Spin Hall Effect Research Articles

Spin Hall Effect in Paraxial Vectorial Light Beams with an Infinite Number of Polarization Singularities.

Elements of micromachines can be driven by light, including structured light with phase and/or polarization singularities. We investigate here a paraxial vector Gaussian beam with an infinite number of polarization singularities residing evenly on a straight line. The intensity distribution is derived analytically and the polarization singularities are shown to exist only in the initial plane and in the far field. The azimuthal angle of the polarization singularities is shown to increase in the far field by π/2. We obtain the longitudinal component of the spin angular momentum (SAM) density and show that it is independent of the azimuthal angle of the polarization singularities. Upon propagation in free space, an infinite number of C-points is generated, where polarization is circular. We show that the SAM density distribution has a shape of four spots, two with left and two with right elliptic polarization. The distance to the transverse plane with the maximal SAM density decreases with decreasing distance between the polarization singularities in the initial plane. Generating such alternating areas with positive and negative SAM density, despite linear polarization in the initial plane, manifests the optical spin Hall effect. Application areas of the obtained results include designing micromachines with optically driven elements.

Controlling the Spin Hall Effect in the Sharp Focus of an Axial Superposition of Two Optical Vortices with Left- and Right-Handed Circular Polarization

We consider sharp focusing of an axial superposition of two optical vortices with identical topological charges, but different amplitudes and circular polarizations of different signs. The ratio of the amplitudes of the two beams is a parameter. When this parameter changes, the polarization state of the superposition changes from linear polarization to right-hand circular polarization. Based on the Richards–Wolf theory, exact expressions are obtained for the longitudinal components of the spin angular momentum (SAM) density and orbital angular momentum (OAM) density at the focus of the considered superposition. It follows from these expressions that the sum of the total longitudinal components of the SAM and OAM is conserved upon focusing, and also that, due to the spin-orbit conversion, the total longitudinal component of the SAM decreases during focusing, while the total longitudinal component of the OAM increases by the same amount. By changing the ratio of the amplitudes of the constituent beams from 1 to 0, one can change the value of the spin-orbit conversion from zero (for linear polarization) to a maximum (for circular polarization). Also, by changing this parameter, one can control the spin Hall effect at the focus, which takes place at the focus of the considered beam. This study can be applied for controlling the rotation velocity of microparticles trapped in the focus.

Spin-to-Charge Conversion in All-Oxide La2/3Sr1/3MnO3/SrIrO3 Heterostructures.

Spin injection and spin-charge conversion processes in all-oxide La2/3Sr1/3MnO3/SrIrO3 (LSMO/SIO) heterostructures with different SIO layer thickness and interfacial features have been studied. Ferromagnetic resonance (FMR) technique has been used to generate pure spin currents by spin pumping (SP) in ferromagnetic (FM) half-metallic LSMO. The change of the resonance linewidth in bare LSMO layers and LSMO/SIO heterostructures suggests a successful spin injection into the SIO layers. However, low values of the spin mixing conductance, compared to more traditional permalloy (Py)/Pt or yttrium iron garnet (YIG)/Pt systems, are found. A thorough analysis of the interfaces by high-resolution scanning transmission electron microscopy (HR-STEM) imaging suggests that they are structurally clean and atomic sharp, but a compositional analysis by energy-dispersive X-ray spectroscopy (EDS) reveals the interdiffusion of La, Ir, and Mn atomic species in the first atomic layers close to the interface. Inverse spin Hall effect (ISHE) measurements evidence that interfacial features play a very relevant role in controlling the effectiveness of the spin injection process and low transversal ISHE voltage signals are detected. In addition, it is found that larger voltage signals are detected for the lowest SIO layer thickness highlighting the role of the spin diffusion length (λsd)/SIO layer thickness ratio. The values of ISHE voltage are rather low but allow us to determine the spin Hall angle of SIO (θSH ≈ 1.12% at T = 250 K), which is remarkably similar to that obtained for the well-known Py/Pt system, therefore suggesting that SIO could be a promising spin-Hall material.

