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.

Spin pumping by higher-order dipole-exchange spin-wave modes

Spin pumping(SP)and inverse spin Hall effect(ISHE)driven by parametrically-excited dipole-exchange spin waves in a yttrium iron garnet film have been systematically investigated.The measured voltage spectrum exhibits a feature of the field-induced transition from parallel pumping to perpendicular pumping because of the inhomogeneous excitation geometry.Thanks to the high precision of the SP-ISHE detection,two sets of fine structures in the voltage spectrum are observed,which can correspond well to two kinds of critical points in the multimode spin-wave spectrum for magnetic films.One is the q=0 point of each higher-order dispersion branch,and the other is the local minimum due to the interplay between the dipolar and exchange interactions.These fine structures on the voltage spectrum confirm the spin pumping by higher-order dipole-exchange spin-wave modes,and are helpful for probing the multimode spin-wave spectrum.

Self-Consistent Spin-Wave Analysis of the 1/3 Magnetization Plateau in the Kagome Antiferromagnet

We propose a modified spin-wave theory to study the 1/3 magnetization plateau of the antiferromagnetic Heisen- berg model on the kagome lattice. By the self-consistent inclusion of quantum corrections, the 1/3 plateau is stabilized over a broad range of magnetic fields for all spin quantum numbers S. The values of the critical mag- netic fields and the widths of the magnetization plateaus are fully consistent with the recent numerical results from exact diagonalization and infinite projected entangled paired states.

A Self-consistent Calculation and an Anisotropic Wavelength Cut off Energy of Spin-wave Spectrumin Magnetic Tunnel Junctions

Temperature dependence of tunnel magnetoresistance (TMR) ratio, resistance, and coercivity from 4.2 K to room temperature (RT), applied de bias voltage dependence of the TMR ratio and resistances at 4.2 K and RT, tunnel current I and dynamic conductance dI/dV as functions of the de bias voltage at 4.2 K, and inelastic electron tunneling (IET) spectroscopy, d(2)I/dV(2) versus V, at 4.2 K for a tunnel junction of Ta(5 nm)/Ni79Fe21(25 nm)/Ir22Mn78(12 nm)/Co75Fe25(4 nm)/Al(0.8 nm)-oxide/Co75Fe25(4 nm)/Ni79Fe21(25 nm)/Ta(5 nm) were systematically investigated. High TMR ratio of 59.2% at 4.2 K and 41.3% at RT were observed for this junction after annealing at 275 degreesC for an hour. The temperature dependence of TMR ratio and resistances from 4.2 to 300 K at 1.0 mV bias and the de bias voltage dependence of TMR ratio at 4.2 K from 0 to 80 mV can be evaluated by a comparison of self-consistent calculations with the experimental data based on the magnon-assisted inelastic excitation model and theory. An anisotropic wavelength cutoff energy of spin-wave spectrum in magnetic tunnel junctions (MTJs) was suggested, which is necessary for self-consistent calculations, based on a series of IET spectra observed in the MTJs.

Shape-manipulated spin-wave eigenmodes of magnetic nanoelements

The magnetization dynamics of nanoelements with tapered ends have been studied by micromagnetic simulations.Several spin-wave modes and their evolutions with the sharpness of the element ends are characterized. The edge mode localized in the two ends of the element can be effectively tuned by the element shape. Its frequency increases rapidly with the tapered parameter h and its localized area gradually expands toward the element center, and it finally merges into the fundamental mode at a critical tapered parameter h0. For nanoelements with h 〉 h0, the edge mode is completely suppressed. The standing spin-wave modes mainly in the internal area of the element are less affected by the element shape.The shifts of their frequencies are small and they display different tendencies. The evolution of the spin-wave modes with the element shape is explained by considering the change of the internal field.

In-plane spin excitation of skyrmion bags

Skyrmion bags are spin structures with arbitrary topological charges, each of which is composed of a big skyrmion and several small skyrmions. In this work, by using an in-plane alternating current(AC) magnetic field, we investigate the spinwave modes of skyrmion bags, which behave differently from the clockwise(CW) rotation mode and the counterclockwise(CCW) rotation mode of skyrmions because of their complex spin topological structures. The in-plane excitation power spectral density shows that each skyrmion bag possesses four resonance frequencies. By further studying the spin dynamics of a skyrmion bag at each resonance frequency, the four spin-wave modes, i.e., a CCW-CW mode, two CW-breathing modes with different resonance strengths, and an inner CCW mode, appear as a composition mode of outer skyrmion–inner skyrmions. Our results are helpful in understanding the in-plane spin excitation of skyrmion bags, which may contribute to the characterization and detection of skyrmion bags, as well as the applications in logic devices.

