Session L31: Focus Session: Spin Dependent Phenomena in Semiconductors: Spin Orbit and Spin Relaxation

Spin-orbit coupling in bulk and low dimensional III-V zinc-blende and wurtzite semiconductors from first principles

We have performed systematic investigations, using first-principles methods, of spin-orbit coupling effects in bulk III-V zinc-blende and wurtzite GaAs, GaSb, InAs, and InSb semiconductors. We have investigated the spin-orbit effects of the surface states of these semiconductors in different technologically important growth directions. Based on symmetry-derived Hamiltonians we have extracted realistic spin-orbit parameters important for spin relaxation, spin transport, optical orientation, and semiconductor-based Majorana states studies.   

Spin Relaxation in III-V Semiconductors in various systems: Contribution of Electron-Electron Interaction

In spintronics, most of the phenomena that we are interested happen at very fast time scales and are rich in structure in time domain. Our understanding, on the other hand, is mostly based on energy domain calculations. Many of the theoretical tools use approximations and simplifications that can be perceived as oversimplifications. We compare the structure, material, carrier density and temperature dependence of spin relaxation time in n-doped III-V semiconductors using Elliot-Yafet (EY) and D'yakanov-Perel'(DP) with real time analysis using kinetic spin Bloch equations (KSBE). The EY and DP theories fail to capture details as the system investigated is varied. KSBE, on the other hand, incorporates all relaxation sources as well as electron-electron interaction which modifies the spin relaxation time in a non-linear way. Since el-el interaction is very fast ($\sim$ fs) and spin-conserving, it is usually ignored in the analysis of spin relaxation. Our results indicate that electron-electron interaction cannot be neglected and its interplay with the other (spin and momentum) relaxation mechanisms (electron-impurity and electron-phonon scattering) dramatically alters the resulting spin dynamics. We use each interaction explicitly to investigate how, in the presence of others, each relaxation source behaves. We use GaAs and GaN for zinc-blend structure, and GaN and AlN for the wurtzite structure.   

Spin Relaxation in Materials Lacking Coherent Charge Transport

As semiconductor spintronics research extends to materials beyond intrinsic or lightly doped semiconductors (e. g. organic materials, amorphous semiconductors, and impurity bands), the need is readily apparent for new theories of spin relaxation that encompass highly disordered materials, where charge transport is incoherent. We describe a broadly applicable theory of spin relaxation in materials with incoherent charge transport. The theory is based on continuous-time-random-walk theory and can incorporate many different relaxation mechanisms. We focus primarily on spin relaxation caused by spin-orbit and hyperfine effects in conjunction with carrier hopping. Analytic and numerical results from the theory are compared in various regimes with Monte Carlo simulations. Three different systems were examined: a polymer (MEH-PPV) [1], amorphous silicon [2], and heavily doped n-GaAs. In the organic and amorphous systems, we predict spin relaxation and spin diffusion dependences on temperature and disorder for three different mechanisms (hyperfine, hopping-induced spin-orbit, and intra-site spin relaxation). The resulting unique experimental signatures predicted by the theory for each mechanism in these disordered systems provide a prescription for determining the dominant spin relaxation mechanism. We find our theory to be in agreement with available measurements in these materials. We also predict that large disorder modifies certain mechanisms to be algebraic instead of exponential in time. Our results should assist in evaluating the suitability of various disordered materials for spintronic devices. All work done in collaboration with Michael E. Flatt\'e. Timothy Peterson and Paul Crowell collaborated as well on the n-GaAs study. \\[4pt] [1] N. J. Harmon and M. E. Flatt\'e, Phys. Rev. Lett., 110, 176602 (2013)\\[0pt] [2] N. J. Harmon and M. E. Flatt\'e, Phys. Rev. B 90, 115203 (2014)   

Electron spin flips due to scattering off substitutional donors in multivalley semiconductors

We elucidate the physical origin of donor-driven spin relaxation in multivalley semiconductors with an emphasis on silicon. This spin flip is dominated by intervalley scattering between non time-reversal related valleys and by spin-orbit interaction from the core region of the donors. By a concise and intuitive explanation, we will present how the crystal symmetries and the multivalley nature of the conduction band set the selection rules for spin flip transitions, and how to decisively associate the microscopic contributions with the empirically found strong dependence of the spin relaxation on the donor identity. These analyses and results are quite general for various other materials with multivalley conduction bands, and they are crucial for optimizing spintronics devices especially in the highly doped region near semiconductor-ferromagnet interfaces.\\[4pt] [1] Yang Song, Oleg Chalaev and Hanan Dery, Phys. Rev. Lett., 113, 167201 (2014).   

