We consider Gaussian fluctuations about domain walls embedded in one- or two-dimensional spin lattices. Analytic expressions for the free energy of one domain wall are obtained. From these, the temperature dependence of experimentally relevant spatia
l scales -- i.e., the correlation length for spin chains and the size of magnetic domains for thin films magnetized out of plane -- are deduced. Stability of chiral order inside domain walls against thermal fluctuations is also discussed.
We discuss time-quantified Monte-Carlo simulations on classical spin chains with uniaxial anisotropy in relation to static calculations. Depending on the thickness of domain walls, controlled by the relative strength of the exchange and magnetic anis
otropy energy, we found two distinct regimes in which both the static and dynamic behavior are different. For broad domain walls, the interplay between localized excitations and spin waves turns out to be crucial at finite temperature. As a consequence, a different protocol should be followed in the experimental characterization of slow-relaxing spin chains with broad domain walls with respect to the usual Ising limit.
