Origin of the multiferroic spiral spin-order in the RMnO3 perovskites

TL;DR

This study explains the origin of spiral spin-order in RMnO3 multiferroic manganites, highlighting the roles of next-nearest-neighbor superexchange and Jahn-Teller distortions in stabilizing the phase.

Contribution

It demonstrates that weak next-nearest-neighbor superexchange and Jahn-Teller distortions are crucial for stabilizing spiral phases in RMnO3, supported by phase diagram simulations.

Findings

Spiral phase stabilized by ~10% next-nearest-neighbor superexchange.

Jahn-Teller distortion essential for realistic spiral period.

Phase transitions from A-type to spiral to E-type antiferromagnet with decreasing R-ion size.

Abstract

The origin of the spiral spin-order in perovskite multiferroic manganites $R$MnO$_{3}$ ($RE=$ Tb or Dy) is here investigated using a two $e_{\rm g}$-orbitals 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 ($\sim10%$ 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.