Domain distributions in tetragonal ferroelectric thin films probed by optical second harmonic generation

Controlling the domain arrangement in a ferroelectric material is the key to accessing its functional properties. However, when a ferroelectric thin film is inserted into a multilayer device architecture, conventional characterization techniques provide limited access to the buried distribution of polar states. Here we show that a combination of nondestructive remote probing by nonlinear optics and symmetry analysis allows the unique distinction of the polar orientations coexisting in tetragonal ferroelectric films. We quantify the volumetric ratio between in-plane and out-of-plane polarized domains, and we further illustrate that our approach incorporates the strain-induced changes to the nonlinear susceptibility tensor. We perform the experiment on $\mathrm{Pb}({\mathrm{Zr}}_{0.2}{\mathrm{Ti}}_{0.8}){\mathrm{O}}_{3}$ thin films, but the generality of the approach permits its extension to other ferroelectric materials.