  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.
