Magnonic Metamaterials Research Articles

Magnonic Metamaterials for Spin-Wave Control with Inhomogeneous Dzyaloshinskii-Moriya Interactions.

A magnonic metamaterial in the presence of spatially modulated Dzyaloshinskii–Moriya interaction is theoretically proposed and demonstrated by micromagnetic simulations. By analogy to the fields of photonics, we first establish magnonic Snell’s law for spin waves passing through an interface between two media with different dispersion relations due to different Dzyaloshinskii–Moriya interactions. Based on magnonic Snell’s law, we find that spin waves can experience total internal reflection. The critical angle of total internal reflection is strongly dependent on the sign and strength of Dzyaloshinskii–Moriya interaction. Furthermore, spin-wave beam fiber and spin-wave lens are designed by utilizing the artificial magnonic metamaterials with inhomogeneous Dzyaloshinskii–Moriya interactions. Our findings open up a rich field of spin waves manipulation for prospective applications in magnonics.

Effects of Cobalt Nanoisland Geometry on Terahertz Negative Refraction: a Numerical Analysis

The architectural framework plays a major role in determining the optical properties of left-handed materials. Most metamaterial so far designed have been based on complicated resonant elements such as split rings and hyperbolic metamaterials. Unfortunately, magnetic response of most of the materials tails off at higher frequencies. Higher frequency excitation in metamaterials requires more complicated designs or toroidal moment. In the proposed magnonic metamaterials, the toroidal excitations are naturally maintained and make it suitable for THz resonances. Magnetism and left-handed behavior are the two extreme phenomena that do not seem to be compatible and the coexistence of both cooperative effects was not foreseen. Terahertz spintronics is an emerging field that bridges the boundary between magnetism and photonics, which make the magnetic material suitable for photonic applications. Here, we present the first numerical realization of a magnonic metamaterial artificial spin ice (ASI), designed to operate at terahertz frequency. The two-dimensional square arrays exhibit a rich spin wave band structure that is tunable both by external electromagnetic fields and the magnetization configuration of individual elements. The ultrafast spin wave resonances have provided a direct gateway to manipulate magnetic field of free-space terahertz pulses. The proposed system consists of two-dimensional square arrays of cobalt nanoislands in four different geometries and the micromagnetic simulations of these systems are carried out using mumax3. From the numerical results, the theoretical prediction of negative permeability is done using Schloemann model.

Reconfigurable and self-biased magnonic metamaterials

In magnonics, magnetic waves and oscillations are exploited for signal and information processing at microwave frequencies. A magnonic metamaterial is employed to configure different microwave bands by spatial engineering of magnetizations using different magnetic states or magnetic couplings. Magnetic field hysteretic variation of microwave responses has conventionally been used for tunable microwave operations. The use of such bias magnetic fields hinders the device integration of microwave magnonic devices. Here, we discuss a route to eliminating the requirement of bias magnetic field and simple initialization process for reconfigurable microwave operations. The distinct microwave responses are associated with different remanent magnetic states which are engineered by shape induced magnetic anisotropy rather than the conventional dipolar coupling driven magnetic states. However, the origin of the shift in the microwave spectra is associated with the variation of dipolar coupling for nanomagnetic networks, multilayer nanomagnets, and their arrays. This perspective provides an outlook on current challenges and potential future scopes of magnonic devices. We discuss some of our recent demonstrations toward the realizations of reconfigurable magnonic devices without any external bias magnetic field. Self-biased nanomagnets are also shown to have applications in designing a waveguide for spin wave transport and spin wave gating which operates without any bias magnetic field.

Hybrid perfect metamaterial absorber for microwave spin rectification applications

Metamaterials provide compelling capabilities to manipulate electromagnetic waves beyond the natural materials and can dramatically enhance both their electric and magnetic fields. The enhanced magnetic fields, however, are far less utilized than the electric counterparts, despite their great potential in spintronics. In this work, we propose and experimentally demonstrate a hybrid perfect metamaterial absorbers which combine the artificial metal/insulator/metal (MIM) metamaterial with the natural ferromagnetic material permalloy (Py) and realize remarkably larger spin rectification effect. Magnetic hot spot of the MIM metamaterial improves considerably electromagnetic coupling with spins in the embedded Py stripes. With the whole hybridized structure being optimized based on coupled-mode theory, perfect absorption condition is approached and an approximately 190-fold enhancement of spin-rectifying photovoltage is experimentally demonstrated at the ferromagnetic resonance at 7.1 GHz. Our work provides an innovative solution to harvest microwave energy for spintronic applications, and opens the door to hybridized magnetism from artificial and natural magnetic materials for emergent applications such as efficient optospintronics, magnonic metamaterials and wireless energy transfer.

