“…Linear magnetoelectricity along z in Cr 2 O 3 , which we discussed earlier, is one example, and further examples of our approach using the tables of dot and cross products, practically handy for the discovery of new phenomena in low-symmetry materials, are discussed in the following. 'toroidal moment + a canted moment', and 'magnetic quadrupole moment + alternating canted moments', respectively, and all have SOS with C. Helical spin states have been observed in numerous magnets such as centrosymmetric compounds such as YMn 6 Sn 6 [20] Gd 2 PdSi 3 [21], MnP [22], and some rare earth metals [23] and crystallographically-chiral compounds such as Co 7 Zn 7 Mn 6 [24], MnSi [25], MnGe [26], Fe 1−x Co x Si [27] with B20 structure, Cu 2 OSeO 3 [28], Cr 1/3 TaS 2 [29], etc 'toroidal moment + a canted moment' has been observed in crystallographically-chiral BaCoSiO 4 [30], and 'magnetic quadrupole moment + alternating canted moments', has been reported in crystallographicallychiral Pb(TiO)Cu 4 (PO 4 ) 4 [31] and Er 2 Ge 2 O 7 [32]. Note that both helical spin state and 'toroidal moment + a canted moment' are 1D objects, and belong to C, but 'magnetic quadrupole moment + alternating canted moments' is 1D objects and belong to C. It turns out that circularly polarized light and vortex light beams with orbital angular momentum are, in fact, chiral (i.e.…”