Arrays Of Nanomagnets Research Articles

Brillouin light scattering spectral fingerprinting of magnetic microstates in artificial spin ice

The family of nanomagnetic arrays termed artificial spin ice (ASI) possess a vast range of metastable microstates. These states exhibit both exotic fundamental physics and more recently applied functionality, garnering attention as reconfigurable magnonic circuits and neuromorphic computing platforms. However, open questions remain on the role of microstate imperfections or angular disorder – particularly in the GHz response of the system. We report a study on the GHz dynamics of a series of five carefully prepared microstates in the same ASI sample, with both coexistence of vortex and uniformly magnetized macrospins, and disorder in the orientation of the macrospins at different vertices. We observe microstate-specific mode frequency shifting, mode creation and mode crossing. This versatility of characteristic spin-wave (SW) peaks for specific magnetic microstates in ASI enables identification of microstate configurations via SW spectral characterization. The wide reconfigurability of microstate-specific SW dynamics also opens avenues for developing rich magnonic devices operating in the GHz frequency regime and advances the understanding of ASI physics.

Ultrastrong magnon-magnon coupling and chiral spin-texture control in a dipolar 3D multilayered artificial spin-vortex ice

Strongly-interacting nanomagnetic arrays are ideal systems for exploring reconfigurable magnonics. They provide huge microstate spaces and integrated solutions for storage and neuromorphic computing alongside GHz functionality. These systems may be broadly assessed by their range of reliably accessible states and the strength of magnon coupling phenomena and nonlinearities. Increasingly, nanomagnetic systems are expanding into three-dimensional architectures. This has enhanced the range of available magnetic microstates and functional behaviours, but engineering control over 3D states and dynamics remains challenging. Here, we introduce a 3D magnonic metamaterial composed from multilayered artificial spin ice nanoarrays. Comprising two magnetic layers separated by a non-magnetic spacer, each nanoisland may assume four macrospin or vortex states per magnetic layer. This creates a system with a rich 16N microstate space and intense static and dynamic dipolar magnetic coupling. The system exhibits a broad range of emergent phenomena driven by the strong inter-layer dipolar interaction, including ultrastrong magnon-magnon coupling with normalised coupling rates of Δfν=0.57\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\frac{\\Delta f}{\ u }=0.57$$\\end{document}, GHz mode shifts in zero applied field and chirality-control of magnetic vortex microstates with corresponding magnonic spectra.

Toroidic phase transitions in a direct-kagome artificial spin ice.

Ferrotoroidicity-the fourth form of primary ferroic order-breaks both space and time-inversion symmetry. So far, direct observation of ferrotoroidicity in natural materials remains elusive, which impedes the exploration of ferrotoroidic phase transitions. Here we overcome the limitations of natural materials using an artificial nanomagnet system that can be characterized at the constituent level and at different effective temperatures. We design a nanomagnet array as to realize a direct-kagome spin ice. This artificial spin ice exhibits robust toroidal moments and a quasi-degenerate ground state with two distinct low-temperature toroidal phases: ferrotoroidicity and paratoroidicity. Using magnetic force microscopy and Monte Carlo simulation, we demonstrate a phase transition between ferrotoroidicity and paratoroidicity, along with a cross-over to a non-toroidal paramagnetic phase. Our quasi-degenerate artificial spin ice in a direct-kagome structure provides a model system for the investigation of magnetic states and phase transitions that are inaccessible in natural materials.

Magnetoresistive Evidence of Degeneracy in Nanomagnets Obtained by Electrodeposition Technique

Inspired in pyrochlore materials presenting residual entropy and featuring collective excitation behaving like emergent monopoles, geometrically frustrated arrays of nanomagnets, denominated artificial spin ices (ASIs), were proposed as an interesting platform to investigate such excitation at room temperature. However, in such artificial systems, emergent magnetic monopoles lack the same freedom present their natural counterpart, once energetic strings connecting opposite magnetic charges arise. In this work, we aim to experimentally investigate the proposed degeneracy obtained in connected square arrays of ASIs, a characteristic that allows a reduction in the string connecting monopole–antimonopole pairs in regular non-connected ASIs and could represent an important development for technological applications of connected nanomagnets. As in general those systems are developed by nanofabrication processes involving expensive and time-consuming physical vapour deposition techniques, we also present a new nanofabrication route using an electrodeposition technique for permalloy growth in different lattice geometries as an alternative for fast and low-cost ASI system production.

