  Hysteretic switching of domain states is a salient character of all ferroic
materials and the foundation for their multifunctional applications.
Ferro-rotational order is emerging as a new type of ferroic order featuring
structural rotations, but its controlled switching remains elusive due to its
invariance under both time reversal and spatial inversion. Here, we demonstrate
electrical switching of ferro-rotational domain states in nanometer-thick
1T-TaS$_2$ crystals in its charge-density-wave phases. Cooling from the
high-symmetry phase to the ferro-rotational phase under an external electric
field induces domain state switching and domain wall formation, realized in a
simple two-terminal configuration using a volt-scale voltage. Although the
electric field does not couple with the order due to symmetry mismatch, it
drives domain wall propagation to give rise to reversible, durable, and
nonvolatile isothermal state switching at room temperature. These results pave
the path for manipulation of the ferro-rotational order and its nanoelectronic
applications.
