Emergent dynamic chirality in a thermally driven artificial spin ratchet

Clocked dynamics in artificial spin ice

Artificial spin ice (ASI) are nanomagnetic metamaterials with a wide range of emergent properties. Through local interactions, the magnetization of the nanomagnets self-organize into extended magnetic domains. However, controlling when, where and how domains change has proven difficult, yet is crucial for technological applications. Here, we introduce astroid clocking, which offers significant control of ASI dynamics in both time and space. Astroid clocking unlocks a discrete, step-wise and gradual dynamical process within the metamaterial. Notably, our method employs global fields to selectively manipulate local features within the ASI. Sequences of these clock fields drive domain dynamics. We demonstrate, experimentally and in simulations, how astroid clocking of pinwheel ASI enables ferromagnetic domains to be gradually grown or reversed at will. Richer dynamics arise when the clock protocol allows both growth and reversal to occur simultaneously. With astroid clocking, complex spatio-temporal behaviors of magnetic metamaterials become easily controllable with high fidelity.

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.

All-electrical reading and writing of spin chirality

Spintronics promises potential data encoding and computing technologies. Spin chirality plays a very important role in the properties of many topological and noncollinear magnetic materials. Here, we propose the all-electrical detection and manipulation of spin chirality in insulating chiral antiferromagnets. We demonstrate that the spin chirality in insulating epitaxial films of TbMnO₃ can be read electrically via the spin Seebeck effect and can be switched by electric fields via the multiferroic coupling of the spin chirality to the ferroelectric polarization. Moreover, multivalued states of the spin chirality can be realized by the combined application of electric and magnetic fields. Our results are a path toward next-generation, low-energy consumption memory and logic devices that rely on spin chirality.

Collective Ferromagnetism of Artificial Square Spin Ice

We study the temperature and magnetic field dependence of the total magnetic moment of large-area permalloy artificial square spin ice arrays. The temperature dependence and hysteresis behavior are consistent with the coherent magnetization reversal expected in the Stoner-Wohlfarth model, with clear deviations due to interisland interactions at small lattice spacing. Through micromagnetic simulations, we explore this behavior and demonstrate that the deviations result from increasingly complex magnetization reversal at small lattice spacing, induced by interisland interactions, and depending critically on details of the island shapes. These results establish new means to tune the physical properties of artificial spin ice structures and other interacting nanomagnet systems, such as patterned magnetic media.

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.

Artificial spin ice systems offer a promising platform to study the motion of emergent magnetic monopoles, but controlled nucleation of monopoles is challenging. Here the authors demonstrate controlled injection and propagation of emergent monopoles in an artificial spin ice utilizing ferromagnetic defects.

Complex free-space magnetic field textures induced by three-dimensional magnetic nanostructures

The design of complex, competing effects in magnetic systems-be it via the introduction of nonlinear interactions^1-4, or the patterning of three-dimensional geometries^5,6-is an emerging route to achieve new functionalities. In particular, through the design of three-dimensional geometries and curvature, intrastructure properties such as anisotropy and chirality, both geometry-induced and intrinsic, can be directly controlled, leading to a host of new physics and functionalities, such as three-dimensional chiral spin states⁷, ultrafast chiral domain wall dynamics^8-10 and spin textures with new spin topologies^7,11. Here, we advance beyond the control of intrastructure properties in three dimensions and tailor the magnetostatic coupling of neighbouring magnetic structures, an interstructure property that allows us to generate complex textures in the magnetic stray field. For this, we harness direct write nanofabrication techniques, creating intertwined nanomagnetic cobalt double helices, where curvature, torsion, chirality and magnetic coupling are jointly exploited. By reconstructing the three-dimensional vectorial magnetic state of the double helices with soft-X-ray magnetic laminography^12,13, we identify the presence of a regular array of highly coupled locked domain wall pairs in neighbouring helices. Micromagnetic simulations reveal that the magnetization configuration leads to the formation of an array of complex textures in the magnetic induction, consisting of vortices in the magnetization and antivortices in free space, which together form an effective B field cross-tie wall¹⁴. The design and creation of complex three-dimensional magnetic field nanotextures opens new possibilities for smart materials¹⁵, unconventional computing^2,16, particle trapping^17,18 and magnetic imaging¹⁹.

