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8
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33750860386
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(1988)
Phys. Rev. Lett.
, vol.61
, pp. 2472
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Baibich, M.N.1
Broto, J.M.2
Fert, A.3
Nguyen Van Dau, F.4
Petroff, F.5
Etienne, P.6
Creuzet, G.7
Friederich, A.8
Chazelas, J.9
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11
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0001259640
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(1991)
Phys. Rev. B
, vol.44
, pp. 5355
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Petroff, F.1
Barthélémy, A.2
Mosca, D.H.3
Lottis, D.K.4
Fert, A.5
Schroeder, P.A.6
Pratt, W.P.7
Loloee, R.8
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27
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84927363828
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The boundary conditions (5) correspond to the situation discussed in BA, Ref. 16, of complete specular reflection at the outer surfaces, P=1.
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32
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84927363827
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It should be noted that the derivation of the equations in Refs. 26–29 require a correlation length longer than the electron Fermi wavelength, so that a vector normal to the surface can be properly defined. In this sense the limit L -> 0 is not strictly valid. It should be understood as the limit in which L is still longer than the Fermi wavelength but shorter than all other lengths in the problem.
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33
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84927363826
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If the geometric random roughness of the interfaces were the only source of scattering, the prefactors in Eq. (11) must all be taken to be Sσ=1. This is, however, not a realistic assumption. Impurities and other defects at the interfaces scatter electrons of opposite spin in a different way. Hence SM and Sm are not equal, and in general both less than one.
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34
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84927363825
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It should be emphasized that ``roughness'' with a single, given periodicity, produces Bragg beams with well-defined directions of propagation, i.e., electron trajectories with their own (positive or negative) contribution to the current. For a smooth, nonuniform, quasiperiodic distribution of geometrical defects at the interface (i.e., a Fourier transform of the topography consisting of a peaked but continuous function), the distribution of velocities of electrons Bragg scattered over the Fermi surface tends to average down to zero, resulting in the electrons being effectively removed from the current-carrying distribution, i.e., relaxing back to equilibrium.
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35
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84927363824
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As in Eq. (7), the masses mi σ and mj σ in Eq. (12) are assumed to be equal. All calculations presented in the paper have mi σ =m, independent of the layer i and the spin sigma.
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