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Lattice modulation expected for various types of spiral magnetic ordering with a propagation vector Q m is discussed in terms of the symmetric ( S i · S j type) and antisymmetric ( S i × 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 2 Q m modulation in lattice, due to the symmetric and antisymmetric interactions. This theoretical prediction was experimentally confirmed for a transverse elliptical antiferromagnet (Tb,Dy)MnO 3 and a transverse conical ferrimagnet CoCr 2 O 4 , both accompanied by ferroelectricity (lattice deformation with Q =0) as well.
Arima et al. (Tue,) studied this question.
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