Influence of a Magnetic Field on the Conductivity of Thin Metallic Films

Abstract

A NEW type of magneto-resistance effect in metals has recently been discovered by D. K. C. MacDonald¹. It occurs in thin wires at low temperatures under conditions such that the diameter of the specimen, the free path of the conduction electrons and the radius of the circular orbits of the electrons in a magnetic field are all of comparable orders of magnitude. MacDonald has given a qualitative theoretical discussion of the effects ; the object of the present note is to point out that a corresponding effect exists, and that a detailed mathematical treatment is possible, for the particular case of a thin film placed in a magnetic field which is normal to the surface of the film. The calculation is based on a free electron model, so that there is no magneto-resistance effect in the bulk metal², and it consists of a generalization of the method given by Fuchs³ for the case of zero magnetic field. Assuming that the electrons suffer diffuse reflexion at the surface of the film, the main results are found to be as follows.