  We describe a new mechanism leading to the formation of rational
magnetization plateau phases, which is mainly due to the anharmonic spin-phonon
coupling. This anharmonicity produces plateaux in the magnetization curve at
unexpected values of the magnetization without explicit magnetic frustration in
the Hamiltonian and without an explicit breaking of the translational symmetry.
These plateau phases are accompanied by magneto-elastic deformations which are
not present in the harmonic case.
