A theoretical study of a possible model of paramagnetic alums at low temperatures

Abstract

An attempt is made to examine theoretically the properties of paramagnetic alums at low temperatures. The model taken is a lattice of freely suspended magnets, all interactions except purely magnetic being neglected. Even with this simplification it is impossible at present to make rigorous calculations of the partition function, either on classical or quantum lines. A simple model is proposed, which is really a generalization of the Bragg - Williams theory enabling one to take account of the effect of a magnetic field. The few configurations whose energies are known are used to fix arbitrary constants in the expression assumed for the energy. The theory predicts that the state of lowest energy is either a spontaneously magnetized, state for a long thin specimen, or a state in which alternate rows of magnets point in opposite directions for a sphere, spontaneous magnetization appearing in an ellipsoid with an eccentricity greater than a certain critical value. The transition curve bounding the region in which the antiparallel state is stable consists partly of a line of Curie points corresponding to transitions of the second, order, passing smoothly into a line of critical points corresponding to a transition of the first order. The effect of shape on the magnetic properties of the specimen seems to be experimentally verified, but the rough nature of the theory prevents it being more than qualitative.