In this thesis, I studied spin and charge transfer properties in graphene with adatoms, focusing on the spin Hall effect originating from the implanted spin-orbital interaction. In graphene with an Au cluster, at a certain carrier concentration, the dominance of the spin Hall effect was observed, causing nonlocal resistance.
Band structure and electrical properties
These points, called Dirac points, are therefore important for the physics of graphene. a) the lattice structure of graphene. The transport properties of graphene are typically investigated via a graphene Hall-bar device, as shown in Figure 3(a).
Spin-orbit coupling
As shown in Figure 5, this intrinsic spin-orbit coupling opens a gap in the Dirac spectrum of magnitude = 2 I24. Meanwhile, Kane and Mele predicted25-26 the quantum spin hall effect in graphene with intrinsic spin-orbit coupling.
Weak localization
B is magnetic field and T is temperature 27-28. a) Resistivity as a function of the carrier density in the graphene hall bar unit. Points are experimental values found from the fitting of the magnetoconductivity using equation (27) in three different regions30.
Strained graphene
In the absence of strain (figure 8 (c,d)), the curvature of the grains of different Dirac points are opposite. It is shown that the Berry curvature (c) in the absence of the stain and the magnetic field, (d) in the presence of the magnetic field, (e) in the presence of the magnetic field and strain36.
Graphene spintronics
Spin-orbit scattering and spin relaxation mechanism in graphene
Local magnetic moment from point defect
So, the possibility of creating magnetic graphene has attracted a lot of interest, because the magnetic moment in graphene can meet the requirements of increasing magnetic information storage density by ultimately engineering thin or two-dimensional magnetic material. This theorem states that the ground state has a magnetic moment with the sublattice site in a bipartite lattice. Then, to replace a site with an adatom or a vacancy should lead to a magnetic moment in the band if the defect is not strongly coupled to the and band63.
In hydrogenated graphene, McCreary et al60 showed that magnetic moment generation can be detected via spin transport with a spin valve device. Also, the sharpening of the Hanle curve after hydrogen exposure indicates the formation of magnetic moments (Fig. 16(b)) because the presence of an exchange field can significantly enhance the spin precession. The sharpening of the Hanle curve is due to the presence of an exchange field due to the atomic hydrogen in graphene60.
Proximity effect on ferromagnetic substrate
Zeeman spin Hall effect in graphene/EuS heterostructures. a) Non-local resistance (this non-local signal will be discussed in detail in the next chapter "spin Hall effect") as a function of gate voltage under different magnetic fields for CVD graphene/EuS heterostructure at 4.2K. The inset is a TEM cross-sectional image of the device. The proximity effect in graphene coupled to a BiFeO3 nanoplate. a) Back gate voltage dependence of resistance of the BFO/graphene heterostructure device.
Spin Hall effect
Intrinsic mechanism
The spin-dependent Hall effect, which are AHE, SHE, ISHE, originates from the intrinsic, oblique and/or lateral hopping mechanism. The intrinsic mechanism can be explained by the anomalous velocity arising from the Berry phase in the momentum space. The Berry phase is similar to the Aharonov-Bohm phase of a charged particle traversing a loop in the presence of a magnetic current81. If R(t) moves slowly along a path C in the parameter space (in an adiabatic evolution of the system), it is useful to introduce an instantaneous orthonormal basis from the eigenstates of H(R) at each value of the R parameter.
Here we can require that the phase of the basis function is smooth and has a single value along the path C in the parameter space. This shows that 𝛾𝑛 can only be changed by an integer multiple of 2 in the gauge transformation and cannot be removed. The approximate Hamiltonian experienced by the wavepacket can be obtained by linearizing the perturbations around the center of the wavepacket rc as 𝐻 ≈ 𝐻𝑐+ ∆𝐻.
Extrinsic mechanism
If the up-spin is scattered down by impurities, 𝑳̂ ∙ 𝑺̂ is subtracted from the nonspin-orbit coupling potential energy V(r). A basic semiclassical argument for this mechanism can be given that an electron wave with an incident wave vector k will undergo a shift transverse to k if we consider the scattering of a Gaussian wave packet from a spherical impurity by spin-orbit coupling (equation 26). A common design for the lateral hopping mechanism can generally be calculated by considering the spin-orbit coupling of the disorder scattering potential.
However, when dealing with materials with strong spin-orbit coupling, there are always two sources of lateral hopping scattering71. One is the external lateral hopping which is the contribution arising from the non-spin-orbit coupled part of the wavepacket scattering out of the spin-orbit coupled disorder. The other is the internal lateral hopping which is the contribution arising from the spin-orbit coupled part of the wavepacket formed by block electrons scattering only the scalar potential without spin-orbit coupling.
Spin hall effect in graphene
In 2013, the spin Hall effect in hydrogenated graphene92, which was used as a model system to improve spin-orbit coupling in graphene, was observed with nonlocal measurement. Here, the non-local measurement method to find spin Hall effect with reverse spin hall effect in an H-rod device was proposed by Hankiewicz et al. From a non-montonic oscillatory dependence of the non-local signal with equation 58, the spin Hall angle of the CVD graphene was ~ 0.2 at room temperature.
