The spin dependent reflection at the interface is the key element to understand the spin transport. By completely solving the scattering problem based on first principles method, we obtained the spin resolved reflectivity spectra. The comparison of our theoretical results with experiment is good in a large energy scale from Fermi level to energy above vacuum level. It is found that interfacial distortion is crucial for understanding the spin dependence of the phase gain at the Cu$|$Co interface. Near the Fermi level, image state plays an important role to the phase accumulation in the copper film.
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