Session Q14: Focus Session: Spins in Semiconductors - Spin Dependent Transport

Determination of Rashba and Dresslhaus coefficient in InGaAs quantum wells

We report the determination of the intrinsic spin-orbit interaction (SOI) parameters for In$_{0.53}$Ga$_{0.47}$As/In$_{0.52}$Al$_{0.48}$As quantum wells (QWs) from the analysis of the weak antilocalization effect measured at dilution temperature [1]. We found that the Dresselhaus SOI is mostly negligible relative to the Rashba SOI in this system. The intrinsic parameter for the Rashba effect, a$_{\rm SO}\equiv \alpha/\langle E_z \rangle$, is determined to be a$_{\rm SO}m^*/m_e = (1.46-1.51 \times 10^{-17}N_{\rm S}$ [m$^{-2}$]) $e${\AA}$^2$, where $\alpha$ is the Rashba SOI coefficient, $\langle E_z \rangle$ is the expected electric field within the QW, $m^*/m_e$ is the electron effective mass ratio, and $N_{\rm S}$ is the sheet carrier density. The $N_{\rm S}$ dependence of a$_{\rm SO}$ corrsponds to the non-parabolic correction in the effective mass or electron g-factor. These values for a$_{\rm SO}m^*$, which are in good agreement with the thoretical prediction by Kane's ${\bf k\cdot p}$ theory, were also confirmed by the observation of beatings in the Shubnikov-de Haas oscillations in our most asymmetric QW sample.\\[4pt] [1] S. Faniel {\it et. al.}, PHYSICAL REVIEW B {\bf 83}, 115309 (2011).   

Spin-dependent scattering in the presence of polarized nuclei in n-GaAs

We report on all-electrical measurements of the inverse spin Hall effect (ISHE) in epitaxial (100) Fe/GaAs heterostructures with a channel doping (Si) of $n =5\times 10^{16}$~cm$^{-3}$ and highly doped Schottky tunnel barriers. Under measurement conditions of large (10-20\%) spin accumulation at the injection electrode, a significant dynamic nuclear polarization (DNP) enhances the size of the ISHE. The electron spin dynamics are shown to match the predictions of the usual drift-diffusion model, including the applied, hyperfine, and Knight fields. The DNP, however, also enhances the scattering of spin-polarized carriers, which is not understood. To separate the roles of the electronic and nuclear spin systems, we have employed a pump-probe method to vary the nuclear spin polarization $\langle I \rangle$ and electron spin polarization $S$ independently. The size of the ISHE is proportional to $\langle I \rangle$ when the DNP is small, but it eventually saturates. When the nuclear polarization is fixed, the ISHE is linear in $S,$ as expected. We conclude therefore that the measured signal scales linearly with the spin current multiplied by a transport skewness parameter that depends strongly on $\langle I \rangle$.   

Nuclear enhancement of the spin Hall angle in $n$-In$_{x}$Ga$_{1-x}$As

We present measurements of the inverse spin Hall effect in vertical Fe/In$_{x}$Ga$_{1-x}$As heterostructures as identified via a Hanle effect in the local Hall voltage. The spin Hall angle is greatly enhanced in the presence of polarized nuclei, achieving typical values of $\gamma\simeq5\times10^{-2}$. Phenomenological modeling of the observed line-shapes shows that the nuclear polarization acts as a linear prefactor to the standard spin Hall conductivity. This enhancement far exceeds expectations based on the energy splitting of the electron or nuclear spin systems. Our samples are doped just above the Mott transition ($n\simeq3n_c$) where metallic impurity band conduction is dominant. A strong coupling between localized moments and delocalized states is evidenced by the temperature dependence and sensitivity to disorder at higher In concentrations. This leads us to interpret our results using an Anderson-like model of polarized impurities whereby both dynamic nuclear polarization and resonant skew scattering arise as a result of a spin polarized doubly occupied $\left(D^{-}\right)$ impurity band.   

