Magnonic Band Gaps Research Articles

Electromagnetic Sensors Based on Magnonic Crystals for Applications in the Fields of Biomedical and NDT

An exploratory investigation of high sensitivity sensors based on magnonic crystals for the measurement of weak magnetic fields at room temperature is presented. The samples are YIG crystals on GGG substrate (Gadolinium-Gallium-Garnet) on which a periodic structure of shallow grooves are etched or gold stripes are deposited. The excitation of surface magnetostatic spin waves (MSSW) which should appear in these structures is obtained by means of microstrip transmission line or microstrip planar antenna.The measurement of the magnonic structure by complex transmission coefficient (S12) shows a significant shift in frequency of the maximum absorption peak related to magnonic band gap which depends on the magnitude of the DC magnetic bias field applied. It shows the possibility of magnonic high Q-value band gap implementation with respect to spin wave propagation band (GHz band) in magnonic crystals applied to spin waves detection of magnetic fields.The influence of the characteristics of the microstrip line or the microstrip antenna on sensor performance (sensitivity and resolution) is studied.

Observation of magnonic band gaps in magnonic crystals with nonreciprocal dispersion relation

An effect of metallization of the magnonic crystal surface on the band gaps formation in the spectra of the surface spin wave (SSW) is studied both theoretically and experimentally. The structures under consideration are one-dimensional magnonic crystals based on yttrium iron garnet with an array of etched grooves with metal screen on the top of the corrugated surface and without it. Due to nonreciprocity of propagation of the SSW the shift of band gap to higher frequency and from the border of the Brillouin zone in presence of conducting overlayer was measured in transmission line experiment. Results of numerical calculations and model analysis are in agreement with experimental data and give further insight into origin of the band gap and properties of the nonreciprocal SSW in metallized magnonic crystals. This gives positive answer to the outstanding question about possibility of detection of magnonic band gaps in the spectra of the spin waves with nonreciprocal dispersion in magnonic crystals and creates potential for new applications and improvements of already existing prototype magnonic devices.

Magnonic Bandgaps in Metalized 1-D YIG Magnonic Crystals

Magnonic Bandgaps in Metalized 1-D YIG Magnonic Crystals

Magnonic Bandgap Control in Coupled Magnonic Crystals

The periodic structure in the form of two coupled magnonic crystals (MCs) was considered for the first time. It was shown that the variation of coupling allows to control effectively the characteristics of the bandgaps in the spectrum of magnetostatic spin waves. Main features of formation of the bandgaps were investigated in the basis of theoretical and experimental results. The comparison with a periodic structure in the form of a single MC was provided. The possibility of formation of two frequency bandgaps and shift of the frequency bandgaps depending on coupling was demonstrated in the frequency region of the first Bragg resonance. It was shown that the control of bandgaps in such structure gives additional opportunities to create microwave filters and phase shifters with desired characteristics.

Monolithic Structure and Multiaxis Magnetic Sensing with Magnonic Crystals

SUMMARYWe aim at the development of high‐sensitivity magnetic sensors with magnonic crystals at room temperature. We fabricated SmCo thin film magnets on magnonic crystals as a monolithic structure. We were able to excite spin waves and develop a magnonic band gap by means of the magnetic field of the thin film magnet. Since magnonic crystals have a high magnetic field dependence, there is potential for their use as magnetic sensors. The maximum response sensitivity of the magnonic crystals with SmCo thin film magnets was found to be 7900%/Oe. We also investigated two‐axis magnetic field sensing by spin waves.

Photonic-magnonic crystals: Multifunctional periodic structures for magnonic and photonic applications

We investigate the properties of a photonic-magnonic crystal, a complex multifunctional one-dimensional structure with magnonic and photonic band gaps in the GHz and PHz frequency ranges for spin waves and light, respectively. The system consists of periodically distributed dielectric magnetic slabs of yttrium iron garnet and nonmagnetic spacers with an internal structure of alternating TiO2 and SiO2 layers which form finite-size dielectric photonic crystals. We show that the spin-wave coupling between the magnetic layers, and thus the formation of the magnonic band structure, necessitates a nonzero in-plane component of the spin-wave wave vector. A more complex structure perceived by light is evidenced by the photonic miniband structure and the transmission spectra in which we have observed transmission peaks related to the repetition of the magnetic slabs in the frequency ranges corresponding to the photonic band gaps of the TiO2/SiO2 stack. Moreover, we show that these modes split to very high sharp (a few THz wide) subpeaks in the transmittance spectra. The proposed novel multifunctional artificial crystals can have interesting applications and be used for creating common resonant cavities for spin waves and light to enhance the mutual influence between them.

