Spin transport and relaxation in graphene

We review our recent work on spin injection, transport and relaxation in graphene. The spin injection and transport in single layer graphene (SLG) were investigated using nonlocal magnetoresistance (MR) measurements. Spin injection was performed using either transparent contacts (Co/SLG) or tunneling contacts (Co/MgO/SLG). With tunneling contacts, the nonlocal MR was increased by a factor of ∼1000 and the spin injection/detection efficiency was greatly enhanced from ∼1% (transparent contacts) to ∼30%. Spin relaxation was investigated on graphene spin valves using nonlocal Hanle measurements. For transparent contacts, the spin lifetime was in the range of 50-100 ps. The effects of surface chemical doping showed that for spin lifetimes in the order of 100 ps, charged impurity scattering (Au) was not the dominant mechanism for spin relaxation. While using tunneling contacts to suppress the contact-induced spin relaxation, we observed the spin lifetimes as long as 771 ps at room temperature, 1.2 ns at 4 K in SLG, and 6.2 ns at 20 K in bilayer graphene (BLG). Furthermore, contrasting spin relaxation behaviors were observed in SLG and BLG. We found that Elliot-Yafet spin relaxation dominated in SLG at low temperatures whereas Dyakonov-Perel spin relaxation dominated in BLG at low temperatures. Gate tunable spin transport was studied using the SLG property of gate tunable conductivity and incorporating different types of contacts (transparent and tunneling contacts). Consistent with theoretical predictions, the nonlocal MR was proportional to the SLG conductivity for transparent contacts and varied inversely with the SLG conductivity for tunneling contacts. Finally, bipolar spin transport in SLG was studied and an electron-hole asymmetry was observed for SLG spin valves with transparent contacts, in which nonlocal MR was roughly independent of DC bias current for electrons, but varied significantly with DC bias current for holes. These results are very important for the use of graphene for spin-based logic and information storage applications.     

Spin relaxation in single-layer and bilayer graphene

We investigate spin relaxation in graphene spin valves and observe strongly contrasting behavior for single-layer graphene (SLG) and bilayer graphene (BLG). In SLG, the spin lifetime (τ(s)) varies linearly with the momentum scattering time (τ(p)) as carrier concentration is varied, indicating the dominance of Elliot-Yafet (EY) spin relaxation at low temperatures. In BLG, τ(s) and τ(p) exhibit an inverse dependence, which indicates the dominance of Dyakonov-Perel spin relaxation at low temperatures. The different behavior is due to enhanced screening and/or reduced surface sensitivity of BLG, which greatly reduces the impurity-induced EY spin relaxation.     

Observation of long spin-relaxation times in bilayer graphene at room temperature

We report on the first systematic study of spin transport in bilayer graphene (BLG) as a function of mobility, minimum conductivity, charge density, and temperature. The spin-relaxation time τ(s) scales inversely with the mobility μ of BLG samples both at room temperature (RT) and at low temperature (LT). This indicates the importance of D'yakonov-Perel' spin scattering in BLG. Spin-relaxation times of up to 2 ns at RT are observed in samples with the lowest mobility. These times are an order of magnitude longer than any values previously reported for single-layer graphene (SLG). We discuss the role of intrinsic and extrinsic factors that could lead to the dominance of D'yakonov-Perel' spin scattering in BLG. In comparison to SLG, significant changes in the carrier density dependence of τ(s) are observed as a function of temperature.     

Resonant tunneling and enhanced Goos–Hänchen shift in a graphene double velocity barrier structure

Resonant transmission and Goos–Hänchen (GH) shift for Dirac fermion beams tunneling through graphene double velocity barrier structures (DVBs) are investigated theoretically. Analytical and numerical results demonstrate that strong resonant tunneling effect occurs in this structure and is highly dependent on the incident angle and the structure of velocity barriers. The resonant tunneling in graphene DVBs belongs to the Fabry–Pérot resonance and leads to oscillated conduction at wide energy range. It is also found that GH shifts in this structure can be enhanced by the resonant tunneling and multi-GH shift peaks with giant magnitudes can occur at these resonant energy positions. These special properties of GH shifts in graphene DVBs may have good application in lateral manipulation of electron beams and valley or spin beam splitter.     

