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In this proceeding, recent theoretical investigations by the authors on the multiferroic RMnO(3) perovskites are briefly reviewed at first. Using the double-exchange model, the realistic spiral spin order in undoped manganites such as TbMnO(3) and DyMnO(3) is well reproduced by incorporating a weak next-nearest neighbor superexchange (similar to 10% of nearest neighbor superexchange) and moderate Jahn-Teller distortion. The phase transitions from the A-type antiferromagnet (as in LaMnO(3)), to the spiral phase (as in TbMnO(3)), and finally to the E-type antiferromagnet (as in HoMnO(3)), with decreasing size of the R ions, were also explained. Moreover, new results of phase diagram of the three-dimensional lattice are also included. The ferromagnetic tendency recently discovered in the LaMnO(3) and TbMnO(3) thin films is explained by considering the substrate stress. Finally, the relationship between our double-exchange model and a previously used J(1)-J(2)-J(3) model is further discussed from the perspective of spin wave excitations.

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