String Phase in an Artificial Spin Ice

One-dimensional strings of local excitations are a fascinating feature of the physical behavior of strongly correlated topological quantum matter. Here we study strings of local excitations in a classical system of interacting nanomagnets, the Santa Fe Ice geometry of artificial spin ice. We measured the moment configuration of the nanomagnets, both after annealing near the ferromagnetic Curie point and in a thermally dynamic state. While the Santa Fe Ice lattice structure is complex, we demonstrate that its disordered magnetic state is naturally described within a framework of emergent strings. We show experimentally that the string length follows a simple Boltzmann distribution with an energy scale that is associated with the system’s magnetic interactions and is consistent with theoretical predictions. The results demonstrate that string descriptions and associated topological characteristics are not unique to quantum models but can also provide a simplifying description of complex classical systems with non-trivial frustration.

Strings of local excitations are interesting features of a strongly correlated topological quantum matter. Here, the authors show that Boltzmann-distributed strings of local excitations also describe the topological physics of the Santa Fe geometry of artificial spin ice, which is a classical thermal system.

Realization of macroscopic ratchet effect based on nonperiodic and uneven potentials

Ratchet devices allow turning an ac input signal into a dc output signal. A ratchet device is set by moving particles driven by zero averages forces on asymmetric potentials. Hybrid nanostructures combining artificially fabricated spin ice nanomagnet arrays with superconducting films have been identified as a good choice to develop ratchet nanodevices. In the current device, the asymmetric potentials are provided by charged Néel walls located in the vertices of spin ice magnetic honeycomb array, whereas the role of moving particles is played by superconducting vortices. We have experimentally obtained ratchet effect for different spin ice I configurations and for vortex lattice moving parallel or perpendicular to magnetic easy axes. Remarkably, the ratchet magnitudes are similar in all the experimental runs; i. e. different spin ice I configurations and in both relevant directions of the vortex lattice motion. We have simulated the interplay between vortex motion directions and a single asymmetric potential. It turns out vortices interact with uneven asymmetric potentials, since they move with trajectories crossing charged Néel walls with different orientations. Moreover, we have found out the asymmetric pair potentials which generate the local ratchet effect. In this rocking ratchet the particles (vortices) on the move are interacting each other (vortex lattice); therefore, the ratchet local effect turns into a global macroscopic effect. In summary, this ratchet device benefits from interacting particles moving in robust and topological protected type I spin ice landscapes.

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.

Configurable Artificial Spin Ice with Site-Specific Local Magnetic Fields

We demonstrate ground state tunability for a hybrid artificial spin ice composed of Fe nanomagnets which are subject to site-specific exchange-bias fields, applied in integer multiples of the lattice along one sublattice of the classic square artificial spin ice. By varying this period, three distinct magnetic textures are identified: a striped ferromagnetic phase; an antiferromagnetic phase attainable through an external field protocol alone; and an unconventional ground state with magnetically charged pairs embedded in an antiferromagnetic matrix. Monte Carlo simulations support the results of field protocols and demonstrate that the pinning tunes relaxation timescales and their critical behavior.

Reconfigurable Pinwheel Artificial-Spin-Ice and Superconductor Hybrid Device

The ability to control the potential landscape in a medium of interacting particles could lead to intriguing collective behavior and innovative functionalities. Here, we utilize spatially reconfigurable magnetic potentials of a pinwheel artificial-spin-ice (ASI) structure to tailor the motion of superconducting vortices. The reconstituted chain structures of the magnetic charges in the pinwheel ASI and the strong interaction between magnetic charges and superconducting vortices allow significant modification of the transport properties of the underlying superconducting thin film, resulting in a reprogrammable resistance state that enables a reversible and switchable vortex Hall effect. Our results highlight an effective and simple method of using ASI as an in situ reconfigurable nanoscale energy landscape to design reprogrammable superconducting electronics, which could also be applied to the in situ control of properties and functionalities in other magnetic particle systems, such as magnetic skyrmions.