Metal Filled Nanostructured Silicon a Platform to Interlink Magnetism and Optics

This presentation deals with the utilization of nanostructured silicon (porous silicon and silicon nanotubes) for deposition of various metals, especially magnetic ones, within the pores/tubes. The novel magnetic properties of the semiconducting/magnetic composites which arise due to the nanoscopic size of the used materials are investigated with respect to optical and magnetic on-chip applications.Porous silicon is fabricated by anodization of a silicon wafer in an aqueous hydrofluoric solution. The morphology of the porous structures depends on the doping density of the used wafer and on the applied current density as well as the electrolyte concentration. The ferromagnetic metals are deposited within the porous structures electrochemically in using the corresponding metal salt solution as electrolyte. A modification of the electrochemical parameters results in adjustable size and shape of the deposits. Ni and Co, both metals are electrodeposited within the nanostructured silicon in using aqueous NiSO4 and CoSO4 solutions by applying a current density between 10 and 20 mA/cm2 and a frequency between 0.05 and 0.2 Hz.One of our key topics is luminescent porous silicon loaded with magnetic metals to enhance the photoluminescence, with the final aim to influence/control the optical properties by a magnetic field. The metal deposits affect the optical properties but also give rise to specific magnetic behavior (1). Due to the metal filling of the porous silicon the photoluminescence is blue-shifted and furthermore an increase of the intensity is observed. The influence of the magnetic metal filling on the optical properties (photoluminescence, decay time) is discussed, and the magnetic characterization of the nanocomposites is presented.A further issue, the deposition of hard and soft magnetic materials within the nanostructures, aiming in the fabrication of arrays of permanent nanomagnets is presented (2). Here the investigation of the magnetic behavior of bi-metal nanostructures within nanostructured silicon with the aim to exploit the magnetic properties of both metals and gain control of the exchange coupling between the two metals especially with respect to their volume ratio is discussed. Furthermore, a variation of the structure size and the proximity of the metal deposits modify the exchange coupling and thus the energy product. Nanocomposite systems with an energy product as high as possible should be achieved to give rise to on-chip applications using permanent nanomagnets, especially arranged in arrays.(1) P. Granitzer, et al, Frontiers in Physics, 8 (2020) 121(2) K. Rumpf, et.al, Phys. Stat. Sol. A, 217 (2020) 1901040

Formation of binary magnon polaron in a two-dimensional artificial magneto-elastic crystal

We observed strong tripartite magnon-phonon-magnon coupling in a two-dimensional periodic array of magnetostrictive nanomagnets deposited on a piezoelectric substrate, forming a 2D magnetoelastic “crystal”; the coupling occurred between two Kittel-type spin wave (magnon) modes and a (non-Kittel) magnetoelastic spin wave mode caused by a surface acoustic wave (SAW) (phonons). The strongest coupling occurred when the frequencies and wavevectors of the three modes matched, leading to perfect phase matching. We achieved this condition by carefully engineering the frequency of the SAW, the nanomagnet dimensions and the bias magnetic field that determined the frequencies of the two Kittel-type modes. The strong coupling (cooperativity factor exceeding unity) led to the formation of a new quasi-particle, called a binary magnon-polaron, accompanied by nearly complete (~100%) transfer of energy from the magnetoelastic mode to the two Kittel-type modes. This coupling phenomenon exhibited significant anisotropy since the array did not have rotational symmetry in space. The experimental observations were in good agreement with the theoretical simulations.

Acousto‐Plasmo‐Magnonics: Coupling Spin Waves with Hybridized Phonon‐Plasmon Waves in a 2D Artificial Magnonic Crystal Deposited on a Plasmonic Material

AbstractCoupling between spin waves (SWs) and other waves in nanostructured media has emerged as an important topic of research because of the rich physics and the potential for disruptive technologies. Herein, a new phenomenon is reported in this family involving coupling between SWs and hybridized phonon‐plasmon waves in a 2D periodic array of magnetostrictive nanomagnets deposited on a silicon substrate with an intervening thin film of aluminium that acts as a source of surface plasmons. Hybridized phonon‐plasmon waves naturally form in this composite material when exposed to ultrashort laser pulses and they non‐linearly couple with SWs to produce a new breed of waves – acousto‐plasmo‐spin waves that can exhibit a “frequency comb” spanning more than one octave. This phenomenon, that we call acousto‐plasmo‐magnonics resulting from tripartite coupling of magnons, phonons and plasmons, is studied with time‐resolved magneto‐optical‐Kerr‐effect microscopy. The findings also reveal the presence of parametric amplification in this system; energy is transferred from the hybridized phonon‐plasmon modes to the acousto‐plasmo‐spin wave modes to amplify the latter. This opens a path to design novel active metamaterials with tailored and enhanced response. It may enable high‐efficiency magneto‐mechanical‐plasmonic frequency mixing in the GHz−THz frequency regime and provide a unique avenue to study non‐linear coupling, parametric amplification, and frequency comb physics.

