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.

Bessel vortices in spin-1 Bose-Einstein condensates with Zeeman splitting and spin-orbit coupling

We investigate the ground states of spin-orbit coupled spin-1 Bose-Einstein condensates in the presence of Zeeman splitting.By introducing the generalized momentum operator,the linear version of the system is solved exactly,yielding a set of Bessel vortices.Additionally,based on linear solution and using variational approximation,the solutions for the full nonlinear system and their ground state phase diagrams are derived,including the vortex states with quantum numbers m=0,1,as well as mixed states.In this work,mixed states in spin-1 spin-orbit coupling(SOC)BEC are interpreted for the first time as weighted superpositions of three vortex states.Furthermore,the results also indicate that under strong Zeeman splitting,the system cannot form localized states.The variational solutions align well with numerical simulations,showing stable evolution and meeting the criteria for long-term observation in experiments.

Spin-orbit torque effect in silicon-based sputtered Mn_(3)Sn film

Noncollinear antiferromagnet Mn_(3)Sn has shown remarkable efficiency in charge-spin conversion,a novel magnetic spin Hall effect,and a stable topological antiferromagnetic state,which has resulted in great interest from researchers in the field of spin-orbit torque.Current research has primarily focused on the spin-orbit torque effect of epitaxially grown noncollinear antiferromagnet Mn_(3)Sn films.However,this method is not suitable for large-scale industrial preparation.In this study,amorphous Mn_(3)Sn films and Mn_(3)Sn/Py heterostructures were prepared using magnetron sputtering on silicon substrates.The spin-torque ferromagnetic resonance measurement demonstrated that only the conventional spin-orbit torque effect generated by in-plane polarized spin currents existed in the Mn_(3)Sn/Py heterostructure,with a spin-orbit torque efficiency of 0.016.Additionally,we prepared the perpendicular magnetized Mn_(3)Sn/CoTb heterostructure based on amorphous Mn_(3)Sn film,where the spin-orbit torque driven perpendicular magnetization switching was achieved with a lower critical switching current density(3.9×10^(7)A/cm^(2))compared to Ta/CoTb heterostructure.This research reveals the spin-orbit torque effect of amorphous Mn_(3)Sn films and establishes a foundation for further advancement in the practical application of Mn_(3)Sn materials in spintronic devices.

Spatial electron-spin splitting in single-layered semiconductor microstructure modulated by Dresselhaus spin-orbit coupling

Combining theory and computation,we explore the Goos–H¨anchen(GH)effect for electrons in a single-layered semiconductor microstructure(SLSM)modulated by Dresselhaus spin–orbit coupling(SOC).GH displacement depends on electron spins thanks to Dresselhaus SOC,therefore electron spins can be separated from the space domain and spinpolarized electrons in semiconductors can be realized.Both the magnitude and sign of the spin polarization ratio change with the electron energy,in-plane wave vector,strain engineering and semiconductor layer thickness.The spin polarization ratio approaches a maximum at resonance;however,no electron-spin polarization occurs in the SLSM for a zero in-plane wave vector.More importantly,the spin polarization ratio can be manipulated by strain engineering or semiconductor layer thickness,giving rise to a controllable spatial electron-spin splitter in the field of semiconductor spintronics.

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.

Transparently manipulating spin-orbit qubit via exact degenerate ground states

By investigating a harmonically confined and periodically driven particle system with spin-orbit coupling(SOC)and a specific controlled parameter,we demonstrate an exactly solvable two-level model with a complete set of spin-motion entangled Schrödinger kitten(or cat)states.In the undriven case,application of a modulation resonance results in the exact stationary states.We show a decoherence-averse effect of SOC and implement a transparent coherent control by exchanging positions of the probability-density wavepackets to create transitions between the different degenerate ground states.The expected energy consisting of quantum and continuous parts is derived,and the energy deviations caused by the exchange operations are much less than the quantum gap.The results could be directly extended to a weakly coupled single-particle chain for transparently encoding spin-orbit qubits via the robust spin-motion entangled degenerate ground states.

Giant interface spin-orbit torque in NiFe/Pt bilayers

The current-induced spin-orbit torque(SOT)plays a dominant role to manipulate the magnetization in a heavy metal/ferromagnetic metal bilayer.We separate the contributions of interfacial and bulk spin-orbit coupling(SOC)to the effective field of field-like SOT in a typical NiFe/Pt bilayer by planar Hall effect(PHE).The effective field from interfacial SOC is directly measured at the transverse PHE configuration.Then,at the longitudinal configuration,the effective field from bulk SOC is determined,which is much smaller than that from interfacial SOC.The giant interface SOT in NiFe/Pt bilayers suggests that further analysis of interfacial effects on the current-induced manipulation of magnetization is necessary.

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.