Highly Sensitive Polydiacetylene Ensembles for Biosensing and Bioimaging

Polydiacetylenes are prepared from amphiphilic diacetylenes first through self-assembly and then polymerization. Different from common supramolecular assemblies, polydiacetylenes have stable structure and very special optical properties such as absorption, fluorescence, and Raman. The hydrophilic head of PDAs is easy to be chemically modified with functional groups for detection and imaging applications. PDAs will undergo a specific color change from blue to red, fluorescence enhancement and Raman spectrum changes in the presence of receptor ligands. These properties allow PDA-based sensors to have high sensitivity and specificity during analysis. Therefore, the PDAs have been widely used for detection of viruses, bacteria, proteins, antibiotics, hormones, sialic acid, metal ions and as probes for bioimaging in recent years. In this review, the preparation, polymerization, and detection mechanisms of PDAs are discussed, and some representative research advances in the field of bio-detection and bioimaging are highlighted.

Relation between microscopic interactions and macroscopic properties in ferroics

The driving force in materials to spontaneously form states with magnetic or electric order is of fundamental importance for basic research and device technology. The macroscopic properties and functionalities of these ferroics depend on the size, distribution and morphology of domains; that is, of regions across which such uniform order is maintained¹. Typically, extrinsic factors such as strain profiles, grain size or annealing procedures control the size and shape of the domains^2-5, whereas intrinsic parameters are often difficult to extract due to the complexity of a processed material. Here, we achieve this separation by building artificial crystals of planar nanomagnets that are coupled by well-defined, tuneable and competing magnetic interactions^6-9. Aside from analysing the domain configurations, we uncover fundamental intrinsic correlations between the microscopic interactions establishing magnetically compensated order and the macroscopic manifestations of these interactions in basic physical properties. Experiment and simulations reveal how competing interactions can be exploited to control ferroic hallmark properties such as the size and morphology of domains, topological properties of domain walls or their thermal mobility.

Magnetization dynamics in artificial spin ice

In this topical review, we present key results of studies on magnetization dynamics in artificial spin ice (ASI), which are arrays of magnetically interacting nanostructures. Recent experimental and theoretical progress in this emerging area, which is at the boundary between research on frustrated magnetism and high-frequency studies of artificially created nanomagnets, is reviewed. The exploration of ASI structures has revealed fascinating discoveries in correlated spin systems. Artificially created spin ice lattices offer unique advantages as they allow for a control of the interactions between the elements by their geometric properties and arrangement. Magnonics, on the other hand, is a field that explores spin dynamics in the gigahertz frequency range in magnetic micro- and nanostructures. In this context, magnonic crystals are particularly important as they allow the modification of spin-wave properties and the observation of band gaps in the resonance spectra. Very recently, there has been considerable progress, experimentally and theoretically, in combining aspects of both fields-artificial spin ice and magnonics-enabling new functionalities in magnonic and spintronic applications using ASI, as well as providing a deeper understanding of geometrical frustration in the gigahertz range. Different approaches for the realization of ASI structures and their experimental characterization in the high-frequency range are described and the appropriate theoretical models and simulations are reviewed. Special attention is devoted to linking these findings to the quasi-static behavior of ASI and dynamic investigations in magnonics in an effort to bridge the gap between both areas further and to stimulate new research endeavors.

Stray-Field Imaging of a Chiral Artificial Spin Ice during Magnetization Reversal

Artificial spin ices are a class of metamaterials consisting of magnetostatically coupled nanomagnets. Their interactions give rise to emergent behavior, which has the potential to be harnessed for the creation of functional materials. Consequently, the ability to map the stray field of such systems can be decisive for gaining an understanding of their properties. Here, we use a scanning nanometer-scale superconducting quantum interference device (SQUID) to image the magnetic stray field distribution of an artificial spin ice system exhibiting structural chirality as a function of applied magnetic fields at 4.2 K. The images reveal that the magnetostatic interaction gives rise to a measurable bending of the magnetization at the edges of the nanomagnets. Micromagnetic simulations predict that, owing to the structural chirality of the system, this edge bending is asymmetric in the presence of an external field and gives rise to a preferred direction for the reversal of the magnetization. This effect is not captured by models assuming a uniform magnetization. Our technique thus provides a promising means for understanding the collective response of artificial spin ices and their interactions.

