Within the framework of the modified semi-classical Fuchs-Sondheimer model, we investigated theoretically the electrical resistivity of multilayered structures (MLS) consisting of alternating metallic layers (of different purity and different thicknesses) in a transverse magnetic field as functions of the ratio of the adjacent layer thicknesses and the magnetic field value. We have derived both a general formula (valid at arbitrary values of layer thicknesses) and asymptotic expressions that are valid when metallic layers are thick or thin compared with the electron mean free path. We found a non-monotonic behavior in the resistivity vs. the value of an applied magnetic field. As we demonstrated, this behavior is sensitive to the characteristics of the electron scattering in the interlayer interfaces in low magnetic fields. Moreover, the MLS resistivity oscillates in high magnetic fields with the field value (or with the layer thicknesses). The oscillation includes the harmonics that correspond both to the each layer thicknesses and the total thickness. The intensity of the oscillation is determined by the diffusive electron scattering in the interfaces, and the oscillation amplitude is proportional to the coefficient of the electron transmission through the interlayer interfaces. We have calculated numerically the resistivity in a wide range of fields and layer thicknesses at various values of the parameters of the interface and bulk electron scattering.
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