Ferro-rotational domain walls revealed by electric quadrupole second harmonic generation microscopy

Domain walls are ubiquitous in materials that undergo phase transitions driven by spontaneous symmetry breaking. Domain walls in ferroics and multiferroics have received tremendous attention recently due to their emergent properties distinct from their domain counterparts, for example, their high mobility and controllability, as well as their potential applications in nanoelectronics. However, it is extremely challenging to detect, visualize and study the ferro-rotational (FR) domain walls because the FR order, in contrast to ferromagnetism (FM) and ferroelectricity (FE), is invariant under both the spatial-inversion and the time-reversal operations and thus hardly couple with conventional experimental probes. Here, an FR candidate $\mathrm{NiTiO_{3}}$ is investigated by ultrasensitive electric quadrupole (EQ) second harmonic generation rotational anisotropy (SHG RA) to probe the point symmetries of the two degenerate FR domain states, showing their relation by the vertical mirror operations that are broken below the FR critical temperature. We then visualize the real-space FR domains by scanning EQ SHG microscopy, and further resolve the FR domain walls by revealing a suppressed SHG intensity at domain walls. By taking local EQ SHG RA measurements, we show the restoration of the mirror symmetry at FR domain walls and prove their unconventional nonpolar nature. Our findings not only provide a comprehensive insight into FR domain walls, but also demonstrate a unique and powerful tool for future studies on domain walls of unconventional ferroics, both of which pave the way towards future manipulations and applications of FR domain walls.