Topologically protected superconducting ratchet effect generated by spin-ice nanomagnets

We have designed, fabricated and tested a robust superconducting ratchet device based on topologically frustrated spin ice nanomagnets. The device is made of a magnetic Co honeycomb array embedded in a superconducting Nb film. This device is based on three simple mechanisms: (i) the topology of the Co honeycomb array frustrates in-plane magnetic configurations in the array yielding a distribution of magnetic charges which can be ordered or disordered with in-plane magnetic fields, following spin ice rules; (ii) the local vertex magnetization, which consists of a magnetic half vortex with two charged magnetic Néel walls; (iii) the interaction between superconducting vortices and the asymmetric potentials provided by the Néel walls. The combination of these elements leads to a superconducting ratchet effect. Thus, superconducting vortices driven by alternating forces and moving on magnetic half vortices generate a unidirectional net vortex flow. This ratchet effect is independent of the distribution of magnetic charges in the array.

Superferromagnetism and Domain-Wall Topologies in Artificial "Pinwheel" Spin Ice

For over ten years, arrays of interacting single-domain nanomagnets, referred to as artificial spin ices, have been engineered with the aim to study frustration in model spin systems. Here, we use Fresnel imaging to study the reversal process in "pinwheel" artificial spin ice, a modified square ASI structure obtained by rotating each island by some angle about its midpoint. Our results demonstrate that a simple 45° rotation changes the magnetic ordering from antiferromagnetic to ferromagnetic, creating a superferromagnet which exhibits mesoscopic domain growth mediated by domain wall nucleation and coherent domain propagation. We observe several domain-wall configurations, most of which are direct analogues to those seen in continuous ferromagnetic films. However, charged walls also appear due to the geometric constraints of the system. Changing the orientation of the external magnetic field allows control of the nature of the spin reversal with the emergence of either one- or two-dimensional avalanches. This property of pinwheel ASI could be employed to tune devices based on magnetotransport phenomena such as Hall circuits.

Dimensional coupling-induced current reversal in two-dimensional driven lattices

We show that the direction of directed particle transport in a two-dimensional ac-driven lattice can be dynamically reversed by changing the structure of the lattice in the direction perpendicular to the applied driving force. These structural changes introduce dimensional coupling effects, the strength of which governs the timescale of the current reversals. The underlying mechanism is based on the fact that dimensional coupling allows the particles to explore regions of phase space which are inaccessible otherwise. The experimental realization for cold atoms in ac-driven optical lattices is discussed.

Effect of FePd alloy composition on the dynamics of artificial spin ice

Artificial spin ices (ASI) are arrays of single domain nano-magnetic islands, arranged in geometries that give rise to frustrated magnetostatic interactions. It is possible to reach their ground state via thermal annealing. We have made square ASI using different FePd alloys to vary the magnetization via co-sputtering. From a polarized state the samples were incrementally heated and we measured the vertex population as a function of temperature using magnetic force microscopy. For the higher magnetization FePd sample, we report an onset of dynamics at T = 493 K, with a rapid collapse into >90% ground state vertices. In contrast, the low magnetization sample started to fluctuate at lower temperatures, T = 393 K and over a wider temperature range but only reached a maximum of 25% of ground state vertices. These results indicate that the interaction strength, dynamic temperature range and pathways can be finely tuned using a simple co-sputtering process. In addition we have compared our experimental values of the blocking temperature to those predicted using the simple Néel-Brown two-state model and find a large discrepancy which we attribute to activation volumes much smaller than the island volume.