Extrinsic Spin-orbit Coupling Research Articles

Accelerated Ultrafast Magnetization Dynamics at Graphene/CoGd Interfaces.

Atomically thin graphene layers can act as a spin-sink material when adjacent to a nanoscale magnetic surface. The enhancement in the extrinsic spin-orbit coupling (SOC) strength of graphene plays an important role in absorbing the spin angular momentum injected from the magnetic surface after perturbation with an external stimulus. As a result, the dynamics of the excited spin system is modified within the magnetic layer. In this paper, we demonstrate the modulation of ultrafast magnetization dynamics at graphene/ferrimagnet interfaces using the time-resolved magneto-optical Kerr effect (TRMOKE) technique. Magnetically modified interfaces with a systematic increase in the number of graphene layers coupled with the 10 nm-thick Co74Gd26 layer are studied. We find that the variation in the dynamical parameters, i.e., ultrafast demagnetization time, remagnetization times, decay time, effective damping, precessional frequency, etc., observed at different time scales is interconnected. The demagnetization time and decay time for the ferrimagnet become approximately two times faster than the corresponding intrinsic values. We found a possible correlation between the demagnetization time and damping. The effect is more pronounced for the interfaces with monolayer graphene and graphite. The spin-mixing conductance is found to be approximately 0.8 × 1015 cm-2. The effect of SOC, pure spin current, the appearance of structural defects, and thermal properties at the graphene/ferrimagnet interface are responsible for the modifications of several dynamical parameters. This work demonstrates some important properties of the graphene/ferrimagnet interface which may unravel the possibilities of designing spintronic devices with elevated performance in the future.

Spin-valley Silin modes in graphene with substrate-induced spin-orbit coupling

In the presence of external magnetic field the Fermi-liquid state supports oscillatory spin modes known as Silin modes. We predict the existence of the generalized Silin modes in a multivalley system, monolayer graphene. A gauge- and Berry-gauge- invariant kinetic equation for a multivalley Fermi liquid is developed and applied to the case of graphene with extrinsic spin-orbit coupling (SOC). The interplay of SOC and Berry curvature allows for the excitation of generalized Silin modes in the spin and valley-staggered-spin channels via an AC electric field. The resonant contributions from these modes to the optical conductivity are calculated.

Supercurrent-induced long-range triplet correlations and controllable Josephson effect in superconductor/ferromagnet hybrids with extrinsic spin-orbit coupling

We predict that long-range triplet correlations (LRTC) in superconductor/ferromagnet (S/F) hybrids with extrinsic impurity spin-orbit coupling can be generated and manipulated by supercurrent flowing in the superconducting leads along the S/F interfaces. The LRTC appear via two basic mechanisms. The essence of the first one is the generation of triplets by the superconducting spin Hall effect. These pairs are long range in the ferromagnet under the appropriate mutual orientation of the condensate momentum and the ferromagnet magnetization. The second mechanism is based on the singlet-triplet conversion at the S/F interface followed by the rotation of the spin of the obtained short-range opposite-spin pairs via the spin current swapping mechanism. The structure of the supercurrent-induced LRTC is studied both for S/F bilayers and superconductor/ferromagnet/superconductor (S/F/S) Josephson junctions. We demonstrate that in S/F/S junctions, where the Josephson coupling is realized via the supercurrent-induced LRTC, the ground state phase can be switched between 0 and $\ensuremath{\pi}$ in a controllable manner. The switching is performed by reversing the supercurrent in one of the superconducting leads, thus realizing a physical principle of the $\text{0-}\ensuremath{\pi}$ shifter.

Dirac imprints on the g -factor anisotropy in graphene

Dirac electrons in graphene are to lowest order spin 1/2 particles, owing to the orbital symmetries at the Fermi level. However, anisotropic corrections in the $g$-factor appear due to the intricate spin-valley-orbit coupling of chiral electrons. We resolve experimentally the $g$-factor along the three orthogonal directions in a large-scale graphene sample. We employ a Hall bar structure with an external magnetic field of arbitrary direction, and extract the effective $g$-tensor via resistively-detected electron spin resonance. We employ a theoretical perturbative approach to identify the intrinsic and extrinsic spin orbit coupling and obtain a fundamental parameter inherent to the atomic structure of $^{12}$C, commonly used in ab-initio models.

