We investigate the skyrmion motion driven by spin waves on magnetic nanotubes through micromagnetic simulations.Our key results include demonstrating the stability and enhanced mobility of skyrmions on the edgeless na...We investigate the skyrmion motion driven by spin waves on magnetic nanotubes through micromagnetic simulations.Our key results include demonstrating the stability and enhanced mobility of skyrmions on the edgeless nanotube geometry,which prevents destruction at boundaries—a common issue in planar geometries.We explore the influence of the damping coefficient,amplitude,and frequency of microwaves on skyrmion dynamics,revealing a non-uniform velocity profile characterized by acceleration and deceleration phases.Our results show that the skyrmion Hall effect is significantly modulated on nanotubes compared to planar models,with specific dependencies on the spin-wave parameters.These findings provide insights into skyrmion manipulation for spintronic applications,highlighting the potential for high-speed and efficient information transport in magnonic devices.展开更多
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 ...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.展开更多
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 ed...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.展开更多
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...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.展开更多
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, tunn...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.展开更多
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 e...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.展开更多
The one dimensional spin 1/2 quantum chain with competing interactions is studied. The ground state energy and the elementary excitations are found by the spin wave theory and the equations of motion with decouplin...The one dimensional spin 1/2 quantum chain with competing interactions is studied. The ground state energy and the elementary excitations are found by the spin wave theory and the equations of motion with decoupling approximation. As required, the excitation energies are triply degenerated.展开更多
The interface spin-wave (ISW) modes or coupled semi-infinitemagnetic superlattices separated by a nonmagnetic layer have been studied by use of the magnetostatic method, A general expression of the ISW dispersion rela...The interface spin-wave (ISW) modes or coupled semi-infinitemagnetic superlattices separated by a nonmagnetic layer have been studied by use of the magnetostatic method, A general expression of the ISW dispersion relation is obtained. Detailed calculations are performed in the special case where the ttwo semi-infinite superlattices is considered to be identical and the external magnetic field is parallel or perpendicular to the surface of the layers. Some results about ISW modes are discussed.展开更多
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 Hamilton...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.展开更多
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 influ...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.展开更多
Tensile-strained epitaxial La0.67Ba0.33MnO3(LBMO)film has been prepared by magnetron sputtering technique on(001)oriented spinel MgAl2O4substrate.The transport and magnetic measurements give an insulator-metal transit...Tensile-strained epitaxial La0.67Ba0.33MnO3(LBMO)film has been prepared by magnetron sputtering technique on(001)oriented spinel MgAl2O4substrate.The transport and magnetic measurements give an insulator-metal transition and paramagnetic-ferromagnetic transition occurring at^150 K and 250 K respectively,which implies the phase separation in such a tensile-strained film.By analyzing the angular and temperature dependences of the ferromagnetic resonance(FMR),we determine the magnetocrystalline anisotropy of the film.It is found that the tensile-strained film is dominated by an easy-axis corresponding to the compressive out-of-plane direction,though the magnitudes of anisotropy constants are relatively small and their temperature dependences are some complex.Furthermore,the FMR spectra show additional spin wave resonance(SWR),and the field positions can be indexed to follow a linear dependence on the square of index n.The scaling gives a spin-wave exchange stiffness D of 20.7 meV 2at low temperature,which is less than half of that in strain-free LBMO films,implying that the double exchange interaction is remarkably suppressed in the tensile-strained LBMO films.展开更多
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,...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.展开更多
The wave/particle duality of particles in Physics is well known. Particles have properties that uniquely characterize them from one another, such as mass, charge and spin. Charged particles have associated Electric an...The wave/particle duality of particles in Physics is well known. Particles have properties that uniquely characterize them from one another, such as mass, charge and spin. Charged particles have associated Electric and Magnetic fields. Also, every moving particle has a De Broglie wavelength determined by its mass and velocity. This paper shows that all of these properties of a particle can be derived from a single wave function equation for that particle. Wave functions for the Electron and the Positron are presented and principles are provided that can be used to calculate the wave functions of all the fundamental particles in Physics. Fundamental particles such as electrons and positrons are considered to be point particles in the Standard Model of Physics and are not considered to have a structure. This paper demonstrates that they do indeed have structure and that this structure extends into the space around the particle’s center (in fact, they have infinite extent), but with rapidly diminishing energy density with the distance from that center. The particles are formed from Electromagnetic standing waves, which are stable solutions to the Schrödinger and Classical wave equations. This stable structure therefore accounts for both the wave and particle nature of these particles. In fact, all of their properties such as mass, spin and electric charge, can be accounted for from this structure. These particle properties appear to originate from a single point at the center of the wave function structure, in the same sort of way that the Shell theorem of gravity causes the gravity of a body to appear to all originate from a central point. This paper represents the first two fully characterized fundamental particles, with a complete description of their structure and properties, built up from the underlying Electromagnetic waves that comprise these and all fundamental particles.展开更多
基金supported by the National Key R&D Program of China(Grant No.2022YFA1402802)the National Natural Science Foundation of China(Grant Nos.12434003,12374103,and 12074057).Tijjani acknowledges the helpful discussions with Dr.Zhejunyu Jin,Mr.Zhaozhuo Zeng and Dr.Huanhuan Yang.
