The Faraday effect in ferromagnetics

Abstract

1. Introduction .—If plane polarised light be transmitted through a medium under the influence of a magnetic field parallel to the direction of propagation, the plane of polarisation is in general rotated. This circumstance is known as the Faraday effect, after its discoverer. For light of a given wave-length, the magnitude of the rotation per unit distance is found to be proportional to the magnetisation. The direction of rotation varies with different substances, being termed diamagnetic, or positive, if in the direction of the current producing the field, and paramagnetic, or negative, if in the opposite sense. The sign of the effect does not depend upon whether the substance is dia- or paramagnetic; negative diamagnetics are, however, infrequent. Thin films of ferromagnetics exhibit an enormous negative rotation, proportional to the magnetisation, and in the following we shall attempt to explain the origin of this by using a very simple model for the substance. We shall consider a single crystal of the metal, and, following Heisenberg, we shall choose the Heitler-London model, where each electron is considered as being attached to an atom, as a first approximation. The interaction of the electrons gives rise to the well-known exchange forces. In a ferromagnetic these exchange forces are of vital importance, and it is therefore necessary to consider states and transitions of the crystal as a whole. Further, it is well known that in a ferromagnetic the average orbital angular momentum is zero. In view of this fact, and in the interest of simplicity, we shall consider a model where each atom possesses one electron in an s -state, outside a closed shell. This, of course, does not correspond to the facts, but any other model would be very much more difficult to handle. Having chosen a model with bound electrons, we shall have no conduction (without including polar states), and shall therefore not have the typical metallic absorption of light, such as is associated with “free” electrons. With the extremely rough model used, it is obvious that we can only expect to obtain the order of magnitude of the rotation, and some idea of its variation with the intensity of magnetisation.