Magnetic Energy Constants of Dipolar Lattices

In this paper, calculations are presented for the determination of the magnetic energy, assuming dipole-dipole interaction, of a macroscopic crystal possessing paramagnetic ions situated on a definite lattice structure. Parallel and antiparallel configurations are considered as well as specimens of different shapes and lattice structures of various types. It is shown that the configuration of lowest energy cannot be strictly defined but is dependent upon the shape of the specimen. This configuration is an antiparallel one for a sphere but changes to a parallel one for a long slender specimen. The transition between the two configurations appears to take place at a certain critical value of the demagnetization factor. For specimens above this value the theory accounts qualitatively for the low values of the magnetization found experimentally and for the apparent constancy of the Curie point with changes of shape. Below the critical value the theory implies a pure ferromagnetic state, which is not in agreement with experiment. Probable reasons for the discrepancy are given.