Electron Spin Dynamics in Semiconductors

F.X. Bronold1; A. Saxena2; D.L. Smith2    1 Institut für Physik, Ernst-Moritz-Arndt Universität Greifswald, D-17487 Greifswald, Germany
2 Theoretical Division, Los Alamos National Lab, Los Alamos, New Mexico 87545 USA

I Introduction

The ability to control and measure electron spin degrees of freedom in solids has been proposed1–12 as the operating principle for a new generation of novel electrical devices with the potential to overcome power consumption and speed limitations associated with conventional electronic circuits, and also as a means to physically implement schemes for quantum information processing and computing. Recent fundamental discoveries related to non-equilibrium electron spin dynamics and transport in solids make the study of these phenomena extremely rich from both basic science and technology points of view.13–37 Devices based on spin-dependent transport in metallic systems, such as giant magneto-resistive structures and magnetic tunnel junctions utilizing spin-dependent tunneling, are having a major technological impact.38–41 Promising new electron-spin-based device concepts utilizing semiconductors have been proposed.42–53 Realizing the full potential of spin-based electronics requires a more complete understanding of non-equilibrium electron-spin-based phenomena than is currently available, and there is extensive on-going research in this area. Essential points of focus for this research area include: generation of non-equilibrium spin-polarized electron distributions; transport of electron spin distributions through a given material and across interfaces between two materials perhaps with different spin-dependent ground states; the relaxation dynamics of a non-equilibrium spin-polarized electron distribution; and the interaction of spin distributions with optical and magnetic probes.

Semiconductors are particularly attractive for studies of spin-based phenomena in solids because circularly polarized light can be used to inject and detect specific spin orientation of electrons and because the use of these materials for integrated electronics is well established. Non-equilibrium spin distributions in semiconductors can be generated by: (1) polarized optical techniques utilizing spin-dependent optical selection rules; (2) spin-polarized electrical injection across interfaces between materials with different magnetic properties; and (3) current transport in spatially inhomogeneous magnetic fields. Spin distributions and currents can be probed and characterized by optical, magnetic, and electrical transport techniques. Non-equilibrium spin distributions can be manipulated by electric and magnetic fields and by semiconductor heterostructure design.42,54,55 The spin coherence lifetimes of electrons in these materials can be quite long and may be optimized by tuning electron density and by selecting specifically designed heterostructures.

Many physical probes, including optical and electrical probes, couple directly to the spatial component of the electron wave function but do not couple directly to the spin component. The spin-orbit interaction mixes the spatial and spin components of the electron wave function and allows, for example, an optical probe to couple to the electron spin. Thus the spin-orbit interaction is useful in allowing the electron spin degrees of freedom to be manipulated and measured using convenient probes. However, the spin-orbit interaction also provides mechanisms for spin decoherence. For example, most scattering processes involve the spatial part of the electron wave function and in the absence of the spin-orbit interaction would not lead to spin decoherence. The spin-orbit interaction allows a loss of spin coherence in scattering events in which the direct coupling is to the spatial part of the wave function. Thus the spin-orbit interaction provides a means to conveniently manipulate the electron spin degree of freedom but also introduces mechanisms for loss of spin coherence. The role of the spin-orbit interaction is a major theme in spin-based device concepts. Controlling the strength of the spin-orbit interaction spatially by heterostructure design is an important approach to spin-based electronic device design.56,57

The coupling between electron spin and orbital motion that results from the spin-orbit interaction produces optical selection rules that allow a non-equilibrium electron spin population to be generated by the absorption of circularly polarized light. Optical transitions across the energy gap of a semiconductor are governed by electric dipole selection rules. Circularly polarized light with a wavelength corresponding to the semiconductor absorption edge induces transitions from the highest energy valence band states to the lowest energy conduction band states, which produce a spin-polarized electron distribution in direct bandgap semiconductors. The same optical selection rules allow the dynamics of a non-equilibrium electron spin population to be probed optically using polarization-sensitive transmission and reflection, Kerr- and Faraday-rotation spectroscopies, respectively. A non-equilibrium spin distribution produces a difference in the index of refraction for left- and right-hand circularly polarized light. As a result, the polarization axis of linearly polarized light, which is a coherent superposition of left- and right-hand circularly polarized light, rotates upon reflection from or transmission through the semiconductor with the spin-polarized electron distribution. These spectroscopies are readily adaptable to time- and spatially-resolved measurements.11 For example, circularly polarized optical pulses can create spin-polarized states in a given spatial region of a bulk semiconductor or a quantum well. A magnetic field can be applied, in which case the spin population precesses in the applied field. The amplitude, phase, and spatial position of the resultant spin population can be tracked in time-resolved experiments using Kerr- or Faraday-rotation spectroscopy. Electron spin polarization can also be detected by polarization-sensitive luminescence measurements because, due to the optical selection rules, a non-equilibrium distribution of spins gives rise to circularly polarized luminescence. In this approach, the spin-polarized electron distribution is allowed to recombine radiatively with a hole distribution—for example, in a p-n junction structure—and the polarization properties of the resulting luminescence are analyzed. Using these optical techniques, electron spin lifetimes have been investigated in a variety of semiconductors under various conditions and long spin lifetimes have been observed.5,13,15–17,58–71 The lifetimes depend strongly on doping levels and temperature. Experiments have identified ranges of doping concentrations in semiconductors where lifetimes are strongly enhanced, in some cases exceeding 100 ns.11 Long electron spin lifetimes can be achieved up to room temperatures in certain nanostructures and quantum dots.1 Because of the long spin coherence times a non-equilibrium electron spin distribution can be driven across macroscopic distances in homogeneous semiconductor crystals and also across heterointerfaces.72,73

A magnetic field couples directly to spin and can be used to create spin polarization. Most semiconductors have effective g-factors of order unity and the magnetic spin splittings are small so that electron spin populations can be significantly polarized only at very low temperature by high magnetic fields. However, in certain Mn-doped II-VI semiconductors, called semimagnetic semiconductors, very large effective g-factors (of order 100) occur and strong electron spin polarization can be achieved with more moderate magnetic fields and temperatures.74 These semimagnetic semiconductors can be incorporated into heterostructures with nonmagnetic semiconductors and used as a source of spin-polarized electrons. Ferromagnetic semiconductors consisting of Mn-doped III-V semiconductors have recently been developed and show many interesting properties.18,75–79 They can also be incorporated into heterostructures to make novel device structures. To date, these ferromagnetic semiconductors have all been p-type doped and have Curie temperatures below room temperature. Current flow in an inhomogeneous magnetic field can be used to create a spin current and a spin current can be manipulated by electrical means. There is also a direct coupling between the electron spin and the nuclear spin through the hyperfine interaction. This interaction enables a non-equilibrium electron spin population to transfer spin polarization to the nuclear spin population. It allows the electron spin polarization to be detected by nuclear spin probes such as nuclear magnetic resonance (NMR). In addition, the optical techniques can be combined with NMR to give an all-optical form of NMR. The latter approach enables an all-optical coherent manipulation of electron spins in a way analogous to nuclear spin echoes.

Semiconductor device concepts that utilize spin-dependent phenomena rely on electrical injection and transport of spin currents. Structures designed to achieve electrical spin injection utilize spin-polarized contacts as the source of polarized electrons. Two main types of spin-polarized contacts...