Vectorial spin-orbital Hall effect of light upon tight focusing and its experimental observation in azopolymer films

Hall effect of light is a result of symmetry breaking in spin and/or orbital angular momentum(OAM)possessing optical system and is caused by e.g.refractive index gradient/interface between media or focusing of a spatially asymmetrical beam,similar to the electric field breaking the symmetry in spin Hall effect for electrons.The angular momentum(AM)conservation law in the ensuing asymmetric system dictates redistribution of spin and orbital angular momentum,and is manifested in spin-orbit,orbit-orbit,and orbit-spin conversions and reorganization,i.e.spin-orbit and orbit-orbit interaction.This AM restructuring in turn requires shifts of the barycenter of the electric field of light.In the present study we show,both analytically and by numerical simulation,how different electric field components are displaced upon tight focusing of an asymmetric light beam having OAM and spin.The relation between field components shifts and the AM components shifts/redistribution is presented too.Moreover,we experimentally demonstrate,for the first time,to the best of our knowledge,the spin-orbit Hall effect of light upon tight focusing in free space.This is achieved using azopolymers as a media detecting longitudinal or z component of the electrical field of light.These findings elucidate the Hall effect of light and may broaden the spectrum of its applications.

Nonlocal Andreev reflection with Rashba spin-orbital interaction in a triple-quantum-dot ring

We theoretically studied the nonlocal Andreev reflection with Rashba spin-orbital interaction in a triple-quantumdot （QD） ring, which is introduced as Rashba spin-orbital interaction to act locally on one component quantum dot. It is found that the electronic current and spin current are sensitive to the systematic parameters. The interdot spin-flip term does not play a leading role in causing electronic and spin currents. Otherwise the spin precessing terra leads to shift of the peaks of the the spin-up and spin-down electronic currents in different directions and results in the spin current. Moreover, the spin-orbital interaction suppresses the nonlocal Andreev reflection, so we cannot obtain the pure spin current.

The Research of Spin-Orbital Interaction in Intermetallic Compounds of System Gd-In on Paramagnetic Area

Normal,R0,and anomalous,RS,components of the Hall coefficient are determined from the results of experimental investigations of temperature dependences of the Hall coefficient,magnetic susceptibility,and specific electrical resistance for intermetallic Gd3In,Gd3In5 and GdIn3 compounds.Effective parameters of spin-orbital interactionλSO of intermetallic compounds are calculated from anomalous components RS of the Hall coefficient and specific electrical resistance.The results calculated for the band parameters and effective parameters of spin-orbital interactionλSO for Gd-In system intermetallides coincide by orders of magnitude with the results obtained from the optical spectra of pure REMs(rare-earth metals).

Wedge-shaped HfO_(2) buffer layer-induced field-free spin-orbit torque switching of HfO_(2)/Pt/Co structure

Field-free spin-orbit torque(SOT)switching of perpendicular magnetization is essential for future spintronic devices.This study demonstrates the field-free switching of perpendicular magnetization in an HfO_(2)/Pt/Co/TaO_(x) structure,which is facilitated by a wedge-shaped HfO_(2)buffer layer.The field-free switching ratio varies with HfO_(2)thickness,reaching optimal performance at 25 nm.This phenomenon is attributed to the lateral anisotropy gradient of the Co layer,which is induced by the wedge-shaped HfO_(2)buffer layer.The thickness gradient of HfO_(2)along the wedge creates a corresponding lateral anisotropy gradient in the Co layer,correlating with the switching ratio.These findings indicate that field-free SOT switching can be achieved through designing buffer layer,offering a novel approach to innovating spin-orbit device.

Ta thickness effect on field-free switching and spin-orbit torque efficiency in a ferromagnetically coupled Co/Ta/CoFeB trilayer

Current induced spin-orbit torque(SOT)switching of magnetization is a promising technology for nonvolatile spintronic memory and logic applications.In this work,we systematically investigated the effect of Ta thickness on the magnetic properties,field-free switching and SOT efficiency in a ferromagnetically coupled Co/Ta/Co Fe B trilayer with perpendicular magnetic anisotropy.We found that both the anisotropy field and coercivity increase with increasing Ta thickness from0.15 nm to 0.4 nm.With further increase of Ta thickness to 0.5 nm,two-step switching is observed,indicating that the two magnetic layers are magnetically decoupled.Measurements of pulse-current induced magnetization switching and harmonic Hall voltages show that the critical switching current density increases while the field-free switching ratio and SOT efficiency decrease with increasing Ta thickness.Both the enhanced spin memory loss and reduced interlayer exchange coupling might be responsible for theβ_(DL)decrease as the Ta spacer thickness increases.The studied structure with the incorporation of a Co Fe B layer is able to realize field-free switching in the strong ferromagnetic coupling region,which may contribute to the further development of magnetic tunnel junctions for better memory applications.

