The direction of magnetisation of single ferromagnetic crystals

The study of the magnetisation of single crystals of ferromagnetic substances has shown that there are definite relations between magnetic properties and crystalline structure. One of the most important, the relation between the crystalline structure and the direction of magnetisation, will be studied in this paper. It is well known that on applying a magnetic field to a crystal the direction of the magnetisation produced does not, in general, coincide with that of the field (here and elsewhere, unless the external field is specifically mentioned, the effective field is to be understood). The phenomenon has been extensively studied experimentally, but hitherto there has been no entirely satisfactory theory. A theory, at least partially successful, was proposed by Mahajani, who assumed that the elementary magnets are electron orbits. Owing to their magnetic interaction, these magnets posses a mutual potential energy which in general depends upon their orientation, and hence leads to deviations between the directions of magnetisation and field. In the case of non-cubic crystals, it is sufficient to consider the elementary magnets as simple dipoles, but in the case of cubic crystals, the dipole energy is independent of the orientation of the dipoles, and it becomes necessary to consider the quadrupole moments. Mahajani showed that this theory accounts qualitatively for the various effects observed in iron (with a cubic structure) and pyrrhotite (with a non-cubic structure).