The spin Hall effect in hydrogenated graphene. a) Measurement schemes for the non-local spin Hall resistance. The spin Hall effect in CVD graphene. a) AFM three-dimensional surface topography of a spin Hall device with details of actual measurement configurations. No spin Hall effect in hydrogenated (a-c)95 and adatom-decorated graphene (d-f) 96. a) SEM image of hydrogenated graphene.
Experimental method
Measurement
Figure 33 (a) indicates the characteristic feature of the field effect, and Figure 33 (b), (c) shows the quantum Hall effect in graphene. As shown in the figure, an out-of-plane magnetic field is used for the quantum Hall effect and quantum interference of graphene. Measurement setup for charge and spin transfer. a) Wiring of a graphene H-bar device on a sample wafer for quantum Hall effect and magnetoresistance.
The conduction of graphene H-bar device on sample puck to spin precession from spin Hall effect. This nano-voltmeter can detect electric potential up to 10-8 V. Field effect property and quantum Hall effect in graphene H-bar device. one). The resistivity as a function of gate voltage at 10K. The neutral charge point is around 2V. b), (c) The resistivity and Hall resistivity as a function of gate voltage with 8.8T at 2K.
Spin Hall induced nonlocal resistance in Au-clustered graphene
Experiment methods
Local and non-local electric transport
The rounding of a region of maximum resistance and the decrease in mobility of the Au-clustered graphene compared to that of the grown CVD graphene imply that the Au clusters introduce significant charged impurity scatterings110. Similar to the local FET curve, RNL displayed the maximum value near the charge neutral point for all channels of device A. Non-local device geometry and RNL measured for device A. a) Schematic representation of the H-rod geometry of the graphene device.
Dominance of the 2D peak over the G peak was observed, suggesting that the studied CVD graphene was mainly a single layer. A small shift of the 2D peak suggests that a partial strain is applied to the graphene layer due to the top Au patch. However, the observed RNL in our device shows something similar to the derivative of the FET peak near the Dirac point.
Gate-dependent spin Hall effect
RNL as a function of the in-plane magnetic field measured at different gate voltages and at T = 3K. The two main processes attributed to spin relaxation in graphene are the D'yakonov-Perel' (DP)52 and EY51 mechanisms. My results show that s-1 is proportional to T2, indicating that EY spin relaxation prevails over DP spin relaxation.
When EY spin relaxation is dominant, the strength of spin–orbit coupling can be deduced from 119–120. The red lines are fits to Eq. b) Temperature dependence of the parameters taken from fitting with Eq. The green and red lines are the predicted temperature dependences for DP and EY spin relaxation mechanisms, respectively.
Symmetry spin-orbit scattering
Spin Halls as Adatom-decorated graphene. a) Schematic representation of the six-terminal graphene used to calculate the nonlocal resistance and Hall spin angle. The gate-dependent nonlocal resistance in the graphene H-bar is not directly related to the spin Hall effect and the inverse spin Hall effect. Quantum Hall effect of Al2O3/Fe/graphene device. a) Resistance as a function of gate voltage under B = 9 T at 2K. The inset is the Hall resistance measured at the gate of 10 V. b) Dependence of the gate voltage on the magnetic field (Vg−VD) for = ±2 states.
Farajollahpour, T.; Phirouznia, A., The role of the strain-induced population imbalance in valley polarization of graphene: Berry curvature perspective. D.; Hoffmann, A., Negative non-local resistance in mesoscopic gold saddle bars: absence of the giant spider neck effect. Gate-dependent spin Hall induced non-local resistance and the symmetry of spin-orbit scattering in Au clustered graphene”.
Discussion and summary
Introduction
Xiaojie Liu and co-workers reported134 that adsorption of transition metals (Fe, Co and Ni) on graphene showed strong covalent bonding with graphene, causing large in-plane lattice distortion in the graphene layer with strong magnetic moment and spin-polarized density of states. It was reported experimentally 137 - 139 that evaporation of alumina on graphene gave rise to defects in graphene. The gate-dependent non-local resistance in the graphene H-bar type is not directly associated with the spin Hall effect, because the non-local signal may contain many contributions such as Valley Hall, ohmic potential, offset voltage and ballistic limits.
Stampfer, C.; Beschoten, B., Nanosecond spin life in single- and minus-layer graphene-hBN heterostructure at room temperature. Wang, Z.; Tang, C.; Sachs, R.; Barlas, Y.; Shi, J., Neighborhood-induced ferromagnetism in graphene reveals anomalous Hall effect. Weke, C.; Hu, J.; Alicea, J.; Franz, M.; Wu, R., Engineering a Robust Quantum Spin Hall State in Graphene via Adatom Deposition.
Metal insulator transition
The splitting of zeroth Landau level
Ojeda-Aristizabal, C.; Monteverde, M.; Weil, R.; Ferrier, M.; Guéron, S.; Bouchiat, H., Conductivity fluctuations and rectification field asymmetry in graphene.
Discussion and summary
Conclusion
