Spin Injection into a Luttinger Liquid

TL;DR

This paper investigates how spin injection affects a Luttinger liquid, revealing unique behaviors in spin-dependent signals and implications for experiments in high-temperature superconductors.

Contribution

It provides a theoretical analysis of spin injection into a Luttinger liquid, highlighting differences from Fermi liquids and implications for experimental detection.

Findings

Spin-charge separation influences spin-dependent signals differently.

In the Ohmic regime, spin voltage depends on Luttinger liquid's spin transport.

Results have implications for high-$T_c$ cuprate experiments.

Abstract

We study the effect of spin injection into a Luttinger liquid. The spin-injection-detection setup of Johnson and Silsbee is considered; here spins injected into the Luttinger liquid induce, across an interface with a ferromagnetic metal, either a spin-dependent current ($I_s$) or a spin-dependent boundary voltage ($V_s$). We find that the spin-charge separation nature of the Luttinger liquid affects $I_s$ and $V_s$ in a very different fashion. In particular, in the Ohmic regime, $V_s$ depends on the spin transport properties of the Luttinger liquid in essentially the same way as it would in the case of a Fermi liquid. The implications of our results for the spin-injection-detection experiments in the high $T_c$ cuprates are discussed.