Current noise generated by spin imbalance in presence of spin relaxation

TL;DR

This paper models and calculates the shot noise generated by spin imbalance in a diffusive conductor with spin relaxation, revealing how noise depends on lead magnetization and conductor length.

Contribution

It introduces a theoretical model for current noise due to spin imbalance in a three-terminal setup considering spin relaxation effects.

Findings

Shot noise increases with spin relaxation.

Noise doubles when conductor length exceeds spin relaxation length.

Parallel magnetization leads to finite shot noise at the normal lead.

Abstract

We calculate current (shot) noise in a metallic diffusive conductor generated by spin imbalance in the absence of a net electric current. This situation is modeled in an idealized three-terminal setup with two biased ferromagnetic leads (F-leads) and one normal lead (N-lead). Parallel magnetization of the F-leads gives rise in spin-imbalance and finite shot noise at the N-lead. Finite spin relaxation results in an increase of the shot noise, which depends on the ratio of the length of the conductor ($L$) and the spin relaxation length ($l_s$). For $L\gg l_s$ the shot noise increases by a factor of two and coincides with the case of the anti-parallel magnetization of the F-leads.