Magnonic Crystals Research Articles

Распространение спиновых волн в управляемом деформациями магнонном кристалле с пьезоэлектрическим слоем

The mechanisms of spin wave propagation in a magnonic-crystalline structure, which is a width-modulated magnetic microwaveguide loaded with a piezoelectric layer with a system of counter-pin electrodes, are considered. Computational modelling based on the finite element method has been used to estimate the transformation of the internal magnetic field in a magnonic crystal under the action of elastic deformations. The shift of the frequency band of the Bragg resonance and the depth of regression of the spin-wave signal at the frequency of the Bragg resonance when an electric potential is applied to the electrodes are observed. It is shown that changing the polarity of the electric field can effectively control the characteristics of the propagating spin waves and the spatial distribution of the dynamic magnetization intensity in the multiferroic structure.

Распространение невзаимных спиновых волн в многослойном магнонном кристалле

The possibility of frequency-selective propagation of spin waves in a magnonic microwave guide with a magnonic crystal consisting of two layers with different values of the saturation magnetization in the layers is demonstrated. It is shown that multimode propagation of spin waves can occur inside a two-layer structure in two frequency ranges, while the presence of a magnonic crystal on the surface of the structure leads to the manifestation of a band gap in one of the frequency ranges. At the same time, the process of propagation of a spin-wave signal is accompanied by a strong nonreciprocity, which manifests itself in a change in the amplitude-frequency characteristics when the direction of the external magnetic field is reversed, while the frequency range of the band gap differs depending on the direction of the field. The proposed concept of a two-layer spin-wave waveguide can underlie the manufacture of multichannel filters or magnonic logic devices.

Propagation of nonreciprocal spin waves in a multilayer magnonic crystal

The possibility of frequency-selective propagation of spin waves in a magnonic microwave guide with a magnonic crystal consisting of two layers with different values of the saturation magnetization in the layers is demonstrated. It is shown that multimode propagation of spin waves can occur inside a two-layer structure in two frequency ranges, while the presence of a magnonic crystal on the surface of the structure leads to the manifestation of a band gap in one of the frequency ranges. At the same time, the process of propagation of a spin-wave signal is accompanied by a strong nonreciprocity, which manifests itself in a change in the amplitude-frequency characteristics when the direction of the external magnetic field is reversed, while the frequency range of the band gap differs depending on the direction of the field. The proposed concept of a two-layer spin-wave waveguide can underlie the manufacture of multichannel filters or magnonic logic devices. Keywords: magnonics, nonlinearity, nonlinear systems, multilayer systems, spin waves.

Наведенный нелинейный сдвиг частоты активного кольцевого резонатора на магнонном кристалле

The nonlinear shift of the resonant frequencies of a microwave active ring resonator (ARR) induced by a pump wave has been studied for the first time. The resonator was designed according to the scheme in the form of a closed ring containing a spin-wave delay line made on the basis of a one-dimensional magnonic crystal, as well as a microwave amplifier in a feedback circuit. It is shown, that with an increase in the power of the pumping wave, the shift of the resonant frequencies of the ARR increases in different ways depending on the position of the pumping frequency. The maximum induced nonlinear frequency shift is observed if the pumping frequency is at the minimum of the ARR transmission coefficient. A model describing the studied effect is developed.

Исследование оптически индуцированного формирования магнонных зон в структуре ЖИГ | периодический арсенид галлия

The present work is devoted to the study of the optically induced formation of the band structure of a magnon crystal consisting of a ferrite microwave diode loaded with a semiconductor with periodic thickness modulation. Using the Brillouin light scattering method, it is demonstrated that an increase in the power of laser radiation illuminating the semiconductor layer leads to the formation of non-transmission bands in the spectrum of surface magnetostatic waves (PMSW) with a simultaneous increase in the central frequency of these bands. Using the finite element method, we connected the formed non-transmission bands with the Bragg resonances of the periodic structure, and also evaluated the effect of changes in the density of semiconductor electrons on the dispersion dependences and non-reciprocal properties of PMSV in such a structure.