Field angle dependent resonant dynamics of artificial spin ice lattices

Artificial spin ice structures which are networks of coupled nanomagnets arranged on different lattices that exhibit a number of interesting phenomena are promising for future information processing. We report reconfigurable microwave properties in artificial spin ice structures with three different lattice symmetries namely square, kagome, and triangle. Magnetization dynamics are systematically investigated using field angle dependent ferromagnetic resonance spectroscopy. Two distinct ferromagnetic resonance modes are observed in square spin ice structures in contrast with the three well-separated modes in kagome and triangular spin ice structures that are spatially localized at the center of the individual nanomagnets. A simple rotation of the sample placed in magnetic field results in the merging and splitting of the modes due to the different orientations of the nanomagnets with respect to the applied magnetic field. Magnetostatic interactions are found to shift the mode positions after comparing the microwave responses from the array of nanomagnets with control simulations with isolated nanomagnets. Moreover, the extent of the mode splitting has been studied by varying the thickness of the lattice structures. The results have potential implications for microwave filter-type applications which can be operated for a wide range of frequencies with ease of tunability.

Topological kinetic crossover in a nanomagnet array

Ergodic kinetics, which are critical to equilibrium thermodynamics, can be constrained by a system's topology. We studied a model nanomagnetic array in which such constraints visibly affect the behavior of the magnetic moments. In this system, magnetic excitations connect into thermally active one-dimensional strings whose motion can be imaged in real time. At high temperatures, our data showed the merging, breaking, and reconnecting of strings, resulting in the system transitioning between topologically distinct configurations. Below a crossover temperature, the string motion is dominated by simple changes in length and shape. In this low-temperature regime, the system is energetically stable because of its inability to explore all possible topological configurations. This kinetic crossover suggests a generalizable conception of topologically broken ergodicity and limited equilibration.

Distinguishing artificial spin ice states using magnetoresistance effect for neuromorphic computing

Artificial spin ice (ASI) consisting patterned array of nano-magnets with frustrated dipolar interactions offers an excellent platform to study frustrated physics using direct imaging methods. Moreover, ASI often hosts a large number of nearly degenerated and non-volatile spin states that can be used for multi-bit data storage and neuromorphic computing. The realization of the device potential of ASI, however, critically relies on the capability of transport characterization of ASI, which has not been demonstrated so far. Using a tri-axial ASI system as the model system, we demonstrate that transport measurements can be used to distinguish the different spin states of the ASI system. Specifically, by fabricating a tri-layer structure consisting a permalloy base layer, a Cu spacer layer and the tri-axial ASI layer, we clearly resolve different spin states in the tri-axial ASI system using lateral transport measurements. We have further demonstrated that the tri-axial ASI system has all necessary required properties for reservoir computing, including rich spin configurations to store input signals, nonlinear response to input signals, and fading memory effect. The successful transport characterization of ASI opens up the prospect for novel device applications of ASI in multi-bit data storage and neuromorphic computing.

Preserving Metamagnetism in Self-Assembled FeRh Nanomagnets.

Preparing and exploiting phase-change materials in the nanoscale form is an ongoing challenge for advanced material research. A common lasting obstacle is preserving the desired functionality present in the bulk form. Here, we present self-assembly routes of metamagnetic FeRh nanoislands with tunable sizes and shapes. While the phase transition between antiferromagnetic and ferromagnetic orders is largely suppressed in nanoislands formed on oxide substrates via thermodynamic nucleation, we find that nanomagnet arrays formed through solid-state dewetting keep their metamagnetic character. This behavior is strongly dependent on the resulting crystal faceting of the nanoislands, which is characteristic of each assembly route. Comparing the calculated surface energies for each magnetic phase of the nanoislands reveals that metamagnetism can be suppressed or allowed by specific geometrical configurations of the facets. Furthermore, we find that spatial confinement leads to very pronounced supercooling and the absence of phase separation in the nanoislands. Finally, the supported nanomagnets are chemically etched away from the substrates to inspect the phase transition properties of self-standing nanoparticles. We demonstrate that solid-state dewetting is a feasible and scalable way to obtain supported and free-standing FeRh nanomagnets with preserved metamagnetism.