Spin Hall effect for detection of spin-currents -- Realization of a Spin transistor

The realization of a viable semiconductor transistor and information processing devices based on the electron spin has fueled intense basic research of three key elements: injection, detection, and manipulation of spins in the semiconductor microchannel. The inverse spin Hall effect (iSHE) detection of spins manipulated by a gate electrode [1] has recently led to the experimental demonstration of a spin transistor device. [2] Here, the spin injection into a 2-dimensional electron gas (2DEG) was done optically in the depletion layer of a reverse biased pn-junction. [3] The iSHE detection is also used for electrical spin injection from a Fe electrode into a lateral GaAs channel combined with a simultaneous non-local spin valve measurement [4-10]. The spins in the channel are manipulated via the Hanle spin precession induced by an applied magnetic field and via a drift of electrons induced by an applied electric field. The output spin signal is suppressed or enhanced depending on the applied electrical bias rendering the device to a spin transitor different from the Datta Das concept. [11] \\[4pt] [1] S. Datta and B. Das, Appl. Phys. Lett. 56, 665 (1990). \\[0pt] [2] J. Wunderlich, et al., Science 330,1801 (2010). \\[0pt] [3] J. Wunderlich, et al., Nature Phys., 5, 675 (2009). \\[0pt] [4] X. Lou, Nature Phys. 3, 197 (2007). \\[0pt] [5] M. Ciorga, et al., Phys. Rev. B 79, 165321 (2009). \\[0pt] [6] C. Awo-Affouda, et al., Appl. Phys. Lett. 94, 102511 (2009). \\[0pt] [7] M. K. Chan, et al., Phys. Rev. B 80, 161206(R) (2009). \\[0pt] [8] G. Salis, et al., Phys. Rev. B 80, 115332 (2009). \\[0pt] [9] G. Salis, et al., Phys. Rev. B 81, 205323 (2010). \\[0pt] [10] E. S. Garlid, et al., Phys. Rev. Lett. 105, 156602 (2010). \\[0pt] [11] K. Olejnik, et al., submitted.   

Measurement by antilocalization of interactions between InAs surface electrons and magnetic surface species

Weak-antilocalization (WAL) low-temperature magnetotransport measurements are sensitive to electron quantum coherence, and can be used as a sensitive probe of surface quantum states. We experimentally study interactions between surface electrons and local magnetic moments on InAs by comparing WAL on patterned InAs accumulation layers where rare earth ions or Co$^{2+}$, Co-phthalocyanine, Fe$^{3+}$, and Fe-phthalocyanine were deposited, with those where no magnetic species were deposited. The magnetic species modify the magnetic spin-flip scattering, which carries information about magnetic interactions, and modify the spin-orbit (SO) scattering, identified via the WAL signal and characterized over temperature. Experiments indicate a mostly temperature-independent magnetic spin-flip scattering, except for Ho$^{3+}$. The SO scattering also displays a weak temperature dependence, and is increased by the heavy ions, Co$^{2+}$ and Co-phthalocyanine, while suppressed by ferromagnetic Fe$^{3+}$ and Fe-phthalocyanine, in agreement with the expected absence of the WAL in ferromagnets.   

A Quantitative Analysis of the Electrical Detection of Spins Via the Spin Hall Effect and the Non-Local Spin Valve Effect Within a Semiconductor Microchannel

Recently, the manipulation of spins via a gate electrode, and their subsequent detection through the Spin Hall Effect, has led to the experimental realization of a spin-based semiconductor transistor. While in this experiment, spin injection was achieved optically via circularly-polarized light, we consider a similar experiment using electrical injection by means of a ferromagnetic contact into a GaAs microchannel instead. The spin current in a lateral semiconductor channel is then detected through the Spin Hall Effect, while the spin accumulation nearby is simultaneously measured through the Non-Local Spin Valve Effect (using another Fe electrode). The spins within the channel are manipulated through the Hanle Effect via an external magnetic field, and through a drift induced by an applied electrical bias. To analyze these results, we use analytical and numerical solutions to the steady-state drift-diffusion equations with a constant magnetic field and a drift velocity modeled by a Heaviside Theta function. Combining these results with the anomalous Hall response function, which takes into account the geometry of the Hall probe in order to obtain the correct Hall angle, we obtain results that are in quantitative agreement with experiments.   