Magnetic Properties of a Mixed Spin-2 and Spin-5/2 Heisenberg Ferrimagnetic System on a Two-Dimensional Honeycomb Lattice： Green＇s Function Approach

The multisublattice Green＇s function technique is applied to study the magnetic properties of a mixed spin-2 and spin-5/2 Heisenberg ferrimagnetic system on a two-dimensional honeycomb lattice. The role of the different interactions in the Hamiltonian is explored. When only the nearest-neighbor interaction and the single-ion anisotropy are included, our results indicate that there are compensation points at finite temperatures. When the next-nearest-neighbor interaction exceeds a minimum value that depends on the other parameters in the Hamiltonian, the compensation point disappears. The next-nearest-neighbor interaction has the effect of changing the compensation temperature.

交换积分变化对低温二维亚铁磁体能谱的影响

运用He isenberg交换作用模型、sp in-wave和G reen's function方法研究了与低维有机磁性系统接近的二维正方晶格绝缘亚铁磁体的自旋波谱,并分析了不同方向上能谱谱线随系数J1/J2增加的变化规律.得到了如下结论:随磁性离子间的交换积分发生改变,磁振子能谱也发生了改变.沿某一方向能谱的变化与此方向上交换积分的变化密切相关.系统沿某一方向上交换积分的变化,导致形成所谓“自旋梯”时,谱线退化成5条能级,除最大的磁振子能谱线与最小的磁振子能谱线外,其余3条磁振子能谱线是二重简并的.系统的磁振子能谱E1、E3、E5、E7与E6、E8、E2、E4关于E/J=0线对称分布.

Discrete modulational instability and bright localized spin wave modes in easy-axis weak ferromagnetic spin chains involving the next-nearest-neighbor coupling

We report a theoretical work on the properties of modulational instability and bright type nonlinear localized modes in one-dimensional easy-axis weak ferromagnetic spin lattices involving next-nearest-neighbor couplings.With a linear stability analysis, we calculate the growth rates of the modulational instability, and plot the instability regions.When the strength of the next-nearest-neighbor coupling is large enough, two new asymmetric modulational instability regions appear near the boundary of the first Brillouin zone.Furthermore, analytical forms of the bright nonlinear localized modes are constructed by means of a quasi-discreteness approach.The influence of the next-nearest-neighbor coupling on the Brillouin zone center mode and boundary mode are discussed.In particular, we discover a reversal phenomenon of the propagation direction of the Brillouin zone boundary mode.

STRUCTURE AND FERROMAGNETIC RESONANCE OF Fe/Cu SUPERLATTICES

Metallic Fe/Cu superlattice films on glass substrates were prepared by a dc-magnetion sputtering system.The modulation behaviors and the crystal structures of the films were ex- amined by X-ray diffraction and transmission electron microscopy(TEM)respectively. Their magnetic properties were studied by means of ferromagnetic resonnance spectrometer and the vibrating sample magnetometer.The results show that there exists a strong magnetic coupling between the neighbouring Fe layers and it is the coupling that affectes the magnetic properties of these superlattice films.

Internal energy and specific antiferromagnetic heat in a ferromagnetic- double layers

The internal energy and specific heat of a Heisenberg ferro- antiferromagnetic double-layer system are studied by using spin-wave theory and the retarded Green function method at low temperatures. Numerical results show that the antiferromagnetic intralayer coupling J2 has an important influence on internal energy and specific heat for a four-sublattice system with antiferromagnetic （or ferrimagnetic） interlayer couplings.

Magnetic Properties of Ferromagnetic Double Layers with Ferrimagnetic Interlayer Coupling at Zero Temperature

Spin-wave theory is used to study magnetic properties of ferromagnetic double layers with a ferrimagnetic interlayer coupling at zero temperature. The spin-wave spectra and four sublattices magnetizations and internal energy are calculated by employing retarded Green function technique. The sublattice magnetizations at ground state are smaller than their classical values, owing to the zero-point quantum fluctuations of the spins.

Intrinsic Localized Spin-Wave Modes in an Anisotropic Ferromagnet with Dzyaloshinsky–Moriya Interaction

The existence and properties of intrinsic localized spin-wave modes in a ferromagnetic XXZ spin chain with Dzyaloshinsky–Moriya interaction are investigated analytically in the semiclassical limit. The model Hamiltonian is quantized by introducing the Dyson–Maleev transformation and the coherent state representation is chosen as the basic representation of the system. By making use of the method of multiple scales combined with a quasidiscreteness approximation, the equation of motion for the coherent-state amplitude is reduced to the nonlinear Schr¨odinger equation.It is shown that a bright intrinsic localized spin-wave mode whose eigenfrequency lies below the bottom of the magnon frequency band can exist in the ferromagnetic system. We also show that the system can produce a dark intrinsic localized spin-wave mode, i.e., nonpropagating kink, whose eigenfrequency is below the upper of the magnon frequency band. In addition, we find that the introduction of the Dzyaloshinsky–Moriya interaction changes wave numbers in the Brillouin-zone corresponding to the appearance of intrinsic localized spin-wave modes.

