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 $\sim 0.2$ kV/mm and at temperatures up to $6{}^{\circ }\mathrm{C}$ 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.

中文翻译：

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钛酸钡中方网畴图形的热和电场稳定性

我们使用偏光显微镜在外部施加电场的情况下原位使用，以在居里温度以上的钛酸钡的顶晶单晶中诱发方阵双折射图案（${Ť}_C$）。图案出现在大于$〜0.2$ kV / mm，温度高达 $6{}^{\circ }\mathrm{C}$ 以上 ${Ť}_C$。我们将此行为映射到伪相图上，该伪相图显示了该域配置稳定的电场和温度空间中的区域。我们观察到电场感应从上面的立方结构转变成周期有序的结构${Ť}_C$ 和下面的四边形结构 ${Ť}_C$。同步加速器X射线互易空间图表明，在一定的电场强度范围内，垂直于电场方向的铁弹性域的存在与我们使用偏振光显微镜观察到的诱导周期性域有序化所需的电场强度相似。结合光学延迟的简单模型，我们表明负责平方网双折射的周期性畴序仅发生在晶体的表面，并且这些畴结构相对于感应它们的电场出乎意料地不变。