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

By viewing current in the detecting lead of a spintronic device as being an ensemble of flowing spins corresponding to a mixed quantum state, where each spin itself is generally described by an improper mixture generated during the transport where it couples to other degrees of freedom due to spin-orbit (SO) interactions or inhomogeneous magnetic fields, we introduce the spin-density operator associated with such current and express it in terms of the spin-resolved Landauer transmission matrix of the device. This formalism, which provides a complete description of coupled spin-charge quantum transport in open finite-size systems attached to external probes, is employed to understand how initially injected pure spin states, comprising fully spin-polarized current, evolve into the mixed ones corresponding to a partially polarized current. We analyze particular routes that diminish spin coherence (signified by decay of the off-diagonal elements of the current spin-density matrix) in two-dimensional-electron-gas-based devices due to the interplay of the Rashba and/or Dresselhaus SO coupling and (i) scattering at the boundaries or lead-wire interface in ballistic semiconductor nanowires; or (ii) spin-independent scattering off static impurities in both weakly and strongly disordered nanowires. The physical interpretation of spin decoherence in the course of multichannel quantum transport in terms of the entanglement of spin to an effectively zero-temperature "environment" composed of open orbital conducting channels offers insight into some of the key challenges for spintronics: controlling decoherence of transported spins and emergence of partially coherent spin states in all-electrical spin manipulation schemes based on the SO interactions in realistic semiconductor structures. In particular, our analysis elucidates why operation of both ballistic and nonballistic spin-field-effect transistors, envisaged to exploit Rashba and Rashba+Dresselhaus SO coupling, respectively, would demand single-channel transport as the only setup ensuring complete suppression of (D'yakonov-Perel'.-type) spin decoherence.