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.

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.

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.

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.

Theory of the magnon Kerr effect in cavity magnonics

We develop a theory for the magnon Kerr effect in a cavity magnonics system, consisting of magnons in a small yttrium iron garnet(YIG) sphere strongly coupled to cavity photons, and use it to study the bistability in this hybrid system. To have a complete picture of the bistability phenomenon, we analyze two different cases in driving the cavity magnonics system, i.e.,directly pumping the YIG sphere and the cavity, respectively. In both cases, the magnon frequency shifts due to the Kerr effect exhibit a similar bistable behavior but the corresponding critical powers are different. Moreover, we show how the bistability of the system can be demonstrated using the transmission spectrum of the cavity. Our results are valid in a wide parameter regime and generalize the theory of bistability in a cavity magnonics system.

Recent progress on optomagnetic coupling and optical manipulation based on cavity-optomagnonics

Recently,the photon–magnon coherent interaction based on the collective spins excitation in ferromagnetic materials has been achieved experimentally.Under the prospect,the magnons are proposed to store and process quantum information.Meanwhile,cavity-optomagnonics which describes the interaction between photons and magnons has been developing rapidly as an interesting topic of the cavity quantum electrodynamics.Here in this short review,we mainly introduce the recent theoretical and experimental progress in the field of optomagnetic coupling and optical manipulation based on cavity-optomagnonics.According to the frequency range of the electromagnetic field,cavity optomagnonics can be divided into microwave cavity optomagnonics and optical cavity optomagnonics,due to the different dynamics of the photon–magnon interaction.As the interaction between the electromagnetic field and the magnetic materials is enhanced in the cavity-optomagnonic system,it provides great significance to explore the nonlinear characteristics and quantum properties for different magnetic systems.More importantly,the electromagnetic response of optomagnonics covers the frequency range from gigahertz to terahertz which provides a broad frequency platform for the multi-mode controlling in quantum systems.

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.

Semiclassical approach to spin dynamics of a ferromagnetic S = 1 chain

Motivated by recent experimental progress on the quasi-one-dimensional quantum magnet Ni Nb2O6, we study the spin dynamics of an S = 1 ferromagnetic Heisenberg chain with single-ion anisotropy by using a semiclassical molecular dynamics approach. This system undergoes a quantum phase transition from a ferromagnetic to a paramagnetic state under a transverse magnetic field, and the magnetic response reflecting this transition is well described by our semiclassical method.We show that at low temperature the transverse component of the dynamical structure factor depicts clearly the magnon dispersion, and the longitudinal component exhibits two continua associated with single-and two-magnon excitations,respectively. These spin excitation spectra show interesting temperature dependence as effects of magnon interactions. Our findings shed light on the experimental detection of spin excitations in a large class of quasi-one-dimensional magnets.

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.

Low Gilbert damping in Bi/In-doped YIG thin films with giant Faraday effect

Magnetic films with low Gilbert damping are crucial for magnonic devices,which provide a promising platform forrealizing ultralow-energy devices.In this study,low Gilbert damping and coercive field were observed in Bi/In-dopedyttrium iron garnet(BiIn:YIG)thin films.The BiIn:YIG(444)films were deposited onto different substrates using pulsedlaser deposition.Low coercivity(<1 Oe)with saturation magnetization of 125.09 emu/cc was achieved along the in-planedirection of BiIn:YIG film.The values of Gilbert damping and inhomogeneous broadening of ferromagnetic resonance inBiIn:YIG films were obtained to be as low as 4.05×10^(-4)and 5.62 Oe,respectively.In addition to low damping,the giantFaraday rotation angles(up to 2.9×10^(4)deg/cm)were also observed in the BiIn:YIG film.By modifying the magneticstructure and coupling effect between Bi^(3+)and Fe^(3+)of Bi:YIG,doped In^(3+)plays a key role on variation of the magneticproperties.The low damping and giant Faraday effect made the BiIn:YIG film an appealing candidate for magnonic andmagneto-optical devices.