Enhanced spin polarization in an asymmetric magnetic graphene superlattice

The authors investigate the spin-resolved transport through an asymmetrical magnetic graphene superlattice (MGS) consisting of the periodic barriers with abnormal one in height. To quantitatively depict the asymmetrical MGS, an asymmetry factor has been introduced to measure the height change of the abnormal barrier. It is shown that the spin filter effect is strongly enhanced by the barrier asymmetry both in the Klein and the classical tunneling regimes. In the presence of abnormal barrier, the conductance with certain spin direction is suppressed with respect to different tunneling regimes, and thus high spin polarization with opposite sign can be achieved.     

Two-dimensional topological insulator state and topological phase transition in bilayer graphene

We show that gated bilayer graphene hosts a strong topological insulator (TI) phase in the presence of Rashba spin-orbit (SO) coupling. We find that gated bilayer graphene under preserved time-reversal symmetry is a quantum valley Hall insulator for small Rashba SO coupling λ(R), and transitions to a strong TI when λ(R)>√[U(2)+t(⊥)(2)], where U and t(⊥) are, respectively, the interlayer potential and tunneling energy. Different from a conventional quantum spin Hall state, the edge modes of our strong TI phase exhibit both spin and valley filtering, and thus share the properties of both quantum spin Hall and quantum valley Hall insulators. The strong TI phase remains robust in the presence of weak graphene intrinsic SO coupling.     

Interplay of spin accumulation and Coulomb blockade in double ferromagnetic junctions

Single-electron tunneling in a double junction in which a nonmagnetic metallic island is separated from two ferromagnetic electrodes by tunnel barriers, is analysed theoretically in the sequential tunneling regime and for an arbitrary intrinsic spin relaxation time on the island. It is shown that nonequilibrium spin polarization of the island results in tunnel magnetoresistance due to rotation of the electrode magnetizations from antiparallel to parallel alignment. It is also shown that discrete charging of the island gives rise to a fine structure in the voltage dependence of the island spin polarization and tunnel magnetoresistance     

Effect of temperature,electric and magnetic field on spin relaxation in single layer graphene: A Monte Carlo simulation study

In this article, we employ the semiclassical Monte Carlo approach to study the spin polarized electron transport in single layer graphene channel. The Monte Carlo method can treat non-equilibrium carrier transport and effects of external electric and magnetic fields on carrier transport can be incorporated in the formalism. Graphene is the ideal material for spintronics application due to very low Spin Orbit Interaction. Spin relaxation in graphene is caused by D'yakonov-Perel (DP) relaxation and Elliott-Yafet (EY) relaxation. We study effect of electron electron scattering, temperature, magnetic field and driving electric field on spin relaxation length in single layer graphene. We have considered injection polarization along z-direction which is perpendicular to the plane of graphene and the magnitude of ensemble averaged spin variation is studied along the x-direction which is the transport direction. This theoretical investigation is particularly important in order to identify the factors responsible for experimentally observed spin relaxation length in graphene.     

Effect of electric field and magnetic field on spin transport in bilayer graphene armchair nanoribbons: A Monte Carlo simulation study

In this article we study the effect of external magnetic field and electric field on spin transport in bilayer armchair graphene nanoribbons (GNR) by employing semiclassical Monte Carlo approach. We include D'yakonov-Perel' (DP) relaxation due to structural inversion asymmetry (Rashba spin-orbit coupling) and Elliott-Yafet (EY) relaxation to model spin dephasing. In the model we neglect the effect of local magnetic moments due to adatoms and vacancies. We have considered injection polarization along z-direction perpendicular to the plane of graphene and the magnitude of ensemble averaged spin variation is studied along the x-direction which is the transport direction. To the best of our knowledge there has been no theoretical investigation of the effects of external magnetic field on spin transport in graphene nanoribbons. This theoretical investigation is important in order to identify the factors responsible for experimentally observed spin relaxation length in graphene GNRs.     

Electrical pump-and-probe study of spin singlet-triplet relaxation in a quantum dot

Spin relaxation from a triplet excited state to a singlet ground state in a semiconductor quantum dot is studied by employing an electrical pump-and-probe method. Spin relaxation occurs via co-tunneling when the tunneling rate is relatively large, confirmed by a characteristic square dependence of the relaxation rate on the tunneling rate. When co-tunneling is suppressed by reducing the tunneling rate, the intrinsic spin relaxation is dominated by spin-orbit interaction. We discuss a selection rule of the spin-orbit interaction based on the observed double-exponential decay of the triplet state.     