Magnonic band gaps in two-dimension magnonic crystals with diffuse interfaces

In this paper, the plane wave method is extended to include the diffuse interface in the calculation of the dispersion of spin waves in two-dimension magnonic crystals. The diffuse interfaces with linear and sinusoidal profiles of variation in the spontaneous magnetization and exchange constant are considered and the effects of the thicknesses and profiles of diffuse interfaces on the magnonic band gaps are investigated. The results show that the thicknesses and profiles of diffuse interfaces are clearly seen to play a significant role in determining the size and position of the magnonic band gaps in the both square and triangular lattices in the exchange interaction regime. The smooth (linear or sinusoidal) interface does not lead to disappearance of the band gaps, instead it may lead to larger band gaps than those in the model with sharp (infinitely thin) diffuse interface under certain conditions.

Magnonic band structure, complete bandgap, and collective spin wave excitation in nanoscale two-dimensional magnonic crystals

We present the observation of a complete bandgap and collective spin wave excitation in two-dimensional magnonic crystals comprised of arrays of nanoscale antidots and nanodots, respectively. Considering that the frequencies dealt with here fall in the microwave band, these findings can be used for the development of suitable magnonic metamaterials and spin wave based signal processing. We also present the application of a numerical procedure, to compute the dispersion relations of spin waves for any high symmetry direction in the first Brillouin zone. The results obtained from this procedure has been reproduced and verified by the well established plane wave method for an antidot lattice, when magnetization dynamics at antidot boundaries is pinned. The micromagnetic simulation based method can also be used to obtain iso--frequency countours of spin waves. Iso--frequency contours are analougous of the Fermi surfaces and hence, they have the potential to radicalize our understanding of spin wave dynamics. The physical origin of bands, partial and full magnonic bandgaps has been explained by plotting the spatial distribution of spin wave energy spectral density. Although, unfettered by rigid assumptions and approximations, which afflict most analytical methods used in the study of spin wave dynamics, micromagnetic simulations tend to be computationally demanding. Thus, the observation of collective spin wave excitation in the case of nanodot arrays, which can obviate the need to perform simulations may also prove to be valuable.

Influence of structural changes in a periodic antidot waveguide on the spin-wave spectra

We demonstrate that the magnonic band structure, including the band gap of a ferromagnetic antidot waveguide, can be significantly tuned by a relatively weak modulation of its structural parameters. We study the magnonic band structure in nanoscale spin-wave waveguides with periodically distributed small antidots along their central line by two independent computational methods, namely, a micromagnetic simulation and a plane-wave method. The calculations were performed with consideration of both the exchange and dipolar interactions. For the exchange dominated regime, we discuss, in details, the impact of the changes of the lattice constant, size, and shape of the antidots on the spin-wave spectra. We have shown that a precise choice of these parameters is crucial for achieving desired properties of antidot waveguides, i.e., a large group velocity and filtering properties due to existence of magnonic band gaps. We discuss different mechanisms of magnonic gap opening resulting from Bragg scattering or anticrossing of modes. We have shown that the dipolar interactions start to assert their role in the spin-wave spectrum when the waveguide is scaled up, but even for a period of few hundreds of nanometers, the magnonic band structure preserves qualitatively the properties found in the exchange dominating regime. The obtained results are important for future development of magnonic crystal based devices.

