Spin polarization via electron tunneling through an indirect-gap semiconductor barrier

Abstract

We study the spin dependent tunneling of electrons through a zinc-blende semiconductor with the indirect X ͑or ⌬͒ minimum serving as the tunneling barrier. The basic difference between tunneling through the ⌫ vs the X barrier is the linear-k spin-orbit splitting of the two spin bands at the X point, as opposed to the k 3 Dresselhaus splitting at the ⌫ point. The linear coefficient of the spin splitting at the X point is computed for several semiconductors using density-functional theory and the transport characteristics are calculated using the barrier tunneling model. We show that both the transmission coefficient as well as the spin polarization can be large, suggesting the potential application of these materials as spin filters. DOI: 10.1103/PhysRevB.72.195347 PACS number͑s͒: 72.25.Ϫb, 71.20.Nr, 73.63.Ϫb An important problem in spintronics is the development of spin polarized current sources. One of the candidates for this is the asymmetric nonmagnetic heterostructure based on the interface-induced Rashba spin-orbit coupling: 1 H SO = ␣͑ ជ ϫ k ជ ͒ · n , which results in a spin-dependent potential for the scattering of the electrons ͑here, is the Pauli spin operator, k ជ is the electron momentum, n is normal to the interface, and ␣ is the coupling strength͒. The spin-dependent potential in turn leads to a net spin polarization for the outgoing electrons tunneled through the asymmetric heterostructure.Recently, Perel' and coworkers 2 have shown that the tunneling process is itself spin dependent and, even for a symmetric heterostructure, a nonzero spin polarization can occur. In their work, tunneling through a potential barrier originating from the ⌫ conduction minimum was considered and a large spin polarization was found for the incident electron energy below the ⌫ minimum. We extend the analysis to tunneling through a barrier formed by the indirect X or the ⌬ minimum. We find that both the transmission coefficient as well as the spin polarization can be large, suggesting the potential use of these materials as spin filters. The basic difference in the physics originates from the spin-orbit coupling term, viz., the k 3 Dresselhaus coupling 3 at the ⌫ point versus the linear-k coupling at the X point.We consider tunneling through a barrier ͑Fig. 1͒, where the barrier material has the zinc-blende structure with no inversion symmetry ͑e.g., AlAs͒. The basic origin of the spin polarization via tunneling lies in the spin-dependent band structure of the barrier material. If the conduction bands are spin split, then an incident electron with energy in the gap will see a spin-dependent barrier, resulting in a spindependent tunneling probability.Consider the spin splitting of the electronic band structure. Quite generally, the time-reversal symmetry demands that the energy eigenvalues of an electron in a crystal must satisfy the conditionwhere k ជ is the Bloch momentum and ↑, ↓ denote the two spin states. If, in addition, the crystal has the inversion symmetry, then the eigenvalues remain unchanged if the Bloch m...

Spin-neutral currents for spintronics

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Strain-induced conduction-band spin splitting in GaAs from first-principles calculations

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Spin tunneling through an indirect barrier: Tight-binding calculations

“…The result shows that the confinement of the X states in the barrier increases the energy threshold at which the tunneling through X states becomes dominant. In the calculations 16 in which the confinement of the X states in the barrier are neglected, the tunneling is predominantly indirect for energies slightly below the top of indirect barrier. Therefore, our calculations suggest that multi-band calculations are needed to fully describe the electron transport in these heterostructures.…”