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Physical reservoir computing has emerged as a powerful framework for exploiting the inherent nonlinear dynamics of physical systems to perform computational tasks. Recently, we presented the magnon-scattering reservoir, whose internal nodes are given by the fundamental wave-like excitations of ferromagnets called magnons. These excitations can be geometrically-quantized and, in response to an external stimulus, show transient nonlinear scattering dynamics that can be harnessed to perform memory and nonlinear transformation tasks. Here, we test a magnon-scattering reservoir in a single magnetic disk in the vortex state towards two key performance indicators for physical reservoir computing, the short-term memory and parity-check tasks. Using time-resolved Brillouin-light-scattering microscopy, we measure the evolution of the reservoir's spectral response to an input sequence consisting of random binary inputs encoded in microwave pulses with two distinct frequencies. Two different output spaces of the reservoir are defined, one based on the time-averaged frequency spectra and another based on temporal multiplexing. Our results demonstrate that the memory and nonlinear transformation capability do not depend on the chosen read-out scheme as long as the dimension of the output space is large enough to capture all nonlinear features provided by the magnon-magnon interactions. This further shows that solely the nonlinear magnons in the physical system, not the read-out, determine the reservoir's capacity.

Using Brillouin light scattering microscopy, we study the rich dynamics in magnetic disks and rings governed by non-linear interactions, focusing on the role of vortex core dynamics on the spin-wave eigenmode spectrum. By strongly exciting quantized magnon modes in magnetic vortices, self-induced magnon Floquet states are populated by the intrinsic nonlinear coupling of magnon modes to the vortex core gyration. In magnetic rings, however, this generation is suppressed even when exciting the system over a large power range. To retrieve the rich nonlinear dynamics in rings, we apply external in-plane magnetic fields by which the vortex core is restored. Our findings demonstrate how to take active control of the nonlinear processes in magnetic structures of different topology., Comment: 6 pages, 4 figures

Nonreciprocal spin-wave propagation in bilayer ferromagnetic systems has attracted significant attention due to its potential to precisely quantify material parameters as well as for applications in magnonic logic and information processing. In this study we investigate the nonreciprocity of spin-wave dispersions in heterostructures consisting of two distinct ferromagnetic materials, focusing on the influence of saturation magnetization and thickness of the magnetic layers. We exploit Brillouin light scattering to confirm numerical calculations which are conducted with the finite element software TETRAX. An extensive numerical analysis reveals that the nonreciprocal behavior is strongly influenced by the changing material parameters, with asymmetry in the spin-wave propagation direction reaching several GHz under optimized conditions. Our findings demonstrate that tailoring the bilayer composition enables precise control over nonreciprocity, providing a pathway for engineering efficient unidirectional spin-wave devices. These results offer a deeper understanding of hybrid ferromagnetic systems and open avenues for designing advanced magnonic circuits., Comment: 10 pages, 10 figures

Driving condensed matter systems with periodic electromagnetic fields can result in exotic states not found in equilibrium. Termed Floquet engineering, such periodic driving applied to electronic systems can tailor quantum effects to induce topological band structures and control spin interactions. However, Floquet engineering of magnon band structures in magnetic systems has proven challenging so far. Here, we present a class of Floquet states in a magnetic vortex that arise from nonlinear interactions between the vortex core and microwave magnons. Floquet bands emerge through the periodic oscillation of the core, which can be initiated by either driving the core directly or pumping azimuthal magnon modes. For the latter, the azimuthal modes induce core gyration through nonlinear interactions, which in turn renormalizes the magnon band structure. This represents a self-induced mechanism for Floquet band engineering and offers new avenues to study and control nonlinear magnon dynamics.

The ultrafast control of magnetisation states in magnetically ordered systems is a key technological challenge for developing memory devices operable at picosecond timescales or terahertz (THz) frequencies. Despite significant efforts in ultrafast magnetic switching, convenient ultrafast readout of magnetic states remains under investigation. Currently, many experiments exploit magneto-optical effects for detecting magnetisation states, necessitating laser sources and optical components. However, energy-efficient and cost-effective electrical detection is preferred for practical applications. Unidirectional spin-Hall magnetoresistance (USMR) was proposed as a simple two-terminal geometry for the electrical detection of the magnetisation state in magnetic heterostructures. Here, we demonstrate that USMR is active at THz frequencies for picosecond time readouts, and can be initiated with light fields. We detect ultrafast USMR in various types of ferromagnet/heavy metal thin film heterostructures through THz second harmonic generation. Our studies, combined with temperature-dependent measurements of USMR, reveal a significant contribution from electron-magnon spin-flip scattering. This suggests possibilities for all-electrical detection of THz magnon modes., Comment: 20 pages, 5 figures

