Role of a spin-flip scatterer in a magnetized Luttinger liquid

TL;DR

This paper investigates how localized magnetic fields affect spin-dependent electron scattering in a magnetized one-dimensional Luttinger liquid, revealing fixed points with spin-flip and spin-preserving reflection behaviors and potential control mechanisms.

Contribution

It introduces a renormalization group analysis of spin-dependent scattering in a magnetized Luttinger liquid, identifying fixed points and the effects of potential scattering and domain walls.

Findings

Two zero-temperature fixed points: spin-preserving and spin-flip reflection.

Finite spin current can occur without charge current at zero temperature.

Potential scattering stabilizes the spin-flip insulator phase, controllable via external gates.

Abstract

We study the spin-dependent scattering of charge carriers in a magnetized one dimensional Luttinger liquid from a localized non-homogeneous magnetic field, which might be brought about by the stray field of magnetic tip near a uniform liquid, or by a transverse domain wall (DW) between two oppositely magnetized liquids. From a renormalization group treatment of the electron interactions we deduce scaling equations for the transmission and reflection amplitudes as the bandwidth is progressively reduced to an energy scale set by the temperature. The repulsive interactions dictate two possible zero temperature insulator fixed points: one in which electrons are reflected in the same spin channel and another where the electron spin is reversed upon reflection. In the latter case, a finite spin current emerges in the absence of a charge current at zero temperature and the Friedel oscillations form a transverse spiraling spin density. Adding a purely potential scattering term has no effect on the fixed points of a uniformly magnetized liquid. For a DW we find that the introduction of potential scattering stabilizes the spin-flip insulator phase even if the single-particle spin-flip scattering produced by the DW is arbitrarily weak. The potential can be induced externally, e.g. by a local gate voltage or a constriction, providing a means for controlling the transport properties of the wire.