Artificial Spin Research Articles

Coupled magnetic nanostructures: Engineering lattice configurations

We present a systematic investigation of tunable magnetization dynamics of coupled magnetic nanostructures, arranged in one-dimensional arrays of horizontally and vertically coupled linear chains and in two-dimensional arrays of square artificial spin ice lattice. The spatial distribution of the demagnetization field is markedly sensitive to the lattice arrangement, leading to a significant modification of the collective behavior of static and dynamic properties of the arrays. Using ferromagnetic resonance spectroscopy, the engineering of demagnetizing factors with various lattice arrangements has been established quantitatively. The signature of distinct spin wave modes, spatially localized in the constituent nanomagnets, was observed and tuned by the lattice arrangements and applied field orientation. The experimental results are well complemented with micromagnetic simulations.

Observation of mode splitting in artificial spin ice: A comparative ferromagnetic resonance and Brillouin light scattering study

We report the dependence of the magnetization dynamics in a square artificial spin-ice lattice on the in-plane magnetic field angle. Using two complementary measurement techniques—broadband ferromagnetic resonance and micro-focused Brillouin light scattering spectroscopy—we systematically study the evolution of the lattice dynamics, for both a coherent radio frequency excitation and an incoherent thermal excitation of spin dynamics. We observe a splitting of modes facilitated by inter-element interactions that can be controlled by the external field angle and magnitude. Detailed time-dependent micromagnetic simulations reveal that the split modes are localized in different regions of the square network. This observation suggests that it is possible to disentangle modes with different spatial profiles by tuning the external field configuration.

Nanomagnonics with artificial spin ice

Traditional electronics employs charge currents to control and transmit information and therefore suffer from energy dissipation due to electron scattering. In the past decade, spin waves (magnons) have been discussed as a more efficient alternative. An important aspect of computing based on magnons is the resonant dynamics' reconfigurability. From this end, nanomagnonics with artificial spin ice offers a wealth of possibilities to control the dynamics. This perspective article reviews experimental and theoretical works on the resonant excitations in the GHz frequency range in artificial spin ice, promising for realizing functional magnonic devices. We discuss both the theoretical formulation and experimental methods to characterize the dynamics in the nanomagnetic arrays. The central part of this perspective is devoted to recent developments targeting full control of the dynamics based on the reprogrammability of the spin-ice microstate with the ultimate goal to realize novel functional devices for logics, computation, and storage concepts based on magnons.

Spin-Wave Dynamics in an Artificial Kagome Spin IceSupported by the State Grid Corporation of China via the Science and Technology Project: Research on Electromagnetic Measurement Technology Based on EIT and TMR (Grant No. JL71-18-007).

Artificial spin ice (ASI) structures have significant technological potential as reconfigurable metamaterials and magnetic storage media. We investigate the field/frequency-dependent magnetic dynamics of a kagome ASI made of 25-nm-thick permalloy nanomagnet elements, combining magnetoresistance (MR) and microscale ferromagnetic resonance (FMR) techniques. Our FMR spectra show a broadband absorption spectrum from 0.2 GHz to 3 GHz at H below 0.3 kOe, where the magnetic configuration of the kagome ASI is in the multidomain state, because the external magnetic field is below the obtained coercive field H c ∼ 0.3 kOe, based on both the low-field range MR loops and simulations, suggesting that the low-field magnetization dynamics of kagome ASI is dominated by a multimode resonance regime. However, the FMR spectra exhibit five distinctive resonance modes at the high-field quasi-uniform magnetization state. Furthermore, our micromagnetic simulations provide additional spatial resolution of these resonance modes, identifying the presence of two high-frequency primary modes, localized in the horizontal and vertical bars of the ASI, respectively; three other low-frequency modes are mutually exclusive and separately pinned at the corners of the kagome ASI by an edge-induced dipolar field. Our results suggest that an ASI structural design can be adopted as an efficient approach for the development of low-power filters and magnonic devices.

