  We use molecular dynamics simulations to understand the mechanisms of
polarization switching in ferroelectric BaTiO$_3$ achieved with external
electric field. For tetragonal and orthorhombic ferroelectric phases, we
determine the switching paths, and show that polarization rotation through
intermediate monoclinic phases (a) facilitates switching at low fields (b) is
responsible for a sharp anisotropy in polarization switching. We develop
understanding of this through determination of detailed electric
field-temperature phase diagrams, that are fundamental to technological
applications based on electromechanical and switching response of
ferroelectrics.