Anderson-Higgs Mass of Magnons in Superconductor-Ferromagnet-Superconductor Systems

The dynamic interplay of superconductivity and magnetism is promising for developing quantum magnonics and spintronics. Recent experiments have reported significant, enigmatic shifts of ferromagnetic resonance frequency in layered SFS structures. The author explains that the origin of this effect is spontaneous generation of magnon mass due to the celebrated Anderson-Higgs mechanism, a cornerstone of the Standard Model of particle physics. Upon cooling below the superconducting critical temperature, the magnons acquire a frequency gap and change their propagation direction. This effect enables the creation of magnon resonators, crystals, parametric amplifiers, and other useful devices.

Lock-in thermographic study of spin-wave propagation in magnonic crystals

We have investigated the spin-wave dynamics in a one-dimensional magnonic crystal (MC) with respect to the heat radiation due to the damping of the spin waves. The spin waves were excited by applying microwaves via a wire antenna. The heat induced by the excitation and propagation of spin waves was measured using the lock-in thermography (LIT) technique by periodically modulating the microwave power. The LIT measurements resolved the heat source distributions inside the MC, which is made of an yttrium iron garnet film and periodic grooves with a sub-mm interval, in the backward volume wave geometry. The temperature distribution induced by the spin-wave excitation notably depends on the frequency or wave number of the spin waves, as a result of the formation of rejection bands in the MC. The observed temperature modulation profiles are complicated, but their behavior is consistent with a calculation based on the microwave transmission line approximation of the MCs, demonstrating the applicability of the LIT measurements to the investigation of the spin-wave dynamics in sub-mm scale MCs.

Spin-wave spectra in antidot lattice with inhomogeneous perpendicular magnetic anisotropy

Magnonic crystals are structures with periodically varied magnetic properties that are used to control collective spin-wave excitations. With micromagnetic simulations, we study spin-wave spectra in a 2D antidot lattice based on a multilayered thin film with perpendicular magnetic anisotropy (PMA). We show that the modification of the PMA near the antidot edges introduces interesting changes to the spin-wave spectra, even in a fully saturated state. In particular, the spectra split into two types of excitations: bulk modes with amplitude concentrated in a homogeneous part of the antidot lattice and edge modes with an amplitude localized in the rims of reduced PMA at the antidot edges. Their dependence on the geometrical or material parameters is distinct, but at resonance conditions fulfilled, we found strong hybridization between bulk and radial edge modes. Interestingly, the hybridization between the fundamental modes in bulk and rim is of magnetostatic origin, but the exchange interactions determine the coupling between higher-order radial rim modes and the fundamental bulk mode of the antidot lattice.

Shaping the spin wave spectra of planar 1D magnonic crystals by the geometrical constraints

We present experimental and numerical studies demonstrating the influence of geometrical parameters on the fundamental spin-wave mode in planar 1D magnonic crystals. The investigated magnonic crystals consist of flat stripes separated by air gaps. The adjustment of geometrical parameters allows tailoring of the spin-wave frequencies. The width of stripes and the width of gaps between them affect spin-wave frequencies in two ways. First, directly by geometrical constraints confining the spin waves inside the stripes. Second, indirectly by spin-wave pinning, freeing the spin waves to a different extent on the edges of stripes. Experimentally, the fundamental spin-wave mode frequencies are measured using an all-optical pump-probe time-resolved magneto-optical Kerr-effect setup. Our studies address the problem of spin-wave confinement and spin-wave dipolar pinning in an array of coupled stripes. We show that the frequency of fundamental mode can be tuned to a large extent by adjusting the width of the stripes and the width of gaps between them.

Tuning of spin-wave transmission and mode conversion in microscopic YIG waveguides with magnonic crystals

We report experimental results on spin-wave propagation, transmission gap tuning, and mode conversion in straight, curved, and Y-shaped yttrium iron garnet waveguides with magnonic crystals made of submicrometer-wide airgrooves. We observe forbidden frequency gaps with sizes up to 200 MHz in straight waveguides and narrowing of the gaps in curved and Y-shaped waveguides. The spin-wave transmission signal is strongly suppressed inside the gaps and remains high at allowed frequencies for all waveguide types. Using super-Nyquist sampling magneto-optical Kerr effect microscopy, we image symmetric and asymmetric spin-wave interference patterns, the self-focusing of propagating spin waves, and interconversions between width modes with different quantization numbers.

