  A toroidal dipole moment appears independent of the electric and magnetic
dipole moment in the multipole expansion of electrodynamics. It arises
naturally from vortex-like arrangements of spins. Observing and controlling
spontaneous long-range orders of toroidal moments are highly promising for
spintronics but remain challenging. Here we demonstrate that a vortex-like spin
configuration with a staggered arrangement of toroidal moments, a ferritoroidal
state, is realized in a chiral triangular-lattice magnet BaCoSiO4. Upon
applying a magnetic field, we observe multi-stair toroidal transitions
correlating directly with metamagnetic transitions. We establish a
first-principles microscopic Hamiltonian that explains both the formation of
toroidal states and the metamagnetic toroidal transition as a combined effect
of the magnetic frustration and the Dzyaloshinskii-Moriya interactions allowed
by the crystallographic chirality in BaCoSiO4.