Tailoring magnetization reversal of a single-domain bar nanomagnet via its end geometry

Nanoscale single-domain bar magnets are building blocks for a variety of fundamental and applied mesoscopic magnetic systems, such as artificial spin ices, magnetic shape-morphing microbots, and magnetic majority logic gates. The magnetization reversal switching field of the bar nanomagnets is a crucial parameter that determines the physical properties and functionalities of their constituted artificial systems. Previous methods on tuning the magnetization reversal switching field of a bar nanomagnet usually relied on modifying its aspect ratio, such as its length, width, and/or thickness. Here, we show that the switching field of a bar nanomagnet saturates when extending its length beyond a certain value, preventing further tailoring of the magnetization reversal via aspect ratios. We showcase a highly tunable switching field of a bar nanomagnet by tailoring its end geometry without altering its size. This provides an easy method to control the magnetization reversal of a single-domain bar nanomagnet. It would enable new research and/or applications, such as designing artificial spin ices with additional tuning parameters, engineering magnetic microbots with more flexibility, and developing magnetic quantum-dot cellular automata systems for low power computing.

Spin contamination in MP2 and CC2, a surprising issue

When calculating the spin multiplicity at either the second-order Møller-Plesset (MP2) or the iterative second-order approximate coupled-cluster singles and doubles (CC2) levels of theory using the same strategy for the calculation of the expectation value as in regular CC theory together with the usual definitions of the MP2 and CC2 density matrices, artificial spin contamination occurs in closed-shell molecules. Non-intuitively, for open-shell systems, results at the MP2 or CC2 levels of theory based on this procedure even suggest stronger contamination at the correlated level than for the Hartree-Fock reference, although treatment of electron correlation should lower spin contamination. In this Communication, the reasons behind this inconsistency are investigated and a solution is proposed, which removes spin contamination for closed-shell molecules and leads to physically meaningful results for open-shell cases. Additionally, we show that CC2 significantly outperforms MP2 in describing systems with a strongly spin-contaminated reference with a performance similar to that of full coupled-cluster with singles and doubles substitutions (CCSD).

Prediction of massless Dirac fermions in a carbon nitride covalent network

Two-dimensional (2D) Dirac materials have received tremendous attention due to their potential applications in spintronics and energy applications. Motivated by recent experimental synthesis of a carbon nitride network with a C22N4 stoichiometry, the N-doped graphdiyne, or pyrazinoquinoxaline-based graphdiyne (PQ-GDY), we studied the electronic and topological properties of the PQ-GDY monolayer using first-principles calculations. Surprisingly, we found that the PQ-GDY monolayer indeed is a 2D Dirac semimetal also known as 2D topologically nontrivial semimetal. The linear band dispersions around the Dirac point are mainly composed of the bonding and antibonding pz-orbitals of C and N atoms. In combination with parity analysis, we found that the mechanism of band inversion in PQ-GDY is similar to the strain-induced Dirac cone in GDY. The underlying physical property of strained GDY is equivalent to expanding the single center benzene into the three benzene rings observed in PQ-GDY. Finally, the formed Dirac cone located on the Y−Γ high-symmetry line is very robust, and a bandgap is opened only after including a large artificial spin–orbit coupling, which transforms it to a 2D topological insulator.

Ice, glass, and solid phases in artificial spin systems with quenched disorder

We present a numerical study on a disordered artificial spin-ice system, which interpolates between the long-range ordered square ice and the fully degenerate shakti ice. Starting from the square-ice geometry, disorder is implemented by adding vertical/horizontal magnetic islands to the center of some randomly chosen square plaquettes of the array at different densities. When no island is added, we have ordered square ice. When all square plaquettes have been modified, we obtain shakti ice, which is disordered yet in a topological phase corresponding to the Rys F-model. In between, geometrical frustration due to these additional center spins disrupts the long-range Ising order of square ice, giving rise to a spin-glass regime at low temperatures. The artificial spin system proposed in our work provides an experimental platform to study the interplay between quenched disorder and geometrical frustration.

Tunable Stochasticity in an Artificial Spin Network.

Metamaterials present the possibility of artificially generating advanced functionalities through engineering of their internal structure. Artificial spin networks, in which a large number of nanoscale magnetic elements are coupled together, are promising metamaterial candidates that enable the control of collective magnetic behavior through tuning of the local interaction between elements. In this work, the motion of magnetic domain-walls in an artificial spin network leads to a tunable stochastic response of the metamaterial, which can be tailored through an external magnetic field and local lattice modifications. This type of tunable stochastic network produces a controllable random response exploiting intrinsic stochasticity within magnetic domain-wall motion at the nanoscale. An iconic demonstration used to illustrate the control of randomness is the Galton board. In this system, multiple balls fall into an array of pegs to generate a bell-shaped curve that can be modified via the array spacing or the tilt of the board. Ananoscale recreation of this experiment using an artificial spin network is employed to demonstrate tunable stochasticity. This type of tunable stochastic network opens new paths toward post-Von Neumann computing architectures such as Bayesian sensing or random neural networks, in which stochasticity is harnessed to efficiently perform complex computational tasks.