Spin thermopower and thermoconductance in a ferromagnetic graphene nanoribbon

The spin thermoelectric properties of a zigzag edged ferromagnetic (FM) graphene nanoribbon are studied theoretically by using the non-equilibrium Green's function method combined with the Landauer-Büttiker formula. By applying a temperature gradient along the ribbon, under closed boundary conditions, there is a spin voltage ΔV(s) inside the terminal as the response to the temperature difference ΔT between two terminals. Meanwhile, the heat current ΔQ is accompanied from the 'hot' terminal to the 'cold' terminal. The spin thermopower S?=?ΔV(s)/ΔT and thermoconductance κ?=?ΔQ/ΔT are obtained. When there is no magnetic field, S versus E(R) curves show peaks and valleys as a result of band selective transmission and Klein tunneling with E(R) being the on-site energy of the right terminal. The results are in agreement with the semi-classical Mott relation. When |E(R)|??M, the quantized value of [Formula: see text] appears. In the quantum Hall regime, because Klein tunneling is suppressed, S peaks are eliminated and the quantized value of κ is much clearer. We also investigate how the thermoelectric properties are affected by temperature, FM exchange split energy and Anderson disorder. The results indicate that S and κ are sensitive to disorder. S is suppressed for even small disorder strengths. For small disorder strengths, κ is enhanced and for moderate disorder strengths, κ shows quantized values.     

Interfacial electronic structure at a metal–phthalocyanine/graphene interface:Copper–phthalocyanine versus iron–phthalocyanine

The energy level alignment of CuPc and FePc on single-layer graphene/Ni(111)(SLG/Ni)substrate was investigated by using ultraviolet and X-ray photoelectron spectroscopy(UPS and XPS).The highest occupied molecular orbitals(HOMOs)in a thick layer of CuPc and FePc lie at 1.04 eV and 0.90 eV,respectively,below the Fermi level of the SLG/Ni substrate.Weak adsorbate–substrate interaction leads to negligible interfacial dipole at the CuPc/SLG/Ni interface,while a large interfacial dipole(0.20 eV)was observed in the case of FePc/SLG/Ni interface,due to strong adsorbate–substrate coupling.In addition,a new interfacial electronic feature was observed for the first time in the case of FePc on SLG/Ni substrate.This interfacial state can be attributed to a charge transfer from the SLG/Ni substrate to unoccupied orbitals of FePc.     

Transport in magnetic graphene superlattice with Rashba spin-orbit interaction

Based on the transfer-matrix method, we have investigated the spin-dependent transport properties of magnetic graphene superlattice in the presence of Rashba spin-orbit interaction (RSOI). It is shown that the angular range of the spin transmission probability through magnetic graphene superlattice can be efficiently controlled by the number of barriers. As the number of magnetic barriers increases, the angular range of the transmission through the magnetic superlattice decreases, the gaps in the transmission and conductivity versus energy become wider. It is also found that the spin conductivities oscillate with the Fermi energy and RSOI strength. Specifically, when a magnetic field is present, the spin polarisation can be observed, whereas for the RSOI alone it is zero. Application of such a phenomenon to design a spin polarised electron device based on the graphene material is anticipated.     

Spin relaxation times in disordered graphene

We consider two mechanisms of spin relaxation in disordered graphene. i) Spin relaxation due to curvature spin orbit coupling caused by ripples. ii) Spin relaxation due to the interaction of the electronic spin with localized magnetic moments at the edges. We obtain analytical expressions for the spin relaxation times τ_SO and τ_J due to both mechanisms and estimate their values for realistic parameters of graphene samples. We obtain that spin relaxation originating from these mechanisms is very weak and spin coherence is expected in disordered graphene up to samples of length .     

Spin relaxation mechanism of hopping transport in a 2D asymmetric quantum dot array

Spin relaxation is studied in the hopping conduction mode in 2D arrays of quantum dots (QDs) with structural asymmetry. It is shown that the absence of the “up-down” symmetry in a QD leads to the emergence of a new spin relaxation mechanism in tunneling in a 2D QD array. The difference in spin relaxation mechanisms for symmetric and asymmetric QDs is demonstrated on the basis of theoretical analysis of an elementary event (jump between two tunnel-coupled dots). It is shown that spin flip during tunneling between QDs is the main spin relaxation mechanism in the transport in dense arrays of QDs in Ge placed in weak (1–10 T) magnetic fields.     

