  We study ferroelectricity in thin films of pseudo-proper ferroelectrics such
as the so-called spiral multiferroics. We find that this type of
ferroelectricity stands better against depolarizing fields than conventional
one. Its single-domain state can be easily preserved by metallic electrodes
even in ultrathin films. In fact, single-domain ferroelectricty can be
generated as a metastable state in the absence of electrodes. We also find a
new regime of small thickness where unscreened films develop unusual
multi-domain states with properties determined by non-electrostatic boundary
conditions.
