First order transitions in simple magnetic systems

A ferromagnet undergoes a first order transition if the rate of change of the exchange integral with the interatomic distance is strong enough compared to the stiffness. If placed in an external field this transition will take place at a different temperature, and with decreasing discontinuity. Beyond a critical field the substance will stay paramagnetic. The dependence of the critical parameters on the compressibility and the rate of change of the exchange constant is calculated for an Ising-like interaction (long range order only) for spin 1 2, 3 2, 21 2 ∞. The transition curve consists of a single line in the H-T plane. The complete phase diagram is shown for spin equal to three halves. The same model is studied for a two sublattice antiferromagnet with nearest and second nearest neighbor interactions. This model predicts transitions from the paramagnetic to the ferromagnetic state as the temperature is decreased. At a certain field one finds that the substance goes directly from the paramagnetic state to the ferromagnetic state. The phase diagram shows a triple point. An attempt was made to fit the experimental data available for dysprosium. The application of these same ideas to a two sublattice ferromagnet is discussed, and it is shown that no triple point exists in this case.