Artificial spin ice: Progress and future directions of the field

The field of artificial spin ice today studies novel, complex geometries that reveal new and unusual phenomena.

Switchable X-Ray Orbital Angular Momentum from an Artificial Spin Ice.

Artificial spin ices (ASI) have been widely investigated as magnetic metamaterials with exotic properties governed by their geometries. In parallel, interest in x-ray photon orbital angular momentum (OAM) has been rapidly growing. Here we show that a square ASI with a patterned topological defect, a double edge dislocation, imparts OAM to scattered x rays. Unlike single dislocations, a double dislocation does not introduce magnetic frustration, and the ASI equilibrates to its antiferromagnetic (AFM) ground state. The topological charge of the defect differs with respect to the structural and magnetic order; thus, x-ray diffraction from the ASI produces photons with even and odd OAM quantum numbers at the structural and AFM Bragg conditions, respectively. The magnetic transitions of the ASI allow the AFM OAM beams to be switched on and off by modest variations of temperature and applied magnetic field. These results demonstrate ASIs can serve as metasurfaces for reconfigurable x-ray optics that could enable selective probes of electronic and magnetic properties.

Artificial spin ice: Paths forward

Artificial spin ice systems are lithographically prepared arrays of interacting nanoscale magnetic moments with collective behavior resulting from the chosen array geometry. These many-body systems are unusual in that their simple constituent elements can be configured to design their interactions with exquisite control. They can then be probed experimentally over a remarkably large range of time scales and length scales, including imaging of the individual moments. The study of artificial spin ice has broadened well beyond the original focus on systems with connection to spin ice and ice models, and now the term is used in reference to many other structures that exhibit a much wider range of physical phenomena. In this Perspective, we review progress in the field of artificial spin ice since its inception more than a decade ago. We then discuss prospects for future directions—continuing the exploration of nanomagnetism, statistical spin models, and the potential for technological devices.

Spin-Wave Dynamics and Symmetry Breaking in an Artificial Spin Ice.

Artificial spin ices are periodic arrangements of interacting nanomagnets which allow investigating emergent phenomena in the presence of geometric frustration. Recently, it has been shown that artificial spin ices can be used as building blocks for creating functional materials, such as magnonic crystals. We investigate the magnetization dynamics in a system exhibiting anisotropic magnetostatic interactions owing to locally broken structural inversion symmetry. We find a rich spin-wave spectrum and investigate its evolution in an external magnetic field. We determine the evolution of individual modes, from building blocks up to larger arrays, highlighting the role of symmetry breaking in defining the mode profiles. Moreover, we demonstrate that the mode spectra exhibit signatures of long-range interactions in the system. These results contribute to the understanding of magnetization dynamics in spin ices beyond the kagome and square ice geometries and are relevant for the realization of reconfigurable magnonic crystals based on spin ices.

Magnetic Normal Mode Calculations in Big Systems: A Highly Scalable Dynamical Matrix Approach Applied to a Fibonacci-Distorted Artificial Spin Ice

We present a new formulation of the dynamical matrix method for computing the magnetic normal modes of a large system, resulting in a highly scalable approach. The motion equation, which takes into account external field, dipolar and ferromagnetic exchange interactions, is rewritten in the form of a generalized eigenvalue problem without any additional approximation. For its numerical implementation several solvers have been explored, along with preconditioning methods. This reformulation was conceived to extend the study of magnetization dynamics to a broader class of finer-mesh systems, such as three-dimensional, irregular or defective structures, which in recent times raised the interest among researchers. To test its effectiveness, we applied the method to investigate the magnetization dynamics of a hexagonal artificial spin-ice as a function of a geometric distortion parameter following the Fibonacci sequence. We found several important features characterizing the low frequency spin modes as the geometric distortion is gradually increased.

