Session X14: Focus Session: Spins in Semiconductors - Spin-Orbit Interaction and Relaxation in Si and Ge

Field-induced negative differential spin lifetime in silicon

Using experimental measurements of spin transport in undoped silicon, we show that the electric field-induced thermal asymmetry between the electron and lattice systems substantially impacts the identity of the dominant spin relaxation mechanism. In contrast to the Elliott-Yafet theory where intraband phonon absorption leads to spin relaxation, here we induce phonon \emph{emission} during which electrons are scattered between conduction band valleys that reside on different crystal axes. This leads to anomalous behavior, where reduction of the transit time between spin-injector and spin-detector with larger electric field is accompanied by a counterintuitive reduction in spin polarization and an apparent \emph{negative} spin lifetime.\\[4pt] Work at UMD is supported by the Office of Naval Research and the National Science Foundation. We acknowledge the support of the Center for Nanophysics and Advanced Materials and Maryland NanoCenter and its FabLab. Work at UR is supported by AFOSR and NSF (No. FA9550-09-1-0493 and No. DMR 1124601).   

Decrease of electron spin lifetime in external electric field due to intervalley phonon scattering in silicon

We derive a simple approximate expression of the spin lifetime of drifting electrons in silicon. This expression agrees well with elaborate Monte Carlo simulations of the charge transport and spin relaxation of conduction electrons heated by the electric field. Already at low temperatures, the drifting electrons become hot enough to undergo $f$-processes (scattering between valleys of different crystal axes following emission of a shortwave phonon). Such a process involves a direct coupling of valence and conduction bands and dominates the spin relaxation. A sharp decrease of spin lifetime can then be expected in intermediate electric fields in between $\sim$100~V/cm and $\sim$1~kV/cm. When electrons are transported between a spin injector and a spin-resolved detector, the decrease of both transit time and spin lifetime results in a non-monotonic behavior of the detected spin polarization with the electric field. The theory shows excellent agreement with empirical results.   

Spin-Polarized Luminescence Across the Indirect Band-Gap of Strained Ge, Si and Their Alloys

We study optical orientation and circularly polarized photoluminescence in germanium, silicon and their alloys. We focus on phonon-assisted optical transitions across the indirect band-gap under conditions of biaxial strain (either compressive or tensile). The signature of strain on the band structure and phonon dispersion is observed in the luminescence spectra where spin properties are better resolved from the change in intensity ratio between left and right circularly polarized emission. The spectra is simulated using the combined results of a spin-dependent empirical pseudopotential method, adiabatic bond charge model, electric-dipole approximation, and rigid-ion model. An additional strain tensor has been introduced in calculating the strain effect. We have used group theory extensively to account for all possible transitions and to provide concise selection rules.   

Spin-orbit interaction and spin relaxation of conduction band electrons in Si and Ge

Group IV element semiconductors, silicon and germanium, are promising material candidates in spintronics due to their intrinsic long electron spin lifetimes. To describe the spin properties of conduction electrons in these indirect band-gap multivalley semiconductors, the method of invariants is employed to build $8 \times 8$ (for Si) and $10 \times 10$ (for Ge) spin-dependent Hamiltonians that capture the symmetries of the zone edge states (X-point of Si [1] and L-point of Ge) and their spin dependent parameters. Concise expressions of the energy bands, and more importantly, of the spin mixed states are derived and verified by numerical results of an empirical pseudopotential method. These analytical state expressions are powerful tools to study the behavior of electron spins similar to the way that the Kane model in being used in direct band-gap semiconductors. Mechanisms of spin relaxation by electron-phonon scattering are studied based on this model. We reveal fundamental differences between spin and momentum relaxation mechanisms. In the case of silicon, intravalley spin flipping is governed by scattering with transverse acoustic (TA) phonons via the interband deformation potential that couples the upper and lower conduction bands (this deformation potential would also break the degeneracy of the conduction band at the X point if off-diagonal stress is applied). The intervalley g-process spin flipping couples the lowest conduction bands of different irreducible representations in opposite valleys via acoustic phonons; the intervalley f-process spin flipping, which is the dominant contribution of spin relaxation in a wide temperature range, couples the conduction and valence band components of the states by scattering with $\Sigma_1$ and $\Sigma_3$ phonons. In the case of germanium, intervalley spin-flip scattering, which is also the main contribution of spin relaxation, couples the lowest and upper conduction bands of different valleys by X-phonons. The intravalley spin flip scattering, which is about two orders of magnitude smaller, couples the conduction and valence bands mostly via TA phonons.\\[4pt] [1] Pengke Li and Hanan Dery, Phys. Rev. Lett. 107, 107203 (2011)   

Group theory analysis of phonon-induced spin relaxation in silicon

Selection rules and leading order matrix element expressions are derived for all important spin flip processes in the multivalley conduction band of bulk silicon. All results are generalized to arbitrary spin orientation directions. Intervalley $f$-process scattering induced by all phonon modes are analyzed using double group irreducible representation matrices of the $\Delta$ axis and independent integrals are identified for transitions between states of either spin. Intervalley $g$-process and intravalley spin flips are analyzed using the $X$ point single group and detailed selection rules are derived using a four-band basis. Together with electronic states obtained by a spin-dependent k$\cdot$p expansion, wavevector dependent spin-flip matrix elements are derived for all phonon modes in intravalley and for the leading order phonon mode in $g$-process scattering. Higher order matrix elements are qualitatively studied. Comparison with deformation potential theory in momentum scattering is made. Integrations for spin relaxation rate are carried out. Symmetry breaking mechanisms such as stress and electric field are discussed and quantified. We benchmark all of our analysis with numerical results of strain-dependent empirical pseudopotential and adiabatic-bond-charge models.   

