Electron scattering from domain walls in ferromagnetic Luttinger liquids

TL;DR

This paper investigates how electron interactions and ferromagnetic domain walls in one-dimensional systems influence electronic phases, revealing that forward scattering dominates at higher temperatures, leading to charge conduction but spin insulation.

Contribution

It introduces a detailed analysis of electron scattering by domain walls in Luttinger liquids, highlighting the dominance of forward scattering and its impact on low-temperature phases.

Findings

Backward scattering affects low-temperature physics only at very low temperatures.

Forward scattering can induce a phase with charge conduction but spin insulation.

Interaction modifies spin and charge densities around the domain wall.

Abstract

We study the properties of interacting electrons in a one-dimensional conduction band coupled to bulk non-collinear ferromagnetic order. The specific form of non-collinearity we consider is that of an extended domain wall. The presence of ferromagnetic order breaks spin-charge separation and the domain wall introduces a spin-dependent scatterer active over the length of the wall l. Both forward and backward scattering off the domain wall can be relevant perturbations of the Luttinger liquid and we discuss the possible low temperature phases. Our main finding is that backward scattering, while determining the ultimate low temperature physics, only becomes important at temperatures T/J < exp(-l/l_+) with J being the magnetic exchange and l_+ the backward scattering length scale. In physical realizations, l >> l_+ and the physics will be dominated by forward scattering which can lead to a charge conducting but spin insulating phase. In a perturbative regime at higher temperatures we furthermore calculate the spin and charge densities around the domain wall and quantitatively discuss the interaction induced changes.