Recent progress on excitation and manipulation of spin-waves in spin Hall nano-oscillators

Spin Hall nano oscillator(SHNO),a new type spintronic nano-device,can electrically excite and control spin waves in both nanoscale magnetic metals and insulators with low damping by the spin current due to spin Hall effect and interfacial Rashba effect.Several spin-wave modes have been excited successfully and investigated substantially in SHNOs based on dozens of different ferromagnetic/nonmagnetic(FM/NM)bilayer systems(e.g.,FM=Py,[Co/Ni],Fe,CoFeB,Y3Fe5O12;NM=Pt,Ta,W).Here,we will review recent progress about spin-wave excitation and experimental parameters dependent dynamics in SHNOs.The nanogap SHNOs with in-plane magnetization exhibit a nonlinear self-localized bullet soliton localized at the center of the gap between the electrodes and a secondary high-frequency mode which coexists with the primary bullet mode at higher currents.While in the nanogap SHNOs with out of plane magnetization,besides both nonlinear bullet soliton and propagating spin-wave mode are achieved and controlled by varying the external magnetic field and current,the magnetic bubble skyrmion mode also can be excited at a low in-plane magnetic field.These spin-wave modes show thermal-induced mode hopping behavior at high temperature due to the coupling between the modes mediated by thermal magnon mediated scattering.Moreover,thanks to the perpendicular magnetic anisotropy induced effective field,the single coherent mode also can be achieved without applying an external magnetic field.The strong nonlinear effect of spin waves makes SHNOs easy to achieve synchronization with external microwave signals or mutual synchronization between multiple oscillators which improve the coherence and power of oscillation modes significantly.Spin waves in SHNOs with an external free magnetic layer have a wide range of applications from as a nanoscale signal source of low power consumption magnonic devices to spin-based neuromorphic computing systems in the field of artificial intelligence.

Synchronization of nanowire-based spin Hall nano-oscillators

The synchronization of the spin Hall nano-oscillator(SHNO)device driven by the pure spin current has been investigated with micromagnetic simulations.It was found that the power spectra of nanowire-based SHNO devices can be synchronized by varying the current flowing in the heavy metal(HM)layer.The synchronized signals have relatively high power and narrow linewidth,favoring the potential applications.We also found that the synchronized spectra are strongly dependent on both the number and length of nanowires.Moreover,a periodic modulation of power spectra can be obtained by introducing interfacial Dzyaloshinskii–Moriya interaction(iDMI).Our findings could enrich the current understanding of spin dynamics driven by the pure spin current.Further,it could help to design novel spintronic devices.

Multi-functional photonic spin Hall effect sensor controlled by phase transition

Photonic spin Hall effect(PSHE), as a novel physical effect in light–matter interaction, provides an effective metrological method for characterizing the tiny variation in refractive index(RI). In this work, we propose a multi-functional PSHE sensor based on VO_(2), a material that can reveal the phase transition behavior. By applying thermal control, the mutual transformation into different phase states of VO_(2) can be realized, which contributes to the flexible switching between multiple RI sensing tasks. When VO_(2) is insulating, the ultrasensitive detection of glucose concentrations in human blood is achieved. When VO_(2) is in a mixed phase, the structure can be designed to distinguish between the normal cells and cancer cells through no-label and real-time monitoring. When VO_(2) is metallic, the proposed PSHE sensor can act as an RI indicator for gas analytes. Compared with other multi-functional sensing devices with the complex structures, our design consists of only one analyte and two VO_(2) layers, which is very simple and elegant. Therefore, the proposed VO_(2)-based PSHE sensor has outstanding advantages such as small size, high sensitivity, no-label, and real-time detection, providing a new approach for investigating tunable multi-functional sensors.

Surface phonon resonance:A new mechanism for enhancing photonic spin Hall effect and refractive index sensor

Metal-based surface plasmon resonance(SPR)plays an important role in enhancing the photonic spin Hall effect(SHE)and developing sensitive optical sensors.However,the very large negative permittivities of metals limit their applications beyond the near-infrared regime.In this work,we theoretically present a new mechanism to enhance the photonic SHE by taking advantage of SiC-supported surface phonon resonance(SPhR)in the mid-infrared regime.The transverse displacement of photonic SHE is very sensitive to the wavelength of incident light and the thickness of SiC layer.Under the optimal parameter setup,the calculated largest transverse displacement of SiC-based SPhR structure reaches up to 163.8 ym,which is much larger than the condition of SPR.Moreover,an NO_(2) gas sensor based on the SPhR-enhanced photonic SHE is theoretically proposed with the superior sensing performance.Both the intensity and angle sensitivity of this sensor can be effectively manipulated by varying the damping rate of SiC.The results may provide a promising paradigm to enhance the photonic SHE in the mid-infrared region and open up new opportunity of highly sensitive refractive index sensors.

