Anisotropy and effective dimensionality crossover of the fluctuation conductivity of hybrid superconductor/ferromagnet structures

TL;DR

This paper investigates how the fluctuation conductivity in a superconductor/ferromagnet structure varies with magnetic domain size and temperature, revealing anisotropic behavior and a crossover in effective dimensionality near the critical temperature.

Contribution

It introduces a detailed analysis of anisotropic fluctuation conductivity in hybrid structures under non-uniform magnetic fields, highlighting the dimensionality crossover and domain size effects.

Findings

Conductivity tensor is highly anisotropic depending on domain size and temperature.

For small domain width, conductivity difference scales as (d/L_{H_0})^4.

For large domain width, a crossover from 2D to 1D fluctuation behavior is observed near T_c.

Abstract

We study the fluctuation conductivity of a superconducting film, which is placed to perpendicular non-uniform magnetic field with the amplitude $H_0$ induced by the ferromagnet with domain structure. The conductivity tensor is shown to be essentially anisotropic. The magnitude of this anisotropy is governed by the temperature and the typical width of magnetic domains $d$. For $d\ll L_{H_0}=\sqrt{\Phi_0/H_0}$ the difference between diagonal fluctuation conductivity components $\Delta\sigma_\parallel$ along the domain walls and $\Delta\sigma_\perp$ across them has the order of $(d/L_{H_0})^4$. In the opposite case for $d\gg L_{H_0}$ the fluctuation conductivity tensor reveals effective dimensionality crossover from standard two-dimensional $(T-T_c)^{-1}$ behavior well above the critical temperature $T_c$ to the one-dimensional $(T-T_c)^{-3/2}$ one close to $T_c$ for $\Delta\sigma_\parallel$ or to the $(T-T_c)^{-1/2}$ dependence for $\Delta\sigma_\perp$. In the intermediate case $d\approx L_{H_0}$ for a fixed temperature shift from $T_c$ the dependence $\Delta\sigma_\parallel(H_0)$ is shown to have a minimum at $H_0\sim\Phi_0/d^2$ while $\Delta\sigma_\perp(H_0)$ is a monotonically increasing function.