Nonlinear spin waves in ferromagnetic/superconductor hybrids

This work is focused on the numerical investigation of spin waves that propagate in nonlinear ferromagnet/superconductor bilayered films and periodic structures. The nonlinearity in these hybrid structures emerges due to the non-monotonous dependence of magnetization of a superconducting subsystem on the magnetic field, which is characterized by the superconducting critical field. It is shown that at relatively high amplitudes of spin waves in comparison to the superconducting critical field, the spin-wave spectrum changes drastically: the spin-wave spectral line can either bifurcate or stretch continuously depending on the type of considered superconductor. In addition, in the case of propagation of spin waves with relatively high amplitude in periodic magnonic metamaterials, additional zero-group-velocity modes appear that are known as flatbands. Overall, these findings suggest a versatile way for tunability of the spin-wave spectrum in nonlinear ferromagnet/superconductor structures by changing the excitation signal in respect to the superconducting critical field.

Magnetic states and dynamics of bistable square Fe nanoislands

The low energy magnetic configurations in square 300 nm Fe islands, having their magneto-crystalline easy axes aligned along the diagonals of the squares, are studied by micromagnetic simulations with the help of the mumax3 package. For thicknesses above 2.4 nm vortex configurations become the lowest energy states. However for the thickness range 1.5–2.5 nm “leaf”, vortex and “C” state configurations have comparable energies and can be all stabilized as the energy barriers that separate them are substantial (209 kBT to 401 kBT) and much larger than their energy differences. Therefore in ordered arrays of such elements different states could be simultaneously present depending on the local interactions and previous history. In view of their use as tunable magnonic metamaterials the high frequency response of each configuration is micromagnetically simulated. The resonance frequencies in single elements as well as for arrays, and the localized spin wave modes that correspond to each resonance, are extracted for each of the low energy micromagnetic states.

Dramatically Enhanced Spin Dynamo with Plasmonic Diabolo Cavity

The applications of spin dynamos, which could potentially power complex nanoscopic devices, have so far been limited owing to their extremely low energy conversion efficiencies. Here, we present a unique plasmonic diabolo cavity (PDC) that dramatically improves the spin rectification signal (enhancement of more than three orders of magnitude) under microwave excitation; further, it enables an energy conversion efficiency of up to ~0.69 mV/mW, compared with ~0.27 μV/mW without a PDC. This remarkable improvement arises from the simultaneous enhancement of the microwave electric field (~13-fold) and the magnetic field (~195-fold), which cooperate in the spin precession process generates photovoltage (PV) efficiently under ferromagnetic resonance (FMR) conditions. The interplay of the microwave electromagnetic resonance and the ferromagnetic resonance originates from a hybridized mode based on the plasmonic resonance of the diabolo structure and Fabry-Perot-like modes in the PDC. Our work sheds light on how more efficient spin dynamo devices for practical applications could be realized and paves the way for future studies utilizing both artificial and natural magnetism for applications in many disciplines, such as for the design of future efficient wireless energy conversion devices, high frequent resonant spintronic devices, and magnonic metamaterials.

Top-down design of magnonic crystals from bottom-up magnetic nanoparticles through protein arrays

We show that chemical fixation enables top-down micro-machining of large periodic 3D arrays of protein-encapsulated magnetic nanoparticles (NPs) without loss of order. We machined 3D micro-cubes containing a superlattice of NPs by means of focused ion beam etching, integrated an individual micro-cube to a thin-film coplanar waveguide and measured the resonant microwave response. Our work represents a major step towards well-defined magnonic metamaterials created from the self-assembly of magnetic nanoparticles.