Anomalous Josephson effect between d-wave superconductors through a two-dimensional electron gas with both Rashba spin-orbit coupling and Zeeman splitting

Based on the Bogoliubov-de Gennes equation and the extended McMillan’s Green’s function formalism,we study theoretically the Josephson effect between two d-wave superconductors bridged by a ballistic two-dimensional electron gas with both Rashba spin-orbit coupling and Zeeman splitting.We show that due to the interplay of Rashba spin-orbit coupling and Zeeman splitting and d-wave pairing,the current-phase relation in such a heterostructure may exhibit a series of novel features and can change significantly as some relevant parameters are tuned.In particular,anomalous Josephson current may occur at zero phase bias under various different situations if both time reversal symmetry and inversion symmetry of the system are simultaneously broken,which can be realized by tuning some relevant parameters of the system,including the relative orientations and the strengths of the Zeeman field and the spin-orbit field in the bridge region,the relative orientations of the a axes in two superconductor leads,or the relative orientations between the Zeeman field in the bridge region and the a axes in the superconductor leads.We show that both the magnitude and the direction of the anomalous Josephson current may depend sensitively on these relevant parameters.

Nonlinear modes coupling of trapped spin-orbit coupled spin-1 Bose-Einstein condensates

We study analytically and numerically the nonlinear collective dynamics of quasi-one-dimensional spin-orbit coupled spin-1 Bose-Einstein condensates trapped in harmonic potential.The ground state of the system is determined by minimizing the Lagrange density,and the coupled equations of motions for the center-of-mass coordinate of the condensate and its width are derived.Then,two low energy excitation modes in breathing dynamics and dipole dynamics are obtained analytically,and the mechanism of exciting the anharmonic collective dynamics is revealed explicitly.The coupling among spin-orbit coupling,Raman coupling and spin-dependent interaction results in multiple external collective modes,which leads to the anharmonic collective dynamics.The cooperative effect of spin momentum locking and spin-dependent interaction results in coupling of dipolar and breathing dynamics,which strongly depends on spin-dependent interaction and behaves distinct characters in different phases.Interestingly,in the absence of spin-dependent interaction,the breathing dynamics is decoupled from spin dynamics and the breathing dynamics is harmonic.Our results provide theoretical evidence for deep understanding of the ground sate phase transition and the nonlinear collective dynamics of the system.

Influence of exchange bias on spin torque ferromagnetic resonance for quantification of spin–orbit torque efficiency

Antiferromagnet(AFM)/ferromagnet(FM)heterostructure is a popular system for studying the spin–orbit torque(SOT)of AFMs.However,the interfacial exchange bias field induces that the magnetization in FM layer is noncollinear to the external magnetic field,namely the magnetic moment drag effect,which further influences the characteristic of SOT efficiency.In this work,we study the SOT efficiencies of IrMn/NiFe bilayers with strong interfacial exchange bias by using spin-torque ferromagnetic resonance(ST-FMR)method.A full analysis on the AFM/FM systems with exchange bias is performed,and the angular dependence of magnetization on external magnetic field is determined through the minimum rule of free energy.The ST-FMR results can be well fitted by this model.We obtained the relative accurate SOT efficiencyξ_(DL)=0.058 for the IrMn film.This work provides a useful method to analyze the angular dependence of ST-FMR results and facilitates the accurate measurement of SOT efficiency for the AFM/FM heterostructures with strong exchange bias.

Magnetic proximity effect in the two-dimensional ε-Fe_(2)O_(3)/NbSe_(2)heterojunction

Two-dimensional(2D)magnet/superconductor heterostructures can promote the design of artificial materials for exploring 2D physics and device applications by exotic proximity effects.However,plagued by the low Curie temperature and instability in air,it is hard to realize practical applications for the reported layered magnetic materials at present.In this paper,we developed a space-confined chemical vapor deposition method to synthesize ultrathin air-stable ε-Fe_(2)O_(3) nanosheets with Curie temperature above 350 K.The ε-Fe_(2)O_(3)/NbSe_(2) heterojunction was constructed to study the magnetic proximity effect on the superconductivity of the NbSe_(2) multilayer.The electrical transport results show that the subtle proximity effect can modulate the interfacial spin–orbit interaction while undegrading the superconducting critical parameters.Our work paves the way to construct 2D heterojunctions with ultrathin nonlayered materials and layered van der Waals(vdW)materials for exploring new physical phenomena.

