Charge accumulation due to spin transport in magnetic multilayers

Starting with the Valet–Fert theory of the current-perpendicular-to-plane giant magnetoresistance, we studied the charge accumulation due to spin transport in magnetic multilayers by solving Poisson׳s equation analytically. Our results show that, in ferromagnetic layers, the charge accumulation has two exponential terms with opposite signs and different decaying lengths: the Thomas–Fermi screening length (on the order of angstrom) and the spin diffusion length (tens of nm in 3d ferromagnetic metals). The charge accumulation on the scale of the screening length is spin-unpolarized and also present in spin-independent transport in nonmagnetic multilayers. However, the charge accumulation on the scale of the spin diffusion length is spin-polarized and shows up only in ferromagnetic layers. Our analysis also provides new insights into the widely used quasi-neutrality approximation, which neglects the charge accumulation.