Interacting topological magnons in a checkerboard ferromagnet

This work is devoted to studying the magnon-magnon interaction effect in a two-dimensional checkerboard ferromagnet with the Dzyaloshinskii-Moriya interaction.Using a first-order Green function method,we analyze the influence of magnon-magnon interaction on the magnon band topology.We find that Chern numbers of two renormalized magnon bands are different above and below the critical temperature,which means that the magnon band gap-closing phenomenon is an indicator for one topological phase transition of the checkerboard ferromagnet.Our results show that the checkerboard ferromagnet possesses two topological phases,and its topological phase can be controlled either via the temperature or the applied magnetic field due to magnon-magnon interactions.Interestingly,it is found that the topological phase transition can occur twice with the increase in the temperature,which is different from the results of the honeycomb ferromagnet.

Tunable dispersion relations manipulated by strain in skyrmion-based magnonic crystals

We theoretically investigate the propagation characteristics of spin waves in skyrmion-based magnonic crystals. It is found that the dispersion relation can be manipulated by strains through magneto-elastic coupling. Especially, the allowed bands and forbidden bands in dispersion relations shift to higher frequency with strain changing from compressive to tensile,while shifting to lower frequency with strain changing from tensile to compressive. We also confirm that the spin wave with specific frequency can pass the magnonic crystal or be blocked by tuning the strains. The result provides an advanced platform for studying the tunable skyrmion-based spin wave devices.

Frequency combs based on magnon-skyrmion interaction in magnetic nanotubes

Within the magnonics community,there has been a lot of interests in the magnon–skyrmion interaction.Magnons and skyrmions are two intriguing phenomena in condensed matter physics,and magnetic nanotubes have emerged as a suitable platform to study their complex interactions.We show that magnon frequency combs can be induced in magnetic nanotubes by three-wave mixing between the propagating magnons and skyrmion.This study enriches our fundamental comprehension of magnon–skyrmion interactions and holds promise for developing innovative spintronic devices and applications.This frequency comb tunability and unique spectral features offer a rich platform for exploring novel avenues in magnetic nanotechnology.

From microelectronics to spintronics and magnonics

In this review,the recent developments in microelectronics,spintronics,and magnonics have been summarized and compared.Firstly,the history of the spintronics has been briefly reviewed.Moreover,the recent development of magnonics such as magnon-mediated current drag effect(MCDE),magnon valve effect(MVE),magnon junction effect(MJE),magnon blocking effect(MBE),magnon-mediated nonlocal spin Hall magnetoresistance(MNSMR),magnon-transfer torque(MTT)effect,and magnon resonant tunneling(MRT)effect,magnon skin effect(MSE),etc.,existing in magnon junctions or magnon heterojunctions,have been summarized and their potential applications in memory and logic devices,etc.,are prospected,from which we can see a promising future for spintronics and magnonics beyond micro-electronics.

Frequency in Middle of Magnon Band Gap in a Layered Ferromagnetic Superlattice

The frequency in middle of magnon energy band in a five-layer ferromagnetic superlattice is studied by using the linear spin-wave approach and Green＇s function technique. It is found that four energy gaps and corresponding four frequencie in middle of energy gaps exist in the magnon band along Kx direction perpendicular to the superlattice plane. The spin quantum numbers and the interlayer exchange couplings all affect the four frequencies in middle of the energy gaps. When all interlayer exchange couplings are same, the effect of spin quantum numbers on the frequency wg1 in middle of the energy gap Δw12 is complicated, and the frequency wg1 depends on the match of spin quantum numbers in each layer. Meanwhile, the frequencies wg2, wg3, and wg4 in middle of other energy gaps increase monotonously with increasing spin quantum numbers. When the spin quantum numbers in each layer are same, the frequencies wg1, wg2, wg3, and wg4 all increase monotonously with increasing interlayer exchange couplings.

Anisotropic Magnon–Magnon Coupling in Synthetic Antiferromagnets

Magnon-magnon coupling in synthetic antiferromagnets advances it as hybrid magnonic systems to explore the quantum information technologies.To induce magnon-magnon coupling,the parity symmetry between two magnetization needs to be broken.Here we experimentally demonstrate a convenient method to break the parity symmetry by the asymmetric structure.We successfully introduce a magnon-magnon coupling in Ir-based synthetic antiferromagnets CoFeB(10 nm)/Ir(t_(Ir)=0.6 nm,1.2 nm)/CoFeB(13 nm).Remarkably,we find that the weakly uniaxial anisotropy field(-20 Oe)makes the magnon-magnon coupling anisotropic.The coupling strength presented by a characteristic anticrossing gap varies in the range between 0.54 GHz and 0.90 GHz for t_(Ir)=0.6 nm,and between 0.09 GHz and 1.4 GHz for t_(Ir)=1.2 nm.Our results demonstrate a feasible way to induce magnon-magnon coupling by an asymmetric structure and tune the coupling strength by varying the direction of in-plane magnetic field.The magnon-magnon coupling in this highly tunable material system could open exciting perspectives for exploring quantum-mechanical coupling phenomena.