Oscillation of Dzyaloshinskii–Moriya interaction driven by weak electric fields

Dzyaloshinskii–Moriya interaction(DMI) is under extensive investigation considering its crucial status in chiral magnetic orders, such as Néel-type domain wall(DW) and skyrmions. It has been reported that the interfacial DMI originating from Rashba spin–orbit coupling(SOC) can be linearly tuned with strong external electric fields. In this work, we experimentally demonstrate that the strength of DMI exhibits rapid fluctuations, ranging from 10% to 30% of its original value, as a function of applied electric fields in Pt/Co/MgO heterostructures within the small field regime(< 10-2V/nm). Brillouin light scattering(BLS) experiments have been performed to measure DMI, and first-principles calculations show agreement with this observation, which can be explained by the variation in orbital hybridization at the Co/MgO interface in response to the weak electric fields. Our results on voltage control of DMI(VCDMI) suggest that research related to the voltage control of magnetic anisotropy for spin–orbit torque or the motion control of skyrmions might also have to consider the role of the external electric field on DMI as small voltages are generally used for the magnetoresistance detection.

A Spin-orbit Coupling Study on the Quinoline-and Porphyrin-based Photosensitizers

The spin-orbit coupling（SOC） of four porphyrin- and quinoline-based compounds has been studied using Pauli-Breit SOC operator with one- and two-electron terms. The results revealed that the yield of singlet oxygen is affected by the spin-orbit coupling matrix element involving the emitting triplet and the perturbing singlet state. Investigated quinoline-based compounds have more high SOC values than those porphyrin-based compounds due to spin parallel electron pairs of oxygen. The open shell d8 of metal Pt can induce the stronger exchange interactions than the closed shell p6 of metal Mg, resulting in bigger SOC matrix element in quinoline-based Pt complex than in the quinoline-based Mg complex. Simultaneously, potential energy curves of the first excited sate and the first triplet sate have been calculated, which proves that all investigated complexes can induce singlet oxygen. These computational findings support quinolin-based compounds have high singlet oxygen yields and provide a rigorous basis for predicting the probability of singlet oxygen yields in plane-type molecules.

Symmetry breaking of photonic spin-orbit interactions in metasurfaces

Spin-orbit optical phenomena pertain to the wider class of electromagnetic effects originating from the interaction of the photon spin with the spatial structure and propagation characteristics of an optical wave,mediated by suitable optical media.There are many emerging photonic applications of spin-orbit interactions(SOI)of light,such as control of the optical wave propagation via the spin,enhanced optical manipulation,and generation of structured optical fields.Unfortunately,current applications are based on symmetric SOI,that is,the behaviours of polarized photons with two opposite spins are opposite,leading to the limit of spin-based multiplexers.The symmetry of SOI can be broken in our proposed metasurfaces,consisting of spatially varying birefringence,which can arbitrarily and independently build SOI for two opposite spins without reduction of optical energy usage.We obtain three kinds of dual-functional metasurfaces at visible and infrared wavelengths with high efficiency.Our concept of generation of asymmetric SOI for two spins,using anisotropic metasurfaces,will open new degrees of freedoms for building new types of spin-controlled multifunctional shared-aperture devices for the generation of complex structured optical fields.

Field-assisted electron transport through a symmetric double-well structure with spin-orbit coupling and the Fano-resonance induced spin filtering

We have investigated theoretically the field-driven electron-transport through a double-quantum-well semiconductor-heterostructure with spin-orbit coupling. The numerical results demonstrate that the transmission spectra are divided into two sets due to the bound-state level-splitting and each set contains two asymmetric resonance peaks which may be selectively suppressed by changing the difference in phase between two driving fields. When the phase difference changes from 0 to π, the dip of asymmetric resonance shifts from one side of resonance peak to the other side and the asymmetric Fano resonance degenerates into the symmetric Breit-Wigner resonance at a critical value of phase difference. Within a given range of incident electron energy, the spin polarization of transmission current is completely governed by the phase difference which may be used to realize the tunable spin filtering.

Spin current and its heat effect in a multichannel quantum wire with Rashba spin-orbit coupling

Using the perturbation method, we theoretically study the spin current and its heat effect in a multichannel quantum wire with Rashba spin-orbit coupling. The heat generated by the spin current is calculated. With the increase of the width of the quantum wire, the spin current and the heat generated both exhibit period oscillations with equal amplitudes. When the quantum-channel number is doubled, the oscillation periods of the spin current and of the heat generated both decrease by a factor of 2. For the spin current js,xy, the amplitude increases with the decrease of the quantum channel; while the amplitude of the spin current js,yx remains the same. Therefore we conclude that the effect of the quantum-channel number on the spin current js,xy is greater than that on the spin current js,yx. The strength of the Rashba spin-orbit coupling is tunable by the gate voltage, and the gate voltage can be varied experimentally, which implies a new method of detecting the. spin current. In addition, we can control the amplitude and the oscillation period of the spin current by controlling the number of the quantum channels. All these characteristics of the spin current will be very important for detecting and controlling the spin current, and especially for designing new spintronic devices in the future.

