Domain-wall profile in the presence of anisotropic exchange interactions: Effective on-site anisotropy

TL;DR

This paper demonstrates that anisotropic exchange interactions in a D-dimensional XXZ ferromagnetic model induce a D-dependent effective on-site anisotropy, affecting domain wall profiles and their contribution to magnetoresistance.

Contribution

It introduces a new effective on-site anisotropy term arising from exchange anisotropy, altering the domain wall profile in higher dimensions.

Findings

Effective on-site anisotropy depends on system dimensionality.

Derived a generalized domain wall profile beyond the standard Landau-Lifshitz form.

Results agree with previous Monte Carlo simulations.

Abstract

Starting from a D-dimensional XXZ ferromagnetic Heisenberg model in an hypercubic lattice, it is demonstrated that the anisotropy in the exchange coupling constant leads to a D-dependent effective on-site anisotropy interaction often ignored for D>1. As a result the effective width of the wall depends on the dimensionality of the system. It is shown that the effective one-dimensional Hamiltonian is not the one-dimensional XXZ version as assumed in previous theoretical work. We derive a new expression for the wall profile that generalizes the standard Landau-Lifshitz form. Our results are found to be in very good agreement with earlier numerical work using the Monte Carlo method. Preceding theories concerning the domain wall contribution to magnetoresistance have considered the role of D only through the modification of the density of states in the electronic band structure. This Brief Report reveals that the wall profile itself contains an additional D dependence for the case of anisotropic exchange interactions.