We demonstrate hydrogen (H2) sensing using Pd/PdO@Fe2O3 nanonetwork powders probed by waveguidebased ferromagnetic resonance (FMR). The nanonetworks possess an open, porous morphology that enables rapid gas diffusion and allows direct integration into a microwave waveguide, which simultaneously functions as the gas-flow channel and sensing element. Exposure to H2 induces great and reproducible changes in the FMR spectra over a wide concentration range (1-100 % H2), with fast response and recovery. Comparative measurements using voltmeter-based and lock-in FMR detection reveal that hydrogen influences both magnetic and non-magnetic (dielectric/conductive) components of the microwave response. A slow post-exposure relaxation ("creep") is observed; control experiments show that the magnetic contribution accounts for approximately 10 % of the total signal and that mechanical immobilisation of the powder effectively suppresses the creep, identifying particle rotation as its dominant origin. These results clarify the respective roles of magnetic and non-magnetic effects in powder-based FMR hydrogen sensing and establish Pd/PdO@Fe2O3 nanonetworks as a promising platform for robust, high-concentration H2 detection.

In this work, we propose a concept of physical reservoir computing based on the three-wave decay of magnetostatic surface spin waves (MSSW) in a thin yttrium iron garnet film and numerically model the operation of a spin-wave active ring resonator (SWARR) under the influence of these three-wave processes as a physical reservoir. To ensure the reliability of our modeling results, we first confirm that, with some modifications, the mathematical model of the Bloembergen Problem for the nonlinear interaction of three waves is in good qualitative agreement with experimental data from the literature on the three-wave decay of short pulses of MSSW. Based on the modified Bloembergen Problem, we then construct a numerical model to simulate the operation of an SWARR under three-wave decay and perform numerical simulations using the developed program code. We find that the performance characteristics of the modeled SWARR-based reservoir are similar to those experimentally measured earlier for an SWARR operating under conditions where three-wave processes are prohibited, and only four-wave processes are allowed. Since the threshold for the three-wave decay of MSSW is considerably lower than that for the four-wave processes, this suggests a significant reduction in power consumption for an SWARR-based physical reservoir if it operates in the mode of three-wave decay of the primary MSSW. We also demonstrate that the proposed physical reservoir network can be used to denoise data sequences. We show this using the example of the Lorenz96 chaotic time series.

The mass-production of fuel-cell vehicles and the eventual transition to the hydrogen economy will require safe, inexpensive and reliable sensors capable of simultaneously detecting low concentrations of leaking hydrogen and measuring broad ranges of hydrogen concentration in storage and energy generating systems. Although several competing sensor technologies can potentially be used in this role, just a few of them have thus far demonstrated a combination of all desirable characteristics. This group of devices also includes magneto-electronic sensors that can detect the presence of hydrogen gas in a range of hydrogen concentrations from zero to 100% at atmospheric pressure with the response time approaching the industry standard of one second. The hydrogen gas sensing mechanism underpinning the operation of magneto-electronic sensors is based on the physical processes of ferromagnetic resonance, magneto-optical Kerr effect and anomalous Hall effect that enable one to measure hydrogen-induced changes in the magnetic properties of structures combining Pd with one or several ferromagnetic metals such as Co, Fe or Ni. In this chapter, we overview the physical foundations of emergent ferromagnetic Pd-alloy-based magneto-electronic hydrogen sensors and compare their characteristics with those of highperforming multilayer thin film-based counterparts that have already demonstrated a potential to find commercial applications.

