Emergence of complex polar order in asymmetric PbTiO$_{\mathrm{3}}$/SrTiO$_{\mathrm{3}}$ superlattices

Recent work has shown the formation of three-dimensional polar vortices in ferroelectric/paraelectric (PbTiO$_{\mathrm{3}})_{n}$/(SrTiO$_{\mathrm{3}})_{n} $superlattices. This novel phase is stabilized by the interplay of lattice, charge, and orbital degrees of freedom. In this work, we employ a systematic study of the electrical polarization in asymmetric superlattices of PbTiO$_{\mathrm{3}}$ and SrTiO$_{\mathrm{3}}$ grown by pulsed laser deposition. In (PbTiO$_{\mathrm{3}})_{m}$/(SrTiO$_{\mathrm{3}})_{n}$ superlattices, phase-field modeling predicts a systemic evolution of the polarization state in the superlattice as a function of SrTiO$_{\mathrm{3}}$ thickness. We will present results of a combined experimental-theoretical study of the emergence of complex topologies of electrical polarization. To study superlattices as a function of SrTiO$_{\mathrm{3}}$ thickness, we map the electrical polarization using high-resolution scanning transmission electron microscopy in conjunction with piezoresponse force microscopy studies of the ferroelectric domain structures.