  The phase transition sequence of SrBi$_2$Ta$_2$O$_9$ is investigated using a
shell model with parameters fitted to first-principles calculations. We show
that the complex interplay between polar and nonpolar instabilities leads to
the presence of two phase transitions, corroborating the existence of an
intermediate orthorhombic paraelectric phase. This phase is characterized by
the rotation of the TaO$_6$ octahedra around the a-axis. We show that this
phase can be also detected from the dielectric response of the material. The
present approach constitutes a powerful tool for a theoretical prediction of
intermediate phases, not yet observed experimentally, in other Aurivillius
compounds.

Materials Science