We calculate the magnetic phases of thin films of helimagnetic materials. T
he surface of the film is perpendicular to the c-axis so that, for H = 0, t
he moments are in the basal plane. We study the effect of external fields,
applied in the basal plane, and find that the field effects are controlled
to a large extent by the c-axis anisotropy. If the c-axis anisotropy is sma
ll, the effect of the external field is to produce small modifications in t
he basal plane projections, which remain nearly in a helical pattern, while
the c-axis components oscillate throughout the film, with the surface regi
ons displaying stronger oscillations. By increasing the external field stre
ngth, this phase evolves to a first order transition to a non-uniform fan p
hase, with major modifications near the surfaces. If the c-axis anisotropy
is strong the out of plane oscillations are inhibited, and depending on the
film thickness, a surface helifan phase is nucleated, starting from the gr
adual alignment of the magnetic moments near the surface region with the ex
ternal field. The phase has twice the period of the helix and nucleates onl
y in films where the thickness fits the double-period structure. (C) 2001 E
lsevier Science B.V. All rights reserved.