  TbMnO$_{3}$ films have been grown under compressive strain on (001)-oriented
SrTiO$_{3}$ crystals. They have an orthorhombic structure and display the (001)
orientation. With increasing thickness, the structure evolves from a more
symmetric (tetragonal) to a less symmetric (bulk-like orthorhombic) structure,
while keeping constant the in-plane compression thereby leaving the
out-of-plane lattice spacing unchanged. The domain microstructure of the films
is also revealed, showing an increasing number of orthorhombic domains as the
thickness is decreased: we directly observe ferroelastic domains as narrow as
4nm. The high density of domain walls may explain the induced ferromagnetism
observed in the films, while both the decreased anisotropy and the small size
of the domains could account for the absence of a ferroelectric spin spiral
phase.
