Origin of multiferroic spiral spin order in the RMnO3 perovskites

The origin of the spiral spin order in perovskite multiferroic manganites RMnO3 (R=Tb or Dy) is here investigated using a two e(g)-orbital double-exchange model. Our main result is that the experimentally observed spiral phase can be stabilized by introducing a relatively weak next-nearest-neighbor superexchange coupling (similar to 10% of the nearest-neighbor superexchange). Moreover, the Jahn-Teller lattice distortion is also shown to be essential to obtain a realistic spiral period. Supporting our conclusions, the generic phase diagram of undoped perovskite manganites is obtained using Monte Carlo simulations, showing phase transitions from the A-type antiferromagnet, to the spiral phase, and finally to the E-type antiferromagnet, with decreasing size of the R ions. These results are qualitatively explained by the enhanced relative intensity of the superexchanges.