Reconstruction of Polarization Vortices by Diffraction Mapping of Ferroelectric PbTiO$_{\mathrm{3}}$/SrTiO$_{\mathrm{3}}$~Superlattice Using a High Dynamic Range Pixelated Detector*

Ferroelectric polarization vortices realized in PbTiO$_{\mathrm{3}}$/SrTiO$_{\mathrm{3}}$ superlattice of complex oxides$^{\mathrm{\thinspace }}$are emerging phenomena that can be used for low-power memory. Here, we apply a high dynamic range electron microscopy pixel array detector (EMPAD) developed at Cornell where convergent beam electron diffraction (CBED) pattern is recorded at 1 ms. Using the EMPAD, we measured \textless P\textgreater of individual diffracted spots where vectorization of \textless Px\textgreater and \textless Py\textgreater reconstructs the polarization vortices at 0.5-1 nm, over an arbitrarily large field of view. Applications of ptychography and careful inspection of \textless P\textgreater help us explore chirality in 3-dimensions and measure the orbital angular momentum of the polarization vortices.