Static and dynamic properties of three-dimensional dot-type magnonic crystals

The static and dynamic magnetization of three-dimensional magnonic metamaterials has been investigated. By numerical means it was analyzed the impact of space dimensionality on the properties of magnonic crystal with unit cell consisting of four dots. It is find out the possibility of multi-vortex core formation which is related to the increasing of the crystal height by three-dimensional periodicity of single crystal layer. Additionally is provided the analysis of ferromagnetic resonance phenomenon for two-dimensional and three-dimensional structures. For the unsaturated magnetization of three-dimensional crystal the several pronounced resonance frequencies were detected.

Spin wave eigenmodes in single and coupled sub-150 nm rectangular permalloy dots

We present the results of a Brillouin light scattering investigation of thermally excited spin wave eigenmodes in square arrays of either isolated rectangular dots of permalloy or twins of dipolarly coupled elements, placed side-by-side or head-to-tail. The nanodots, fabricated by e-beam lithography and lift-off, are 20 nm thick and have the major size D in the range between 90 nm and 150 nm. The experimental spectra show the presence of two main peaks, corresponding to modes localized either at the edges or in the center of the dots. Their frequency dependence on the dot size and on the interaction with adjacent elements has been measured and successfully interpreted on the basis of dynamical micromagnetic simulations. The latter enabled us also to describe the spatial profile of the eigenmodes, putting in evidence the effects induced by the dipolar interaction between coupled dots. In particular, in twinned dots the demagnetizing field is appreciably modified in proximity of the “internal edges” if compared to the “external” ones, leading to a splitting of the edge mode. These results can be relevant for the exploitation of sub-150 nm magnetic dots in new applications, such as magnonic metamaterials, bit-patterned storage media, and nano-magnetic logic devices.

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.

Adjustable microwave permeability of nanorings: A micromagnetic investigation

Abstract Based on the three-dimensional micromagnetic simulations, we present a method to tailor the microwave permeabilities of magnonic metamaterials cells by a designed nanoring structure. The results show that the permeabilities and resonant frequency are depended on the wallʼs thickness of nanorings. The underlying mechanism is ascribed to the presence of strong demagnetization fields, which are associated to the ringʼs wall. In addition, the products of magnetic susceptibility and resonant frequency are larger than that predicted from Snoekʼs law in polycrystalline particles. These results are direct manifestations of the bi-anisotropy model.

Calculation of high-frequency permeability of magnonic metamaterials beyond the macrospin approximation

We present a method of calculation of the effective magnetic permeability of magnonic metamaterials containing arrays of magnetic inclusions of arbitrary shapes. The method fully takes into account the spectrum of spin waves confined in the inclusions. We evaluate the method by considering a particular case of a metamaterial formed by a stack of identical two-dimensional (2D) periodic hexagonal arrays of disk-shaped magnetic inclusions in a nonmagnetic matrix. Two versions of the method are considered. The first approach is based on a simple semianalytical theory that uses the numerically calculated susceptibility tensor of an isolated inclusion as input data for an analytical calculation in which the magnetodipole interaction between inclusions within each 2D array is taken into account. In the second approach, we employ micromagnetic packages with periodic boundary conditions to calculate the susceptibility of the whole 2D periodic array of such inclusions. The comparison of the two approaches reveals the necessity of retaining higher-order terms in the analytical calculation of the magnetodipole interaction via the multipole expansion. Models limited to the dipolar term can lead to remarkable underestimation of the effect of the magnetodipole interaction, in particular, for modes localized near the edge regions of inclusions. To calculate the susceptibility tensor of an isolated inclusion, we have implemented two different methods: (a) a method based on micromagnetic simulations, in which we have compared three different micromagnetic packages: the finite-element package nmag and the two finite differences packages oommf and micromagus; and (b) the modified dynamical matrix method (DMM). The comparison of the different micromagnetic packages and the DMM (based on the calculation of the susceptibility tensor of an isolated inclusion) demonstrate that their results agree to within 3$%$. Frequency regions in which the metamaterial is characterized by the negative permeability are identified. We speculate that the proposed methodology could be generalized to more complex arrangements of magnetic inclusions, e.g., to those with multiple periods or fractal arrangements, as well as to arrays of inclusions with a distribution of properties.