Geometric spin Hall effect and polarization-dependent transformations in the oblique section of a paraxial light beam

The spatial structure of light beams is usually considered in the transverse cross sections but supplementary analysis of the field pattern across an oblique plane may disclose additional details of the internal beam structure and energy flow distributions. Their manifestations are known as ‘geometric spin Hall effect of light’ (gSHEL). We analyze the ‘practical’ gSHEL scheme in which the light energy distribution is registered by a detector whose input plane is inclined with respect to the propagation axis. Based on the vector beam model and using the formalism of optical Wigner matrices, we find that the oblique-plane energy distribution differs from that observed in the transverse cross section. This difference is associated with the azimuthal energy circulation and the orbital angular momentum (AM) of the beam; it can be expressed as the lateral shift of the mean-weighted beam position (beam centroid). The similar effect can be observed in elliptically polarized beams without orbital AM: there, the oblique-section projection reveals a specific asymmetry induced by the spin AM in the longitudinal field components of such beams. The polarization-induced oblique-section beam shift is rather weak in paraxial approximation but can be observable if the light-detecting procedure is selectively sensitive to the longitudinal optical-field component.

Out-of-plane spin-to-charge conversion at low temperatures in graphene/MoTe2 heterostructures

Multi-directional spin-to-charge conversion—in which spin polarizations with different orientations can be converted into a charge current in the same direction—has been demonstrated in low-symmetry materials and interfaces. This is possible because, in these systems, spin-to-charge conversion can occur in unconventional configurations in which charge current, spin current, and polarization do not need to be mutually orthogonal. Here, we explore, in the low temperature regime, the spin-to-charge conversion in heterostructures of graphene with the low-symmetry 1T' phase of MoTe2. First, we observe the emergence of charge conversion for out-of-plane spins at temperatures below 100 K. This unconventional component is allowed by the symmetries of both MoTe2 and graphene and likely arises from spin Hall effect in the spin–orbit proximitized graphene. Moreover, we examine the low-temperature evolution of non-local voltage signals arising from the charge conversion of the two in-plane spin polarizations, which have been previously observed at higher temperature. As a result, we report omni-directional spin-to-charge conversion—for all spin polarization orientations—in graphene/MoTe2 heterostructures at low temperatures.

Magnon Hall effect in antiferromagnetic lattices

Topology applied to condensed matter is an important area of research and technology, and topological magnetic excitations have recently become an active field of study. This paper presents a general discussion of magnon Hall transport in two-dimensional antiferromagnets. Although the Chern number is zero for a collinear antiferromagnet, we offer a general discussion that can be used in the more general case. First, we study the Union Jack lattice, where an effective time-reversal symmetry is broken, making the system display the magnon Hall effect. Then, we investigate the brick-wall lattice where such symmetry is present. Consequently, we have a phenomenon similar to the quantum spin Hall effect in electronic systems. Both lattices have not yet been studied from the topological point of view. The coexistence of opposite spin polarization in an antiferromagnet resembles the electron spin in various transport phenomena. We study magnon transport in the lattices mentioned above with Dzyaloshinskii-Moriya interaction and easy-axis single-ion anisotropy. We calculate the Berry curvature from the eigenvalues of the Hamiltonian. From that, we plot the spin Hall and thermal Hall conductivities, as well as the spin Nernst coefficient, as functions of the temperature. In the Union Jack lattice, we treat the effect of anharmonic interactions using a mean-field spin wave theory where the Hamiltonian becomes implicitly temperature-dependent. We determine self-consistently the renormalized dispersion and the staggered magnetization as a function of temperature. Our calculations can be applied to other antiferromagnetic lattices.

Efficient charge to spin conversion in iridium oxide thin films

Many 5d transition metal oxides have a unique electronic structure, where the density of states near the Fermi level is dominated by only 5d electrons with strong spin–orbit coupling. IrO2, a Dirac nodal line semi-metal, is the simplest of these oxides. The presence of 5d electrons and gap opening of Dirac nodal lines via strong spin–orbit coupling allows for the hybridization of the 5d electrons of the oxide with the itinerant d electrons of a ferromagnet, while simultaneously increasing the intrinsic spin Hall effect. We report large charge-to-spin conversion in thin films of this material using spin-torque ferromagnetic resonance experiments. By independently performing line shape analysis and linewidth modulation experiments, we conclusively determine the spin Hall angle of optimized IrO2 films to be ∼8 times larger than that of Pt.

