Polarization rotation transitions in anisotropically strained $SrTiO3$ thin films

Commensurately strained epitaxial $SrTiO3$ thin films on a $GdScO3$ substrate with anisotropic in-plane tensile strains of 1.46% and 1.59% were grown. By using optical second harmonic generation and polarization measurements, a ferroelectric transition from a tetragonal $4∕mmm$ phase to a ferroelectric $mm2$ phase at $∼400K$ and an antiferrodistortive transition to a multiferroic phase at $150–175K$ are observed, which are in agreement with thermodynamic calculations. In addition, a series of polarization rotation transitions between $⟨100⟩p$ to $⟨l00⟩p$ $(0<l<1)$ is observed in the $4–400K$ temperature range.