Radiation-free and non-Hermitian topology inertial defect states of on-chip magnons

Radiative damping is a strong dissipation source for the quantum emitters hybridized with propagating photons, electrons, or phonons, which is not easily avoidable for on-chip magnonic emitters as well that can radiate via the surface acoustic waves of the substrate. Here we demonstrate in an array of on-chip nanomagnets coupled in a long range via exchanging the surface acoustic waves that a point defect in the array, which can be introduced by the local magnon frequency shift by a local biased magnetic field or the absence of a magnetic wire, strongly localizes the magnons, in contrast to the well spreading Bloch-like collective magnon modes in such an array setting. The radiation of the magnon defect states is exponentially suppressed by the distance of the defect to the array edges. Moreover, this defect state is strikingly inertial to the non-Hermitian topology that localizes all the extended states at one boundary. Such configuration robust magnon defect states towards radiation-free limit may be suitable for high-fidelity magnon quantum information storage in the future on-chip magnonic devices.

Generation of Microwaves With Tuneable Frequencies in Ultracompact “Magnon Microwave Antenna” via Phonon-Magnon-Photon Coupling

Here, we report a “magnon microwave antenna” (MMA) for the generation of microwaves with tuneable frequencies, based on modulation of confined spin waves (SWs) in the patterned array of magnetostrictive nanomagnets/piezoelectric heterostructures caused by the surface acoustic waves (SAWs). A SAW launched on a piezoelectric substrate produces a periodic strain within the nanomagnets patterned on it, which, in turn, stimulates magnetization precession resulting in different magneto-dynamical resonance modes in the array of nanomagnets with a rich SW texture. The generated SWs (magnons) further interact with the EM radiation (photons) at the SAW frequency. The phonon-magnon-photon coupling in the patterned array of nanowires (NWs) generates a 0.56 GHz microwave frequency with a 13.9 MHz linewidth and a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${Q}$ </tex-math></inline-formula> -factor of 40, while that in a matrix of nanodots (having same overall area) provides tuneable frequencies leading up to 30 GHz with a linewidth of 59.1 MHz and an enhanced <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${Q}$ </tex-math></inline-formula> -factor of 439; having nonvolatile spin textures in both the cases. The generated nonvolatile spin textures of the NWs/nanodots can also be useful in energy-efficient logic and low-power computing applications.

Crystal size dependence of dipolar ferromagnetic order between Mn6 molecular nanomagnets

We study how crystal size influences magnetic ordering in arrays of molecular nanomagnets coupled by dipolar interactions. Compressed fluid techniques have been applied to synthesize crystals of ${\mathrm{Mn}}_{6}$ molecules (spin $S=12$) with sizes ranging from $28\phantom{\rule{0.16em}{0ex}}\ensuremath{\mu}\mathrm{m}$ down to 220 nm. The onset of ferromagnetic order and the spin thermalization rates have been studied by means of ac susceptibility measurements. We find that the ordered phase remains ferromagnetic, as in the bulk, but the critical temperature ${T}_{\mathrm{c}}$ decreases with crystal size. Simple magnetostatic energy calculations, supported by Monte Carlo simulations, account for the observed drop in ${T}_{\mathrm{c}}$ in terms of the minimum attainable energy for finite-sized magnetic domains limited by the crystal boundaries. Frequency-dependent susceptibility measurements give access to the spin dynamics. Although magnetic relaxation remains dominated by individual spin flips, the onset of magnetic order leads to very long spin thermalization time scales. The results show that size influences the magnetism of dipolar systems with as many as ${10}^{11}$ spins and are relevant for the interpretation of quantum simulations performed on finite lattices.

Straintronic Nanomagnetic Logic Using Self-Biased Dipole Coupled Elliptical Nanomagnets

This work delineates the thermally stable, self-biased straintronic nanomagnetic logic (NML) by leveraging the dipole coupling between an array of nanomagnets using only two electrodes that discard the intricate voltage mechanism of multi-electrode systems. For efficient NML operation, the self-biased elliptical nanomagnets with fixed aspect ratio can be designed over a particular thickness range, limited by the thermal stability and shape anisotropy energy. Micromagnetic simulations show that the 180° magnetization switching of the nanomagnet is assisted by an external applied voltage and the dipole coupling, allowing controlled NML operations. The relationship between the critical switching frequency and critical strain is used to select the appropriate nanomagnets for different logic operations.

