Theory of spin loss at metallic interfaces

Interfacial spin-flip scattering plays an important role in magnetoelectronic devices. Spin loss at metallic interfaces is usually quantified by matching the magnetoresistance data for multilayers to the Valet-Fert model, while treating each interface as a fictitious bulk layer whose thickness is $\delta$ times the spin-diffusion length. By employing the properly generalized circuit theory and the scattering matrix approaches, we derive the relation of the parameter $\delta$ to the spin-flip transmission and reflection probabilities at an individual interface. It is found that $\delta$ is proportional to the square root of the probability of spin-flip scattering. We calculate the spin-flip transmission probability for flat and rough Cu/Pd interfaces using the Landauer-B\"uttiker method based on the first-principles electronic structure and find $\delta$ in reasonable agreement with experiment.