  Piezoelectrics interconvert mechanical energy and electric charge and are
widely used in actuators and sensors. The best performing materials are
ferroelectrics at a morphotropic phase boundary (MPB), where several phases can
intimately coexist. Switching between these phases by electric field produces a
large electromechanical response. In the ferroelectric BiFeO$_3$, strain can be
used to create an MPB-like phase mixture and thus to generate large electric
field dependent strains. However, this enhanced response occurs at localized,
randomly positioned regions of the film, which potentially complicates
nanodevice design. Here, we use epitaxial strain and orientation engineering in
tandem - anisotropic epitaxy - to craft a hitherto unavailable low-symmetry
phase of BiFeO$_3$ which acts as a structural bridge between the
rhombohedral-like and tetragonal-like polymorphs. Interferometric displacement
sensor measurements and first-principle calculations reveal that under external
electric bias, this phase undergoes a transition to the tetragonal-like
polymorph, generating a piezoelectric response enhanced by over 200%, and
associated giant field-induced reversible strain. These results offer a new
route to engineer giant electromechanical properties in thin films, with
broader perspectives for other functional oxide systems.
