Magnonic Crystals Research Articles

Tunable magnonic crystal in a hybrid superconductor–ferrimagnet nanostructure

One of the most intriguing properties of magnonic systems is their reconfigurability, where an external magnetic field alters the static magnetic configuration to influence magnetization dynamics. In this paper, we present an alternative approach to tunable magnonic systems. We studied theoretically and numerically a magnonic crystal induced within a uniform magnetic layer by a periodic magnetic field pattern created by the sequence of superconducting strips. We showed that the spin-wave spectrum can be tuned by the inhomogeneous stray field of the superconductor in response to a small uniform external magnetic field. Additionally, we demonstrated that modifying the width of superconducting strips and separation between them leads to the changes in the internal field which are unprecedented in conventional magnonic structures. The paper presents the results of semi-analytical calculations for realistic structures, which are verified by finite-element method computations.

Spin-wave mode coupling in the presence of the demagnetizing field in cobalt-permalloy magnonic crystals

We present the results of studies on the non-uniform frequency shift of spin wave spectrum in a two-dimensional magnonic crystal of cobalt/permalloy under the influence of external magnetic field changes. We investigate the phenomenon of coupling of modes and, as a consequence, their hybridization. By taking advantage of the fact that compressing the crystal structure along the direction of the external magnetic field leads to an enhancement of the demagnetizing field, we analyse its effect on the frequency shift of individual modes depending on their concentration in Co. We show that the consequence of this enhancement is a shift in the coupling of modes towards higher magnetic fields. This provides a potential opportunity to design which pairs of modes and in what range of fields hybridization will occur.

Reconfigurable spin-wave properties in two-dimensional magnonic crystals formed of diamond and triangular shaped nanomagnets

Two-dimensional ferromagnetic nanodot structures exhibit intriguing magnetization dynamics and hold promise for future magnonic devices. In this study, we present a comparative experimental investigation into the reconfigurable magnetization dynamics of non-ellipsoidal diamond and triangular-shaped nanodot structures, employing broadband ferromagnetic resonance spectroscopy. Our findings reveal substantial variations in the spin wave (SW) spectra of these structures under different bias field strengths (H) and angles (φ). Notably, the diamond nanodot structure exhibits a variation from nearly symmetric W-shaped dispersion to a skewed dispersion and subsequent transition to a discontinuous dispersion with subtle variation in bias field angle. On the other hand, in the triangular nanodot array a SW mode anti-crossing appears at φ = 15° which is starkly modified with the increase in φ to 30°. By analyzing the static magnetic configurations, we unveil the nature of the SW spectra in these two shapes. We reinforce our observations with simulated spatial power and phase maps. This study underscores the critical impact of dot shape and inversion symmetry on SW dynamical response, highlighting the significance of selecting appropriate structures and bias field strength and orientation for required functionalities. The remarkable tunability demonstrated by the magnonic crystals underscores their potential suitability for future magnonic devices.

Designed Spin-Texture-Lattice to Control Anisotropic Magnon Transport in Antiferromagnets.

Spin waves in magnetic materials are promising information carriers for future computing technologies due to their ultra-low energy dissipation and long coherence length. Antiferromagnets are strong candidate materials due, in part, to their stability to external fields and larger group velocities. Multiferroic antiferromagnets, such as BiFeO3 (BFO), have an additional degree of freedom stemming from magnetoelectric coupling, allowing for control of the magnetic structure, and thus spin waves, with the electric field. Unfortunately, spin-wave propagation in BFO is not well understood due to the complexity of the magnetic structure. In this work, long-range spin transport is explored within an epitaxially engineered, electrically tunable, 1D magnonic crystal. A striking anisotropy is discovered in the spin transport parallel and perpendicular to the 1D crystal axis. Multiscale theory and simulation suggest that this preferential magnon conduction emerges from a combination of a population imbalance in its dispersion, as well as anisotropic structural scattering. This work provides a pathway to electrically reconfigurable magnonic crystals inantiferromagnets.

Solutions to the Landau–Lifshitz–Gilbert equation in the frequency space: Discretization schemes for the dynamic-matrix approach

The dynamic matrix method addresses the Landau–Lifshitz–Gilbert (LLG) equation in the frequency domain by transforming it into an eigenproblem. Subsequent numerical solutions are derived from the eigenvalues and eigenvectors of the dynamic matrix. In this work we explore discretization methods needed to obtain a matrix representation of the dynamic operator, a fundamental counterpart of the dynamic matrix. Our approach opens a new set of linear algebra tools for the dynamic matrix method and expose the approximations and limitations intrinsic to it. Moreover, our discretization algorithms can be applied to various discretization schemes, extending beyond micromagnetism problems. We present some application examples, including a technique to obtain the dynamic matrix directly from the magnetic free energy function of an ensemble of macrospins, and an algorithmic method to calculate numerical micromagnetic kernels, including plane wave kernels. We also show how to exploit symmetries and reduce the numerical size of micromagnetic dynamic-matrix problems by a change of basis. This procedure significantly reduces the size of the dynamic matrix by several orders of magnitude while maintaining high numerical precision. Additionally, we calculate analytical approximations for the dispersion relations in magnonic crystals. This work contributes to the understanding of the current magnetization dynamics methods, and could help the development and formulations of novel analytical and numerical methods for solving the LLG equation within the frequency domain.

