Theory of Magnetothermomechanics

We show that in both ferromagnetic and antiferromagnetic systems with weak magnetostrictive coupling the coefficient of thermal expansion gives a useful measure of the magnetic specific heat. We also analyze the strong coupling situation by means of our simplified, but solube model, and find it possible to introduce an effective temperature $T^{*}$ and an effective magnetic susceptibility. The exact pressure dependence of the thermodynamic functions can be found, and the pressure dependence of the Curie temperature is given explicitly. In strong coupling, a novel first-order thermodynamic phase transformation can occur which is manifested by a discontinuity in $T^{*}$ as a function of $T$. An equal area rule for determining the transition is derived, which is reminiscent of the laws of condensation of nonideal gases. It is also shown that in its simple version the theory is not directly applicable to a one-dimensional chain, which is separately analyzed in an Appendix.