  Multiferroic BiFeO$_3$ (BFO) possesses a rich phase diagram that allows
strain tuning of its properties in thin-film form. In particular, at large
compressive strain, a supertetragonal (T) phase with giant polarization is
stabilized over the more common rhombohedral (R) structure. To utilize the
functionality of such metastable BFO phases in device applications, it is
essential to understand the ferroelectric phase evolution upon insertion in
nanoscale heterostructures. Here, we explore the emergence of ferroelectric
phases close to the morphotropic phase boundary in compressively strained BFO
during thin-film growth using in-situ optical second harmonic generation. We
find that the epitaxial films form at the growth temperature in the ideal T
phase without critical thickness for the polarization. Signatures of T-like and
R-like monoclinically distorted phases only appear upon sample cooling. We
furthermore demonstrate a robustness of single-domain polarization in the
high-temperature T phase during the growth of capacitor-like
metal|ferroelectric|metal heterostructures. Here, a reduction in tetragonality
of the T phase, rather than domain formation, lowers the electrostatic energy.
At this lower tetragonality, density-functional calculations and scanning
transmission electron microscopy point to the stabilization of a new metastable
R-like monoclinic structure upon cooling the heterostructure down to room
temperature. Our results thus show that the combination of strain and
electrostatic phase stabilization in BFO heterostructures yields a prominent
platform for exploring ferroelectric phases and realizing ultrathin
ferroelectric devices.
