  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.
