Electron scattering from domain walls in ferromagnetic Luttinger liquids

Abstract

We study the properties of interacting electrons in a one-dimensional conduction band coupled to bulk noncollinear ferromagnetic order. The specific form of noncollinearity 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 $\ensuremath{\lambda}$. 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 $T/J<\mathrm{exp}(\ensuremath{-}\ensuremath{\lambda}/{\ensuremath{\lambda}}_{+})$, with $J$ being the magnetic exchange and ${\ensuremath{\lambda}}_{+}$ the backward scattering length scale. In physical realizations, $\ensuremath{\lambda}\ensuremath{\gg}{\ensuremath{\lambda}}_{+}$ 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.