We demonstrate piezostrain-induced frequency pulling in stacked double-vortex structures, magnetostatically coupled through the nonmagnetic spacer. We study the effect of the Cu spacer thickness on the strain-induced gyrotropic frequency shift in double-vortex structures comprising of magnetostrictive CoFeB and nonmagnetostricitve Py layers. For the two stacked vortices with different eigen-frequencies, the strain-induced magnetoelastic anisotropy leads to the downshift of the gyration frequency of the magnetostricitve vortex. We show that for increased dipolar coupling between the layers (i.e. decreased spacer thickness), a strain-induced frequency pulling regime is obtained, where the resonance frequency of the nonmagnetostrictive Py vortex is upshifted towards the gyration resonance of the magnetostrictive CoFeB vortex. This result offers an additional degree of freedom for the manipulation of the dynamical regimes and synchronization conditions in spintronic oscillators, controlled by voltage and tunable by strain, Comment: 5 pages, 4 figures

It is known that singular values of idempotent matrices are either zero or larger or equal to one \cite{HouC63}. We state exactly how many singular values greater than one, equal to one, and equal to zero there are. Moreover, we derive a singular value decomposition of idempotent matrices which reveals a tight relationship between its left and right singular vectors. The same idea is used to augment a discovery regarding the singular values of involutory matrices as presented in \cite{FasH20}.

A class of (block) rational Krylov subspace based projection method for solving large-scale continuous-time algebraic Riccati equation (CARE) $0 = \mathcal{R}(X) := A^HX + XA + C^HC - XBB^HX$ with a large, sparse $A$ and $B$ and $C$ of full low rank is proposed. The CARE is projected onto a block rational Krylov subspace $\mathcal{K}_j$ spanned by blocks of the form $(A^H - s_kI)^{-1}C^H$ for some shifts $s_k, k = 1, \ldots, j.$ The considered projections do not need to be orthogonal and are built from the matrices appearing in the block rational Arnoldi decomposition associated to $\mathcal{K}_j.$ The resulting projected Riccati equation is solved for the small square Hermitian $Y_j.$ Then the Hermitian low-rank approximation $X_j = Z_jY_jZ_j^H$ to $X$ is set up where the columns of $Z_j$ span $\mathcal{K}_j.$ The residual norm $\|R(X_j )\|_F$ can be computed efficiently via the norm of a readily available $2p \times 2p$ matrix. We suggest to reduce the rank of the approximate solution $X_j$ even further by truncating small eigenvalues from $X_j.$ This truncated approximate solution can be interpreted as the solution of the Riccati residual projected to a subspace of $\mathcal{K}_j.$ This gives us a way to efficiently evaluate the norm of the resulting residual. Numerical examples are presented.

The interplay of electric charge, spin, and orbital polarizations, coherently driven by picosecond long oscillations of light fields in spin-orbit coupled systems, is the foundation of emerging terahertz spintronics and orbitronics. The essential rules for how terahertz light interacts with these systems in a nonlinear way are still not understood. In this work, we demonstrate a universally applicable electronic nonlinearity originating from spin-orbit interactions in conducting materials, wherein the interplay of light-induced spin and orbital textures manifests. We utilized terahertz harmonic generation spectroscopy to investigate the nonlinear dynamics over picosecond timescales in various transition metal films. We found that the terahertz harmonic generation efficiency scales with the spin Hall conductivity in the studied films, while the phase takes two possible values (shifted by {\pi}), depending on the d-shell filling. These findings elucidate the fundamental mechanisms governing non-equilibrium spin and orbital polarization dynamics at terahertz frequencies, which is relevant for potential applications of terahertz spin- and orbital-based devices., Comment: 11 pages, 4 figures

