  Controlling the preferred direction of the magnetic moments is essential for
the design of spintronic devices based on ultrathin films and heterostructures.
As the film thickness or the temperature is increased, the easy anisotropy axis
is typically reoriented from an out-of-plane direction preferred by surface and
interface energy contributions to an in-plane alignment favored by the volume
anisotropy terms. We study the temperature-driven spin reorientation transition
in two atomic layers of Fe on W(110) using well-tempered metadynamics
simulations based on a spin model parametrized by ab initio calculations and
find that the transition only takes place in the presence of the
Dzyaloshinsky--Moriya interaction (DMI). This demonstrates that the chiral DMI
does not only differentiate between noncollinear spin structures of different
rotational senses, but it also influences the magnetic orientation of collinear
magnetic configurations.
