(a) Helicoidal spin spiral in which the spin rotation axis and the induced polarization are parallel to the spiral wave vector. (b) Cycloidal spin spiral in which spins (red arrows) rotate around an axis normal to the spiral wave vector Q. The induced electric polarization P is normal to both the wave vector and the spin rotation axis. Green curve is the cyloid. (c) Propellerlike structure of - octahedra in , which changes the rotation direction when the sample is turned around.