Coupling between lattice vibrations and magnetism in ising-like systems

In this paper the bond proportion model is introduced as a prototype of a system with coupled magnetic and vibrational degrees of freedom. This model is generalized within the framework of cluster expansions in order to achieve invariance of the potential energy to a rotation of the crystal. First, the original bond proportion model is solved in the mean-field approximation and by means of numerical simulations. It has been found that the temperature and the smoothness of the magnetic phase transition depend on the strength of the magnetoelastic coupling. For a large enough entropy difference between the magnetic phases the phase transition becomes first order. This is evidenced by means of the computation of the magnetization, the elastic constants, and the total entropy. The numerical simulation of the modified bond proportion model has revealed significant differences with respect to the bond proportion model in the heat capacity around the phase transition and, consequently, in the entropy difference between the magnetic phases. Small differences in the elastic constants are also detected.