Double-exchange model study of multiferroic $R$MnO$_3$ perovskites

TL;DR

This paper reviews theoretical studies on multiferroic RMnO3 perovskites using a double-exchange model, successfully reproducing complex magnetic orders and explaining phase transitions and thin film behaviors.

Contribution

It demonstrates that the double-exchange model can accurately reproduce spiral spin order and phase transitions in RMnO3, incorporating realistic interactions and substrate effects.

Findings

Reproduces spiral spin order in undoped manganites.

Explains phase transitions with decreasing R ion size.

Accounts for ferromagnetic tendencies in thin films.

Abstract

In this proceeding, recent theoretical investigations by the authors on the multiferroic $R$MnO$_3$ 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 ($\sim10%$ 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.