Spin-gating of a conventional aluminum single electron transistor

We report the realization of a single electron transistor in which electron transport from an aluminum source electrode to an aluminum drain electrode via an aluminum island is controlled by spins in a capacitively coupled magnetic gate electrode. The origin of the effect is in the change of the chemical potential on the gate, formed by the ferromagnetic semiconductor GaMnAs, with changing the direction of the magnetization. In agreement with experimental observations, microscopically calculated anisotropies of the chemical potential with respect to the magnetization orientation are of the order of 10$\mu$V which is comparable to the electrical gate voltages required to control the on and off state of the single electron transistor. Our phenomenon belongs to the family of anisotropic magnetoresistance effects which can be observed in ohmic, tunneling or other device geometries. In our case, the entire phenomenon is coded in the dependence of the chemical potential on the spin orientation which allowed us to remove the spin functionality from all current contacts and channels and place it in the capacitively coupled gate electrode. Our spintronic device therefore operates without spin current.   

Spin injection from into InSb from CoFe

The strong spin-orbit interaction in InSb is an asset for spin manipulation using electric fields. In order to electrically characterize spin injection and detection in InSb, we experimentally investigate spin injection into InSb from ferromagnetic CoFe electrodes, via non-local spin valve measurements at low temperature. We observe non-local transresistance switching around zero in-plane external magnetic field. We characterize the magnetic properties of the CoFe layer by the Hall signal of the fringing fields and confirm 3-state switching. We verify that the non-local signal is not related to the physical or geometrical magnetoresistance due to the CoFe fringing fields. The non-local spin valve signal is, as typical, dependent on the specific CoFe/InSb interfaces, while the temperature dependence points to a contribution beyond the spin coherence length. We further observe a modification of weak-antilocalization by spin injected carriers and the same phenomenon may contribute to the spin valve transresistance (partial support from DOE DE-FG02-08ER46532).   

Top- and Side-Gated InAs Spinfilter Cascades in Magnetic Fields

We present results from transport experiments on two-stage Y-shaped spin-filter cascades fabricated from InAs heterostructures. The first Y junction acts as a generator of two oppositely spin-polarized currents by employing the intrinsic spin-Hall effect. When the second filter that is attached to one of the first filter's outputs in a distance corresponding to a multiple of the spin-precession length, the spin polarization is revealed as a conductance imbalance at the outputs. To achieve the required quasi one-dimensional transport modes we reduce either the effective width of the cascade's five wires by side-gate quantum-point contacts or we reduce the carrier concentration by means of a top gate. The latter yields the advantage to keep the width along the cascade's wires constant and thus, by ensuring higher homogeneity of the potential, reduces spurious effects in the measured conductances. The application of a magnetic field perpendicular to the cascade's plane results in a Lorentz force acting on the electrons in the cascade and thereby changing the measured conductance imbalance and the spin polarization. This can be used to quantify the strength of the spin-Hall effect in InAs heterostructures.   

Tunable Zeeman-like Spin Splitting with Liquid Gated Field Effect Transistors

Generation of spin polarized electrons is the most critical step for developing spintronics applications. As an electric and nonmagnetic way to realize spin polarization in energy bands, spin-orbit interaction (SOI) has been widely used for spin manipulation in two-dimensional systems. For example, Rashba-type energy splitting with in-plane-polarized spins near \textit{$\Gamma $} point of Brillouin zone (BZ) is able to be modulated by electric field through tuning spatial inversion asymmetry. However, Zeeman-type energy splitting with out-of-plane spin polarization is known to be sensitive only to magnetic field and supposed never to be affected by external electric field. In this paper, we theoretically uncover and experimental confirm a perpendicular-electric-field induced giant Zeeman spin splitting at low symmetric $K$ and $K'$ points in a layered chalcogenide, 2H-WSe$_{2}$. \textit{Ab initio} band calculation and spin texture indicate that an electric field can make low-energy carriers spin-polarized in a out-of-plane Zeeman-type way and a tunable SOI is able to selectively control the size of splitting. A gate-induced crossover from weak localization to weak antilocalization in the magnetotransport serves as an experimental proof for the tunable SOI and spin polarization. The splitting energy deduced from quantum correction of magnetoconductance is as large as 120 meV and satisfied well with the band calculation for Zeeman-type splitting. This finding directly provides us with a new path-way for electrically initializing and manipulating electron spins for spintronics applications.   

