  In this paper, we explore magneteoelectricity of rare earth orthochromites
from the symmetry point of view. We determine the principal structural order
parameters and find their couplings with ferroelectric and magnetic orderings.
Our calculations showed that electric dipole moments emerge in the vicinity of
Cr3+ ions in the unit cell of RCrO3 due to the displacements of oxygen ions
from their highly symmetric positions in the parent perovskite phase
(structural instability). We find that the electric dipole moments are arranged
in an antiferroelectric mode, so, in essence, RCrO3 are antiferroelectric
materials. By classifying the order parameters according to the irreducible
representations of the RCrO3 symmetry group (D2h16), we determine the possible
couplings between distortive, ferroelectric and magnetic orderings and explore
the emerging magnetoelectric structures in these terms. Our analysis makes it
possible to explain experimentally observed polarization reversal and the
concomitant reorientation of spins in a series of RCrO3 compounds and to
predict the possible scenarios of phase transitions in RCrO3.