Structure of Essential Spectrum and Discrete Spectrum of the Energy Operator of Three-Magnon Systems in the Isotropic Ferromagnetic Non-Heisenberg Model with Spin One and Nearest-Neighbor Interactions

We consider a three-magnon system in the isotropic ferromagnetic Non-Heisenberg model with spin one and with a coupling between nearest-neighbors. The structure of essential spectrum and discrete spectrum of the systems in a ν-dimensional lattice are investigated. We obtain the lower and upper estimates for the number of three-magnon bound states of the system.

Effects of rotating noncircular scatterers on spin-wave band gaps of two-dimensional magnonic crystals

Using the plane-wave expansion method, the spin-wave band structures of two-dimensional magnonic crystals consisting of square arrays of different shape scatterers are calculated numerically, and the effects of rotating rectangle and hexagon scaterers on the gaps are studied, respectively. The results show that the gaps can be substantially opened and tuned by rotating the scatterers. This approach should be helpful in designing magnonic crystals with desired gaps.

Topological magnon insulator with Dzyaloshinskii–Moriya interaction under the irradiation of light

The topological magnon insulator on a honeycomb lattice with Dzyaloshinskii–Moriya interaction(DMI) is studied under the application of a circularly polarized light.At the high-frequency regime, the effective tight-binding model is obtained based on Brillouin–Wigner theory.Then, we study the corresponding Berry curvature and Chern number.In the Dirac model, the interplay between a light-induced handedness-dependent effective DMI and intrinsic DMI is discussed.

Magnon energy gap in a four-layer ferromagnetic superlattice

The magnon energy band in a four-layer ferromagnetic superlattice is studied by using the linear spin-wave approach and Green＇s function technique. It is found that three modulated energy gaps exist in the magnon energy band along Kx direction perpendicular to the superlattice plane. The spin quantum numbers and the interlayer exchange couplings all affect the three energy gaps. The magnon energy gaps of the four-layer ferromagnetic superlattice are different from those of the three-layer one. For the four-layer ferromagnetic superlattice, the disappearance of the magnon energy gaps △ω12, △ω23 and △ω34 all correlates with the symmetry of this system. The zero energy gap △ω23 correlates with the symmetry of interlayer exchange couplings, while the vanishing of the magnon energy gaps △ω12 and △ω34 corresponds to a translational symmetry of x-direction in the lattice. When the parameters of the system deviate from these symmetries, the three energy gaps will increase.

Squeezing States of Magnons in a Ferromagnet

In this paper, we conduct an investigation into magnon self-squeezing states in a ferromagnet. In these states, the quantum fluctuations of the spin components can be lower than the zero-point quantum fluctuations of the coherent states. Through calculating the expectation values of spin fluctuations we gain the condition of achieving magnon self-squeezing. We introduce the mean-field theory for dealing with the nonlinear interaction term of Hamiltonian of magnon system.

Observation of nonlinearity and heating-induced frequency shifts in cavity magnonics

When there is a certain amount of field inhomogeneity,the biased ferrimagnetic crystal can exhibit the higher-order magnetostatic(HMS)mode in addition to the uniform-precession Kittel mode.In cavity magnonics,we show the nonlinearity and heating-induced frequency shifts of the Kittel mode and HMS mode in a yttrium-iron-garnet(YIG)sphere.When the Kittel mode is driven to generate a certain number of excitations,the temperature of the whole YIG sample rises and the HMS mode can display an induced frequency shift,and vice versa.This cross effect provides a new method to study the magnetization dynamics and paves a way for novel cavity magnonic devices by including the heating effect as an operational degree of freedom.

Eigenstates and temporal dynamics in cavity optomagnonics

Many studies of magnon–photon coupling are performed in the frequency domain for microwave photons.In this work,we present analytical results of eigenfrequency,eigenstates,and temporal dynamics for the coupling between ferromagnetic magnon and visible photon.In contrast to microwave photons,optical photons can be coupled with magnon in a dispersive interaction which produces both level repulsion and attraction by varying the magnon–photon frequency detuning.At resonance,the hybridized states are of linear polarization and circular polarization for level repulsion and level attraction respectively.As the detuning increases,the polarizations of level repulsion remain linear but those of level attraction vary from elliptical to linear polarizations.The temporal dynamics of level repulsion presents the beat-like behavior.The level attraction presents monotonous decay in the weak coupling regime but gives rise to instability in the strong coupling regime due to the magnon amplification.As the detuning is large,both magnon and photon amplitudes present a synchronizing oscillation.Our results are important for exploring the temporal evolution of magnon–photon coupling in the range of optical frequency and designing magnon-based timing devices.

