Novel magnetic arrangement and structural phase transition induced by spin-lattice coupling in multiferroics

Using an effective Hamiltonian of mutiferroic BiFeO$_3$ (BFO) as a toy model, we explore the effect of the coefficient, C, characterizing the strength of the spin-current interaction, on physical properties. We observe that for larger C values and below a critical temperature, the magnetic moments organize themselves in a novel cycloid which propagates along a low-symmetry direction and is associated with a structural phase transition from polar rhombohedral to a polar triclinic state. We emphasize that both of these magnetic and structural transitions are results of a remarkable self-organization of different solutions of the spin-current model.