Zero-Magnetic-Field Oscillation of Spin Transfer Nano-Oscillator with a Second-Order-Perpendicular-Anisotropy Free Layer

The zero-magnetic-field oscillation behavior of spin torque nano-oscillator （STNO） with a perpendicularly mag- netized free layer with second-order uniaxial anisotropy is studied theoretically based on the Landau-Lifshitz- Cilbert-Slonczewski equation. It is demonstrated numerically that the second-order uniaxial anisotropy plays a significant role in the occurrence of a zero-magnetic-field steady-state precession, which can be understood in terms of the energy balance between the energy accumulation due to the spin torque and the energy dissipation due to the Gilbert damping. In particular, a relatively large zero-magnetic-field-oscillation current region, in which the corresponding microwave frequency is increased while the threshold current still maintains an almost constant value, can be obtained by modulating the second-order uniaxial anisotropy of the free layer. These results suggest a tunable zero-magnetic-field STNO, and it may be a promising configuration for STNO＇s applications in future wireless communications.

Spin torque nano-oscillators with a perpendicular spin polarizer

We present an overview in the understanding of spin-transfer torque(STT) induced magnetization dynamics in spintorque nano-oscillator(STNO) devices. The STNO contains an in-plane(IP) magnetized free layer and an out-of-plane(OP) magnetized spin polarizing layer. After a brief introduction, we first use mesoscopic micromagnetic simulations,which are based on the Landau–Lifshitz–Gilbert equation including the STT effect, to specify how a spin-torque term may tune the magnetization precession orbits of the free layer, showing that the oscillator frequency is proportional to the current density and the z-component of the free layer magnetization. Next, we propose a pendulum-like model within the macrospin approximation to describe the dynamic properties in such type of STNOs. After that, we further show the procession dynamics of the STNOs excited by IP and OP dual spin-polarizers. Both the numerical simulations and analytical theory indicate that the precession frequency is linearly proportional to the spin-torque of the OP polarizer only and is irrelevant to the spin-torque of the IP polarizer. Finally, a promising approach of coordinate transformation from the laboratory frame to the rotation frame is introduced, by which the nonstationary OP magnetization precession process is therefore transformed into the stationary process in the rotation frame. Through this method, a promising digital frequency shift-key modulation technique is presented, in which the magnetization precession can be well controlled at a given orbit as well as its precession frequency can be tuned with the co-action of spin polarized current and magnetic field(or electric field) pulses.

Inverse spin Hall effect in ITO/YIG exited by spin pumping and spin Seebeck experiments

Spin currents, which are excited in indium tin oxide(ITO)/yttrium iron garnet(YIG) by the methods of spin pumping and spin Seebeck effect, are investigated through the inverse spin Hall effect(ISHE). It is demonstrated that the ISHE voltage can be generated in ITO by spin pumping under both in-plane and out-of-plane magnetization configurations.Moreover, it is observed that the enhancement of spin Hall angle and interfacial spin mixing conductance can be achieved by an appropriate annealing process. However, the ISHE voltage is hardly seen in the presence of a longitudinal temperature gradient. The absence of the longitudinal spin Seebeck effect can be ascribed to the almost equal thermal conductivity of ITO and YIG and specific interface structure, or to the large negative temperature dependent spin mixing conductance.

Hydrogenated antimonene as quantum spin Hall insulator:A first-principles study

Using first-principles calculations based on density functional theory(DFT), the structural and electronic properties of hydrogenated antimonene have been systematically investigated. Phonon dispersion and molecular dynamics(MD)simulation reveal that fully hydrogenated(FH) antimonene has high dynamic stability and could be synthesized. A newσ-type Dirac cone related to Sb-px,y orbitals is found in FH antimonene, which is robust to tensile strain. Noticeably, the spin orbital coupling(SOC) opens a quantum spin Hall(QSH) gap of 425 meV at the Dirac cone, sufficiently large for practical applications at room temperature. Semi-hydrogenated antimonene is a non-magnetic metal. Our results show that FH antimonene may have great potential applications in next generation high-performance devices.