Magnonic band structures in two-dimensional bi-component magnonic crystals with in-plane magnetization

We investigate the magnonic band structure of in-plane magnetized two-dimensional magnonic crystals composed of cobalt dots embedded into a permalloy antidot lattice. Our analysis is based on the results of numerical calculations carried out by the plane wave method. The complex magnonic band structure found in square-lattice magnonic crystals is explained on the basis of the spin wave dispersion relations calculated in the empty lattice model. We show that four principal effects influence the formation of a magnonic band structure in planar two-dimensional bi-component magnonic crystals: a folding effect, Bragg scattering, hybridization between various spin wave modes, and a demagnetizing field. While the first two effects are found for other types of waves in periodic composites, the third one exists in an anisotropic medium and the last one is specific to spin waves propagating in magnonic crystals with magnetization in the film plane. The strong anisotropy in the dispersion relation of spin waves in thin ferromagnetic films results in the crossing and anti-crossing of the fast, Damon–Eshbach-like mode with a number of other spin waves folded to the first Brillouin zone. The demagnetizing field can induce the formation of channels for spin waves which are propagating perpendicular to the external magnetic field direction, but this property exists only in the limiting range of the thicknesses and the lattice constants of the bi-component magnonic crystals. Based on the model analysis we propose a modification of the magnonic crystal structure by changing its thickness, lattice constant and aspect ratio along the direction of the applied magnetic field to significantly modify the magnonic band structure and obtain partial magnonic band gaps.

Nonreciprocity of spin waves in metallized magnonic crystal

The nonreciprocal properties of spin waves in metallized one-dimensional bi-component magnonic crystal composed of two materials with different magnetizations are investigated numerically. Nonreciprocity leads to the appearance of indirect magnonic band gaps for magnonic crystals with both low and high magnetization contrast. Specific features of the nonreciprocity in low contrast magnonic crystals lead to the appearance of several magnonic band gaps located within the first Brillouin zone for waves propagating along the metallized surface. Analysis of the spatial distribution of dynamic magnetization amplitudes explains the mechanism of dispersion band formation and hybridization between magnonic bands in magnonic crystals with metallization.

Magnonic band gaps in waveguides with a periodic variation of the saturation magnetization

We present a micromagnetic analysis of spin-wave propagation in a magnonic crystal realized as a permalloy spin-wave waveguide with a spatial periodical variation of its saturation magnetization. Frequency band gaps were clearly observed in the spin-wave transmission spectra, and their origin is traced back to an overlap of individual band gaps of the fundamental and higher-order spin-wave width modes. The control of the depth, width, and position in frequency and space of the rejection band gaps by the width areas with a reduced magnetization and by the modulation level is discussed in this study.

Comment on “Physical Origin and Generic Control of Magnonic Band Gaps of Dipole-Exchange Spin Waves in Width-Modulated Nanostrip Waveguides”

In Ref. [PRL 102, 127202 (2009)] Lee et al. reported the existence of large magnonic bandgaps in one-dimensional width-modulated Permalloy nanostripe waveguides based on OOMMF simulations. However, as the symmetry of the magnetic field pulse they applied to excite the spin waves (SWs) was not general, the entire set of SW branches with A symmetry was omitted from the magnonic band structures (see below). This omission has unfortunately led to misleading conclusions of, for instance, the number, width and position of the bandgaps. We present here the full band structure based on three different theoretical approaches that gave consistent predictions, thus corroborating the methods employed, namely, a microscopic approach, OOMMF simulations, and a method based on the linearized Landau-Lifshitz equation. Further, we provide a physical interpretation using group theory.

Magnonic Band Engineering by Intrinsic and Extrinsic Mirror Symmetry Breaking in Antidot Spin-Wave Waveguides

We theoretically study the spin-wave spectra in magnonic waveguides periodically patterned with nanoscale square antidots. We show that structural changes breaking the mirror symmetry of the waveguide can close the magnonic bandgap. The effect of these intrinsic symmetry breaking can be compensated by adjusted asymmetric external bias magnetic field, i.e., by an extrinsic factor. This allows for the recovery of the magnonic bandgaps. The described methods can be used for developing parallel models for recovering bandgaps closed due to a fabrication defect. The model developed here is particular to magnonics, an emerging field combining spin dynamics and spintronics. However, the underlying principle of this development is squarely based upon the translational and mirror symmetries, thus, we believe that this idea of correcting an intrinsic defect by extrinsic means, should be applicable to spin-waves in both exchange and dipolar interaction regimes, as well as to other waves in general.