In this work, we carried out a theoretical analysis of the dispersion relation omega(k) for spin waves in a layered structure comprising two ferromagnetic layers and a nonmagnetic spacer sandwiched between them. The spin-wave configuration considered is that of the Damon-Eshbach magnetostatic surface spin wave, characterized by a static magnetic field applied in the structure plane and perpendicular to the direction of wave propagation. We assumed that, in addition to the conventional ferromagnetic interlayer Heisenberg exchange via the Ruderman-Kittel-Kasuya-Yosida interaction, the ferromagnetic layers are also coupled by the recently discovered interlayer Dzyaloshinskii-Moriya interaction (IL-DMI). We found that the presence of IL-DMI modifies the eigenfrequencies of both fundamental modes of the structure-acoustic and optical. The acoustic mode experiences a downward shift in frequency and a reduction in slope. Conversely, the optical mode is shifted upward and develops a significant positive slope, whereas it remains dispersionless across most of the wave-number range accessible with Brillouin light-scattering spectroscopy in the absence of IL-DMI. Numerical calculations of the dispersion relation demonstrate that it will be possible to experimentally identify the presence of IL-DMI in such layered structures using Brillouin light scattering. Additionally, the value of the Dzyaloshinskii constant for the ferromagnetic/nonmagnetic/ferromagnetic interface pair can be extracted from the measurement results.

Interfacial Dzyaloshinskii-Moriya interaction (IFDMI) leads to noncollinear spin configurations within the magnetic layers of multilayer heterostructures, while its interlayer counterpart (ILDMI) minimizes chiral states between the layers. Here, we demonstrate that the symmetries of these interactions are very different, even though both arise from pairwise exchange interactions between magnetic sites mediated by nonmagnetic atoms. By deriving respective boundary conditions for the exchange operator and solving the associated boundary value problem, we show that, unlike IFDMI, which does not contribute to the FMR frequencies, ILDMI alters the frequencies of the fundamental FMR modes and can be separated from other contributions in an FMR experiment.

We demonstrated resonance-based detection of magnetic nanoparticles employing novel designs based upon planar (on-chip) microresonators that may serve as alternatives to conventional magnetoresistive magnetic nanoparticle detectors. We detected 130 nm sized magnetic nanoparticle clusters immobilized on sensor surfaces after flowing through PDMS microfluidic channels molded using a 3D printed mold. Two detection schemes were investigated: (i) indirect detection incorporating ferromagnetic antidot nanostructures within microresonators, and (ii) direct detection of nanoparticles without an antidot lattice. Using scheme (i), magnetic nanoparticles noticeably downshifted the resonance fields of an antidot nanostructure by up to 207 G. In a similar antidot device in which nanoparticles were introduced via droplets rather than a microfluidic channel, the largest shift was only 44 G with a sensitivity of 7.57 G/ng. This indicated that introduction of the nanoparticles via microfluidics results in stronger responses from the ferromagnetic resonances. The results for both devices demonstrated that ferromagnetic antidot nanostructures incorporated within planar microresonators can detect nanoparticles captured from dispersions. Using detection scheme (ii), without the antidot array, we observed a strong resonance within the nanoparticles. The resonance’s strength suggests that direct detection is more sensitive to magnetic nanoparticles than indirect detection using a nanostructure, in addition to being much simpler.

Physical reservoir computers based on principles of magnonics promise energy efficient data processing and a reduction in the size and weight of the neuromorphic computing devices. The present work is a major step toward all-magnonic implementation of the recently proposed concept of a physical reservoir based on the spin wave active ring. The main component of the ring is a spin wave delay line employing a thin film of yttrium iron garnet (YIG) as the spin wave guiding medium. We propose controlling spin wave propagation in the YIG film electronically to enter input data into the reservoir. To this end, we exploit a physical effect of scattering of backward volume spin waves from a highly localized Oersted field of a dc current flowing through a metallic strip sitting on top of the YIG film. We find experimentally that a very small current (on the order of several milliamps) through the strip is able to control the amplitude of auto-oscillations in the ring. The use of the current control of spin wave propagation as a means to enter input data into the reservoir reduces the number of non-magnetic components of the reservoir to just one (a microwave amplifier). In addition, the proposed current-controlled magnonic reservoir demonstrates a record-high short-term memory capacity of 5.53, as our experiments show. Our findings open up an avenue for reduction of energy consumption by magnonic active-ring-based physical reservoirs, their micro-miniaturization, and all-magnonic implementation.

