Probing Ferroelectric Phase Transitions in Barium Titanate Single Crystals via $\it{in-situ}$ Second Harmonic Generation Microscopy

Ferroelectric materials play a crucial role in a broad range of technologies due to their unique properties that are deeply connected to the pattern and behavior of their ferroelectric (FE) domains. Chief among them, barium titanate (BaTiO$_3$; BTO) sees widespread applications such as in electronics but equally is a ferroelectric model system for fundamental research, e.g., to study the interplay of such FE domains, the domain walls (DWs), and their macroscopic properties, owed to BTO's multiple and experimentally accessible phase transitions. Here, we employ Second Harmonic Generation Microscopy (SHGM) to $\it{in-situ}$ investigate the cubic-to-tetragonal (at $\sim$126$^\circ$C) and the tetragonal-to-orthorhombic (at $\sim$5$^\circ$C) phase transition in single-crystalline BTO via 3-dimensional (3D) DW mapping. We demonstrate that SHGM imaging provides the direct visualization of FE domain switching as well as the domain dynamics in 3D, shedding light on the interplay of the domain structure and the phase transition. These results allow us to extract the different transition temperatures locally, to unveil the hysteresis behavior, and to determine the type of phase transition at play (1st/2nd order) from the recorded SHGM data. The capabilities of SHGM in uncovering these crucial phenomena can easily be applied to other ferroelectrics to provide new possibilities for $\it{in-situ}$ engineering of advanced ferroic devices.