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 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 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.