Phase Coherence and Spin Dynamics

Abstract

The recent advances in manipulating electronic spins in semiconductors provide a strong incentive for understanding the dynamics and transport properties of spin-based semiconducting electronics [1, 2, 3]. There has been a great deal of effort pursuing spin injection in high mobility but low dimensionality systems where spin transport is expected to be enhanced. However, most of the studies on spin transport and spin precession has been based on spin diffusive transport [4, 5]. For submicrons devices, where electronic mean free paths can easily exceed the length of the device, transport is in the ballistic regime. Furthermore, in the case of narrow conductors, only a few channels are involved in the spin transport and interchannel scattering becomes inconsequential and the electron can propagate phase coherently. It is at present unclear how the spatial part of the wavefunction can affect its spin counterpart. Indeed the quantum equation of motion for a spin in a magnetic field B is

$$ \partial _t S + \partial _x J = g\mu _B S \times B, $$

((1))

where S and J are the spin density and spin-current density operators respectively and g, μ _B are the gyromagnetic factor and Bohr magneton. In absence of spin flip scattering, the previous equation remains valid in a semiclassical sense where the operators are replaced by their expectation values. This raises the question, “Does phase coherence affect spin dynamics?” In this paper, we investigate this question and answer by the affirmative. Using a scattering approach, we study spin dynamics in a double barrier system. The continuous transition from fully coherent to fully incoherent propagation is described by a conceptually simple approach presented by Buttiker [6, 7]. In this model, incoherent propagation is achieved by inserting localized phase randomizing scatterers between elastic scatterers. Our results, which describe spin transport in the partially coherent regime, illustrate the importance of quantum effects. We show that quantum interference between multiples partial waves shifts the semiclassical spin resonance. Moreover, we demonstrate that spin and charge can mix, a phenomena with no classical analog.