Notes on magneto-optics

Abstract

The present work was originally undertaken as a sequel to a recent paper in which I discussed certain questions connected with the refractive index, but its scope has widened out considerably. The presence of a static magnetic field in no way effects the central difficulty of the earlier work, and it seemed therefore worth while to make the small extension which would include such fields. But a study of the literature of magneto-optics suggested that the whole subject ought to be presented in a more systematic way than has hitherto been usual, and so the first part of the paper develops a formal method suitable for the discussion of magneto-optics, no matter what the underlying atomic theory may be. There follows a discussion of the magneto-optics effects of material of any atomic character, which is worked out with the same quasi-classical model as was used in I. The formulae are then applied to an examination of the Kerr magneto-optics effect, and the experimental results are tested. The experimental measures are very variable and discrepant, and the test cannot be regarded as satisfactory; but it does seem rather probable that it is fulfilled, so that the Kerr effect may be treated as if due to the disturbance of the ordinary optical effects by a strong intrinsic magnetic field, though this proves to be quite different from the Weiss field. The model used are mainly classical. It is not, of course, claimed that they are as close to actuality as would be models making explicit use of the quantum theory; nevertheless, there are pronounced advantages in the present method. In the ordinary treatment in the quantum theory of the refraction of light, the argument leads, after the Raman scattering has been removed from consideration, to formulae involving “virtual electrons’ which obey the laws of classical electromagnetics. Things are a little different , for magnetic gyration, and the changes will be briefly described; but these differences are not the main interest of the subject. The main difficulty is the same for the quantum as for the classical theory. This is the question of the Lorentz correction, which arises whenever what is essentially a problem of many electrons is simplified into a problem of a single electron. In metals the effect can hardly be called a correction, as it entirely alters the numerical magnitudes. Some writers have maintained that the correction should not be applied in metals; but in a recent paper Kronig and Groenewold, using the methods of quantum theory, show that some correction of the kind is demanded, and though they have not evaluated it, their work does not exclude the possibility that the result of the classical model is correct. The problem must certainly be solved properly before we can feel any confidence in theories of metallic optics. In the meantime there is still perhaps room, here as in many other branches of atomic theory, for work that simplifies the problem by the use of classical models.