Dependence of WAL effect and enhancement of spin-orbit coupling effect in Bi1.2Sb0.8Te0.4Se2.6 low-temperature magnetic transport

The strong spin-orbit coupling and time-reversal symmetry in topological insulators (TIs) produce a new quantum state known as the topological surface state (TSS). The study of low-temperature magnetic transport in the TSS provides opportunities to explore exotic physical phenomena such as the spin Hall effect and the topological phase transition. An important goal in obtaining intrinsic TI systems is to eliminate internal defects and thereby reduce the contributions of metallic states in transport measurements. In this work, we are committed to overcoming this difficulty by elemental alloying. This paper reports the successful preparation of high-quality and stoichiometrically stable Bi1.2Sb0.8Te0.4Se2.6 (BSTS) thin films by innovatively combining the hybrid target structure with the laser molecular beam epitaxy (LMBE) system and low-temperature magnetic transport tests conducted on BSTS thin films of different thicknesses. Due to stronger spin-orbit coupling, we observed a weak anti-localization (WAL) effect, and the strength of the effect was affected by the film thickness and temperature in the low-temperature magnetic transport study. The dependence of the WAL effect provides a way to regulate the TSS.

Spin-charge separation and quantum spin Hall effect of beta-bismuthene

Multiple works suggest the possibility of classification of quantum spin Hall effect with magnetic flux tubes, which cause separation of spin and charge degrees of freedom and pumping of spin or Kramers-pair. However, the proof of principle demonstration of spin-charge separation is yet to be accomplished for realistic, ab initio band structures of spin-orbit-coupled materials, lacking spin-conservation law. In this work, we perform thought experiments with magnetic flux tubes on beta-bismuthene, and demonstrate spin-charge separation, and quantized pumping of spin for three insulating states, that can be accessed by tuning filling fractions. With a combined analysis of momentum-space topology and real-space response, we identify important role of bands supporting even integer invariants, which cannot be addressed with symmetry-based indicators. Our work sets a new standard for the computational diagnosis of two-dimensional, quantum spin-Hall materials by going beyond the mathbb {Z}_{2} paradigm and providing an avenue for precise determination of the bulk invariant through computation of quantized, real-space response.

Power efficient ReLU design for neuromorphic computing using spin Hall effect

We demonstrate that a magnetic tunnel junction injected with a spin Hall current can exhibit linear rotation of the magnetization of the free-ferromagnet using only the spin current. Using the linear resistance change of the magnetic tunnel junction (MTJ), we devise a circuit for the rectified linear activation (ReLU) function of the artificial neuron. We explore the role of different spin Hall effect (SHE) heavy metal (HM) layers on the power consumption of the ReLU circuit. We benchmark the power consumption of the ReLU circuit with different SHE layers by defining a new parameter called the spin Hall power factor. It combines the spin Hall angle, resistivity, and thickness of the HM layer, which translates to the power consumption of the different SHE layers during spin-orbit switching/rotation of the free FM. We employ a hybrid spintronics-CMOS simulation framework that couples Keldysh non-equilibrium Green’s function formalism with Landau–Lifshitz–Gilbert–Slonzewski equations and the HSPICE circuit simulator to account for the diverse physics of spin-transport and the CMOS elements in our proposed ReLU design. We also demonstrate the robustness of the proposed ReLU circuit against thermal noise and a non-trivial power-error trade-off that enables the use of an unstable free-ferromagnet for energy-efficient design. Using the proposed circuit, we evaluate the performance of the convolutional neural network for MNIST datasets and demonstrate comparable classification accuracies to the ideal ReLU with an energy consumption of 75 pJ per sample.

Topological phase transition on the ruby lattice with Rashba spin–orbit coupling and an exchange field

We investigate the topological phases in a ruby lattice when considering the effects of the intrinsic spin–orbit coupling, the Rashba spin–orbit coupling and an exchange field. The combination of the Rashba coupling and the exchange field leads to the quantum anomalous Hall effect characterized by a nonzero Chern number. We show that the variation of the exchange field drives interesting topological phase transitions between different topological insulating phases, including the quantum spin Hall insulator with spin Chern number Cs=±1, the quantum anomalous Hall insulator with Chern number C=±1 and C=±2. Particularly, the quantum anomalous Hall phases with high Chern numbers C=−4 and C=6 can be realized by tuning the strength of the exchange field. Each phase transition is accompanied by closing of the bulk gap. Furthermore, we find a new topological phase which exhibits the electronic characteristics of both the quantum spin Hall effect and the quantum anomalous Hall effect. The band structures of the edge states confirm the classification of various topological gapped phases.

Effect of the spin–orbit interaction in nanotubes

In this work, we study the electronic properties of nanotubes with spin–orbit interaction that exhibit a spin Hall effect. Nanoribbons made of these materials are expected to have topologically protected states. The lack of edge states in a seamless tube eliminates the possibility of finding a topological edge state. The spin–orbit interaction breaks the degeneracy of Dirac’s cones and eliminates the chance of finding a metal nanotube. As a consequence, this makes all nanotubes with spin–orbit interaction trivial band insulators. We focus our attention on two features. First, we study the energy band gap as a function of the diameter of the nanotubes. Then, we concentrate on controlling the bandgap of a nanotube by applying an external radial electric field. Finally, we discuss the possibility of using one of these tubes as a field-effect transistor.

