Conductivity of thin metallic films in a longitudinal magnetic field

The size-effect conductivity of thin metallic films in a longitudinal magnetic field is calculated following Chambers' kinetic formulation. We assume (i) that the electron Fermi surface is a single sphere in momentum space, (ii) purely diffuse scattering at the boundary surfaces, and (iii) an isotropic relaxation time in the bulk material. The calculation is based on a study of the trajectory of electrons scattered from the surfaces. The computed size-effect magnetoresistance exhibits a maximum in low magnetic fields and a monotonic decrease in higher magnetic fields. The resistivity maximum may be utilized to obtain information on the bulk mean free path or the cyclotron radius of the conduction electrons. The gross feature of the calculated size-effect variation of magnetoresistance (the galvanomagnetomorphic effect) is found in agreement with some experimental results.