Fig. 4

Reciprocity of ferro-rotational (“Yin”-type) materials, including the propagation of objects with angular momentum. See the main text for the definition of “Yin” and “Yang” in this perspective. a Time reversal connects reciprocal situations for an object moving perpendicular to the ferro-rotational plane, so this case is reciprocal. b Even if the ferro-rotational system is ferromagnetic with magnetization (M) along the ferro-rotational axis, it is reciprocal since two reciprocal situations can be connected by a mirror operation. In addition, ferro-rotation, combined with polarization along the ferro-rotational axis, is reciprocal, since time reversal links two relevant reciprocal situations. c However, ferro-rotation, combined with magnetization (M) and polarization along the ferro-rotational axis, can be non-reciprocal since two reciprocal situations cannot be related by any symmetry operation. d An object with non-zero angular momentum moving along the magnetization (M) direction of a ferro(ferri)magnet can be non-reciprocal, since two relevant reciprocal situations cannot be connected by symmetry operations