A numerical model for a spin wave delay-line active ring resonator is presented. Spin wave dynamics along a one-dimensional strip of magnetic material are modeled using the nonlinear Schrödinger equation. The equation is solved numerically in Fourier space using the fourth-order Runge–Kutta method and yields qualitative agreement with experimental measurements of spin wave dynamics in two different regimes. The model provides a useful tool for performing experiments based on neuromorphic computing and logic gates in traveling spin wave devices.

A magnonic active ring oscillator based on an yttrium iron garnet (YIG) is a promising hardware platform for physical reservoir computing. It meets the required conditions for the availability of fading memory and nonlinearity. However, its performance still needs further improvement. Two methods can be employed to improve the performance. One is increasing the time of establishing steady self-oscillations in the auto-oscillator. The second one is increasing the amplitude of spin waves propagating in the YIG film. In this work, we achieve an increase of the amplitude of the reservoir response by broadening the available range for the ring gain coefficient. We use a metallized YIG film as a waveguide in which spin waves propagate. This shifts up the amplitude threshold for the development of spin wave modulation instability in the ring. The threshold defines the upper limit of the gain range for the ring. Binary pulse sequence is entered into the ring by switching its gain between upper and lower levels. The modulation instability threshold then sets the upper limit for the higher gain level. In addition, in this work, we set the lower level of the gain to negative values. This is one more improvement with respect to earlier works. Switching the gain between a negative and a positive value increases the amplitude of the reservoir response and the depth of its fading memory. We employ the standard short-term memory and parity-check tests to quantify the performance of the reservoir computer. Both tests demonstrate an increase in the computational efficiency of the magnonic reservoir.

In this work, we investigate the effects of H2 on the physical properties of Fe25Pd75. Broadband ferromagnetic resonance (FMR) spectroscopy revealed a significant FMR peak shift induced by H2 absorption for the FCC phased Fe25Pd75. The peak shifted towards higher applied fields, which is contrary to what was previously observed for CoPd alloys. Additionally, we conducted structural and magneto-optical Kerr ellipsometric studies on the Fe25Pd75 film and performed density functional theory calculations to explore the electronic and magnetic properties in both hydrogenated and dehydrogenated states. In the final part of this study, we deposited a Fe25Pd75 layer on top of a microscopic coplanar transmission line and investigated the FMR response of the layer while driven by a microwave current in the coplanar line. We observed a large amplitude FMR response upon hydrogen absorption, as well as desorption rates when cycling between pure N2 and a mixture of 3

A numerical model describing a magnonic active ring oscillator (MARO) based on a microscopic spin-wave delay line is proposed. The model considers excitation, propagation, and reception of the magnetostatic surface waves in a yttrium iron garnet (YIG) magnetic film with a thickness in the nanometer range. The waves are excited and received with a microscopic coplanar antenna. We employed the model to analyze the influence of the YIG-film thickness and the distance between the antennas on the MARO performance characteristics. We showed that an increase in the delay time inserted by the delay line reduces the phase noise of the MARO and increases the auto-oscillation threshold. In addition, we found a relation between the auto-oscillation threshold, the thickness of the YIG film, and the distance between the antennas. The relation helps design miniature MAROs and suggests a way to reduce the phase noise of the device. The model predicts a phase noise level of −115 dBc/Hz at a 10 kHz offset from an oscillation frequency in the vicinity of 5 GHz for the MARO based on a 100 nm-thick YIG film and 56 μm of distance between the coplanar nano-antennas of the YIG-film based delay line. We believe that this is a clear way forward to microminiaturize the time-delay feedback microwave auto-oscillators. A further reduction in the phase noise down to −125 dBc/Hz at a 10 kHz offset is found in a model of cascaded connection of several microscopic spin-wave delay lines.