The role of non-uniform magnetization texture for magnon–magnon coupling in an antidot lattice

We numerically study the spin-wave dynamics in an antidot lattice based on a Co/Pd multilayer structure with reduced perpendicular magnetic anisotropy at the edges of the antidots. This structure forms a magnonic crystal with a periodic antidot pattern and a periodic magnetization configuration consisting of out-of-plane magnetized bulk and in-plane magnetized rims. Our results show a different behavior of spin waves in the bulk and in the rims under varying out-of-plane external magnetic field strength, revealing complex spin-wave spectra and hybridizations between the modes of these two subsystems. A particularly strong magnon–magnon coupling, due to exchange interactions, is found between the fundamental bulk spin-wave mode and the second-order radial rim modes. However, the dynamical coupling between the spin-wave modes at low frequencies, involving the first-order radial rim modes, is masked by the changes in the static magnetization at the bulk–rim interface with magnetic field changes. The study expands the horizons of magnonic-crystal research by combining periodic structural patterning and non-collinear magnetization texture to achieve strong magnon–magnon coupling, highlighting the significant role of exchange interactions in the hybridization.

Strain-induced multi-band spin-wave logic gate based on alligator-type magnonic crystal/PZT structure

Here, we report the results of strain-controlled spin-wave propagation regimes in a double-period multiferroic structure. It consists of an alligator-type magnonic crystal with a period of 250 μm and a piezoelectric layer, featuring a periodic counter-pin-type electrode system with a period of 125 μm. Employing microwave measurements, we acquired the transmission and dispersion of spin waves under various external electric field configurations applied to the piezoelectric layer. The formation of bandgaps in the magnon spectrum and the variation of the spin-wave transmission when altering the configurations of the external electric field are demonstrated. A finite element method reveals that the combination of the non-uniformity in the initial internal magnetic field of the magnonic crystal, which is caused by the presence of periodic alligator-type regions, together with elastic deformations, heightens the amplitude of the modulation of the internal magnetic field. Micromagnetic modeling has demonstrated that this modulation enhancement results in the variation of the spin-wave transmission at the frequency of the magnonic bandgap center of the magnonic crystal. The proposed design of the reconfigurable magnonic crystal creates a condition for the nucleation of the spin-wave bandgap, with further enhancement of the spin-wave reflection from the periodic grating induced by strain. We demonstrate the potential use of the proposed device as a multi-band NAND/NXOR spin-wave based logic gate.

Exciting High‐Frequency Short‐Wavelength Spin Waves using High Harmonics of a Magnonic Cavity Mode

AbstractSpin waves (SWs) are promising objects for signal processing and future quantum technologies due to their high microwave frequencies with corresponding nanoscale wavelengths. However, the nano‐wavelength SWs generated so far are limited to low frequencies. In the paper, using micromagnetic simulations, it is shown that a microwave‐pumped SW mode confined to the cavity of a thin film magnonic crystal (MC) can be used to generate waves at tens of GHz and wavelengths well below 50 nm. These multi‐frequency harmonics of the fundamental cavity mode are generated when the amplitude of the pumping microwave field exceeds a threshold, and their intensities then scale linearly with the field intensity. The frequency of the cavity mode is equal to the ferromagnetic resonance frequency of the planar ferromagnetic film, which overlaps with the magnonic bandgap, providing an efficient mechanism for confinement and magnetic field tunability. The effect reaches saturation when the microstrip feed line covers the entire cavity, making the system feasible for realization.

Nanoscaled magnon transistor based on stimulated three-magnon splitting

Magnonics is a rapidly growing field, attracting much attention for its potential applications in data transport and processing. Many individual magnonic devices have been proposed and realized in laboratories. However, an integrated magnonic circuit with several separate magnonic elements has yet not been reported due to the lack of a magnonic amplifier to compensate for transport and processing losses. The magnon transistor reported in Chumak et al. [Nat. Commun. 5, 4700 (2014)] could only achieve a gain of 1.8, which is insufficient in many practical cases. Here, we use the stimulated three-magnon splitting phenomenon to numerically propose a concept of magnon transistor in which the energy of the gate magnons at 14.6 GHz is directly pumped into the energy of the source magnons at 4.2 GHz, thus achieving the gain of 9. The structure is based on the 100 nm wide YIG nano-waveguides, a directional coupler is used to mix the source and gate magnons, and a dual-band magnonic crystal is used to filter out the gate and idler magnons at 10.4 GHz frequency. The magnon transistor preserves the phase of the signal, and the design allows integration into a magnon circuit.