Coexistence of Fano and electromagnetically induced transparency resonance line shapes in photonic topological insulators

Due to the bending resistance and defect immunity of the topological optical structure, topological photonics is extended to researching Fano line shapes or electromagnetically induced transparency-like (EIT-like) line shapes. In this paper, two-dimensional photonic crystal with Kekule´ distortion is designed to realize quantum spin Hall effect and quantum valley Hall effect simultaneously. The stable topological corner states and edge states are obtained. Corner states as dark modes interfere with edge states as bright mode to induce Fano or EIT-like line shapes. As far as we know, we first realize the coexistence of Fano and EIT-like line shapes based on the coexistence of quantum spin Hall effect and quantum valley Hall effect. Our results provide a new way to realize multi-channel sensing technology.

Spin Hall magnetoresistance across a paramagnetic Pt/NdGaO3 interface

In recent years, spin Hall magnetoresistance (SMR) has emerged as an efficient way to probe the spontaneous magnetization state in ordered magnetic systems by electrical current. Less known is its versatility as a probe of materials that do not possess spontaneous magnetization, such as in paramagnets. In this work, SMR is used to probe paramagnetic NdGaO3 (NGO), a rare earth oxide, possessing a sizable spin–orbit interaction (L = 6). NGO has not been investigated earlier for its efficiency in propagating spins. We have performed extensive temperature and angle dependent-magnetoresistance (ADMR) studies along different crystallographic axes in NGO, using platinum (Pt) as a spin injector and a detector and utilizing (inverse) spin Hall effect. We find a close correlation between the temperature dependence of the ADMR response with magnetization in NGO and a linear current bias dependence of the ADMR amplitudes. These are characteristics of the SMR effect in Pt/NGO, arising from the torque acting on localized moments in NGO and considering crystal field induced intermultiplet transitions with temperature. Control experiments on Pt/SrTiO3 and Pt/SiO2 devices were also carried out in order to validate the observed SMR response in the Pt/NGO bilayer and to rule out magnetoresistive contributions from Pt.

Spin Hall effects in the sky

In many areas of physics, the propagation of wave packets carrying intrinsic angular momentum is generally influenced by spin–orbit interactions. This is the main mechanism behind spin Hall effects, which result in wave packets following spin-dependent trajectories. Spin Hall effects have been observed in several experiments for electrons in condensed matter systems and for light propagating in inhomogeneous optical media. Similar effects have also been predicted for wave packets propagating in inhomogeneous gravitational fields. We give a brief introduction to gravitational spin Hall effects, emphasizing the analogies with the spin Hall effect of light in optics. Furthermore, we review the most promising astrophysical avenues that could lead to experimental observations of the gravitational spin Hall effect.

Topological edge state-induced enhancement of photonic spin Hall effect in a heterostructure with monolayer graphene

Photonic spin Hall effect (PSHE) of the transmitted wave presents promising applications in photonic spintronic devices, including inter-chip optical circuitry and quantum computing devices. These applications can benefit from phenomena such as the photon tunneling effect, frustrated total internal reflection, and the resonant optical tunneling effect. However, the mechanisms for enhancing PSHE of the transmitted wave are limited. In this study, an alternative strategy is proposed, which involves the utilization of topological edge states to enhance PSHE without relying on the aforementioned means. To demonstrate this effect, a heterostructure is designed, comprising two one-dimensional photonic crystals (PhCs) and a monolayer graphene. By leveraging the topological edge state, a significant enhancement of PSHE in the transmitted wave is observed, surpassing several times the incident wavelength. Furthermore, it is shown that the enhanced PSHE can be controlled and fine-tuned by adjusting the Fermi energy of monolayer graphene and the repetition numbers of the two PhCs. The enhanced and controlled PSHE in this heterostructure introduces possibilities for the development of novel optical components, such as switches, filters, modulators, and sensors.