The symmetric (Heisenberg) exchange interaction is fundamental to magnetism and assumes critical importance in designing magnetic materials for novel emergent phenomena and device applications. However, quantifying exchange is extremely challenging for ultrathin ($\sim$ 1 nm) magnetic films, as techniques and approximations reliably used for bulk materials are largely inapplicable in the two-dimensional (2D) limit. Here we present and contrast the measurement of exchange stiffness, $A$, by several methods on a series of five Co/Pt-based ultrathin ($1-2$ nm) films. We compare results from (a) spin-wave spectroscopy by Brillouin light scattering (BLS), (b) three analytical models describing the temperature dependence of magnetization obtained by magnetometry, (c) microscopic domain periodicity measurements and simulations, and (d) ab initio density functional theory (DFT) calculations. While different methods present some qualitatively consistent trends across samples, we note, for any given sample, considerable differences (up to $5\times$) in the absolute values of $A$ across the techniques, consistent with discrepancies of $A$ reported in literature for nominally similar samples. We analyze possible sources of the discrepancies across various methods, notably including their relationship to the spin-wave dispersion, and the wave-vector ranges probed. We compare the strengths and limitations of the techniques, and outline directions for their future use in characterizing exchange interactions in ultrathin films.

The influence of an external magnetic field upon the capture of 130 nm magnetic nanoparticles (MNPs) by ferromagnetic nanostructures was investigated. The magnetophoretic forces acting upon a nanoparticle were simulated in external magnetic fields parallel and perpendicular to ferromagnetic nanostructures consisting of arrays of antidots and dots. Changing the direction of the external field was found to dramatically alter the magnetophoretic forces acting on the particle and the trajectories of the MNPs. A field parallel to the nanostructures' surfaces generated magnetophoretic forces that directed the nanoparticle into the nanostructures. A perpendicular field produced forces directing particles onto the structures' surfaces. Nanostructures were etched into the surfaces of Permalloy films using ion beam lithography. MNPs were then deposited onto the films' surfaces under a parallel or perpendicular magnetic field. The distributions of particles in the nanostructures were analysed to obtain the capture efficiencies of each structure which indicate the proportion of particles trapped inside. Without an external field, the highest efficiency was displayed by arrays of circular antidots with circular dot arrays displaying the lowest. Antidot arrays displayed higher capture efficiencies than dot arrays. Addition of a field parallel to the surface significantly increased the capture efficiencies and addition of a field perpendicular to the surface decreased the efficiencies. Under the perpendicular field, the particles were instead caught on the outer edges of the nanostructures. These results suggest that application of a parallel external magnetic field promotes the capture of MNPs within ferromagnetic nanostructures and a perpendicular field increases the capture of MNPs onto the outer surface and edges of nanostructures.

We report on the coupling of spin waves propagating as guided modes of yttrium iron garnet stripes. Three stripes are placed parallel to each other and separated by gaps that are small enough to provide nearest-neighbor coupling. We term this geometry ``bilateral stripes.'' The origin of the coupling is the long-ranging dynamic, stray (dipole) field of the precessing magnetization vector. We propose controlling characteristics of this coupling through variation of the static magnetization angle with respect to the main axes of the geometry. We verified the functionality of the proposed magnonic coupler with a micromagnetic simulation of spin-wave propagation along the bilateral stripes. The micromagnetic numerical simulation yielded spectra of transmission of spin waves through the device prototype. Analysis of those spectra revealed that the bilateral stripes can be used as a functional unit in planar magnonic networks---they can be employed as a directional coupler, spin-wave multiplexer, or microwave power divider. Using Brillouin light scattering spectroscopy, we experimentally demonstrated spin-wave transport along the bilateral stripes. We were able to control the spin-wave routing between the stripes (``magnetic channels'') by varying the angle of the bias magnetic field.