文摘We investigate the skyrmion motion driven by spin waves on magnetic nanotubes through micromagnetic simulations.Our key results include demonstrating the stability and enhanced mobility of skyrmions on the edgeless nanotube geometry,which prevents destruction at boundaries—a common issue in planar geometries.We explore the influence of the damping coefficient,amplitude,and frequency of microwaves on skyrmion dynamics,revealing a non-uniform velocity profile characterized by acceleration and deceleration phases.Our results show that the skyrmion Hall effect is significantly modulated on nanotubes compared to planar models,with specific dependencies on the spin-wave parameters.These findings provide insights into skyrmion manipulation for spintronic applications,highlighting the potential for high-speed and efficient information transport in magnonic devices.
基金the National Natural Science Foundation of China(Grant No.11904194).
文摘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.
基金Project supported by the National Natural Science Foundation of China(Grant No.11374373)the Doctoral Fund of Ministry of Education of China(Grant No.20120162110020)+1 种基金the Natural Science Foundation of Hunan Province of China(Grant No.13JJ2004)the Science and Technology Planning of Yiyang City of Hunan Province of China(Grant No.2014JZ54)
文摘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.
基金Supported by the National Natural Science Foundation of China under Grant Nos 10934008,10874215 and 11174365the National Basic Research Program of China under Grant Nos 2012CB921704 and 2011CB309703
文摘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.
文摘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.
基金Project supported by the National Key Research and Development Program of China(Grant No.2016YFA0300803)the National Natural Science Foundation of China(Grant Nos.11774150,12074178,and 12004171)+1 种基金the Applied Basic Research Programs of Science and Technology Commission Foundation of Jiangsu Province,China(Grant No.BK20170627)the Open Research Fund of Jiangsu Provincial Key Laboratory for Nanotechnology.
文摘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.
文摘The one dimensional spin 1/2 quantum chain with competing interactions is studied. The ground state energy and the elementary excitations are found by the spin wave theory and the equations of motion with decoupling approximation. As required, the excitation energies are triply degenerated.
文摘The interface spin-wave (ISW) modes or coupled semi-infinitemagnetic superlattices separated by a nonmagnetic layer have been studied by use of the magnetostatic method, A general expression of the ISW dispersion relation is obtained. Detailed calculations are performed in the special case where the ttwo semi-infinite superlattices is considered to be identical and the external magnetic field is parallel or perpendicular to the surface of the layers. Some results about ISW modes are discussed.
基金Supported by the National Natural Science Foundation of China under Grant No.11264012Hunan Provincial Innovation Foundation for Postgraduate under Grant No.CX2013B264
文摘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.
文摘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.
基金supported by the National Natural Science Foundation of China (11174261)
文摘Tensile-strained epitaxial La0.67Ba0.33MnO3(LBMO)film has been prepared by magnetron sputtering technique on(001)oriented spinel MgAl2O4substrate.The transport and magnetic measurements give an insulator-metal transition and paramagnetic-ferromagnetic transition occurring at^150 K and 250 K respectively,which implies the phase separation in such a tensile-strained film.By analyzing the angular and temperature dependences of the ferromagnetic resonance(FMR),we determine the magnetocrystalline anisotropy of the film.It is found that the tensile-strained film is dominated by an easy-axis corresponding to the compressive out-of-plane direction,though the magnitudes of anisotropy constants are relatively small and their temperature dependences are some complex.Furthermore,the FMR spectra show additional spin wave resonance(SWR),and the field positions can be indexed to follow a linear dependence on the square of index n.The scaling gives a spin-wave exchange stiffness D of 20.7 meV 2at low temperature,which is less than half of that in strain-free LBMO films,implying that the double exchange interaction is remarkably suppressed in the tensile-strained LBMO films.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 12104124 and 12274111)the Natural Science Foundation of Hebei Province, China (Grant Nos. A2021201001 and A2021201008)+4 种基金the Central Guidance Fund on the Local Science and Technology Development of Hebei Province, China (Grant No. 236Z0601G)the Post-graduate’s Innovation Fund Project of Hebei Province, China (Grant No. CXZZSS2023007)the Advanced Talents Incubation Program of the Hebei University, China (Grant Nos. 521000981395, 521000981423, 521000981394, and 521000981390)the Research Foundation of Chongqing University of Science and technology, China (Grant No. ckrc2019017)the High-Performance Computing Center of Hebei University, China。
文摘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.
文摘The wave/particle duality of particles in Physics is well known. Particles have properties that uniquely characterize them from one another, such as mass, charge and spin. Charged particles have associated Electric and Magnetic fields. Also, every moving particle has a De Broglie wavelength determined by its mass and velocity. This paper shows that all of these properties of a particle can be derived from a single wave function equation for that particle. Wave functions for the Electron and the Positron are presented and principles are provided that can be used to calculate the wave functions of all the fundamental particles in Physics. Fundamental particles such as electrons and positrons are considered to be point particles in the Standard Model of Physics and are not considered to have a structure. This paper demonstrates that they do indeed have structure and that this structure extends into the space around the particle’s center (in fact, they have infinite extent), but with rapidly diminishing energy density with the distance from that center. The particles are formed from Electromagnetic standing waves, which are stable solutions to the Schrödinger and Classical wave equations. This stable structure therefore accounts for both the wave and particle nature of these particles. In fact, all of their properties such as mass, spin and electric charge, can be accounted for from this structure. These particle properties appear to originate from a single point at the center of the wave function structure, in the same sort of way that the Shell theorem of gravity causes the gravity of a body to appear to all originate from a central point. This paper represents the first two fully characterized fundamental particles, with a complete description of their structure and properties, built up from the underlying Electromagnetic waves that comprise these and all fundamental particles.