Electron Momentum Spectroscopy of Valence Orbitals of n-Propyl Iodide： Spin-Orbit Coupling Effect and Intramolecular Orbital Interaction

The binding energy spectrum and electron momentum distributions for the outer valence orbitals of n-propyl iodide molecule have been measured using the electron momentum spectrometer employing non-coplanar asymmetric geometry at impact energy of 2.5 keV plus binding energy. The ionization bands have been assigned in detail via the high accuracy SACCI general-R method calculation and the experimental momentum profiles are compared with the theoretical ones calculated by Hartree-Fock and B3LYP/aug-cc-pVTZ（C,H）6-311G？？（I）. The spin-orbit coupling effect and intramolecular orbital interaction have been analyzed for the outermost two bands, which are assigned to the iodine 5p lone pairs, using NBO method and non-relativistic as well as relativistic calculations. It is found that both of the interactions will lead to the observed differences in electron momentum distributions. The experimental results agree with the relativistic theoretical momentum profiles, indicating that the spin-orbit coupling effect dominates in n-propyl iodide molecule.

Zero-Magnetic-Field Spin Splitting of Polaron＇s Ground State Energy Induced by Rashba Spin-Orbit Interaction

We study theoretically the ground state energy of a polaron near the interface of a polar-polar semiconductor by considering the Rashba spin-orbit （SO） coupling with the Lee-Low-Pines intermediate coupling method. Our numerical results show that the Rashba SO interaction originating from the inversion asymmetry in the heterostructure splits the ground state energy of the polaron. The electron area/density and vector dependence of the ratio of the SO interaction to the total ground state energy or other energy composition are obvious. One can see that even without any external magnetic field, the ground state energy can be split by the Rashba SO interaction, and this split is not a single but a complex one. Since the presents of the phonons, whose energy gives negative contribution to the polaron＇s, the spin-splitting states of the polaron are more stable than electron＇s.

Spin-Orbit Scattering Effects on Hall Conductivity in a Layered Disordered Electron System

Spin-orbit scattering effects in a layered quasi-2D disordered electron system have been investigated by the diagrammatic techniques in perturbation theory. The expression of Cooperon (propagator in particle-particle channel) is obtained as the function of interlayer coupling. The analytical result for the quantum correction to Hall conductivity has been obtained as functions of elastic, inelastic and spin-orbit scattering times. It is shown that the strong and weak couplings correspond, respectively, to the 3D and 2D situations. The Hall coefficient is shown to vanish. The relevant dimensional crossover behavior from 3D to 2D with decreasing the interlayer coupling has been discussed, and the condition for the crossover has been obtained. The present theory is expected to apply for the electronic transport in tunneling superlattices.

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-Tunneling Time in Ferromagnetic/Semiconductor/Ferromagnetic Three-Terminal Heterojunction in the Presence of Rashba Spin-Orbit Coupling

We study theoretically the transmission coefficients and the spin-tunneling time in ferromagnetic/semiconductor/ferromagnetic three-terminal heterojunction in the presence of Rashba spin-orbit interaction, in which onedimensional quantum waveguide theory is developed and applied. Based on the group velocity concept and the particle current conservation principle, we calculate the spin-tunneling time as the function of the intensity of Rashba spinrblt coupling and the length of the semiconductor. We find that as the length of the semiconductor increases, the spintunneling time does not increase linearly but shows behavior of slight oscillation, i;brthermore, with the increasing of the soin-orbit coupling, the spin-tunneling time increases.

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.

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-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.

Mitigating the Jahn-Teller distortion driven by the spin-orbit coupling of lithium manganate cathode

Spinel LiMn_(2)O_(4)is recognized as one of the most competitive cathode candidates for lithium-ion batteries ascribed to environmentally benign and rich sources.However,the wholesale application of LiMn_(2)O_(4)is predominately plagued by its severe capacity degradation,mainly associated with the innate Jahn-Teller effect.Herein,single-crystalline LiMn_(2)O_(4)with Eu^(3+) doping is rationally designed to mitigate the detrimental Jahn-Teller distortion by tuning the chemical environment of MnO_(6) octahedra and accommodating localized electron,based on the unique aspheric flexible 4f electron orbit of rare-earth metal ions.Notably,the stretching of MnO_(6) octahedron stemmed from the Jahn-Teller effect in Eu-doped LiMn_(2)O_(4)is effectively suppressed,confirmed by theoretical calculation.Meanwhile,the structural stability of the material has been significantly enhanced due to the robust Mn–O band coherency and weakened phase transition,proved by synchrotron radiation absorption spectrum and operando X-ray diffraction.The corresponding active cathode manifests superior long-cycle stability after 300 loops at 2C and displays only a 0.011%capacity drop per cycle even at 5C.Given this,this modification tactic sheds new light on achieving superior long-cycle performances by suppressing distortion in various cathode materials.