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Scattering formulations of transport in ferromagnetic systems will in general require the consistent evaluation of scalar and spin exchange fields using an approach similar to that developed by
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note
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The transport orbitals will also, in general, contribute to the total spin-density component in the direction of the magnetization. This effect alters the exchange field along the magnetization direction and does not produce a spin torque.
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note
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S O = ({ λ, over(p, →) } × over(z, ̂)) · over(s, →), where the symbol {·,·} denotes the operator anticonmutator.
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