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Magno and Pifer (Ref. 7) were the first to perform experiments on the interface in a bimetal sample studying lithium on copper, lithium on manganese, and sodium on aluminum. They analyzed their results using six coefficients in a kinetic model. Their coefficients are directly related to transmission and reflection coefficients. However, there is no experimental configuration that can independently measure any one of the coefficients. The results of Fredkin et al. may be expressed as linear combinations of Magno and Pifer's coefficients. Magno and Pifer found the probability of electron transmission, with or without spin scattering, to be small, of the order of 10-3 or less. They found the probability of spin scattering in a reflection to be temperature dependent; curlep = curlep (T) which is of the order of (1 – 20 ) times 10-3. Flesner et al. used reflection and transmission ESR on lithium on copper samples to probe the interface. When they interpret their results in terms of a kinetic model, they find a single probability, curlep = 2.5 times 10-3, for a spin relaxation for any interaction with the surface, and a probability of t = 0.02 for an electron to cross the interface with or without spin scattering. We will neglect interfacial spin relaxation as a negligible effect.
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13
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Most generally, J vece is a vector and J bdyadM is a second-rank tensor; the component ( JM )ij describes the transport along the jth axis of the projection of the magnetization on the ith axis. Under the simplifying assumptions that Je is normal to the interface, that the magnetization of the film is in the plane of the film along a direction m ^, and that JM is oriented along m ^, both Je and JM may be treated as scalars.
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14
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Note that eta can have either sign; in the simplest picture of Fig. 2(b) we see that it is positive (negative) if the minority (majority) spin subband has a larger density of states at the Fermi surface. Thus, one could use subscripts ""minmaj interchangeably with "" u p d own in the ferromagnet. The former are more informative than the latter, because the majority subband is well defined by the direction of equilibrium magnetization, and then the sign of eta would identify which subband is dominating the transport. However, ""minmaj are inappropriate in the paramagnet. In order to avoid confusion, we will use the arbitrary choice "" u p d own throughout.
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15
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In the following, we will use the free electron value g =2.
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19
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Mark Johnson, Ph.D. dissertation, Cornell University, 1986.
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21
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P. M. Platzman and P. A. Wolff, Waves and Interactions in Solid State Plasmas (Academic, New York, 1973), Eq. (53.25).
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22
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84927858650
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A. G. M. Jansen et al., J. Phys. C 13, 6073.
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24
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Neil W. Ashcroft and N. David Mermin, Solid State Physics (Holt, Rinehart and Winston, New York, 1976), Eqs. (2.21), (2.86), and (8.63).
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25
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We have been neglecting interfacial spin relaxation. However, we could include this effect by defining a conditional probability that a spin which is transmitted has not undergone a spin flip interaction in the process; this probability would most generally be different for each subband bs.
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26
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J. M. Ziman, Principles of the Theory of Solids, 2nd ed. (Cambridge University Press, Cambridge, 1972), p. 215.
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