Magnon bands in twisted bilayer honeycomb quantum magnets

We study the magnon bands of twisted bilayer honeycomb quantum magnets using linear spin wave theory.Although the interlayer coupling can be ferromagnetic or antiferromagnetic,we keep the intralayer one ferromagnetic to avoid possible frustration.For the interlayer ferromagnetic case,we find the magnon bands have similar features with the corresponding electronic energy spectrums.Although the linear dispersions near the Dirac points are preserved in the magnon bands of twisted bilayer magnets,their slopes are reduced with the decrease of the twist angles.On the other hand,the interlayer antiferromagnetic couplings generate quite different magnon spectra.The two single-layered magnon spectra are usually decoupled due to the opposite orientations of the spins in the two layers.We also develop a low-energy continuous theory for very small twist angles,which has been verified to fit well with the exact tight-binding calculations.Our results may be experimentally observed due to the rapid progress in two-dimensional magnetic materials.

High-fidelity quantum sensing of magnon excitations with a single electron spin in quantum dots

Single-electron spins in quantum dots are the leading platform for qubits,while magnons in solids are one of the emerging candidates for quantum technologies.How to manipulate a composite system composed of both systems is an outstanding challenge.Here,we use spin-charge hybridization to effectively couple the single-electron spin state in quantum dots to the cavity and further to the magnons.Through this coupling,quantum dots can entangle and detect magnon states.The detection efficiency can reach 0.94 in a realistic experimental situation.We also demonstrate the electrical tunability of the scheme for various parameters.These results pave a practical pathway for applications of composite systems based on quantum dots and magnons.

Solitary Magnon Localization in Antiferromagnet RbFeBr_3

Introducing the Dyson-Maleev transformation. the coherent state ansatz and the time-dependent variation principle, we obtain two partial different equations of motion from Hamiltonian. Employing the method of multiple scales. we reduce these equations into the envelope function equations and force the amplitude function to satisfy a nonlinear Schrodinger equation. Using the inverse- scat-tering transformation, we obtain the single soliton solution and discuss the solitary magnon localization in antiferromagnet RbFeBr3

Laser-field-induced magnon amplification in a magnetic semiconductor quantum well under an external magnetic field

The laser-field induced magnon amplification in a magnetic semiconductorquantum well under an external magnetic field was discussed, it is shown that when the laserfrequency is near to the electron cyclotron frequency, no matter how weaker the laser field is, themagnon amplification always occurs. In case of fixed laser frequency, the optical absorption ofmagnons obeys the definite selection rule to the laser field strength. The rate of change of magnonoccupation is calculated, and the amplification condition is given.

Itinerant Topological Magnons in SU (2) Symmetric Topological Hubbard Models with Nearly Flat Electronic Bands

We show that a suitable combination of flat-band ferromagnetism,geometry and nontrivial electronic band topology can give rise to itinerant topological magnons.An SU(2) symmetric topological Hubbard model with nearly flat electronic bands,on a Kagome lattice,is considered as the prototype.This model exhibits ferromagnetic order when the lowest electronic band is half-filled.Using the numerical exact diagonalization method with a projection onto this nearly flat band,we can obtain the magnonic spectra.In the flat-band limit,the spectra exhibit distinct dispersions with Dirac points,similar to those of free electrons with isotropic hoppings,or a local spin magnet with pure ferromagnetic Heisenberg exchanges on the same geometry.Significantly,the non-flatness of the electronic band may induce a topological gap at the Dirac points,leading to a magnonic band with a nonzero Chern number.More intriguingly,this magnonic Chern number changes its sign when the topological index of the electronic band is reversed,suggesting that the nontrivial topology of the magnonic band is related to its underlying electronic band.Our work suggests interesting directions for the further exploration of,and searches for,itinerant topological magnons.

Determination of the Range of Magnetic Interactions from the Relations between Magnon Eigenvalues at High-Symmetry k Points

Magnetic exchange interactions(MEIs) define networks of coupled magnetic moments and lead to a surprisingly rich variety of their magnetic properties. Typically MEIs can be estimated by fitting experimental results.Unfortunately, how many MEIs need to be included in the fitting process for a material is unclear a priori,which limits the results obtained by these conventional methods. Based on linear spin-wave theory but without performing matrix diagonalization, we show that for a general quadratic spin Hamiltonian, there is a simple relation between the Fourier transform of MEIs and the sum of square of magnon energies(SSME). We further show that according to the real-space distance range within which MEIs are considered relevant, one can obtain the corresponding relationships between SSME in momentum space. By directly utilizing these characteristics and the experimental magnon energies at only a few high-symmetry k points in the Brillouin zone, one can obtain strong constraints about the range of exchange path beyond which MEIs can be safely neglected. Our methodology is also generally applicable for other Hamiltonian with quadratic Fermi or Boson operators.

Weyl and Nodal Ring Magnons in Three-Dimensional Honeycomb Lattices

We study the topological properties of magnon excitations in a wide class of three-dimensional （3D） honeycomb lattices with ferromagnetic ground states. It is found that they host nodal ring magnon excitations. These rings locate on the same plane in the momentum space. The nodal ring degeneracy can be lifted by the Dzyaloshinskii- Moriya interactions to form two Weyl points with opposite charges. We explicitly discuss these physics in the simplest 3D honeycomb lattice and the hyperhoneycomb lattice, and show drumhead and are surface states in the nodal ring and Weyl phases, respectively, due to the bulk-boundary correspondence.