Thermal nanoconversion of ferromagnetic nanoislands

In this work, we investigate the use of post-fabrication thermal nanoconversion (TNC), using a heated scanning probe tip, to modify the magnetic properties of Ni80Fe20 elliptical nanoislands with varying aspect ratio. Despite Ni80Fe20 being unoptimized for TNC, by comparing quasistatic and dynamic magneto-optical Kerr effect microscopy measurements, we demonstrate that TNC at a contact temperature of 250 °C increases the saturation magnetization of the treated nanoislands, reaching a value close to 800 kA/m. Micromagnetic simulations of the nanoislands indicate that the TNC technique can be used to alter the remanent state, from a single domain to a vortex. These results demonstrate the opportunities afforded by TNC to modify the properties of selected areas in a thin film or a patterned sample, particularly when designing magnonic crystals and other nanomagnetic devices.

Dirac points and flat bands in two-dimensional magnonic crystals with honeycomb–kagome structure

Based on the model of magnonic crystals (MCs) with honeycomb structure, we propose another model of two-dimensional MCs with honeycomb–kagome structure that is a periodic magnetic composite system composed of Fe, Co, or Py ferromagnetic cylindrical scatterers arranged in the EuO matrix as the honeycomb–kagome structure. The band structures of magnons in these systems are studied numerically by using the plane-wave expansion method. The results show that the Dirac points of magnons will be generated at the Brillouin region points if the scatterers are close-packed, that is to say, the edges of cylindrical scatterers are in contact with each other. The frequency of Dirac points can be indirectly adjusted by changing the radius ratio of close-packed cylinders. In addition, in the case of a large difference in the radius between the close-packed cylindrical scatterers, there will be a magnonic flat band in the band structure, which is a phenomenon of so-called compact localized states different from the impurity state in the crystal, and it is formed by the highly interference superposition of spin waves in the honeycomb–kagome structure. The research on the generation and modulation of magnonic Dirac points and flat bands not only expands the research content of condensed matter topological physics but also provides a promising platform for the application of artificial MCs in the fabrication of spin-wave topological devices.

Nano-Magnonic Crystals by Periodic Modulation of Magnetic Parameters

Magnonic crystals are metamaterials whose magnon behavior can be controlled for specific applications. To date, most magnonic crystals have relied on nanopatterning and magnetostatic waves. Here, we analytically and numerically investigate magnonic crystals defined by modulating magnetic parameters at the nanoscale, which predominantly act on exchange-dominated, sub-100 nm magnons. We focus on two cases: the variation in the exchange constant, and the DMI constant. We found that the exchange constant modulation gives rise to modest band gaps in the forward volume wave and surface wave configurations. The modulation of the DMI constant was found to have little effect on the magnonic band structure, leading instead to a behavior expected for unpatterned thin films. We believe that our results will be interesting for future experimental investigations of nano-designed magnonic crystals and magnonic devices, where material parameters can be locally controlled, e.g., by thermal nano-lithography.

Excitation and Tuning of Spin Waves in Magnonic Crystals by Magnetic Coupling

Magnonic crystals with artificial micro/nanomagnetic pattern act as low‐loss information carriers in many microwave devices. The excitation and control of spin waves inside is essential and fundamental in magnonic crystal applications. Herein, permalloy micro‐disk patterns are constructed on a continuous permalloy film, and they succeed in exciting spin waves in this bilayer‐structured magnonic crystal. The spin‐wave modes can be effectively tuned by varying the periodic parameter (P) of upper‐layer disk pattern, which is confirmed by the transition from single‐peak to multi‐peak in ferromagnetic resonance (FMR) spectra with P decreased from 4 to 0.5 μm. The split in FMR spectra is reconstructed by micromagnetic simulation, revealing that three spin‐wave modes are respectively excited by the domain walls of below‐layer continuous film, geometrical restriction of permalloy micro‐disk, and magnetic coupling between neighboring permalloy micro‐disks. The tunable spin‐wave behavior in this bilayer‐structured magnonic crystal presents broad application prospect in programmable spintronic devices at micro/nanoscale.

Hopfion based magnonic crystal

We conduct a numerical analysis to explore the magnonic band structure of spin waves (SWs) within a unique magnonic crystal. The latter is composed of a waveguide hosting a linear array of hopfions, evenly spaced along its center, generated through micromagnetic simulations. The computed dispersion relationship of spin waves (SWs) in the envisioned hopfions magnonic crystal, illustrating the frequency versus wave vector, demonstrates a periodic attribute, a hallmark of conventional magnonic crystal band structures. Likewise, the computed magnonic spectra reveal both permitted frequency bands and restricted frequency bandgaps. These results may inspire additional exploration into the diverse functionalities offered by magnonic crystals built on periodic Hopfion lattices.