Spin relaxation in strained n-type silicon

The impurity-induced spin-relaxation mechanism in heavily doped n-type silicon has been recently reported in Phys. Rev. Lett. \textbf{113}, 167201. The leading contribution to the spin-relaxation rate occurs due to electron transitions between momentum-space valleys that reside on different crystallographic axes (the so-called f-process). This spin relaxation mechanism can be suppressed by applying uniaxial compressive strain that lifts the valley degeneracy. By calculating the next-order contribution to the spin-relaxation rate due to intravalley scattering and intervalley scattering between opposite valleys (the so-called g-process), we find a significant enhancement of the spin lifetime.   

Theory of copper induced spin-orbit coupling in graphene: substrate, clusters, and adatoms

We present a DFT study of graphene functionalized by copper adatoms and clusters, as well as of graphene on the (111) Cu surface, focussing on spin-orbit coupling effects. In the single copper adatom limit we study two energetically favored adsorption positions: the top and bridge positions and their corresponding diffusion barrier. Based on symmetry arguments we propose an effective tight-binding model Hamiltonian to describe low energy electronic states and determine realistic orbital and spin-orbit coupling parameters. We consider also copper clusters adsorbed on graphene and graphene on the Cu (111) surface, for which we as well fit to a model Hamiltonian to extract Rashba and intrinsic spin-orbit coupling strengths.   

Intervalley mixing and skew scattering in graphene systems

The scattering of electrons in graphene from impurities that preserve the point symmetries of the lattice is known to be anisotropic, with a transport to elastic time ratio $\xi=2$ at low energies [1]. In systems in which the spin orbit interactions (SOI) are locally enhanced and do not lead to K-K$'$ intervalley mixing, we have shown that the scattering becomes isotropic, and can be experimentally detected through the drop in $\xi\simeq1$ at low carrier concentrations [2]. These systems have been also shown to exhibit skew scattering and associated spin Hall Effect (SHE) [3]. In this study we extend our analysis to defects described by time reversal invariant interactions (TRIs) that reduce the lattice symmetries of graphene and may cause intervalley scattering. We show that the presence of such defects also leads to the suppression of $\xi$, with carrier concentration dependence similar to those produced by the intrinsic SOI, but qualitatively different from the effects of Rashba SOI, allowing their simultaneous determination. Finally, we show the effects of such defects on skew scattering, and the dependence of the SH angle on the relative strength of such disorder.\\[4pt] [1] Monteverde et al.,PRL 104, 126801(2010)\\[0pt] [2] Asmar and Ulloa, PRL 112, 136602(2014)\\[0pt] [3] Ferreira et al.,PRL 112, 066601(2014)   

Extrinsic Spin Hall Effect Induced by Resonant Skew Scattering in Graphene

We show that the extrinsic spin Hall effect can be engineered in monolayer graphene by decoration with small doses of adatoms, molecules, or nanoparticles originating local spin-orbit perturbations. The analysis of the single impurity scattering problem shows that intrinsic and Rashba spin-orbit local couplings enhance the spin Hall effect via skew scattering of charge carriers in the resonant regime. The solution of the transport equations for a random ensemble of spin-orbit impurities reveals that giant spin Hall currents are within the reach of the current state of the art in device fabrication. The spin Hall effect is robust with respect to thermal fluctuations and disorder averaging.   

