For example, in Lvov's model , the Gibbs potential includes Helmholtz free energy, free energy of magnetic subsystem of the crystal, the energy of magnetoelastic coupling
, and mechanical energy, which makes the calibration of model parameters very difficult.
In other words, the magnetoelastic coupling allowed the atoms to undergo an isostructural transition, which has been regarded as the primary source of the magnetoelectric phenomena.
In other words, the disappearance of optical phonon mode might be attributed to the magnetoelastic coupling. In temperature-dependent Raman studies, the lowest frequency [A.sub.1] mode also shows anomaly at [T.sub.N] in YMn[O.sub.3] , ErMn[O.sub.3] , and LuMn[O.sup.3] [80, 82]which support close relation between phonon and spin systems.