Scattering of Conduction Electrons by a Ferromagnetic Domain Wall

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 Schrödinger equation for conduction electrons. This equation coincides with a conventional phenomenological Schrödinger equation which was derived in a classical treatment of spins of a domain wall. By solving the Schrödinger 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.