Scattering of Conduction Electrons by a Ferromagnetic Domain Wall

TL;DR

This paper analytically derives and numerically solves an effective Schrödinger equation to study how conduction electrons scatter off a ferromagnetic domain wall modeled by the XXZ quantum spin chain, revealing energy-dependent transmission properties.

Contribution

It provides an exact analytical derivation of the effective electron Schrödinger equation in a quantum spin chain domain wall and numerically investigates the transmission coefficient.

Findings

Transmission coefficient vanishes at low electron energy.

Effective Schrödinger equation matches classical phenomenological models.

Numerical results depend on Hund coupling and anisotropy.

Abstract

We study the scattering of an electron by a ferromagnetic domain wall of the quantum Heisenberg-Ising model (XXZ model) with certain boundary conditions. The spin of the electron interacts with the spins of the XXZ model by the Hund coupling. Using the exact domain wall ground states of the XXZ model, we analytically obtain the exact effective Schr\"odinger equation for conduction electrons. This equation coincides with a conventional phenomenological Schr\"odinger equation which was derived in a classical treatment of spins of a domain wall. By solving the Schr\"odinger equation numerically, we have calculated the transmission coefficient which is a function of the Hund coupling and of the anisotropy of the XXZ model. It turns out that the transmission coefficient is vanishing in the low energy limit for the electron.