  An electric ferro-axial moment, which is characterized by a nonzero
expectation value of a time-reversal-even axial vector, exhibits distinct
spatial-inversion and time-reversal properties from conventional ferroelectric,
ferromagnetic, and ferro-magnetoelectric orders. Nevertheless, physical
properties characteristic of the electric ferro-axial moment have been obscure
owing to the absence of its conjugate electromagnetic fields. We theoretically
investigate consequences of the presence of the ferro-axial moment on the basis
of the symmetry and microscopic model analyses. We show that atomic-scale
electric toroidal multipoles are the heart of the ferro-axial moment, which act
as a nanometric rotator against external stimuli. Furthermore, we propose an
intrinsic generation of a spin current parallel to an applied electric field in
both metals and insulators. Our results not only provide a deep microscopic
understanding of the role of the ferro-axial moment but also stimulate a new
development for functional materials with use of the electric toroidal moment.