Tunable 2-D magnonic crystals: effect of packing density.

Magnonic crystals, periodic arrays of magnetic structures, have emerged as a promising platform for manipulating and controlling spin waves in magnetic materials. Magnetic antidot nanostructures, representing 2-D magnonic crystals, are versatile platforms for controlling and manipulating magnons. In this work, we systematically investigate the effects of inter-hole spacing and lattice (rhombic and honeycomb) arrangements on the dynamic properties of Ni80Fe20 antidot structures. The dynamic responses of antidot lattices of fixed hole diameter (d = 280 nm) and inter-hole spacing (s) between 90 and 345 nm are investigated using broadband ferromagnetic spectroscopy. Multiple resonance modes sensitive to s are observed due to the inhomogeneous internal field distribution induced by the presence of holes. There is a marked variation in mode frequency, mode intensity and the number of modes for rhombic antidot lattice as the inter-hole spacing and applied field direction are varied. Our experimental results are in good agreement with micromagnetic simulations. Our findings may find application in the design of magnonic-based devices.

Influence of nonlinearity on the Bragg resonances in coupled magnon crystals

Purpose. The purpose of this paper is to investigate the effect of nonlinearity on formation mechanism and characteristics of Bragg resonances in vertically coupled magnon crystals with periodic groove system on the surface. In this paper a wave model is constructed, a nonlinear dispersion relation for surface magnetostatic waves in such a structure is obtained and the characteristics of each of the Bragg resonances are numerically studied with increasing input signal power. Methods. Theoretical methods of investigation of spin-wave excitations in a wide class of structures with ferromagnetic layers have been used. In particular, the following theoretical models have been used: coupled wave method, long-wave approximation. Results. This paper presents the results of a theoretical investigation of the effect of magnetic nonlinearity on Bragg resonances in a sandwich structure based on magnon crystals with periodic grooves on the surface separated by a dielectric layer. A mechanism for the formation of band gaps at the Bragg resonance frequencies in the presence of media nonlinearity has been revealed. It is shown that with increasing input power the frequency interval between the band gaps decreases. With increasing magnetization difference of magnon crystals, the effect of nonlinear convergence is more pronounced. Conclusion. The identified features extend the capabilities of sandwich structures based on magnon crystals for frequency selective signal processing by controlling the frequency selectivity, both via static coupling parameters, periodicity and layer magnetisation, and dynamically via the input signal power.

Specific Features of Bragg Resonances in a Magnonic Crystal with Two Periods

Specific features of Bragg resonances in a magnonic crystal with a metallic grating on the surface with two periods have been revealed. A theoretical model describing the spectral characteristics of magnetostatic waves has been constructed by matching the permeabilities of the metal layer and the ferromagnetic film at the interface between them and using the coupled-wave analysis. The distribution of the magnetization amplitude at each Bragg resonance frequency has been calculated by the finite-element method. It has been shown that three Bragg resonances in the first Brillouin zone for the grating with a smaller period and one resonance in the first Brillouin zone for the grating with a larger period are formed in this structure. Resonance frequencies are determined by the ratio of the large and small periods.

Спиновые волны в одномерных магнонных кристаллах с двумя пространственными периодами

The propagation of surface and backward volume magnetostatic waves in a one-dimensional magnonic crystal in the form of a yttrium iron garnet film with two periodic lattices of grooves with different periods etched on its surface was experimentally studied. It is shown that the form of the frequency dependence of the transmission coefficient of magnetostatic waves in such crystal is not a simple superposition of similar dependences for two magnonic crystals with the same lattice periods.

Specific Features of Bragg Resonances in a Magnonic Crystal with Two Periods

Specific Features of Bragg Resonances in a Magnonic Crystal with Two Periods

The influence of the demagnetizing field on the concentration of spin wave energy in two-dimensional magnonic crystals

We use the Plane Wave Method to theoretically study thin-film magnonic crystals (MCs) composed of two very common magnetic materials: cobalt and permalloy. In both cases, we consider Co inclusions in the Py matrix and Py inclusions in the Co matrix. An external magnetic field is applied in the plane of the structure, leading to the formation of a demagnetizing field at the interface between the inclusions and matrix. Previous studies have shown that this field strongly affects the spectrum of spin waves, including the position and width of bandgaps. In this study, we exploit the in-plane squeezing of the MC structure to enhance the demagnetizing field. This results in the transfer of low-frequency spin waves from Py to Co, affecting the energy distribution (i.e., the spin-wave profile). The change in the concentration of spin-wave profiles leads to certain peculiarities in the spin-wave frequency spectrum. These include modes repulsion caused by hybridization, which in turn leads to the reordering of modes in the spectrum.