Field-Induced Magnetic Monopole Plasma in Artificial Spin Ice

Artificial spin ices (ASIs) are interacting arrays of lithographically-defined nanomagnets in which novel frustrated magnetic phases can be intentionally designed. A key emergent description of fundamental excitations in ASIs is that of magnetic monopoles -- mobile quasiparticles that carry an effective magnetic charge. Here we demonstrate that the archetypal square ASI lattice can host, in specific regions of its magnetic phase diagram, high-density plasma-like regimes of mobile magnetic monopoles. By passively "listening" to spontaneous monopole noise in thermal equilibrium, we reveal their intrinsic dynamics and show that monopole kinetics are minimally correlated (that is, most diffusive) in the plasma phase. These results open the door to on-demand monopole regimes having field-tunable densities and dynamic properties, thereby providing a new paradigm for probing the physics of effective magnetic charges in synthetic matter.

Spin wave spectral probing of degenerate microstates in building-block of square artificial spin ice

We have investigated the spin wave modes of dipolar coupled, highly shape anisotropic magnetic nanoislands forming square artificial spin ice system by performing micromagnetic simulations using MuMax3 in combination with Matlab coding. Here, artificial spin ice is considered to be formed by the four identical square ring-type structure of elliptical shaped nanoislands of permalloy. Our results demonstrate a direct relation between the spin wave modes generated and the micro-states formed in the system. Thus, we show that single ring type structure may alone be adequately used to understand the spin wave modes of square artificial spin ice.

Chiral switching and dynamic barrier reductions in artificial square ice

Collective dynamics in lithographically-defined artificial spin ices offer profound insights into emergent correlations and phase transitions of geometrically-frustrated Ising spin systems. Their temporal and spatial evolution are often simulated using kinetic Monte Carlo (kMC) simulations, which rely on the precise knowledge of the switching barriers to obtain predictive results in agreement with experimental observations. In many cases, however, the barriers are derived from simplified assumptions only, and do not take into account the full physical picture of nanomagnetic switching. Here we describe how the immediate magnetic square- or kagome-ice environment of a nanomagnet reversing via quasi-coherent rotation can induce clockwise and counter-clockwise switching channels with different barrier energies. This energy splitting for chiral reversal channels can be sizeable and, as string-method micromagnetic simulations show, is relevant for artificial spin ice systems made of both exchange- as well as magnetostatically-dominated units. Due to the barrier splitting and further reductions due to non-uniform reversal, transition rates can be exponentially enhanced by several orders of magnitude compared to mean-field predictions, especially in the limit of rare switching events where thermal excitation is less likely. This leads to significantly faster relaxation time scales and modified spatial correlations. Our findings are thus of integral importance to achieve realistic kMC simulations of emergent correlations in artificial spin systems, magnonic crystals, or the evolution of nanomagnetic logic circuits.

Emergent Spin Dynamics Enabled by Lattice Interactions in a Bicomponent Artificial Spin Ice.

Artificial spin ice (ASI) networks are arrays of nanoscaled magnets that can serve both as models for frustration in atomic spin ice as well as for exploring new spin-wave-based strategies to transmit, process, and store information. Here, we exploit the intricate interplay of the magnetization dynamics of two dissimilar ferromagnetic metals arranged on complementary lattice sites in a square ASI to modulate the spin-wave properties effectively. We show that the interaction between the two sublattices results in unique spectra attributed to each sublattice, and we observe inter- and intralattice dynamics facilitated by the distinct magnetization properties of the two materials. The dynamic properties are systematically studied by angular-dependent broadband ferromagnetic resonance and confirmed by micromagnetic simulations. We show that combining materials with dissimilar magnetic properties enables the realization of a wide range of two-dimensional structures, potentially opening the door to new concepts in nanomagnonics.

Magnetic charge's relaxation propelled electricity in two-dimensional magnetic honeycomb lattice

SummaryEmerging new concepts, such as magnetic charge dynamics in two-dimensional magnetic material, can provide novel mechanism for spin-based electrical transport at macroscopic length. In artificial spin ice of single domain elements, magnetic charge's relaxation can create an efficient electrical pathway for conduction by generating fluctuations in local magnetic field that couple with conduction electron spins. In a first demonstration, we show that the electrical conductivity is propelled by more than an order of magnitude at room temperature due to magnetic charge defects sub-picosecond relaxation in artificial magnetic honeycomb lattice. The direct evidence to the proposed electrical conduction mechanism in two-dimensional frustrated magnet points to the untapped potential for spintronic applications in this system.

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.