  The revisited theoretical phase diagrams for thin films of cubic helimagnets
with the easy-plane anisotropy are shown to have different topology as
previously reported [Phys. Rev. B 85, 094429 (2012)]. For both in-plane and
out-of-plane directions of an applied magnetic field, the phase diagrams
exhibit extensive areas of stable skyrmions, which overlap for a wide range of
anisotropy parameters. Although the existence of the out-of-plane skyrmions was
contradicted within the previous theoretical models, we prove that additional
surface twists lead to their stability, while the moderate easy-plane
anisotropy increases the stability range of in-plane skyrmions. Moreover, the
interplay between the anisotropy and the surface twists gives rise to a stable
spiral state canted with respect to the surfaces. Being absent in bulk
helimagnets, this oblique spiral occupies vast areas at the phase diagrams in
thin-film nanosystems and serves as a connecting-link between cones and
helicoids. Our theory gives clear directions for renewed experimental studies
of in-plane and out-of-plane skyrmions in epitaxial MnSi(111)/Si(111) thin
films.
