Spin-lattice coupling in ferroelectric spiral magnets:: Comparison between the cases of (Tb,Dy)MnO3 and CoCr2O4

Lattice modulation expected for various types of spiral magnetic ordering with a propagation vector Q(m) is discussed in terms of the symmetric ((SiSj)-S-. type) and antisymmetric (S-i x S-j type) exchange interactions between neighboring spins (S-i and S-j). We show that the conical ordering causes the superlattice modulation with Q(m) via the antisymetric interaction, while the elliptical deformation of spiral induces a 2Q(m) modulation in lattice, due to the symmetric and antisymmetric interactions. This theoretical prediction was experimentally confirmed for a transverse elliptical antiferromagnet (Tb,Dy)MnO3 and a transverse conical ferrimagnet CoCr2O4, both accompanied by ferroelectricity (lattice deformation with Q = 0) as well.