Omnidirectional flat bands in chiral magnonic crystals

The magnonic band structure of two-dimensional chiral magnonic crystals is theoretically investigated. The proposed metamaterial involves a three-dimensional architecture, where a thin ferromagnetic layer is in contact with a two-dimensional periodic array of heavy-metal square islands. When these two materials are in contact, an anti-symmetric exchange coupling known as the Dzyaloshinskii–Moriya interaction (DMI) arises, which generates nonreciprocal spin waves and chiral magnetic order. The Landau–Lifshitz equation and the plane-wave method are employed to study the dynamic magnetic behavior. A systematic variation of geometric parameters, the DMI constant, and the filling fraction allows the examination of spin-wave propagation features, such as the spatial profiles of the dynamic magnetization, the isofrequency contours, and group velocities. In this study, it is found that omnidirectional flat magnonic bands are induced by a sufficiently strong Dzyaloshinskii–Moriya interaction underneath the heavy-metal islands, where the spin excitations are active. The theoretical results were substantiated by micromagnetic simulations. These findings are relevant for envisioning applications associated with spin-wave-based logic devices, where the nonreciprocity and channeling of the spin waves are of fundamental and practical scientific interest.

Topological magnons in one-dimensional ferromagnetic Su–Schrieffer–Heeger model with anisotropic interaction

Topological magnons in a one-dimensional (1D) ferromagnetic Su–Schrieffer–Heeger (SSH) model with anisotropic exchange interactions are investigated. Apart from the intercellular isotropic Heisenberg interaction, the intercellular anisotropic exchange interactions, i.e. Dzyaloshinskii–Moriya interaction and pseudo-dipolar interaction, also can induce the emergence of the non-trivial phase with two degenerate in-gap edge states separately localized at the two ends of the 1D chain, while the intracellular interactions instead unfavors the topological phase. The interplay among them has synergistic effects on the topological phase transition, very different from that in the two-dimensional (2D) ferromagnet. These results demonstrate that the 1D magnons possess rich topological phase diagrams distinctly different from the electronic version of the SSH model and even the 2D magnons. Due to the low dimensional structural characteristics of this 1D topological magnonic system, the magnonic crystals can be constructed from bottom to top, which has important potential applications in the design of novel magnonic devices.

Resonant and nonlinear phenomena during the propagation of magnetostatic waves in multiferroid, semiconductor and metallized structures based on ferromagnetic films and magnonic crystals

Purpose of this work is to compile an overview of a new and fruitful scientific direction in magnonics, which grew out of the works of Ph.D., Professor Yuri Pavlovich Sharaevsky, and related to the study of resonant and nonlinear phenomena during the propagation of magnetostatic waves in ferromagnetic films, ferromagnetic films with periodic inhomogeneities (magnonic crystals), coupled (layered and lateral) ferromagnetic structures, as well as ferromagnetic structures with layers of a different physical nature (semiconductor, ferroelectric, piezoelectric, normal metal layers). Methods. Experimental and theoretical methods have been used to study spin-wave excitations in a wide class of structures with ferromagnetic layers. In particular, experimental radiophysical methods of microwave measurements and optical methods of Mandelstam-Brillouin spectroscopy. For the construction of theoretical models, the following methods are used: the method of coupled waves, the method of crosslinking magnetic permeability at the boundaries of layers, the method of transmission matrices, long-wave approximation. Results. The presented results are of general scientific importance for understanding the basic laws of the joint influence of coupling, periodicity and interactions of different physical nature (the influence on the magnetostatic wave of deformation in periodic structures with piezoelectric, electromagnetic wave in structures with ferroelectric, electric current in structures with semiconductor, spin current in structures with normal metal). In applied terms, the identified effects open up wide opportunities for creation of new devices of spin-wave electronics with the possibility of dynamic control of characteristics when changing the electric and magnetic fields, as well as the power of the input signal. Conclusions. The review of the most interesting results obtained by the authors together with Yuri Pavlovich and which are an ideological continuation of the foundations laid by him is given.