Influence of spin polarization on resistivity of a two-dimensional electron gas in Si MOSFET at metallic densities

Positive magnetoresistance (PMR) of a silicon MOSFET in parallel magnetic fields $B$ has been measured at high electron densities $n \gg n_{\rm c}$ where $n_{\rm c}$ is the critical density of the metal-insulator transition (MIT). It turns out that the normalized PMR curves, $R(B)/R(0)$, merge together when the field is scaled according to $B/B_{\rm c}(n)$ where $B_{\rm c}$ is the field in which electrons become fully spin polarized. The values of $B_{\rm c}$ have been calculated from the simple equality between the Zeeman splitting energy and the Fermi energy taking into account the experimentally measured dependence of the spin susceptibility on the electron density. This extends the range of validity of the scaling all the way to a deeply metallic regime far away from MIT. The subseqent analysis of PMR for low $n\stackrel{>}{\sim} n_{\rm c}$ demonstrated that the merging of the initial parts of curves can bee achieved only with taking into account the temperature dependence of $B_{\rm c}$. It is shown that the shape of the PMR curves at strong magnetic fields is affected by a crossover from a purely two-dimensional (2D) electron transport to a regime where out-of-plane carrier motion becomes important (quasi-three-dimensional regime).   

Spin phase coherence of donor nuclear spins in silicon: the influence of electrical readout

Storing information in spin underpins the operation of a wide range of emerging technologies. However, the ability to interact with, and thus control electron spin implies a reasonable coupling to the environment, and a correspondingly limited spin coherence time. This problem can be overcome by using nuclear spins for long term information storage, and significant experimental progress in this direction has been seen recently. Readout of stored information can be achieved in a variety of ways, with electrical approaches offering substantial benefit with regard to integration of spintronic and classical electronic applications. Here, we discuss electrical readout of coherent nuclear spin states of donor nuclei in silicon. By utilizing nuclear Hahn echo sequences, we are able to demonstrate that nuclear spin phase coherence can exceed 3 ms with electrical readout. We find that the spin phase coherence is in this case limited by the spin lifetime of the donor electron which mediates our readout scheme, and discuss approaches to ameliorate this effect.   

Optical Orientation and Spin Relaxation of electrons and holes in Strained Germanium Quantum Wells

We demonstrate optical orientation in strained Ge/SiGe quantum wells and study their spin properties. The energy proximity between the center of the Brillouin zone to its edge allows us to achieve high spin-polarization efficiency and to resolve the spin dynamics of holes and electrons. The circular polarization degree of the direct-gap photoluminescence is 37\% and 86\% for transitions with heavy and light holes states, respectively. Considering the ultrafast transition of electrons to L valleys, the extracted spin lifetime of holes at the top of the valence band is found to be 0.5 ps. This lifetime is governed by transitions between heavy and light hole states. The indirect-gap photoluminescence via the no-phonon line and its LA phonon replica allows us to study spin properties of electrons at the bottom of the conduction band. Taking into account the recombination lifetime of electrons (radiative and non-radiative channels), we find that their spin lifetime exceeds 5 ns below 150 K. Theoretical analysis of the electrons spin relaxation indicates that phonon-induced intervalley scattering by the X point phonon modes dictates the spin lifetime.   

Infrared Kerr measurements in ferromagnetic silicon carbide

We measure the infrared (100-1000 meV) polar Kerr angle in ferromagnetic silicon carbide (SiC). The Kerr angle is sensitive to the Hall conductivity $\sigma _{xy}$ and measures the difference of optical responses for left and right circularly polarized light, which makes it a sensitive spectral probe for small changes in the symmetry of the system due to magnetic order. Both neutron-irradiated and Al-doped samples are studied in the 10-300K temperature range. This study provides new insights into the mechanisms by which non-magnetic impurities and defects can produce magnetic order. Strong frequency dependence and hysteresis are observed in the Kerr measurements. Work supported by NSF-DMR1006078.   

Low-temperature scattering-Scanning Near-field Optical Microscopy of Strongly Correlated Materials

Strongly correlated electron materials display diverse complex phenomena such as metal-insulator transitions and ferroelectric and ferromagnetic ordering, with characteristic lengths on the nanometer scale. In order to directly access and study the associated nano-phase behavior and domains for a wide range of materials, we have developed a low temperature tip-enhanced scattering-type scanning near-field optical microscope (s-SNOM). A microscopy flow cryostat reservoir is coupled to a shear-force atomic force microscope, with illumination of electrochemically etched Au tips provided by an on-axis high numerical aperture parabolic mirror. We will discuss the use of this system for the study and imaging of ferroic ordering in multiferroic and ferroelectric materials through the symmetry selectivity provided by tip-enhanced second harmonic generation (SHG) and nano-Raman crystallography via the tensor based selection rules.