Magnetotransport in conducting composite films with a disordered columnar microstructure and an in-plane magnetic field

Some exact relations are found between different elements of the bulk effective resistivity tensor of a two-component composite medium with a columnar microstructure. A self-consistent effective-medium approximation is constructed that incorporates those relations. This is then used to conduct a theoretical study of magnetotransport in such a medium, which can be implemented experimentally as a thin conducting film with perpendicular cylindrical inclusions. Detailed, explicit results are obtained for a conductor/insulator random mixture and a normal conductor/perfect conductor random mixture that are above the two-dimensional percolation threshold of the normal conducting constituent. At large magnetic fields B, the in-plane magnetoresistance components increase as B² without any saturation in mixtures of the first kind, but tend to constant asymptotic values in mixtures of the second kind. The Clausius-Mossotti or Maxwell Garnett type of approximation, which predicts a different behavior, is shown to be unreliable at strong magnetic fields even for very dilute mixtures.