  It has recently been shown that domain walls in ferromagnets can be moved in
the presence of thermal gradients. In this work we study the motion of narrow
domain walls in low-dimensional systems when subjected to thermal gradients.
The system chosen is a monolayer of Fe on W(1 1 0) which is known to exhibit a
large anisotropy while having a soft exchange, resulting in a very narrow
domain wall. The study is performed by means of atomistic spin dynamics
simulations coupled to first-principles calculations. By subjecting the systems
to a thermal gradient we observe a temperature dependent movement of the domain
wall as well as changes of the spatial magnetization profile of the system. The
thermal gradient always makes the domain wall move towards the hotter region of
the sample with a velocity proportional to the gradient. The material specific
study is complemented by model simulations to discern the interplay between the
thermal gradient, magnetic anisotropy and the exchange interaction, and shows
that the larger DW velocities are found for materials with low magnetic
anisotropy. The relatively slow DW motion of the Fe/W(1 1 0) system is hence
primarily caused by its large magnetic anisotropy.