Anomalous Hall effect in the Presence of Strong Spin-orbit Coupling and Non-trivial Magnetization

AHE in ferromagnets with strong spin-orbit coupling (SOC) and homogeneous magnetization has been studied extensively, using both Kubo formalism and semi-classical Boltzmann equation. In the opposite limit of weak SOC in the presence of non-trivial magnetization texture and strong exchange coupling with the carriers (adiabatic limit), the electron spins always align themselves with the direction of the local magnetization and they experience an effective magnetic field arising from this non-trivial magnetization, giving rise to the topological anomalous Hall effect. We study here the transition between the two limits and the joint effect that a strong SOC and non-trivial magnetic textures have on the AHE. We will report on results from both perturbative analytical approaches and bulk numerical simulations. Some of these effects may be present and exploited in current induced manipulation and detection of domain walls.   

Spin diffusion and precession at the multiferroic interface and InAs quantum wells

We study spin diffusion and precession in a two-dimensional electron gas at the multiferroic interface and InAs quantum wells respectively by means of the kinetic spin Bloch equation approach [Wu {\it et al.}, Physics reports {\bf 493}, 61 (2010)]. At the AlO$_3$/SrTiO$_3$/TbMnO$_3$ heterostructure with a temperature being as low as 15~K, the two-dimensional electron gas at the LaAlO$_3$/SrTiO$_3$ interface interacts with the spiral magnetic moments of Mn$^{3+}$ in TbMnO$_3$ via the Heisenberg exchange interaction. It is demonstrated that the spin diffusion length at the interface is always finite, despite the polarization direction of the injected spins. It is also revealed that the Coulomb scattering plays an important role and effectively suppresses the spin diffusion. The spin precession in InAs quantum wells is investigated with the Rashba spin-orbit coupling being modulated by a gate voltage. The gate-voltage dependence of spin diffusion under different temperatures is studied with all the scattering explicitly included. Our result partially supports the claim of the realization of the Datta-Das spin-injected field effect-transistor by Koo {\it et al.} [Science {\bf 325}, 1515 (2009)]. We also show that the scattering plays an important role in spin diffusion in such a system.   

Enhanced photon-assisted spin transport in a quantum dot attached to ferromagnetic leads

Time-dependent transport in quantum dot system (QDs) has received significant attention due to a variety of new quantum physical phenomena emerging in transient time scale.[1] In the present work [2] we investigate real-time dynamics of spin-polarized current in a quantum dot coupled to ferromagnetic leads in both parallel and antiparallel alignments. While an external bias voltage is taken constant in time, a gate terminal, capacitively coupled to the quantum dot, introduces a periodic modulation of the dot level. Using non equilibrium Green's function technique we find that spin polarized electrons can tunnel through the system via additional photon-assisted transmission channels. Owing to a Zeeman splitting of the dot level, it is possible to select a particular spin component to be photon-transferred from the left to the right terminal, with spin dependent current peaks arising at different gate frequencies. The ferromagnetic electrodes enhance or suppress the spin transport depending upon the leads magnetization alignment. The tunnel magnetoresistance also attains negative values due to a photon-assisted inversion of the spin-valve effect. [1] F. M. Souza, Phys. Rev. B 76, 205315 (2007). [2] F. M. Souza, T. L. Carrara, and E. Vernek, Phys. Rev. B 84, 115322 (2011).