The photon does not couple strongly to the spin degree of freedom. To lowest order a photon will drive electric dipole-allowed transitions. It is, however, possible to use the spin-orbit coupling in most crystals to generate spin polarized distributions. For example, in semiconductor systems with zincblende symmetry, (crudely) the conduction band has an orbital angular momentum of zero, whereas the valence band has an orbital angular momentum of 1. Circularly polarized photons, through an electric dipole transition, will change the angular momentum projected along the direction of light propagation by 1. Now assume for the moment that all three valence bands (heavy-hole, light-hole, and split-off-hole) are separate in energy. Then by fixing the photon energy it is possible to individually address transitions involving the heavy hole to the conduction band. The heavy hole has total angular momentum 3/2 and projected angular momentum +3/2 or -3/2. In the both cases the orbital angular momentum and the spin angular momentum are parallel (orbital +1, spin +1/2 or orbital -1, spin -1/2) . Thus the orbital selection rule is transformed into a spin selection rule through the spin-orbit interaction in the crystal. The maximum spin polarization that could be generated this way is 100%
Even in the case of a bulk semiconductor where the heavy and light holes are degenerate, because the J=1/2 band (split-off hole) is at a different energy, spin polarization can be generated. The light hole has a component where the spin and orbit angular momentum are antiparallel, but it is only 1/3 of the state's probability density. Thus 50% polarization can be achieved.
The essence, then, of probing spin dynamics, is to generate a spin polarized distribution in this fashion, and then probe it with light at a later time, again relying on the coupling of the orbital selection rule to the spin selection rule to allow probing of the spin degree of freedom.
In order to understand the evolution of the spin population two different spin coherence times must be distinguished. The longitudinal time T1 is an incoherent time and describes the change in occupation of the two spin states. The transverse time T2 is a coherence time. A spin oriented perpendicular to the magnetic field involves an equal occupation of spin states parallel and antiparallel to the field, but with a definite phase relationship between them. As a result, the decay of that phase coherence is a measure of the decay of the spin polarization perpendicular to the magnetic field. Note that the decay of phase coherence does not change the occupations of the two spin states.
In the systems described below T1 and T2 are often found to be similar. They are not always equal, but they are often related. Why does this occur, even though one describes coherence and the other does not? The principal difference between them, then, is that a longitudinal decay involves a change in occupation, with a related change in energy of the system. A transverse decay is purely elastic - no energy is required. In nuclear systems the T1 and T2 are very different because energy transfer into or out of the spin system is difficult. This energy bottleneck implies that T1 and T2 differ by several orders of magnitude.
In bulk or quantum well semiconductors (as is the case for electrons in metals), there is no energy bottleneck. Consider a scattering event involving a spin flip where an electron goes from k to k'. The energy required to change the spin state occupation can always be easily absorbed by slightly changing the value of the final-state momentum k'.
Perhaps it is the case that the energy bottleneck can be established in a semiconductor system by converting the spectrum to a discrete spectrum. That discrete spectrum can perhaps be achieved in a quantum dot, in which the T1 and T2 times may differ by orders of magnitude.
A central property of the electronic system in a semiconductor is the amount of time for a spin disturbance to relax to equilibrium. Near room temperature the dominant mechanism for this in III-V semiconductors is precession of the electron spin in the effective magnetic field produced by the crystal field of the zincblende material. This effective magnetic field is dependent on the carrier momentum. As the carrier is scattered from momentum state to momentum state the effective magnetic field fluctuates.
There are two definite regimes of fluctuation. One is when the precession time is shorter than the orbital scattering time. In this situation the decoherence time is roughly the orbital scattering time. The second regime is when the precession time is much longer than the orbital scattering time. Then the electron spin cannot fully precess 180 degrees before scattering, so it performs a random walk, and the decoherence time depends linearly on the orbital scattering rate, instead of the time. In this "motional narrowing" regime the longitudinal and transverse decoherence times depend on different crystallographic components of the fluctuating fields (relative to the magnetic field). In particular, in a cubic crystal where the fluctuating fields are identical along x, y, and z axes, the times T1=T2.
The origins of inversion asymmetry can usually be categorized into three categories. Bulk inversion asymmetry originates from the zincblende crystal structure. Structural inversion asymmetry arises in the presence of either an external electric field or a quasi-electric field (such as originating in an asymmetric heterostructure). The third category, interface asymmetry, comes from the bonding character of interfaces. In a structure with no common atom, such as the InAs/GaSb system, there are bonds at the interface which differ from those in the bulk constituents (either InSb or GaAs). Of course, if these are different at the two interfaces there is an obvious source of asymmetry. In the case below, the bonds are InSb at both interfaces. However, the bonds are rotated relative to each other by 90 degrees. Thus there is an orientational bonding asymmetry.
The effective field can be determined from an electronic structure model which includes the inversion asymmetry of the zincblende lattice. We use a fourteen-band restricted basis set model (shown below for GaAs).
The results of these calculations are shown below for bulk III-V semiconductors, including GaAs, InAs, and GaSb. Also shown are experimental results on GaAs from J. Kikkawa and D. D. Awschalom [PRL 80, (1998)].
In the case of bulk the symmetry requires T1 to be equal to T2. In quantum wells the symmetry is reduced. In the case of (001) quantum wells the fluctuating field along the growth direction vanishes, and thus T2=2T1. In the case of (110) quantum wells the fluctuating field is entirely along the growth direction. Hence T1 is infinite for this mechanism. T2, however, depends on the fluctuating field along all three axes, so it does not become infinite.
The times which appears in the expression for T1 is the fluctuating field coherence time, defined as the time required for the field to change direction by 180 degrees. This time can differ depending on the angular dependence of the fluctuating field. An L=1 component of the fluctuating field requires the momentum to change 180 degrees for the fluctuating field to change sign, whereas an L=3 component only requires the momentum to change 60 degrees. For certain scattering processes, therefore, these field coherence times will differ. Previous theories of the spin coherence in (100) quantum wells focused on the L=1 fluctuating field entirely, and assumed it had a simple functional form (proportional to the square root of the energy). With this functional form the expression for the spin coherence time becomes independent of the scattering process, and only depends on the mobility.
We find that these approximations are not appropriate for typical quantum wells at room temperature. Our calcualtions are shown in comparison with this DK theory for the L=1 fluctuating field above. In addition, DK theory neglects entirely the L=3 fluctuating field, which we show above to be comparable to the L=1 term, and comparable to bulk GaAs.
Shown below are results for the spin coherence time in this system. Results have been calculated for optical phonon scattering as well as neutral impurity scattering. The roughly order of magnitude discrepancy of the DK theory has been corrected. Also, deviations from the trends obtained by DK theory are found to be well reproduced by our calculations.
On the lower right is shown the temperature dependence of the spin coherence time for this structure, assuming a particular room-temperature mobility and extending to lower temperature according to the energy dependence of the particular scattering process. Thus temperature-dependent measurements of the mobility are absolutely essential in attempting to understand the trends in spin coherence times.
