Charge and spin transport through a metallic ferromagnetic-paramagnetic-ferromagnetic junction

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Abstract
Using a pair of weakly coupled drift-diffusion equations for spin-up and spin-down electrons, we compute the signal of recent spin-injection experiments by Johnson on ferromagnetic-paramagnetic-ferromagnetic films. In the limit of large junction resistance, our results coincide with those of earlier calculations. As the junction resistance decreases, there are correction terms which provide a cutoff to the size of the signal for films much thinner than the spin-diffusion length. The physical origin of this cutoff is the leakage of nonequilibrium magnetization out of the paramagnet into the current and voltage probes. Although our calculation can explain the sample thickness dependence of the experiments, it cannot account for the large magnitude of the signal observed.