The modulation of the next-nearest-neighbor spin interaction in RMnO3-type manganites is considered and its effect on the multiferroic behaviors is investigated within the framework of classical Heisenberg model using Monte Carlo simulation. Two types of the modulations, i.e., the symmetric perturbations in which the interactions over the lattice are symmetrically modulated with an equal distribution to maintain the mean interaction invariant and the asymmetric perturbations in which the interactions over the lattice are randomly modulated with variable mean interaction, are taken into account. It is shown that both the types of modulations can drive the reorientation of the spiral spin order and thus lead to the coexistence of two cycloid-phases within appropriate magnitudes of modulation. The two multiferroic phase coexistence can be understood as the consequence of the competition between the single-ion anisotropy and the Dzyaloshinskii-Mariya interaction. A comparison of the simulated results with recent relevant experiments on multiferroic manganites is also presented. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4707756]
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