Fig. 6
From: Broken symmetries, non-reciprocity, and multiferroicity
Different entities behave similarly under all five symmetry operations (translation, rotation, mirror reflection, space inversion and time reversal) in terms of invariance (whether it changes or is invariant). a The handedness of helical spins behaves identically with that of chirality with chiral axis along the helical axis. b Cycloidal spins act similar to polarization in the cycloidal plane and perpendicular to the cycloidal modulation direction. c Ferro-rotation, combined with helical spins with helical axis along the ferro-rotational axis, behaves similar to polarization along the ferro-rotational axis. d Ferro-rotation, combined with polarization along the ferro-rotational axis, acts similar to chirality with chiral axis along the ferro-rotational axis. e Ferro-toroidal moment behaves similar to velocity (linear momentum, wavevector) under all symmetry operations, which is the origin of common non-reciprocity in ferro-toroidal materials
