  In order to investigate nature of the antiferromagnetic structures in
perovskite RMnO3, we study a Heisenberg J1-J2 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 up-up-down-down spin 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.