Experimental methods for the study of spin waves

Purpose of this paper is to give an overview of various experimental methods for investigation of spin waves characteristics. Methods. The paper presents a description of a number of experimental techniques, such as the probing method, the phase shift method, the method of measure of equiphase dependences, the method of intersecting wave beams, and the use of Fourier analysis of the complex transfer coefficient of spin waves to determine their spatial spectrum. The conditions for using the listed methods and the characteristics of spin waves that one can measure by means of these methods are discussed in detail. Results. The paper presents a number of fundamental results that have been obtained on the basis of described methods. For example, the probing method was successfully used to visualize the amplitude and phase distribution of spin waves in the ferrite film plane and, in particular, it was used to experimentally confirm the previously predicted appearance of super-directed propagation of surface and backward volume spin wave beams. The phase-shift measurement method made it possible to measure the dispersion dependence of spin waves in ferrite structures such as ferrite – metal and ferrite – dielectric – metal, where measurements cannot be made by the probing method. The method of measuring equiphase dependences of spin waves made it possible, in particular, to measure for the first time with great accuracy the value of an external magnetic field magnetizing an yttrium iron garnet film to saturation in various crystallographic directions. The method of intersecting wave beams has made it possible to clarify the mechanism of parametric instability of surface spin waves. Fourier analysis of the complex transfer coefficient of spin waves allowed to determine the spatial spectrum of these waves; in particular, dispersion dependences of higher modes of the backward volume spin wave were first measured using this method. Conclusion. The methods described in this paper may continue to be successfully used for investigations of spin waves characteristics in various magnon crystals, ferrite structures and meta-structures.

Spectrum of exchange spin waves in a one-dimensional magnonic crystal with antiferromagnetic ordering

Purpose of the study is to show that the conditions for the propagation of exchanged spin waves (ESWs) in an asymmetric superlattice with antiferromagnetically ordered cells depend significantly on the chirality of the precession of the ESW magnetization (polarization, “magnon pseudospin”). Method. When constructing the EWS spectra, the Croning– Penny model (transfer-matrix method) and the Landau–Lifshitz equation are used to determine the nature of the waves in the cells. In the case of a uniaxial medium, there is only one type of ESW, therefore, when fields are joined at the boundary, the conservation of chirality is an essential factor due to which the ESW in one cell is always traveling, and in the other — evanescent. Thus, a superlattice for ESW is an effective periodic “potential” in which asymmetry can be realized either by applying an external field, or by a difference in the thickness and/or physical properties of the cell materials. Results. Based on the analysis of the spectrum, maps of the transmission zones for ESW of different chirality were constructed in three representations — “Bloch wave number – frequency”, “frequency – relative cell thickness”, as well as in the plane of cell wave numbers. It is shown that the presence of asymmetry leads to a difference in the width of the transmission zones for waves of different chirality. For a finite structure, the frequency dependences of the transmission and reflection coefficients of the ESW are plotted. An increase in the attenuation of the ESW near the boundaries of the transmission zones was also found. Conclusion. The results of the study can be used in the design of magnon valves and other devices based on ESW, in which their chirality can be controlled.

Inverse design of magnonic filter

Monochromatic spin wave (SW) is the substrates for the realizing the practical function of magnonic devices, however the generating perfect monochromatic SW is still a unsolved but fundamental problems. In our latest work (Xing et al., 2022), the resonant tunneling effect was found in a magnonic crystals (MCs), which demonstrates a similar effect of Fabry–Pérot interferometer, and shows a promising application of band-pass magnonic filter (MF) for generating perfect monochromatic SW. The optimization of such MF is a complex problem, due to that the natural nonlinearity of spin-wave scattering behavior enhances sensitivity to device parameters. In this work, the inverse design (ID) approach is developed for designing the magnonic filters (MFs). To determine the optimizable variables, the fundamental properties of antiferromagnetically coupled heterojunction based MCs were theoretically investigated. The particle swarm algorithms (PSA) is used for automatically finding MFs which meet the inputting requirements. Here, the input of algorithms is a vector of SW frequency and output is a vector of parameters of MFs. Besides, the PSA is further optimized to be self-adapting to required accuracies, showing a higher computing efficiency than the convectional one. Finally, the output data of predicted MFs with various filtering characteristics are briefly summarized in a table as an alternative proposal for the future experimental design. These encouraging results show high potential of using ID approach in magnetism and boosting optimization of magnetic multilayer heterojunction devices, such as magnon transistor and magnon space–time crystals.