Spin-Wave Analysis of the Spin-1 Two-Dimensional Frustrated Heisenberg Antiferromagnet with the Single-Ion Anisotropy

In this paper, the lowtemperature properties of the spin1 twodimensionM frustrated Heisenberg antifer romagnet with the singleion anisotropy are investigated on a square lattice by using the spinwave theory. The influence of the frustration and anisotropy is found in the thermodynamics of the model, such as the temperature dependence of the staggered magnetization and specific heat. For some selected values of the frustration and anisotropy parameters, the results for the specific heat are compared with those of existing theories and numerical estimates. Within a spinwave analysis, we have found the evidence for an intermediate magnetically disorder phase to separate the Nel and collinear phases.

Magnetic field enhanced thermal conductivity and origin of large thermopower in layered cobaltates

Cobalt oxide,as one of the most fascinating examples of correlated electronic system,exhibits several exotic transport characteristics,such as superconductivity,charge ordering,and topological frustration.In this study,we are reporting the observation of another intriguing transport phenomenon in calcium cobaltates.Specifically,under a large magnetic field of 7 T,we observed an anomalously enhanced thermal conductivity that was accompanied with a largely suppressed thermopower.This observation reveals a hitherto undiscovered correlation between the two transport factors.Within the premise of Heisenberg model,we have shown that the observed experimental results can be explained consistently only if the magnon excitation is taken into account.Our study offers an insight into the puzzling origin of large thermopower observed in layered cobaltates and provides a specific strategy for further optimization of thermopower.

Electronic and magnetic structures of chain structured ironselenide compounds

Electronic and magnetic structures of iron selenide compounds Ce2O2FeSe2 （2212＊） and BaFe2Se3 （123＊） are studied by the first-principles calculations. We find that while all these compounds are composed of one-dimensional （1D） Fe chain （or ladder） structures, their electronic structures are not close to be quasi-lD. The magnetic exchange couplings between two nearest-neighbor （NN） chains in 2212＊ and between two NN two-leg-ladders in 123＊ are both antiferromagnetic （AFM）, which is consistent with the presence of significant third NN AFM coupling, a common feature shared in other iron-chalcogenides, FeTe （11＊） and KyFe2-xSe2 （122＊）. In magnetic ground states, each Fe chain of 2212＊ is ferromagnetic and each two-leg ladder of 123＊ form a block-AFM structure. We suggest that all magnetic structures in iron-selenide compounds can be unified into an extended J1-J2-J3 model. Spin-wave excitations of the model are calculated and can be tested by future experiments on these two systems.

Generation of polarization-entangled photon pairs in a cold atomic ensemble

We report an experimental generation of polarization-entangled photon pairs in a cold atomic ensemble. A single Stokes photon and one spin-wave excitation are simultaneously created via spontaneous Raman scattering. The spin-wave excitation is then converted into an anti-Stokes photon via an electromagnetic-induced-transparency reading process. The measured cross-correlation functions between the Stokes and anti-Stokes photons for two orthogonal polarizations are -75 and 74, respectively, at a generation rate of the photon pair of -60/s. Based on such correlations, we obtain polarization-entangled photon pairs, whose Bell parameter is S = 2.77 4- 0.01, violating Bell-CHSH inequality by -77 standard deviations. The presented polarization-entangled photon source has high entanglement degree and fast generation rate, which will promise us to apply it in future quantum repeater.

Hard-Core Bosons on a Two-Dimensional Square Optical Superlattice

In this work,we theoretically study hard-core bosons on a two-dimensional square optical superlattice at T = 0.First of all,we present the mean field phase diagram of this model in terms of the chemical potential μ and the alternating potential strength △.Besides a superfluid(SF) phase at △ = 0 and a charge density wave(CDW)phase in the large △ at half filling,we demonstrate that a supersolid(SS) phase emerges in the moderate △.Then,we focus on the μ = 0,e.g.,half filling case,using large-S semi-classical spin-wave approximation to study the SS to CDW quantum phase transition.In particular,we calculate the ground-state energy and the superfluid density at the level of1/S correction.We then compare the spin-wave results with the large scale quantum Monte Carlo(QMC) simulations using the cluster stochastic series expansion(CSSE) algorithm,and find that while the spin wave method is intuitive with clear physical pictures,the quantum critical point is quite different from that of numerical results which is believed to be accurate.We suggest that as simple as it is,this model still exhibits strong quantum fluctuations near the quantum critical point beyond the power of semiclassical spin-wave approach.