Electric Ferro-Axial Moment as Nanometric Rotator and Source of Longitudinal Spin Current

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