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By viewing current in the detecting lead of a spintronic device as being anensemble of flowing spins corresponding to a mixed quantum state, where eachspin itself is generally described by an improper mixture generated during thetransport where it couples to other degrees of freedom due to spin-orbit (SO)interactions or inhomogeneous magnetic fields, we introduce the spin densityoperator associated with such current expressed in terms of the spin-resolvedLandauer transmission matrix of the device. This formalism, which providescomplete description of coupled spin-charge quantum transport in openfinite-size systems attached to external probes, is employed to understand howinitially injected pure spin states, comprising fully spin-polarized current,evolve into the mixed ones corresponding to partially polarized current. Weanalyze particular routes that diminish spin coherence (signified by decay ofthe off-diagonal elements of the current spin density matrix) intwo-dimensional electron gas-based devices due to the interplay of the Rashbaand/or Dresselhaus SO coupling and: (i) scattering at the boundaries orlead-wire interface in ballistic semiconductor nanowires; or (ii)spin-independent scattering off static impurities in both weakly and stronglylocalized disordered nanowires. The physical interpretation of spin decoherencein the course of multichannel quantum transport in terms of the entanglement ofspin to an effectively zero-temperature ``environment'' composed of more thanone open orbital conducting channels offers insight into some of the keychallenges for spintronics: controlling decoherence of transported spins andemergence of partially coherent spin states in all-electrical spin manipulationschemes based on the SO interactions in realistic semiconductor structures.Comment: 16 pages, 9 color figure

physical review. b, condensed matter and materials physics

Decoherence of transported spin in multichannel spin-orbit-coupled spintronic devices: Scattering approach to spin-density matrix from the ballistic to the localized regime