Roles of Bond Alternation in Magnetic Phase Diagram of RMnO3

In order to investigate the nature of the antiferromagnetic structures in perovskite RMnO3, we study a Heisenberg J(1)-J(2) model with bond alternation using analytical and numerical approaches. The magnetic phase diagram which includes incommensurate spiral states and commensurate collinear states is reproduced. We discuss that the magnetic structure with spin up arrow up arrow down arrow down arrow configuration (E-type structure) and the ferroelectricity emerge cooperatively to stabilize this phase. Magnetoelastic couplings are crucial to understand the magnetic and electric phase diagram of RMnO3.