Spin and valley dependent delay time in MoS2 junction

Spin and valley-dependent delay times, including the group delay time and dwell time, in a MoS2-based junction with extrinsic Rashba spin-orbit coupling (ERSOC) are studied theoretically. We show that the dwell and group delay time strongly dependent on the spin and valley degree of freedom. The effects of the electrostatic barrier height and the angles of incidence of the electrons on the group delay and the dwell time are investigated. The results of these evaluations provide the ability to adjust the delay times with applications in highly efficient spintronic and valleytronic MoS2-based devices. We also found that the spin and valley-dependent transmission probability and the valley and spin polarization can be effectively controlled with the ERSOC and electrostatic potential strength.

Intrinsic and extrinsic spin-orbit coupling and spin relaxation in monolayer PtSe2

Monolayer PtSe$_2$ is a semiconducting transition metal dichalcogenide characterized by an indirect band gap, space inversion symmetry, and high carrier mobility. Strong intrinsic spin-orbit coupling and the possibility to induce extrinsic spin-orbit fields by gating make PtSe$_2$ attractive for fundamental spin transport studies as well as for potential spintronics applications. We perform a systematic theoretical study of the spin-orbit coupling and spin relaxation in this material. Specifically, we employ first principles methods to obtain the basic orbital and spin-orbital properties of PtSe$_2$, also in the presence of an external transverse electric field. We calculate the spin mixing parameters $b^2$ and the spin-orbit fields $\Omega$ for the Bloch states of electrons and holes. This information allows us to predict the spin lifetimes due to the Elliott-Yafet and D'yakonov-Perel mechanisms. We find that $b^2$ is rather large, on the order of $10^{-2}$ and $10^{-1}$, while $\Omega$ varies strongly with doping, being about $10^{3} - 10^{4}$\,ns$^{-1}$ for %typical Fermi levels in the interval $(10-100)$ meV, carrier density in the interval $10^{13}-10^{14}$\,cm$^{-2}$ at the electric field of 1 V/nm. We estimate the spin lifetimes to be on the picosecond level.

Universal conductance dips and fractional excitations in a two-subband quantum wire

We theoretically investigate a quasi-one-dimensional quantum wire, where the lowest two subbands are populated, in the presence of a helical magnetic field. We uncover a backscattering mechanism involving the helical magnetic field and Coulomb interaction between the electrons. The combination of these ingredients results in scattering resonances and partial gaps which give rise to non-standard plateaus and conductance dips at certain electron densities. The positions and values of these dips are independent of material parameters, serving as direct transport signatures of this mechanism. Our theory applies to generic quasi-one-dimensional systems, including a Kondo lattice and a quantum wire subject to intrinsic or extrinsic spin-orbit coupling. Observation of the universal conductance dips would identify a strongly correlated fermion system hosting fractional excitations, resembling the fractional quantum Hall states.

Valley and spin dependent group delay time in silicene superlattice

In this paper, the valley- and spin-dependent transport properties, the tunneling time and the Hartman effect in a silicene superlattice under extrinsic Rashba spin-orbit coupling is theoretically studied. It is found that the transmission probability and the group delay time depend on the degree of freedom of the valley and spin, and that they have an oscillatory behavior with respect to the extrinsic Rashba spin-orbit interaction (ERSOI). Furthermore, the difference of the group delay time between two inequivalent valleys, and also between spin-up and spin-down can be efficiently tuned via the ERSOI strength and the number of superlattice barriers. Thus, valley-spin filtering can be achieved in the time domain in silicene superlattice with ERSOI. Especially, in contrast to the graphene superlattice, the Hartman effect or the superluminal tunneling can be observed in silicene superlattice even for the normal angle of incidence.

