α,ε) as functions of the transport current density j, temperature t, the angle α between the directions of the current and the twins, and the relative volume fraction ε occupied by the twins. In light of the great variety of types of nonlinear resistive dependences contained in these expressions for ρ ^±_‖,⊥ the most characteristic of them are presented in the form of graphs with commentary. The desired nonlinear dependences ρ ^±_‖,⊥ are linear combinations of the even and odd parts of the function v(j,t, α,ε), which has the sense of the probability of overcoming the potential barrier of the twins; this makes it possible to give a simple physical treatment of the nonlinear regimes. New scaling relations for the Hall conductivity are obtained and investigated which differ from the previously known relations for isotropic pinning. The interaction of vortex motion directed along the twins and the Hall effect is considered for Hall constants which are arbitrary in magnitude and sign, and it is shown that in the case of small Hall viscosity vortex motion directed along the twins has an effect on the odd magnetoresistivities ρ ⁻_‖ and ρ ⁻_⊥ , whereas the reverse effect can be neglected. It is shown that pinning anisotropy is sufficient to manifest the new nonlinear (in the current) magnetoresistivities ρ ⁺_⊥ and ρ ⁻_‖ .