  The effect of octahedral tilting on the acentric structural transitions in
AGaO$_{3}$/A'GaO$_{3}$ [001], [110], and [111] superlattices (A, A' = La, Pr,
Nd) is studied using density functional theory. We find the displacive
transitions are driven by two octahedral rotations modes (a$^{-}$a$^{-}$c$^{0}$
and a$^{0}$a$^{0}$c$^{+}$ tilting), with amplitudes that depend on the A and A'
chemistry and cation ordering direction. We find the ground states structures
of the [001] and [111] ordered superlattices are polar. The coupling of
octahedral tilting modes through a hybrid improper ferroelectric mechanism
induces the polar displacements and produces the macroscopic electric
polarizations.