Spin-valley transport properties in a silicene velocity superlattice

Abstract Using the transfer matrix method, the valley- and spin-dependent transport properties in a silicene velocity superlattice under extrinsic Rashba spin-orbit coupling, are theoretically investigated. Silicene velocity superlattice includes the silicene sheet, in which the electrostatic potential and the Fermi velocity vary in space. It was found that through adjusting the Fermi velocity, number of velocity barriers and Rashba spin-orbit interaction, the transmission probability, with and without the spin-flip can be controlled. The results show that increasing the Fermi velocity results in the reduction and enhancement of the oscillation amplitude and oscillation period of the spin-dependent conductance, respectively. Specifically, in the case of Fermi velocity ratio (the Fermi velocity inside barriers over the Fermi velocity outside barriers) being smaller than one, fully valley polarized current can be observed. However, when the Fermi velocity ratio exceeds one, increasing the Fermi velocity leads to the decrement of valley polarization. Furthermore, the spin polarization is controllable via the Fermi velocity ratio.

Extrinsic spin-orbit coupling and spin relaxation in phosphorene

An effective Hamiltonian is derived to describe the conduction band of monolayer black phosphorus (phosphorene) in the presence of spin-orbit coupling and external electric field. Envelope function approximation along with symmetry arguments and Lowdin partitioning are utilized to derive extrinsic spin-orbit coupling. The resulting spin splitting appears in fourth order perturbation terms and is shown to be linear in both the magnitude of the external electric field and the strength of the atomic spin-orbit coupling, similar to the Bychkov-Rashba expression but with an in-plane anisotropy. The anisotropy depends on the coupling between conduction band and other bands both close and distant in energy. The spin relaxation of conduction electrons is then calculated within the Dyakonov-Perel mechanism where momentum scattering randomizes the polarization of a spin ensemble. We show how the anisotropic Fermi contour and the anisotropic extrinsic spin splitting contribute to the anisotropy of spin-relaxation time. Scattering centers in the substrate are considered to be charged impurities with screened Coulomb potential.

Weak localization in boron nitride encapsulated bilayer MoS2

We present measurements of weak localization on hexagonal boron nitride encapsulated bilayer MoS$_2$. From the analysis we obtain information regarding the phase-coherence and the spin diffusion of the electrons. We find that the encapsulation with boron nitride provides higher mobilities in the samples, and the phase-coherence shows improvement, while the spin relaxation does not exhibit any significant enhancement compared to non-encapsulated MoS$_2$. The spin relaxation time is in the order of a few picoseconds, indicating a fast intravalley spin-flip rate. Lastly, the spin-flip rate is found to be independent from electron density in the current range, which can be explained through counteracting spin-flip scattering processes based on electron-electron Coulomb scattering and extrinsic Bychkov-Rashba spin-orbit coupling.

Direct observation of unusual interfacial Dzyaloshinskii-Moriya interaction in graphene/NiFe/Ta heterostructures

Graphene/ferromagnet interface promises a plethora of new science and technology. The interfacial Dzyaloshinskii Moriya interaction (iDMI) is essential for stabilizing chiral spin textures, which are important for future spintronic devices. Here, we report direct observation of iDMI in graphene/Ni80Fe20/Ta heterostructure from non-reciprocity in spin-wave dispersion using Brillouin light scattering (BLS) technique. Linear scaling of iDMI with the inverse of Ni80Fe20 thicknesses suggests primarily interfacial origin of iDMI. Both iDMI and spin-mixing conductance increase with the increase in defect density of graphene obtained by varying argon pressure during sputter deposition of Ni80Fe20. This suggests that the observed iDMI originates from defect-induced extrinsic spin-orbit coupling at the interface. The direct observation of iDMI at graphene/ferromagnet interface without perpendicular magnetic anisotropy opens new route in designing thin film heterostructures based on 2-D materials for controlling chiral spin structure such as skyrmions and bubbles, and magnetic domain-wall-based storage and memory devices.