Immersed boundary methods simplify mesh generation by embedding the domain of interest into an extended domain that is easy to mesh, introducing the challenge of dealing with cells that intersect the domain boundary. Combined with explicit time integration schemes, the finite cell method introduces a lower bound for the critical time step size. Explicit transient analyses commonly use the spectral element method due to its natural way of obtaining diagonal mass matrices through nodal lumping. Its combination with the finite cell method is called the spectral cell method. Unfortunately, a direct application of nodal lumping in the spectral cell method is impossible due to the special quadrature necessary to treat the discontinuous integrand inside the cut cells. We analyze an implicit-explicit (IMEX) time integration method to exploit the advantages of the nodal lumping scheme for uncut cells on one side and the unconditional stability of implicit time integration schemes for cut cells on the other. In this hybrid, immersed Newmark IMEX approach, we use explicit second-order central differences to integrate the uncut degrees of freedom that lead to a diagonal block in the mass matrix and an implicit trapezoidal Newmark method to integrate the remaining degrees of freedom (those supported by at least one cut cell). The immersed Newmark IMEX approach preserves the high-order convergence rates and the geometric flexibility of the finite cell method. We analyze a simple system of spring-coupled masses to highlight some of the essential characteristics of Newmark IMEX time integration. We then solve the scalar wave equation on two- and three-dimensional examples with significant geometric complexity to show that our approach is more efficient than state-of-the-art time integration schemes when comparing accuracy and runtime.

We present a study of the piezostrain-tunable gyrotropic dynamics in Co$_{40}$Fe$_{40}$B$_{20}$ vortex microstructures fabricated on a 0.7PMN-0.3PT single crystalline substrate. Using field-modulated spin rectification measurements, we demonstrate large frequency tunability (up to 45 %) in individual microdisks accessed locally with low surface voltages, and magnetoresistive readout. With increased voltage applied to the PMN-PT, we observe a gradual decrease of the vortex core gyrotropic frequency associated with the strain-induced magnetoelastic energy contribution. The frequency tunability strongly depends on the disk size, with increased frequency downshift for the disks with larger diameter. Micromagnetic simulations suggest that the observed size effects originate from the joint action of the strain-induced magnetoelastic and demagnetizing energies in large magnetic disks. These results enable a selective energy-efficient tuning of the vortex gyrotropic frequency in individual vortex-based oscillators with all-electrical operation.

We use a pure spin current originating from the spin Hall effect to generate a spin-orbit torque (SOT) strongly reducing the effective damping in an adjacent ferromagnet. Due to additional microwave excitation, large spin-wave amplitudes are achieved exceeding the threshold for 4-magnon scattering, thus resulting in additional spin-wave signals at discrete frequencies. Two or more modes are generated below and above the directly pumped mode with equal frequency spacing. It is shown how this nonlinear process can be controlled in magnonic waveguides by the applied dc current and the microwave pumping power. The sudden onset of the nonlinear effect after exceeding the thresholds can be interpreted as spiking phenomenom which makes the effect potentially interesting for neuromorphic computing applications. Moreover, we investigated this effect under microwave frequency and external field variation. The appearance of the additional modes was investigated in the time-domain revealing a time delay between the directly excited and the simultaneously generated nonlinear modes. Furthermore, spatially resolved measurements show different spatial decay lengths of the directly pumped mode and nonlinear modes.

In [3] it was shown that four seemingly different algorithms for computing low-rank approximate solutions $X_j$ to the solution $X$ of large-scale continuous-time algebraic Riccati equations (CAREs) $0 = \mathcal{R}(X) := A^HX+XA+C^HC-XBB^HX $ generate the same sequence $X_j$ when used with the same parameters. The Hermitian low-rank approximations $X_j$ are of the form $X_j = Z_jY_jZ_j^H,$ where $Z_j$ is a matrix with only few columns and $Y_j$ is a small square Hermitian matrix. Each $X_j$ generates a low-rank Riccati residual $\mathcal{R}(X_j)$ such that the norm of the residual can be evaluated easily allowing for an efficient termination criterion. Here a new family of methods to generate such low-rank approximate solutions $X_j$ of CAREs is proposed. Each member of this family of algorithms proposed here generates the same sequence of $X_j$ as the four previously known algorithms. The approach is based on a block rational Arnoldi decomposition and an associated block rational Krylov subspace spanned by $A^H$ and $C^H.$ Two specific versions of the general algorithm will be considered; one will turn out to be a rediscovery of the RADI algorithm, the other one allows for a slightly more efficient implementation compared to the RADI algorithm (in case the Sherman-Morrision-Woodbury formula and a direct solver is used to solve the linear systems that occur). Moreover, our approach allows for adding more than one shift at a time.

