Non-linear optical probing of strain-enabled ferroelectricity in CaTiO$_{3}$ thin films

First principles calculations predict CaTiO$_{3}$, under tensile strain, to become ferroelectric with a spontaneous polarization of up to 0.5 C/m$^{2}$.~ Comparative second harmonic generation (SHG) studies of a series of strained CaTiO$_{3}$ thin films were undertaken in order to determine their transition temperature and point group symmetry. The epitaxial strain ranged from -1.7{\%} to 3.3{\%}. Symmetry analysis of the SHG polar plots confirms that for the samples under tensile strain, the polarization is along the $<$110$>_{p }$directions and the point group of the ferroelectric phase is \textit{mm2}. SHG ``hysteresis'' loops were also obtained; these show clear switching. The experimental results are in excellent agreement with the first principles calculations predictions, and low temperature dielectric measurements that were performed on the same samples.