LAUSR

We use polarized light microscopy in situ with an externally applied electric field to induce square-net birefringence patterns in top-seeded single crystals of barium titanate above the Curie temperature (${T}_{C}$). The patterns occur under a wide range of electric field magnitudes larger than $\ensuremath{\sim}0.2$ kV/mm and at temperatures up to $6{\phantom{\rule{0.16em}{0ex}}}^{\ensuremath{\circ}}\mathrm{C}$ above ${T}_{C}$. We mapped this behavior on a pseudophase diagram showing the region in electric field and temperature space where this domain configuration is stable. We observed the electric field induced transformation into the periodically ordered structure from both the cubic structure above ${T}_{C}$ and the tetragonal structure below ${T}_{C}$. Synchrotron x-ray reciprocal space maps indicate the presence of ferroelastic domains perpendicular to the electric field direction at a range of electric field magnitudes similar to those required to induce the periodic domain ordering we observe using polarized light microscopy. Combined with a simple model of the optical retardation, we show that the periodic domain ordering responsible for the square-net birefringence occurs only at the surfaces of the crystals and that these domain structures are unexpectedly invariant with respect to the electric field that induces them.