  The degenerate Blume-Emery-Griffiths model for martensitic transformations is
extended by including both structural and magnetic degrees of freedom in order
to elucidate premartensitic effects. Special attention is paied to the effect
of the magnetoelastic coupling in Ni2MnGa. The microscopic model is constructed
and justified based on the analysis of the experimentally observed strain
variables and precursor phenomena. The description includes the (local)
tetragonal distortion, the amplitude of the plane-modulating strain, and the
magnetization. The model is solved by means of mean-field theory and Monte
Carlo simulations. The results show that a variety of premartensitic effects
may appear due to the magnetoelastic coupling. For large values of the
magnetoelastic coupling parameter we find a premartensitic first-order
transition line ending in a critical point. This critical point is responsible
for the existence of large premartensitic fluctuations which manifest as broad
peaks in the specific heat, not always associated with a true phase transition.
The main conclusion is that premartensitic effects result from the interplay
between the softness of the anomalous phonon driving the modulation and the
magnetoelastic coupling. In particular, the premartensitic transition occurs
when such coupling is strong enough to freeze the involved mode phonon.