Pump wavelength-dependent terahertz spin-to-charge conversion in CoFeB/MgO Rashba interface

Spin/charge interconversion mechanisms provide an essential handle to generate and detect spin currents. Their applications at different timescales are critical in spintronics since they cover a technologically relevant broadband spectrum. While the inverse spin Hall effect is known to be robust from quasi-static to sub-picosecond timescales, the conversion efficiency evolution of the inverse Edelstein effect has not been addressed yet. In this work, we report that while the quasi-static response of the inverse Edelstein effect can be comparable to that of the most efficient inverse spin Hall systems, a drastic drop of efficiency is observed in the terahertz (THz) regime. This behavior at the sub-picosecond timescale is qualitatively understood from the dependence of the inverse Edelstein effect on the energy distribution of spin-carrier entities, which is different between thermalized carriers in the quasi-static regime and hot carriers generated by light pulses. This finding is supported by the pump-laser wavelength dependence in the THz regime for the inverse Edelstein effect, which offers a promising route for tunability of spintronic devices.

Orthogonal Spin Current Injected Magnetic Tunnel Junction for Convolutional Neural Networks

We propose that a spin Hall effect (SHE) driven magnetic tunnel junction (MTJ) device can be engineered to provide a continuous change in the resistance across it when injected with orthogonal spin currents. Using this concept, we develop a hybrid device-circuit simulation platform to design a network that realizes multiple functionalities of a convolutional neural network (CNN). At the atomistic level, we use the Keldysh nonequilibrium Green’s function (NEGF) technique that is coupled self-consistently with the stochastic Landau-Lifshitz-Gilbert–Slonczewski (LLGS) equations, which in turn is coupled with the HSPICE circuit simulator. We demonstrate the simultaneous functionality of the proposed network to evaluate the rectified linear unit (ReLU) and max-pooling functionalities. We present a detailed power and error analysis of the designed network against the thermal stability factor of the free ferromagnets (FMs). Our results show that there exists a nontrivial power-error trade-off in the proposed network, which enables an energy-efficient network design based on unstable free FMs with reliable outputs. The static power for the proposed ReLU circuit is 0.56 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mu $</tex-math> </inline-formula> W and whereas the energy cost of a nine-input ReLU -max-pooling network with an unstable free FM ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\sf\Delta$</tex-math> </inline-formula> <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$=$</tex-math> </inline-formula> 15) is 3.4 pJ in the worst case scenario. We also rationalize the magnetization stability of the proposed device by analyzing the vanishing torque gradient points.

Photocurrents, inverse Faraday effect, and photospin Hall effect in Mn2Au

Among antiferromagnetic materials, Mn2Au is one of the most intensively studied, and it serves as a very popular platform for testing various ideas related to antiferromagnetic magnetotransport and dynamics. Since recently, this material has also attracted considerable interest in the context of optical properties and optically-driven antiferromagnetic switching. In this work, we use first principles methods to explore the physics of charge photocurrents, spin photocurrents, and the inverse Faraday effect in antiferromagnetic Mn2Au. We predict the symmetry and magnitude of these effects and speculate that they can be used for tracking the dynamics of staggered moments during switching. Our calculations reveal the emergence of large photocurrents of spin in collinear Mn2Au, whose properties can be understood as a result of a non-linear optical version of the spin Hall effect, which we refer to as the photospin Hall effect, encoded into the relation between the driving charge and resulting spin photocurrents. Moreover, we suggest that even a very small canting in Mn2Au can give rise to colossal spin photocurrents that are chiral in flavor. We conclude that the combination of staggered magnetization with the structural and electronic properties of this material results in a unique blend of prominent photocurrents, which makes Mn2Au a unique platform for advanced optospintronics applications.

Symmetry-breaking enabled topological phase transitions in spin-orbit optics.

The topological phase transitions (TPT) of light refers to a topological evolution from one type of spin-orbit interaction to another, which has been recently found in beam scattering at optical interfaces and propagation in uniaxial crystals. In this work, the focusing of off-axis and partially masked circular-polarization Gaussian beams are investigated by using of a full-wave theory. Moreover, two different types of spin-orbit interactions (i.e., spin-dependent vortex generation and photonic spin-Hall effect) in the focusing system are unified from the perspective of TPT. It is demonstrated that as the off-axis distance or the masked area increases, a TPT phenomenon in the focused optical field takes place, evolving from the spin-dependent vortex generation to the spin-Hall shift of the beam centroids. The intrinsic mechanism is attributed to the cylindrical symmetry-breaking of the system. This symmetry-breaking induced TPT based on the method of vortex mode decomposition is further examined. The main difference between the TPT phenomenon observed here and that trigged by oblique incidence at optical interfaces or oblique propagation in uniaxial crystals is also uncovered. Our findings provide fruitful insights for understanding the spin-orbit interactions in optics, providing an opportunity for unifying the TPT phenomena in various spin-orbit photonics systems.