Magnetotransport in a graphene monolayer with two tunable magnetic barriers

The magnetotransport property for a monolayer graphene with two turnable magnetic barriers has been investigated by the transfer-matrix method. We show that the parameters of barrier height, width, and interval between two barriers affect the electron wave decaying length, which determine the conductance with parallel or antiparallel magnetization configuration, and consequently the tunneling magnetoresistance (TMR) for the system. Interestingly, a graphene attached by two barriers with different heights can produce a resonant TMR peak at low energy region one order of magnitude larger than that for the system with two same height barriers because that the asymmetry of magnetic barriers block the electron transmission in the case of antiparallel magnetization configuration. The results obtained here may be useful in understanding of electron tunneling in graphene and in designing of graphene-based nanodevices.     

Spin-polarized tunneling in a ferromagnetic graphene junction: Interplay between the exchange interaction and the orbital effect of the magnetic field

The influence of magnetic vector potential barrier (MVPB) on the spin-polarized transport of massless Dirac particles in ferromagnetic graphene is studied theoretically. The phenomenon of Klein tunneling of relativistic particles across a rectangular potential barrier prevents any of the massless fermions from being confined but they can be electrically confined by quantum dots with integrable dynamics (Bardarson et al., 2009) [36]. Utilization of only the in-plane exchange splitting in the ferromagnetic graphene cannot produce 100% spin polarization. This tunneling can be confined using the magnetic vector potential barrier, which leads to high degree of spin polarization. By combining the orbital effect and the Zeeman interaction in graphene junction, it is found that the junction mimics behavior of half-metallic tunneling junction, in which it acts as a metal to particles of one spin orientation but as an insulator or a semiconductor to those of the opposite orientation. The idea of the half-metallic tunneling junction can provide a source of ∼100% spin-polarized current, which is potentially very useful. Adjustment of the position of the Fermi level in ferromagnetic layer by placing a gate voltage on top of the ferromagnetic layer shows that reverse of the orientation of the completely spin-polarized current passing through the junction is controlled by adjusting the gate voltage. These interesting characteristics should lead to a practical gate voltage controlled spin filtering and spin-polarized switching devices as a perfect spin-polarized electron source for graphene-based spintronics.     

Tunneling of Dirac fermions through magnetic barriers in graphene

We have studied the tunneling of Dirac fermions through magnetic barriers in graphene. Magnetic barriers are produced via delta function-like inhomogeneous magnetic fields in which Dirac fermions in graphene experience the tunneling barrier in the real sense in contrast to Klein paradox caused by electrostatic barriers. The transmission through the magnetic barriers as functions of incident energy and angle of incoming fermions shows characteristic oscillations associated with tunneling resonances. We have also found the confined states in the magnetic barrier region which turn out to correspond to the total internal reflection in the usual optics.     

Resonant tunneling through double-barrier structures on graphene

Quantum resonant tunneling behaviors of double-barrier structures on graphene are investigated under the tightbinding approximation. The Klein tunneling and resonant tunneling are demonstrated for the quasiparticles with energy close to the Dirac points. The Klein tunneling vanishes by increasing the height of the potential barriers to more than 300 meV. The Dirac transport properties continuously change to the Schro¨dinger ones. It is found that the peaks of resonant tunneling approximate to the eigen-levels of graphene nanoribbons under appropriate boundary conditions. A comparison between the zigzag- and armchair-edge barriers is given.     

Time domain capacitance spectroscopy of tunneling electrons in the two-dimensional electron gas

We have developed a technique capable of measuring the tunneling current into both localized and conducting states in a 2D electron system (2DES). The method yields I-V characteristics for tunneling with no distortions arising from low 2D in-plane conductivity. We have used the technique to determine the pseudogap energy spectrum for electron tunneling into and out of a 2D system and, further, we have demonstrated that such tunneling measurements reveal spin relaxation times within the 2DEG. Pseudogap: In a 2DEG in perpendicular magnetic field, a pseudogap develops in the tunneling density of states at the Fermi energy. We resolve a linear energy dependence of this pseudogap at low excitations. The slopes of this linear gap are strongly field dependent. No existing theory predicts the observed behavior. Spin relaxation: We explore the characteristics of equilibrium tunneling of electrons from a 3D electrode into a high mobility 2DES. For most 2D Landau level filling factors, we find that electrons tunnel with a single, well-defined tunneling rate. However, for spin-polarized quantum Hall states (ν=1, 3 and 1/3) tunneling occurs at two distinct rates that differ by up to two orders of magnitude. The dependence of the two rates on temperature and tunnel barrier thickness suggests that slow in-plane spin relaxation creates a bottleneck for tunneling of electrons.