Application of Magnonic Crystals in Magnetic Bead Detection.

This paper aims at studying a sensor concept for possible integration in magnetic field-based lab-on-chip devices that exploit ferromagnetic resonance (FMR) phenomena in magnonic crystals. The focus is on 2D magnetic antidot arrays, i.e., magnetic thin films with periodic non-magnetic inclusions (holes), recently proposed as magnetic field sensor elements operating in the gigahertz (GHz) range. The sensing mechanism is here demonstrated for magnetic nano/microbeads adsorbed on the surface of permalloy (Ni80Fe20) antidot arrays with a rhomboid lattice structure and variable hole size. Through extensive micromagnetic modelling analysis, it is shown that the antidot arrays can be used as both bead traps and high-sensitivity detectors, with performance that can be tuned as a function of bead size and magnetic moment. A key parameter for the detection mechanism is the antidot array hole size, which affects the FMR frequency shifts associated with the interaction between the magnetization configuration in the nanostructured film and the bead stray field. Possible applications of the proposed device concept include magnetic immunoassays, using magnetic nano/microbeads as probes for biomarker detection, and biomaterial manipulation.

Interaction between the First Mode of Backward Bulk Spin Waves and a Low-Contrast Magnon Crystal

Interaction between the First Mode of Backward Bulk Spin Waves and a Low-Contrast Magnon Crystal

Reconfigurable Magnonic Crystals Based on Imprinted Magnetization Textures in Hard and Soft Dipolar-Coupled Bilayers.

Reconfigurable magnetization textures offer control of spin waves with promising properties for future low-power beyond-CMOS systems. However, materials with perpendicular magnetic anisotropy (PMA) suitable for stable magnetization-texture formation are characterized by high damping, which limits their applicability in magnonic devices. Here, we propose to overcome this limitation by using hybrid structures, i.e., a PMA layer magnetostatically coupled to a low-damping soft ferromagnetic film. We experimentally show that a periodic stripe-domain texture from a PMA layer is imprinted upon the soft layer and induces a nonreciprocal dispersion relation of the spin waves confined to the low-damping film. Moreover, an asymmetric bandgap features the spin-wave band diagram, which is a clear demonstration of collective spin-wave dynamics, a property characteristic for magnonic crystals with broken time-reversal symmetry. The composite character of the hybrid structure allows for stabilization of two magnetic states at remanence, with parallel and antiparallel orientation of net magnetization in hard and soft layers. The states can be switched using a low external magnetic field; therefore, the proposed system obtains an additional functionality of state reconfigurability. This study offers a link between reconfigurable magnetization textures and low-damping spin-wave dynamics, providing an opportunity to create miniaturized, programmable, and energy-efficient signal processing devices operating at high frequencies.

Magnetization process and ordering of the S=12 pyrochlore Heisenberg antiferromagnet in a magnetic field

We study the $S=\frac{1}{2}$ pyrochlore Heisenberg antiferromagnet in a magnetic field. Using large-scale density-matrix renormalization group calculations for clusters with up to 128 spins, we find indications of a finite triplet gap, causing a threshold field to nonzero magnetization in the magnetization curve. We obtain a robust saturation field consistent with a magnon crystal, although the corresponding $5/6$ magnetization plateau is very slim and possibly unstable. Most remarkably, there is a pronounced and apparently robust $1/2$ magnetization plateau where the ground state breaks the rotational symmetry of the lattice, exhibiting oppositely polarized spins on alternating kagome and triangular planes. Reminiscent of the kagome ice plateau of the pyrochlore Ising antiferromagnet known as spin ice, it arises via a much more subtle ``quantum order by disorder'' mechanism.