  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.