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.

Dissipationless spin-Hall current contribution in the extrinsic spin-Hall effect

This paper shows that a substantial amount of dissipationless spin-Hall current contribution may exist in the extrinsic spin-Hall effect,which originates from the spin-orbit coupling induced by the applied external electric field itself that drives the extrinsic spin-Hall effect in a nonmagnetic semiconductor （or metal）.By assuming that the impurity density is in a moderate range such that the total scattering potential due to all randomly distributed impurities is a smooth function of the space coordinate,it is shown that this dissipationless contribution shall be of the same orders of magnitude as the usual extrinsic contribution from spin-orbit dependent impurity scatterings （or may even be larger than the latter one）.The theoretical results obtained are in good agreement with recent relevant experimental results.

Photonic spin Hall effect:fundamentals and emergent applications

The photonic spin Hall effect(SHE)refers to the transverse spin separation of photons with opposite spin angular momentum,after the beam passes through an optical interface or inhomogeneous medium,manifested as the spin-dependent splitting.It can be considered as an analogue of the SHE in electronic systems:the light’s right-circularly polarized and left-circularly polarized components play the role of the spin-up and spin-down electrons,and the refractive index gradient replaces the electronic potential gradient.Remarkably,the photonic SHE originates from the spin-orbit interaction of the photons and is mainly attributed to two different geometric phases,i.e.,the spin-redirection Rytov-Vlasimirskii-Berry in momentum space and the Pancharatnam-Berry phase in Stokes parameter space.The unique properties of the photonic SHE and its powerful ability to manipulate the photon spin,gradually,make it a useful tool in precision metrology,analog optical computing and quantum imaging,etc.In this review,we provide a brief framework to describe the fundamentals and advances of photonic SHE,and give an overview on the emergent applications of this phenomenon in different scenes.

Magnetization-direction-dependent inverse spin Hall effect observed in IrMn/NiFe/Cu/YIG multilayer structure

The magnetization-direction-dependent inverse spin Hall effect(ISHE) has been observed in NiFe film during spin Seebeck measurement in IrMn/NiFe/Cu/yttrium iron garnet(YIG) multilayer structure, where the YIG and NiFe layers act as the spin injector and spin current detector, respectively. By using the NiFe/IrMn exchange bias structure, the magnetization direction of YIG(MYIG) can be rotated with respect to that of NiFe(MNiFe) with a small magnetic field, thus allowing us to observe the magnetization-direction-dependent inverse spin Hall effect voltage in NiFe layer. Compared with the situation that polarization direction of spin current(σs) is perpendicular to MNiFe, the spin Seebeck voltage is about 30% larger than that when σs and MNiFe are parallel to each other. This phenomenon may originate from either or both of stronger interface or bulk scattering to spin current when σs and MNiFe are perpendicular to each other. Our work provides a way to control the voltage induced by ISHE in ferromagnets.

Intrinsic Hall effect and separation of Rashba and Dresselhaus spin splittings in semiconductor quantum wells

We have proposed a method to separate Rashba and Dresselhaus spin splittings in semiconductor quantum wells by using the intrinsic Hall effect. It is shown that the interference between Rashba and Dresselhaus terms can deflect the electrons in opposite transverse directions with a change of sign in the macroscopic Hall current, thus providing an alternative way to determine the different contributions to the spin-orbit coupling.

Switching the direction of spin accumulation in the spin Hall effect of light by adjusting the optical axis of an uniaxial crystal

We theoretically and experimentally investigate a switchable spin Hall effect（SHE） of light in reflection near the Brewster angle at an air-uniaxial crystal interface.We find a large transverse spin splitting near the Brewster angle,whose sign can be altered by rotating the optical axis.As an analogy of the SHE in an electronic system,a switchable spin accumulation in the SHE of light is detected.We are able to switch the direction of the spin accumulation by adjusting the optical axis angle of the uniaxial crystal.These findings may give opportunities for photon spin manipulating and developing a new generation of nano-photonic devices.

