  Recent developments have led to an explosion of activity on skyrmions in
three-dimensional (3D) chiral magnets. Experiments have directly probed these
topological spin textures, revealed their nontrivial properties, and led to
suggestions for novel applications. However, in 3D the skyrmion crystal phase
is observed only in a narrow region of the temperature-field phase diagram. We
show here, using a general analysis based on symmetry, that skyrmions are much
more readily stabilized in two-dimensional (2D) systems with Rashba spin-orbit
coupling. This enhanced stability arises from the competition between field and
easy-plane magnetic anisotropy and results in a nontrivial structure in the
topological charge density in the core of the skyrmions. We further show that,
in a variety of microscopic models for magnetic exchange, the required
easy-plane anisotropy naturally arises from the same spin-orbit coupling that
is responsible for the chiral Dzyaloshinskii-Moriya interactions. Our results
are of particular interest for 2D materials like thin films, surfaces, and
oxide interfaces, where broken surface-inversion symmetry and Rashba spin-orbit
coupling naturally lead to chiral exchange and easy-plane compass anisotropy.
Our theory gives a clear direction for experimental studies of 2D magnetic
materials to stabilize skyrmions over a large range of magnetic fields down to
T=0.