XDCP0044.0-2033 is the most massive galaxy cluster known at z>1.5 and its core shows a high density of galaxies which are experiencing mergers and hosting nuclear activity. We present a multi-wavelength study of a region located 157 kpc from the center of this galaxy cluster, for which we have photometric and spectroscopic multi-wavelength observations (high resolution HST images in F105W, F140W and F160W bands, NIR KMOS data in H and YJ bands and Chandra ACIS-S X-ray data). Our main goal is to investigate the environmental effects acting on the galaxies inhabiting this high density region. We find that the analyzed region hosts at least nine different sources, six of them confirmed to be cluster members within a narrow redshift range 1.5728

Magnons are elementary excitations in magnetic materials and undergo nonlinear multimode scattering processes at large input powers. In experiments and simulations, we show that the interaction between magnon modes of a confined magnetic vortex can be harnessed for pattern recognition. We study the magnetic response to signals comprising sine wave pulses with frequencies corresponding to radial mode excitations. Three-magnon scattering results in the excitation of different azimuthal modes, whose amplitudes depend strongly on the input sequences. We show that recognition rates above 95\% can be attained for four-symbol sequences using the scattered modes, with strong performance maintained with the presence of amplitude noise in the inputs.

1D spin-wave conduits are envisioned as nanoscale components of magnonics-based logic and computing schemes for future generation electronics. `A-la-carte methods of versatile control of the local magnetization dynamics in such nanochannels are highly desired for efficient steering of the spin waves in magnonic devices. Here, we present a study of localized dynamical modes in 1-$\mu$m-wide Permalloy conduits probed by microresonator ferromagnetic resonance technique. We clearly observe the lowest-energy edge mode in the microstrip after its edges were finely trimmed by means of focused Ne$^+$ ion irradiation. Furthermore, after milling the microstrip along its long axis by focused ion beams, creating consecutively $\sim$50 and $\sim$100 nm gaps, additional resonances emerge and are attributed to modes localized at the inner edges of the separated strips. To visualize the mode distribution, spatially resolved Brillouin light scattering microscopy was used showing an excellent agreement with the ferromagnetic resonance data and confirming the mode localization at the outer/inner edges of the strips depending on the magnitude of the applied magnetic field. Micromagnetic simulations confirm that the lowest-energy modes are localized within $\sim$15-nm-wide regions at the edges of the strips and their frequencies can be tuned in a wide range (up to 5 GHz) by changing the magnetostatic coupling (i.e. spatial separation) between the microstrips., Comment: 10 pages, 4 figures

Ionic and molecular selectivity is considered unique for the nanoscale and not realizable in microfluidics. This is due to the scale-matching problem -- a difficulty to match the dimensions of ions and electrostatic potential screening lengths with the micron-sized confinements. Here, we demonstrate a microscale realization of the ionic transport processes closely resembling those specific to ionic channels or in nanofluidic junctions, including selectivity, guidance through complex geometries and flow focusing. As a model system, we explore electrokinetic spherical Janus micromotors moving over charged surfaces with a complex spatial charge distribution and without any topographical wall. We discuss peculiarities of the long-range electrostatic interaction on the behavior of the system including interface crossing and reflection of positively charged particles from negatively charged interfaces. These results are crucial for understanding the electrokinetic transport of biochemical species under confinement, have the potential to increase the precision of lab-on-chip-based assays, as well as broadening use cases and control strategies of nano-/micromachinery., Comment: 15 pages, 6 figures

Ongoing efforts in quantum engineering have recently focused on integrating magnonics into hybrid quantum architectures for novel functionalities. While hybrid magnon-quantum spin systems have been demonstrated with nitrogen-vacancy (NV) centers in diamond, they have remained elusive on the technologically promising silicon carbide (SiC) platform mainly due to difficulties in finding a resonance overlap between the magnonic system and the spin centers. Here we circumvent this challenge by harnessing nonlinear magnon scattering processes in a magnetic vortex to access magnon modes that overlap in frequency with silicon-vacancy ($\textrm{V}_{\mathrm{Si}}$) spin transitions in SiC. Our results offer a route to develop hybrid systems that benefit from marrying the rich nonlinear dynamics of magnons with the advantageous properties of SiC for scalable quantum technologies., Comment: 17 pages, 4 figures

