We theoretically study origins of the ferroelectricity in the multiferroic phases of the rare-earth (R) Mn perovskites, RMnO3, by constructing a realistic spin model including the spin-phonon coupling, which reproduces the entire experimental phase diagram in the plane of temperature and Mn-O-Mn bond angle for the first time. Surprisingly we reveal a significant contribution of the symmetric (S•S)-type magnetostriction to the ferroelectricity even in a spin-spiral-based multiferroic phase, which can be larger than the usually expected antisymmetric (S×S)-type contribution. This explains well the nontrivial behavior of the electric polarization. We also predict the noncollinear deformation of the E-type spin structure and a wide coexisting regime of the E and spiral states, which resolve several experimental puzzles.
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