Time-dependent exchange creates the time-frustrated state of matter

Magnetic systems governed by exchange interactions between magnetic moments harbor frustration that leads to ground state degeneracy and results in the new topological state often referred to as a frustrated state of matter (FSM). The frustration in the commonly discussed magnetic systems has a spatial origin. Here we demonstrate that an array of nanomagnets coupled by the real retarded exchange interactions develops a new state of matter, time frustrated matter (TFM). In a spin system with the time-dependent retarded exchange interaction, a single spin-flip influences other spins not instantly but after some delay. This implies that the sign of the exchange interaction changes, leading to either ferro- or antiferromagnetic interaction, depends on time. As a result, the system’s temporal evolution is essentially non-Markovian. The emerging competition between different magnetic orders leads to a new kind of time-core frustration. To establish this paradigmatic shift, we focus on the exemplary system, a granular multiferroic, where the exchange transferring medium has a pronounced frequency dispersion and hence develops the TFM.

Focused surface acoustic wave induced nano-oscillator based reservoir computing

We demonstrate using micromagnetic simulations that a nanomagnet array excited by surface acoustic waves (SAWs) can work as a reservoir. An input nanomagnet is excited with focused SAW and coupled to several nanomagnets, seven of which serve as output nanomagnets. To evaluate memory effect and computing capability, we study the short-term memory (STM) and parity check (PC) capacities, respectively. The SAW (4 GHz carrier frequency) amplitude is modulated to provide a sequence of sine and square waves of 100 MHz frequency. The responses of the selected output nanomagnets are processed by reading the envelope of their magnetization states, which is used to train the output weights using the regression method. For classification, a random sequence of 100 square and sine wave samples is used, of which 80% are used for training, and the rest are used for testing. We achieve 100% training and 100% testing accuracy. The average STM and PC are calculated to be ∼4.69 and ∼5.39 bits, respectively, which is indicative of the proposed acoustically driven nanomagnet oscillator array being well suited for physical reservoir computing applications. The energy dissipation is ∼2.5 times lower than a CMOS-based echo-state network. Furthermore, the reservoir is able to accurately predict Mackey-Glass time series up to several time steps ahead. Finally, the ability to use high frequency SAW makes the nanomagnet reservoir scalable to small dimensions, and the ability to modulate the envelope at a lower frequency (100 MHz) adds flexibility to encode different signals beyond the sine/square waves classification and Mackey-Glass predication tasks demonstrated here.

Defect-induced monopole injection and manipulation in artificial spin ice

Lithographically defined arrays of nanomagnets are well placed for application in areas such as probabilistic computing or reconfigurable magnonics due to their emergent collective dynamics and writable magnetic order. Among them are artificial spin ice (ASI), which are arrays of binary in-plane macrospins exhibiting geometric frustration at the vertex interfaces. Macrospin flips in the arrays create topologically protected magnetic charges, or emergent monopoles, which are bound to an antimonopole to conserve charge. In the absence of controllable pinning, it is difficult to manipulate individual monopoles in the array without also influencing other monopole excitations or the counter-monopole charge. Here, we tailor the local magnetic order of a classic ASI lattice by introducing a ferromagnetic defect with shape anisotropy into the array. This creates monopole injection sites at nucleation fields below the critical lattice switching field. Once formed, the high energy monopoles are fixed to the defect site and may controllably propagate through the lattice under stimulation. Defect programing of bound monopoles within the array allows fine control of the pathways of inverted macrospins. Such control is a necessary prerequisite for the realization of functional devices, e. g. reconfigurable waveguide in nanomagnonic applications.

Entropy and order work together in an artificial spin ice

The very factor that propels most of the universe toward disorder pushes an array of nanomagnets into a visibly ordered state.

Entropy-driven order in an array of nanomagnets

Long-range ordering is typically associated with a decrease in entropy. Yet, it can also be driven by increasing entropy in certain special cases. We demonstrate that artificial spin ice arrays of single-domain nanomagnets can be designed to produce entropy-driven order. We focus on the tetris artificial spin ice structure, a highly frustrated array geometry with a zero-point Pauli entropy, which is formed by selectively creating regular vacancies on the canonical square ice lattice. We probe thermally active tetris artificial spin ice both experimentally and through simulations, measuring the magnetic moments of the individual nanomagnets. We find two-dimensional magnetic ordering in one subset of these moments, which we demonstrate to be induced by disorder (i.e., increased entropy) in another subset of the moments. In contrast with other entropy-driven systems, the discrete degrees of freedom in tetris artificial spin ice are binary and are both designable and directly observable at the microscale, and the entropy of the system is precisely calculable in simulations. This example, in which the system's interactions and ground state entropy are well-defined, expands the experimental landscape for the study of entropy-driven ordering.