Extrinsic spin-orbit coupling induced enhanced spin pumping in few-layer MoS2/Py

We report on broadband ferromagnetic resonance spectroscopy studies of permalloy (Py) thin films grown on large area pulse laser deposited MoS2. We observe an enhancement of the effective damping constant of the Py layer grown on few-layer MoS2. The spin mixing conductance is found to be an order of magnitude larger in the case of 3.5 (average of the 3–4 layer)-layer-MoS2/Py compared to the case of 2-layer-MoS2/Py. The results are interpreted as a consequence of the extrinsic defect induced spin-orbit coupling at the 3.5-layer-MoS2/Py interface evidenced by a higher variation of Raman intensity across the sample as compared to the 2-layer-MoS2/Py system.

Extrinsic spin-charge coupling in diffusive superconducting systems

We present a theoretical study of diffusive superconducting systems with extrinsic spin-orbit coupling and arbitrarily strong impurity potential. We derive from a microscopic Hamiltonian a diffusion equation for the quasi-classical Green function, and demonstrate that all mechanisms related to the spin-orbit coupling are expressed in terms of three kinetic coefficients: the spin Hall angle, the spin current swapping coefficient, and the spin relaxation rate due to Elliott-Yafet mechanism. The derived diffusion equation contains a hitherto unknown term describing a spin-orbit torque that appears exclusively in the superconducting state. As an example, we provide a qualitative description of a magnetic vortex in a superconductor with triplet correlations, and show that the novel term describes a spin torque proportional to the vector product between the spectral angular momentum of the condensate and the triplet vector. Our equation opens up the possibility to explore spintronic effects in superconductors with no counterparts in the normal metallic state.

Quasiclassical theory of the spin–orbit magnetoresistance of three-dimensional Rashba metals

The magnetoresistance of a three-dimensional Rashba metal placed on top of a ferromagnetic insulator is theoretically investigated. In addition to the intrinsic Rashba spin–orbit interaction, we consider extrinsic spin–orbit coupling via side-jump and skew scattering, as well as Elliott–Yafet spin relaxation. The latter is anisotropic due to the mass anisotropy which reflects the noncentrosymmetric crystal structure. A quasiclassical approach is employed to derive coupled spin-diffusion equations, which are supplemented by boundary conditions that account for the spin-transfer torque at the interface of the bilayer. The magnetoresistance is fully determined by the current-induced spin polarization, i.e., it cannot in general be ascribed to a single (bulk) spin Hall angle. Our theory reproduces several features of the experiments, at least qualitatively, and contains established phenomenological results in the relevant limiting cases. In particular, the anisotropy of the Elliott–Yafet spin relaxation mechanism plays a major role for the interpretation of the observed magnetoresistance.

Spin Hall and Spin Swapping Torques in Diffusive Ferromagnets.

A complete set of the generalized drift-diffusion equations for a coupled charge and spin dynamics in ferromagnets in the presence of extrinsic spin-orbit coupling is derived from the quantum kinetic approach, covering major transport phenomena, such as the spin and anomalous Hall effects, spin swapping, spin precession, and relaxation processes. We argue that the spin swapping effect in ferromagnets is enhanced due to spin polarization, while the overall spin texture induced by the interplay of spin-orbital and spin precession effects displays a complex spatial dependence that can be exploited to generate torques and nucleate or propagate domain walls in centrosymmetric geometries without the use of external polarizers, as opposed to the conventional understanding of spin-orbit mediated torques.

Spin-dependent magneto-thermopower of narrow-gap lead chalcogenide quantum wells

A semi-classical analysis of magneto-thermopower behaviour, namely, the Seebeck and Nernst effect (NE) in quantum wells of IV-VI lead salts with significant extrinsic Rashba spin-orbit coupling (RSOC) is performed in this report. In addition to the spin-dependent Seebeck effect that has been observed before, we also theoretically predict a similar spin-delineated behavior for its magneto-thermal analog, the spin-dependent NE. The choice of lead salts follows from a two-fold advantage they offer, in part, to their superior thermoelectric properties, especially PbTe, while their low band gaps and high spin-orbit coupling make them ideal candidates to study RSOC governed effects in nanostructures. The calculations show a larger longitudinal magneto-thermopower for the spin-up electrons while the transverse components are nearly identical. In contrast, for a magnetic field free case, the related power factor calculations reveal a significantly higher contribution from the spin-down ensemble and suffer a reduction with an increase in the electron density. We also discuss qualitatively the limitations of the semi-classical approach for the extreme case of a high magnetic field and allude to the observed thermopower behaviour when the quantum Hall regime is operational. Finally, techniques to modulate the thermopower are briefly outlined.

