Generation of Spin Currents via Raman Scattering

Abstract

We show theoretically that stimulated spin flip Raman scattering can be used to inject spin currents in doped semiconductors with spin split bands. A pure spin current, where oppositely oriented spins move in opposite directions, can be injected in zincblende crystals and structures. The calculated spin current should be detectable by pump-probe optical spectroscopy and anomalous Hall effect measurement.PACS numbers: 71.70.Ej Spintronics is the strategy of using the spins of carriers in solid state structures as a new degree of freedom to carry and transform information [1]. An important capability is the generation of spin currents, which couple spin and charge. Suggestions for the generation of spin currents have included proposals based on the use of the extrinsic and intrinsic spin Hall effects, as well as spin pumping [2,3,4]. All-optical generation and control of spin currents have also been proposed and observed [5,6,7,8,9]. In these optical schemes, the generation of the spin current is accompanied by the deposition of photon energies of about 1 eV per carrier in the system. Most of this energy is used simply to generate the electron-hole pairs, and is lost in the sense that it does not contribute to the motion of the carriers. An obvious goal for the alloptical manipulation of spin is the minimization of such energy loss.Here we propose a new scheme for generating spin currents in doped semiconductors via a two photon Raman scattering process [10,11], which can be understood as the absorption of a photon of frequency ω 1 and the emission of a photon at ω 2 . This process deposits an energy ofhΩ =h (ω 1 − ω 2 ) per carrier in the crystal, which for GaAs is only about 0.5 meV. In the presence of spin splitting of the bands, stimulated spin-flip Raman scattering can produce a pure spin current, where electrons with opposite spins move in opposite directions. Hence no net charge current is injected.Crucial to this effect is the spin-splitting of states, which results from the lack of inversion symmetry of the crystal. A schematic picture of the conduction states is shown in Fig. 1, where E F denotes the Fermi energy. For simplicity we take the temperature to be zero [12]. The proposal in this letter is based on optically inducing transitions between states d(±k) and u(±k) at ±k wavevectors, as depicted in Fig. 1, via Raman scattering. As an example, we first consider an optical field E = E(ω 1 )e −iω1t + E(ω 2 )e −iω2t + c.c. in the material, where c.c. denotes complex conjugation and ω 1 > ω 2 and then present an experimentally relevant scenario of pulse excitation. The interaction of this field with the crystal in the dipole approximation is described by H int = −(e/mc)p · A(t), where e(m) is the charge(mass) of an electron, c is the speed of light and A(t) is the vector potential associated with the field. In the ground state |0 , electrons occupy states up to the Fermi level. The wavefunction of the perturbed system at time t is then written as |Ψ(t) = c 0 (t)|0 + k c k (t)|ehk , where |ehk , denote...

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