  We study the interplay of structural and polar distortions in hexagonal YMnO3
and short-period PbTiO3/SrTiO3 superlattices by means of first-principles
calculations at constrained electric displacement field D. We find that in
YMnO3 the tilts of the oxygen polyhedra produce a robustly polar ground state,
which persists at any choice of the electrical boundary conditions. Conversely,
in PTO/STO the antiferrodistortive instabilities alone do not break inversion
symmetry, and open-circuit bundary conditions restore a non-polar state. We
suggest that this qualitative difference naturally provides a route to
rationalizing the concept of "improper ferroelectricity" from the point of view
of first-principles theory. We discuss the implications of our arguments for
the design of novel multiferroic materials with enhanced functionalities, and
for the symmetry analysis of the phase transitions.