Weyl Nodes in Trigonal Tellurium and Selenium

Singular points in the momentum space (Dirac nodes) have been under intensive investigation recently. Among various Dirac systems, materials having three-dimensional Dirac nodes without spin degeneracy (Weyl nodes) are of particular interest because of their topological nature. We study trigonal Te and Se as systems having both strong spin-orbit interaction (SOI) and broken inversion symmetry, which is necessary for the Weyl node. We calculate the electronic structure by using QMAS [1] based on relativistic density functional theory, and add the self-energy correction in the GW approximation. Te and Se are insulating at ambient pressure. The conduction bands have a spin splitting similar to the Rashba splitting around the H points, but unlike the Rashba splitting the spin directions are radial, forming a hedgehog spin texture. The energy gap decreases with increasing pressure. In the metallic phase, the spin rotates twice around H on the k$_{\mathrm{z}} = \pm \pi$/c plane, which can be explained by the motion of the Weyl nodes under pressure [2]. We also find that trigonal Te shows the Weyl semimetal phase with time-reversal symmetry under pressure [2].\\[4pt] [1] http://www.qmas.jp/\\[0pt] [2] M. Hirayama, R. Okugawa, S. Ishibashi, S. Murakami, and T. Miyake: arXiv 1409.6399.   

Spin relaxation and transport mechanics in ZnO thin films

Zinc oxide has been widely used in optoelectronic and lasing application due to its wide-bandgap and large exciton binding energy. In recent studies, it has also been studied for spintronic device applications due to its relatively large spin-orbit coupling and potential as a dilute magnetic semiconductor. However, a fundamental understanding of spin transport and relaxation mechanisms has not yet been reached. Knowledge of these mechanisms is required in order to accurately explain and enhance spin-based effects in ZnO. To study spin transport and relaxation in ZnO, four-probe non-local Hanle measurements were performed on thin film samples. These samples were grown using a pulsed laser deposition technique under low ambient oxygen pressure. Under these conditions, the films grown are degenerately doped, with a carrier concentration on the order of 10$^{\mathrm{19}}$ cm$^{\mathrm{-3}}$. Taking this into account, the spin lifetime results can be explained by Dyakonov-Perel (DP) relaxation mechanisms using Fermi-Dirac statistics.   

Hyperfine-induced spin relaxation of a hopping carrier: implications for spin transport in 1-D vs 3-D organic semiconductors

The hyperfine coupling of a carrier spin to a nuclear spin bath is a predominant channel for the carrier spin relaxation in organic semiconductors. We investigate the hyperfine-induced spin relaxation of a carrier performing a random walk on a $d$-dimensional regular lattice theoretically, in a transport regime typical for organic semiconductors. We show that in $d=1$ and $d=2$ the time dependence of spin polarization, $P(t)$, is dominated by a superexponential decay, crossing over to an exponential tail at long times. The faster decay is attributed to multiple self-intersections (returns) of the random walk trajectories, which occur more often in lower dimensions. We also show, analytically and numerically, that the returns lead to sensitivity of $P(t)$ to external electric and magnetic fields, and this sensitivity strongly depends on dimensionality of the system ($d=1$ vs. $d=3$). Furthermore, we consider the coordinate dependence of spin polarization, $\sigma(r)$, in a hypothetic lateral or vertical organic spin-valve device. We demonstrate that, while $\sigma(r)$ is essentially exponential, the effect of multiple self-intersections can be identified in transport measurements from the specific field-dependence of spin relaxation length.   

Dissecting the mechanisms of magnetocrystalline anisotropy in alloys: Electronic structure analysis tools and applications to (Fe$_{1-x}$Co$_x$)$_2$B and Li$_{3-x}$Fe$_x$N alloys

We describe a first-principles code and a set of tools providing detailed information about the mechanisms of the magnetocrystalline anisotropy (MCA) in alloys. The spin-orbit coupling (SOC) is included in the Green's function-based linear muffin-tin orbital (LMTO) method combined with the coherent potential approximation. Third-order correspondence with the LMTO Hamiltonian is formally demonstrated. The analysis tools include the identification of contributions from different spin channels, single-ion and two-ion terms and alloy components by computing the SOC energy with scaled SOC parameters, as well as a full reciprocal-space resolution of MCA in the Brillouin zone. Application of these tools is illustrated for the (Fe$_{1-x}$Co$_x$)$_2$B system, where the complicated non-monotonic concentration dependence of MCA is attributed to the combination of band filling and SOC selection rules. For Li$_{3-x}$Fe$_x$N we demonstrate the interplay between chemical disorder, orbital polarization, and correlation effects in a doubly degenerate impurity band.