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The Smoluchowski effect [1] Focuses on the total electron charge density and it neglects did electrons carry a spin. In spin-polarized material, it is not clear how majority and minority states contribute to the spin-dependence of this effect. To elucidate this point we perform spin-polarized scanning tunneling microscopy at the step edge of a bilayer high Co Iceland on Cu (111) at 8 K. We measure Maps of the differential conductance (dI / dV) for States of parallel (P) and anti-parallel (AP) orientation between tip and sample magnetization. From These maps we extract the asymmetry A of the differential conductance A = (dI / dVAP-dI / dV) / (dI / dVAP + dI / dV). This quantity is proportional to the spin polarization of the sample. We reveal striking spatial variations of the spin-polarization at the transition between the step and the Co Cu substrates with sub-nm spatial resolution and investigate its energy dependence. We find a variation of the tunnel magnetoresistance ratio of more than 20% on a length scale of few angstroms. We discuss our results on the basis of ab initio calculations, spin-dependent electron charge flow supports our findings [2]. [1] R. Smoluchowski, Phys. Rev. 60, 661 (1941). [2] OP Polyakov et al., Phys. Rev. B, Accepted (2012).