Asymmetric scattering behaviors of spin wave dependent on magnetic vortex chirality

We investigate asymmetric spin wave scattering behaviors caused by vortex chirality in a cross-shaped ferromagnetic system by using the micromagnetic simulations.In the system,four scattering behaviors are found:(i)asymmetric skew scattering,depending on the polarity of vortex core,(ii)back scattering(reflection),depending on the vortex core stiffness,(iii)side deflection scattering,depending on structural symmetry of the vortex circulation,and(iv)geometrical scattering,depending on waveguide structure.The first and second scattering behaviors are attributed to nonlinear topological magnon spin Hall effect related to magnon spin-transfer torque effect,which has value for magnonic exploration and application.

Liquid phase epitaxy magnetic garnet films and their applications

Liquid phase epitaxy （LPE） is a mature technology. Early experiments on single magnetic crystal films fabricated by LPE were focused mainly on thick films for microwave and magneto-optical devices. The LPE is an excellent way to make a thick film, low damping magnetic garnet film and high-quality magneto-optical material. Today, the principal challenge in the applied material is to create sub-micrometer devices by using modern photolithography technique. Until now the magnetic garnet films fabricated by LPE still show the best quality even on a nanoscale （about 100 nm）, which was considered to be impossible for LPE method.

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.

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.

Review of Raman spectroscopy of two-dimensional magnetic van der Waals materials

Ultrathin van der Waals(vdW)magnets provide a possibility to access magnetic ordering in the two-dimensional(2D)limit,which are expected to be applied in the spintronic devices.Raman spectroscopy is a powerful characterization method to investigate the spin-related properties in 2D vdW magnets,including magnon and spin–lattice interaction,which are hardly accessible by other optical methods.In this paper,the recent progress of various magnetic properties in 2D vdW magnets studied by Raman spectroscopy is reviewed,including the magnetic transition,spin-wave,spin–lattice interaction,symmetry tuning induced by spin ordering,and nonreciprocal magneto-phonon Raman scattering.

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.

Microscopic Theory of Nonlinear Spin Waves in Ferromagnets

Considering the attractive interaction between ferromagnet, we propose the model of magnon-pairs, which two magnons with opposite wave vectors in a Heisenberg is suitable for low-temperature environment. A dressed magnon is an energy quantum of the magnon-pairs whose energy is a monotonically increasing function of absolute temperature. Based on the model, we re-investigate the excitation mechanism and thermodynamic properties of the Heisenberg ferromagnet. The correction factor e（O） plays an important role in studying the low-temperature properties of a ferromagnet.

An Explicit Function Expression for dc Bias and Temperature Dependence of Magnetoresistances in Magnetic Tunnel Junctions

An explicit function expression for the bias voltage or/and temperature dependences of tunnel magnetoresistance ratio and resistances were obtained with a unique set of intrinsic parameters. Two of these intrinsic parameters are the Curie temperature TC and the density of state (DOS) for itinerant majority and minority electrons ξ(ρM/ρm), which are the eigen parameters of ferromagnetic electrodes. Others are the spin-dependent matrix-element ratio (i.e., |Td|2/|TJ|2 ) and the anisotropic-wavelength-cutoff energy ECγ of spin-wave spectrum in magnetic tunnel junction (MTJ), which are the structure parameters of an MTJ. These intrinsic parameters can be predetermined using the experimental measurement or, in principle, using the first-principle calculation method for an MTJ with the three key layers of FM/I/FM. Furthermore, a series of experimental data for an MTJ, for example, a spin-valve-type MTJ of Ta (5 nm)/Ni79Fe21(25 nm)/lr22Mn78(12 nm)/Co75Fe25(4 nm)/AI(0.8 nm)-oxide/Co75Fe25(4 nm)/Ni79Fe21(20 nm)/Ta (5 nm) in this work, can be self-consistently evaluated and explained using such concise explicit function formulations.

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.

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.