Easy axis antiferromagnets are robust against external magnetic fields of moderate strength. Spin reorientations in strong fields can provide an insight into more subtle properties of antiferromagnetic materials, which are often hidden by their high ground state symmetry. Here, we investigate theoretically effects of curvature in ring-shaped antiferromagnetic achiral anisotropic spin chains in strong magnetic fields. We identify the geometry-governed helimagnetic phase transition above the spin-flop field between vortex and onion states. The curvature-induced Dzyaloshinskii-Moriya interaction results in the spin-flop transition being of first- or second-order depending on the ring curvature. Spatial inhomogeneity of the N\'eel vector in the spin-flop phase generates weak ferromagnetic response in the plane perpendicular to the applied magnetic field. Our work contributes to the understanding of the physics of curvilinear antiferromagnets in magnetic fields and guides prospective experimental studies of geometrical effects relying on spin-chain-based nanomagnets., Comment: 11 pages, 6 figures

Surface curvature of magnetic systems can lead to many static and dynamic effects which are not present in flat systems of the same material. These emergent magnetochiral effects can lead to frequency nonreciprocity of spin waves, which has been shown to be a bulk effect of dipolar origin and is related to a curvature-induced symmetry breaking in the magnetic volume charges. So far, such effects have been investigated theoretically mostly for thin shells, where the spatial profiles of the spin waves can be assumed to be homogeneous along the thickness. Here, using a finite-element dynamic-matrix approach, we investigate the transition of the spin-wave spectrum from thin to thick curvilinear shells, at the example of magnetic nanotubes in the vortex state. With increasing thickness, we observe the appearance of higher-order radial modes which are strongly hybridized and resemble the perpendicular-standing-waves (PSSWs) in flat films. Along with an increasing dispersion asymmetry, we uncover the curvature-induced non-reciprocity of the mode profiles. This is explained in a very simple picture general for thick curvilinear shells, considering the inhomogeneity of the emergent geometric volume charges along the thickness of the shell. Such curvature-induced mode-profile asymmetry also leads to non-reciprocal hybridization which can facilitate unidirectional spin-wave propagation. With that, we also show how curvature allows for nonlinear three-wave splitting of a higher-order radial mode into secondary modes which can also propagate unidirectionally. We believe that our study provides a significant contribution to the understanding of the spin-wave dynamics in curvilinear magnetic systems, but also advertises these for novel magnonic applications.

An algorithm for constructing a $J$-orthogonal basis of the extended Krylov subspace $\mathcal{K}_{r,s}=\operatorname{range}\{u,Hu, H^2u,$ $ \ldots, $ $H^{2r-1}u, H^{-1}u, H^{-2}u, \ldots, H^{-2s}u\},$ where $H \in \mathbb{R}^{2n \times 2n}$ is a large (and sparse) Hamiltonian matrix is derived (for $r = s+1$ or $r=s$). Surprisingly, this allows for short recurrences involving at most five previously generated basis vectors. Projecting $H$ onto the subspace $\mathcal{K}_{r,s}$ yields a small Hamiltonian matrix. The resulting HEKS algorithm may be used in order to approximate $f(H)u$ where $f$ is a function which maps the Hamiltonian matrix $H$ to, e.g., a (skew-)Hamiltonian or symplectic matrix. Numerical experiments illustrate that approximating $f(H)u$ with the HEKS algorithm is competitive for some functions compared to the use of other (structure-preserving) Krylov subspace methods.

A digital platform is a networked infrastructure that allows people to engage in various kinds of interactions: social, economic, political, educational. Digital platforms can play a fundamental part of today's English language arts (ELA) classroom. Students read, write, view, connect, and interact with, on, and through a kaleidoscope of digital platforms. Google Docs, Turnitin, and Flip, among many others, have become part of the very infrastructure of classroom life (Garcia & Nichols, 2021). These same platforms are further used by educators, administrators, and third-party companies to instruct, assess, track, communicate with, respond to, and discipline students. This policy brief examines how digital platforms have been used in ELA Education and concludes with recommendations for teachers, administrators, and policymakers who implement digital platforms in the ELA classroom.