Magnetic nanoparticles (MNPs) have many applications which require MNPs to be captured and immobilized for their manipulation and sensing. For example, MNP sensors based on detecting changes to the ferromagnetic resonances of an antidot nanostructure exhibit better performance when the nanoparticles are captured within the antidot inclusions. This study investigates the influence of microfluidics upon the capture of MNPs by four geometries of antidot array nanostructures hollowed into 30 nm-thick Permalloy films. The nanostructures were exposed to a dispersion of 130 nm MNP clusters which passed through PDMS microfluidic channels with a 400 {\mu}m circular cross-section fabricated from wire molds. With the microfluidic flow of MNPs, the capture efficiency - the ratio between the number of nanoparticles captured inside of the antidot inclusions to the number outside the inclusions - decreased for all four geometries compared to previous results introducing the particles via droplets on the film surface. This indicates that most MNPs were passing over the nanostructures, since there were no significant magnetophoretic forces acting upon the particles. However, when a static magnetic field is applied, the magnetophoretic forces generated by the nanostructure are stronger and the capture efficiencies are significantly higher than those obtained using droplets. In particular, circular antidots demonstrated the highest capture efficiency among the four geometries of almost 83.1% when the magnetic field is parallel to the film plane. In a magnetic field perpendicular to the film, the circle antidots again show the highest capture efficiency of about 77%. These results suggest that the proportion of nanoparticles captured inside antidot inclusions is highest under a parallel magnetic field. Clearly, the geometry of the nanostructure has a strong influence on the capture of MNPs.

We carried out numerical simulations of propagation of spin waves (magnons in quantum language) in a yttrium-iron garnet film. The numerical model is based on an original formalism. We demonstrated that a potential barrier for magnons, created by an Oersted field of a dc current flowing through a wire sitting on top of the film, is able to act as an electrically controlled partly transparent mirror for the magnons. We found that the mirror transparency can be set to 50% by properly adjusting the current strength, thus creating a semi-transparent mirror. A strong Hong-Ou-Mandel Effect for single magnons is expected in this configuration. The effect must be seen as two single magnons, launched simultaneously into the film from two transducers located from the opposite sides of the mirror, creating a two-microwave-photon state at the output port of one of the transducers. The probability of seeing those two-photon states at the output port of either transducer must be the same for both transducers.

The efficacy of a physical reservoir computer model based on traveling spin waves in a spin-wave delay-line active-ring resonator was demonstrated recently. In the present work, we investigate how this neuromorphic device can be adapted for sensing applications. In this "reservoir computing for sensing" framework, we exploit strong coupling of the physical reservoir to its environment to utilize the reservoir as a sensing element. The dynamics of traveling spin waves in delay-line active rings are strongly depen-dent on the magnetic field and carrier frequency of those spin waves. Treating the spin-wave frequency as an environmental variable, we excite the active ring into different dynamical states by modulating the carrier frequency of a drive signal of microwave pulses injected into the ring. Training a linear regression on the time-multiplexed output from the ring allows the periodic amplitude patterns of the spin waves to be mapped reproducibly onto two-dimensional trajectories, representing periodic "behavioral" targets. Our work demonstrates the versatility of a magnonic resonator as a multipurpose computing and sensing device.

A fully self-consistent model for the excitation and reception of magnetostatic surface waves in thin ferromagnetic films by a set of coplanar antennas was developed and implemented numerically. The model assumes that the ferromagnetic film is highly conducting and is interfaced with non-magnetic metallic films, but is also suitable for modeling magneto-insulating films. Perpendicular magnetic anisotropy and Dzyaloshinskii-Moriya interaction can be included at both interfaces of the ferromagnetic layer. The model calculates the coupling impedances between the different strips constituting the coplanar antennas. In some situations, this leads to a frequency non-reciprocity between counter-propagating waves even in the case of no asymmetry in the spin-wave dispersion relation. Several intermediate results of the model were checked numerically and the final output of the model, given as the scattering parameters, $S_{11}$, $S_{12}$, and $S_{21}$ of the antenna system, were in good agreement with previous experimental studies.