Design of nanostrip magnonic crystal waveguides with a single magnonic band gap

A novel planar structure of magnonic-crystal waveguide (MCW) with periodic rectangular-shaped holes embedded in a magnetic nanostrip film was designed. The effects of the distance between rectangular-shaped holes in the width direction of MCW on magnonic band structures were studied by micromagnetic simulations. The results show that a MCW with a single magnonic band gap can be obtained by adjusting the distance to meet the condition of Bragg reflection of spin waves in the width direction of MCW. Moreover, the center frequency and width of magnonic gap can be regulated by changing the period and length of rectangular-shaped holes.

Magnetostatic surface wave propagation in a one-dimensional magnonic crystal with broken translational symmetry

Magnetostatic surface wave propagation through the one-dimensional magnonic crystal with broken translational symmetry developed in an yttrium iron garnet film was experimentally studied. Magnonic crystals were prepared in the form of lattices of etched grooves in yttrium iron garnet film where structural defect was inserted in the center of the lattice in the form of a single defective crest or groove with the width different from those in the lattices. The defect modes within the magnonic bandgaps were detected under conditions corresponding to excitation of the Bragg reflecting resonator formed by the defect.

Large magnonic band gaps and spectra evolution in three-dimensional magnonic crystals based on magnetoferritin nanoparticles

Large magnonic band gaps and spectra evolution in three-dimensional magnonic crystals based on magnetoferritin nanoparticles

Magnonic band gap design by the edge modulation of micro-sized waveguides

The potential to control the number of the spin-wave band gaps of a magnonic crystal (MC) by variation of its geometry is investigated by numerical simulations. The MC is represented by a micro-sized planar ferromagnetic waveguide with periodically variable width. By choosing a step-like or sinusoidal variation of the width, the MC reveals multiple or single band gaps, respectively. This allows for additional degrees of freedom in the design of MC-based microwave filters and phase shifters with desired characteristics. The MCs' band gaps have been studied in the space and frequency domains exploring the spin-wave spectrum dependence on the probing position inside the MC.

Materials Optimization of the Magnonic Bandgap in Two-Dimensional Bi-Component Magnonic Crystal Waveguides

We present the results of micromagnetic study of magnonic band structures for exchange spin waves propagating in two-dimensional magnonic crystal waveguides. The studied waveguides are in the form of a regular square lattice array of square dots of a ferromagnetic material embedded in a matrix of another ferromagnetic material. Large magnonic bandgaps with widths of tens of GHz are observed. The bandgaps are also studied as a function of in-plane applied magnetic field, and the width of the square dots. The widths of the first three bandgaps are dependent on the material configurations of the waveguides, but are independent of applied field strength.

Magnonic and plasmonic band gaps in films with periodically modified surfaces

It is of current interest to understand the electromagnetic response of different nanostructures. In this study, we focus on the role of geometry, in the so-called static limit. In this limit, the incoming wavelength is much greater than the relevant scales of the object, retardation can be neglected, there are no inductive effects, and the electric and magnetic problems decouple, thus one studies plasmonic and magnonic responses separately. In particular, it is of interest to study enhancements of the fields associated with geometric features of the samples as well as the development of artificial structures that may show desired behaviors. With this in mind, in this work, we study a structure with a periodic geometric perturbation that shows a behavior of interest: plasmons and magnons propagate in it with band gaps associated with the geometry, i.e., they may be controlled by design. The structures in question are dielectric or ferromagnetic thin films whose surfaces are modulated periodically in one direction: we study modes of infinite wavelength along the nonmodulated direction. The results are analogous to those found for electronic wave functions in periodic potentials, i.e., one can introduce a reduced Brillouin zone scheme to describe the modes (its width is $2\ensuremath{\pi}/A$, with $A$ the period of the geometric perturbations), which are of the Bloch type. Different bands are identified, and they are calculated numerically. For small geometric perturbations, we develop a perturbation theory that agrees well with our numerical results, and we do obtain analytic expressions for the band gaps at the edges of the Brillouin zone (proportional to the amplitudes of the geometric perturbation of the surfaces and very simple in the case of plasmons). The underlying theory used to calculate the modes was previously developed and relies on solving integral equations along the edges of the sample for the electrostatic and magnetostatic potentials, respectively. Interesting features of this method are that it is practical and computationally nonintensive, film perturbations of arbitrary shapes and amplitudes can be addressed, and it merges in one framework the study of magnons and plasmons.