Spin properties of black phosphorus and phosphorene, and their prospects for spincalorics

Semiconducting black phosphorus attracts a lot of attention due to its extraordinary electronic properties. Its application to spincalorics requires the knowledge about the spin and thermal properties. Here, we describe first principles calculations of the spin–orbit coupling and spin scattering in phosphorene and bulk black phosphorus. We find that the intrinsic spin–orbit coupling is of the order of 20 meV for the valence and conduction band, both for phosphorene and bulk black phosphorus, and induces spin mixing with the probability –10−4. A strong anisotropy of b2 is observed. The calculated Elliott–Yafet spin relaxation times reach nanoseconds for realistic values of the momentum relaxation times. The extrinsic spin–orbit coupling, enabling the D’yakonov–Perel’ spin relaxation mechanism, is studied for phosphorene by application of a transverse electric field. We observe a strong anisotropy of the extrinsic effects for the valence band and much weaker for the conduction band. It is shown, that for small enough electric fields the spin relaxation is dominated by the Elliott–Yafet mechanism, while the D’yakonov–Perel’ matters for higher electric fields. Our theoretical results stay in a good agreement with the experimental findings, and indicates that long spin lifetimes in black phosphorus and phosphorene makes them prospective materials for spincalorics and spintronics.

Dielectric properties of graphene on transition metal dichalcogenide substrate

The tunability of the dielectric properties induced by the substrate driven interactions (SDI) and the exchange field (M) due to the ferro-magnetic impurities in graphene monolayer on transition metal dichalcogenide (TMDC) (viz., XY2 , X = Mo, W; Y = S, Se) around K and K prime points is reported here. The cavalcade of interactions involve sub-lattice-resolved, strongly enhanced intrinsic spin-orbit couplings(SOC), the extrinsic Rashba spin-orbit coupling (RSOC), and the orbital gap related to the transfer of the electronic charge from graphene to XY2. The RSOC allows for external tuning of the band gap in graphene and connects the nearest neighbors with spin-flip. We obtain the usual gapped bands with an effective, RSOC-dependent Zeeman field due to the interplay of SDI. Using these bands we obtain the closed analytical expression of the dielectric function in the finite doping case. The zero of the dielectric function corresponds to the collective mode. Upon including the full dispersion of graphene on TMDC, we find that there is in fact only one collective mode and it corresponds to charge plasmons. The dispersion of the latter yields the q^2/3 behavior and not the well known q^1/2 behavior. We also find that the plasmon frequency could be changed by the tuning of the chemical potential.

Spin- and valley-dependent electronic band structure and electronic heat capacity of ferromagnetic silicene in the presence of strain, exchange field and Rashba spin-orbit coupling

We studied how the strain, induced exchange field and extrinsic Rashba spin-orbit coupling (RSOC) enhance the electronic band structure (EBS) and electronic heat capacity (EHC) of ferromagnetic silicene in presence of external electric field (EF) by using the Kane-Mele Hamiltonian, Dirac cone approximation and the Green’s function approach. Particular attention is paid to investigate the EHC of spin-up and spin-down bands at Dirac K and K′ points. We have varied the EF, strain, exchange field and RSOC to tune the energy of inter-band transitions and consequently EHC, leading to very promising features for future applications. Evaluation of EF exhibits three phases: Topological insulator (TI), valley-spin polarized metal (VSPM) and band insulator (BI) at given aforementioned parameters. As a new finding, we have found a quantum anomalous Hall phase in BI regime at strong RSOCs. Interestingly, the effective mass of carriers changes with strain, resulting in EHC behaviors. Here, exchange field has the same behavior with EF. Finally, we have confirmed the reported and expected symmetry results for both Dirac points and spins with the study of valley-dependent EHC.