Spin Seebeck effect and spin Hall magnetoresistance in the Pt/Y_3Fe_5O_(12) heterostructure under laser-heating

In the previous study of longitudinal spin Seebeck effect（LSSE）, the thermal gradient was often generated by inserting the sample between the cool bath and the hot bath. For practical use, this method is too cumbersome to be easily integrated into modern electrical circuits. Since the laser can be easily focused into a small region, it will be more convenient and friendly to the integrated circuit. In this paper, we systematically investigate the LSSE and spin Hall magnetoresistance（SMR） of the Pt/Y_3 Fe_5 O_（12） heterostructure under focused laser-heating. We find that the extremely large voltage of inverse spin Hall effect（VISHE） can be obtained by reducing the diameter of laser or increasing the number of light spots.Meanwhile, even under the illumination of the ultraviolet light which will excite the electron from the valence band to the conduction band in yttrium iron garnet（YIG）, the magnitude of SMR is nearly constant. It indicates that the spin transport behavior of the adjacent Pt is independent of the electron configuration of YIG. The laser-heating method to generate LSSE will be very promising for modern integrated electronic circuits and will promote the application of spin caloritronics in practice.

Spin Chern numbers and time-reversal-symmetry-broken quantum spin Hall effect

The quantum spin Hall （QSH） effect is considered to be unstable to perturbations violating the time-reversal （TR） symmetry. We review some recent developments in the search of the QSH effect in the absence of the TR symmetry. The possibility to realize a robust QSH effect by artificial removal of the TR symmetry of the edge states is explored. As a useful tool to characterize topological phases without the TR symmetry, the spin-Chern number theory is introduced.

Interfacial spin Hall current in a Josephson junction with Rashba spin-orbit coupling

We theoretically investigate the spin transport properties of the Cooper pairs in a conventional Josephson junction with Rashba spin-orbit coupling considered in one of the superconducting leads.It is found that an angle-resolved spin supercurrent flows through the junction and a nonzero interfacial spin Hall current driven by the superconducting phase difference also appears at the interface.The physical origin of this is that the Rashba spin-orbit coupling can induce a triplet order parameter in the s-wave superconductor.The interfacial spin Hall current dependences on the system parameters are also discussed.

Quantum spin Hall and quantum valley Hall effects in trilayer graphene and their topological structures

The present study pertains to the trilayer graphene in the presence of spin orbit coupling to probe the quantum spin/valley Hall effect. The spin Chern-number Cs for energy-bands of trilayer graphene having the essence of intrinsic spin-orbit coupling is analytically calculated. We find that for each valley and spin, Cs is three times larger in trilayer graphene as compared to single layer graphene. Since the spin Chern-number corresponds to the number of edge states, consequently the trilayer graphene has edge states, three times more in comparison to single layer graphene. We also study the trilayer graphene in the presence of both electric-field and intrinsic spin-orbit coupling and investigate that the trilayer graphene goes through a phase transition from a quantum spin Hall state to a quantum valley Hall state when the strength of the electric field exceeds the intrinsic spin coupling strength. The robustness of the associated topological bulk-state of the trilayer graphene is evaluated by adding various perturbations such as Rashba spin-orbit （RSO） interaction αR, and exchange-magnetization M. In addition, we consider a theoretical model, where only one of the outer layers in trilayer graphene has the essence of intrinsic spin-orbit coupling, while the other two layers have zero intrinsic spin-orbit coupling. Although the first Chern number is non-zero for individual valleys of trilayer graphene in this model, however, we find that the system cannot be regarded as a topological insulator because the system as a whole is not gaped.

Spin Hall effect of a light beam in anisotropic metamaterials

We theoretically investigate a switchable spin Hall effect of light （SHEL） in reflection for three specific dispersion relations at an air-anisotropic metamaterial interface. The displacements of horizontal and vertical polarization compo- nents vary with the incident angle at different dispersion relations. The transverse displacements can be obtained with the relevant metamaterial whose refractive index can be arbitrarily tailed. The results of the SHEL in the metamaterial provide a new way for manipulating the transverse displacements of a specific polarization component.

The spin Hall effect in single-crystalline gold thin films

The spin Hall effect has been investigated in 10-nm-thick epitaxial Au(001) single crystal films via H-pattern devices,whose minimum characteristic dimension is about 40 nm. By improving the film quality and optimizing the in-plane geometry parameters of the devices, we explicitly extract the spin Hall effect contribution from the ballistic and bypass contribution which were previously reported to be dominating the non-local voltage. Furthermore, we calculate a lower limit of the spin Hall angle of 0.08 at room temperature. Our results indicate that the giant spin Hall effect in Au thin films is dominated not by the interior defects scattering, but by the surface scattering. Besides, our results also provide an additional experimental method to determine the magnitude of spin Hall angle unambiguously.