The upper critical field of superconducting superlattices is calculated by taking account of spatial variations of the following quantities of conduction electrons: the density of states, the diffusion constant, the attractive interaction constant responsible for superconductivity, and the spin polarization. For applied magnetic fields parallel to the layers, these spatial variations cause a dimensional crossover in the temperature dependence of the upper critical field Hc2?. The spatial variation of the density of states is most important for the effect of the dimensional crossover observed in Nb/Cu superlattices. For applied magnetic fields perpendicular to layers, a new type of crossover is predicted in the temperature dependence of Hc2 for superlattices composed of a high-Hc2 material and a low-Hc2 material. The anisotropic spin polarization of conduction electrons induced by applied magnetic fields explains the anomalous behavior of Hc2 observed in V/Ni superlattices.
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