  We investigate the oxygen octahedral rotations that occur in two perovskites,
SrTiO3 and PbTiO3, as a function of applied three-dimensional electric
displacement field, allowing us to map out the phase diagram of rotations in
both the paraelectric and ferroelectric regions of the polar response.
First-principles calculations at fixed electric displacement field are used to
extract parameters of a Landau-Devonshire model that is analyzed to identify
the phase boundaries between different rotational states. The calculations
reveal a rich phase diagram of rotations versus applied field in both SrTiO3
and PbTiO3, although the details are quite different in the two cases.
