Andreev Reflection and Spin Injection into $s-$ and $d-$wave Superconductors

TL;DR

This paper investigates how spin injection affects superconductors with different pairing symmetries, highlighting the roles of boundary and bulk transport, with implications for high-temperature superconductor experiments.

Contribution

It provides a detailed analysis of spin injection effects in $s$- and $d$-wave superconductors, emphasizing the dependence on boundary and bulk properties and simplifying conditions.

Findings

Andreev reflection influences magnetization, spin current, and boundary voltage differently.

In certain limits, quantities depend only on bulk spin transport properties.

Results have implications for interpreting spin injection experiments in high-$T_c$ cuprates.

Abstract

We study the effect of spin injection into $s-$ and $d-$wave superconductors, with an emphasis on the interplay between boundary and bulk spin transport properties. The quantities of interest include the amount of non-equilibrium magnetization ($m$), as well as the induced spin-dependent current ($I_s$) and boundary voltage ($V_s$). In general, the Andreev reflection makes each of the three quantities depend on a different combination of the boundary and bulk contributions. The situation simplifies either for half-metallic ferromagnets or in the strong barrier limit, where both $V_s$ and $m$ depend solely on the bulk spin transport/relaxation properties. The implications of our results for the on-going spin injection experiments in high $T_c$ cuprates are discussed.