Spin-orbit interaction in coupled quantum wells

We theoretically investigate the spin-orbit interaction in GaAs/AlxGal_xAs coupled quantum wells. We consider the contribution of the interface-related Rashba term as well as the linear and cubic Dresselhaus terms to the spin splitting. For the coupled quantum wells which bear an inherent structure inversion asymmetry, the same probability density distribution of electrons in the two step quantum wells results in a large spin splitting from the interface term. If the widths of the two step quantum wells are different, the electron probability density in the wider step quantum well is considerably higher than that in the narrower one, resulting in the decrease of the spin splitting from the interface term. The results also show that the spin splitting of the coupled quantum well is not significantly larger than that of a step quantum well.

Electron resonance-transmission through a driven quantum well with spin-orbit coupling

We have studied the spin-dependent electron transmission through a quantum well driven by both dipole-type and homogeneous oscillating fields. The numerical evaluations show that Dresselhaus spin-orbit coupling induces the splitting of asymmetric Fano-type resonance peaks in the conductivity, in which the dipole modulation and the homogeneous modulation are equivalent. Therefore, we predict that the dipole-type oscillation, which is more practical in the experimental setup, can be used to realize the tunable spin filters by adjusting the field oscillation-frequency and the amplitude as well.

A pure spin-current injector of semiconductor quantum dots with Andreev reflection and Rashba spin-orbit coupling

We propose a four-terminal device consisting of two parallel quantum dots with Rashba spin-orbit interaction （RSOI）, coupled to two side superconductor leads and two common ferromagnetic leads, respectively. The two ferromagnetic leads and two quantum dots form a ring threaded by Aharonov-Bohm （AB） flux. This device possesses normal quasiparticle transmission between the two ferromagnetic leads, and normal and crossed Andreev reflections providing conductive holes. For the appropriate spin polarization of the ferromagnetic leads, RSOI and AB flux, the pure spin-up （or spin-down） current without net charge current in the right lead, which is due to the equal numbers of electrons and holes with the same spin-polarization moving along the same direction, can be obtained by adjusting the gate voltage, which may be used in practice as a pure spin-current injector.

Transport properties in a multi-terminal regular polygonal quantum ring with Rashba spin-orbit coupling

Transport properties in a multi-terminal regular polygonal quantum ring with Rashba spin-orbit coupling （SOC） are investigated analytically using quantum networks and the transport matrix metLod. The results show that conduc- tances remain at exactly the same values when the output leads are located at axisymmetric positions. However, for the nonaxisymmetrical case, there is a phase difference between the upper and lower arm, which leads to zero conductances appearing periodically. An isotropy of the conductance is destroyed by the Rashba SOC effect in the axisymmetric case. In addition, the position of zero conductance is regulated with the strength of the Rashba SOC.

Characteristics of anomalous Hall effect in spin-polarized two-dimensional electron gases in the presence of both intrinsic,extrinsic,and external electric-field induced spin-orbit couplings

The various competing contributions to the anomalous Hall effect in spin-polarized two-dimensional electron gases in the presence of both intrinsic, extrinsic and external electric-field induced spin-orbit coupling were investigated theoretically. Based on a unified semiclassical theoretical approach, it is shown that the total anomalous Hall conductivity can be expressed as the sum of three distinct contributions in the presence of these competing spin-orbit interactions, namely an intrinsic contribution determined by the Berry curvature in the momentum space, an extrinsic contribution determined by the modified Bloch band group velocity and an extrinsic contribution determined by spin-orbit-dependent impurity scattering. The characteristics of these competing contributions are discussed in detail in the paper.

Spin transport in a chain of polygonal quantum rings with Dresselhaus spin-orbit coupling

Using a transfer matrix method, we investigate spin transport through a chain of polygonal rings with Dresselhaus spin-orbit coupling（DSOC）. The spin conductance is dependent on the number of sides in the polygons. When DSOC is considered in a chain which also has Rashba spin-orbit coupling（RSOC） of the same magnitude, the total conductance is the same as that for the same chain with no SOC. However, when the two types of SOC have different values, there results a unique anisotropic conductance.