The non-random walk of chiral magnetic charge carriers in artificial spin ice

Artificial Magnetic Tripod Ice

We study the collective behavior of interacting arrays of nanomagnetic tripods. These objects have six discrete moment states, in contrast to the usual two states of an Ising-like moment. Our experimental data demonstrate that triangular lattice arrays form a "tripod ice" that exhibits charge ordering among the effective vertex magnetic charges, in direct analogy to artificial kagome spin ice. The results indicate that the interacting tripods have effective moments that act as emergent local variables, with strong connections to the well-studied Potts and clock models. In addition, the tripod moments display a tendency toward a nearest neighbor alignment in our thermalized samples that separates this system from kagome spin ice. Our results open a path toward the study of the collective behavior of nonbinary moments that is unavailable in other physical systems.

Comparison of Spin-Wave Modes in Connected and Disconnected Artificial Spin Ice Nanostructures Using Brillouin Light Scattering Spectroscopy

Artificial spin ice systems have seen burgeoning interest due to their intriguing physics and potential applications in reprogrammable memory, logic, and magnonics. Integration of artificial spin ice with functional magnonics is a relatively recent research direction, with a host of promising results. As the field progresses, direct in-depth comparisons of distinct artificial spin systems are crucial to advancing the field. While studies have investigated the effects of different lattice geometries, little comparison exists between systems comprising continuously connected nanostructures, where spin-waves propagate via dipole-exchange interaction, and systems with nanobars disconnected at vertices, where spin-wave propagation occurs via stray dipolar field. Gaining understanding of how these very different coupling methods affect both spin-wave dynamics and magnetic reversal is key for the field to progress and provides crucial system-design information including for future systems containing combinations of connected and disconnected elements. Here, we study the magnonic response of two kagome spin ices via Brillouin light scattering, a continuously connected system and a disconnected system with vertex gaps. We observe distinct high-frequency dynamics and magnetization reversal regimes between the systems, with key distinctions in spin-wave localization and mode quantization, microstate trajectory during reversal and internal field profiles. These observations are pertinent for the fundamental understanding of artificial spin systems and broader design and engineering of reconfigurable functional magnonic crystals.

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. A nanoscale 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.

Use of Two-Photon Lithography with a Negative Resist and Processing to Realise Cylindrical Magnetic Nanowires

Cylindrical magnetic nanowires have been shown to exhibit a vast array of fascinating spin textures, including chiral domains, skyrmion tubes, and topologically protected domain walls that harbor Bloch points. Here, we present a novel methodology that utilizes two-photon lithography in order to realize tailored three-dimensional (3D) porous templates upon prefabricated electrodes. Electrochemical deposition is used to fill these porous templates, and reactive ion etching is used to free the encased magnetic nanowires. The nanowires are found to have a diameter of 420 nm, length of 2.82 μm, and surface roughness of 7.6 nm. Magnetic force microscopy in an externally applied field suggests a complex spiraling magnetization state, which demagnetizes via the production of vortices of alternating chirality. Detailed micro-magnetic simulations confirm such a state and a qualitative agreement is found with respect to the switching of experimental nanowires. Surprisingly, simulations also indicate the presence of a Bloch point as a metastable state during the switching process. Our work provides a new means to realize 3D magnetic nanowires of controlled geometry and calculations suggest a further reduction in diameter to sub-200 nm will be possible, providing access to a regime of ultrafast domain wall motion.

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.

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.

A Micromagnetic Protocol for Qualitatively Predicting Stochastic Domain Wall Pinning

Understanding dynamically-induced stochastic switching effects in soft ferromagnetic nanowires is a critical challenge for realising spintronic devices with deterministic switching behaviour. Here, we present a micromagnetic simulation protocol for qualitatively predicting dynamic stochastic domain wall (DW) pinning/depinning at artificial defect sites in Ni₈₀Fe₂₀ nanowires, and demonstrate its abilities by correlating its predictions with the results of focused magneto-optic Kerr effect measurements. We analyse DW pinning configurations in both thin nanowires (t = 10 nm) and thick nanowires (t = 40 nm) with both single (asymmetric) and double (symmetric) notches, showing how our approach provides understanding of the complex DW-defect interactions at the heart of stochastic pinning behaviours. Key results explained by our model include the total suppression of stochastic pinning at single notches in thick nanowires and the intrinsic stochasticity of pinning at double notches, despite their apparent insensitivity to DW chirality.

A novel method for the injection and manipulation of magnetic charge states in nanostructures

Realising the promise of next-generation magnetic nanotechnologies is contingent on the development of novel methods for controlling magnetic states at the nanoscale. There is currently demand for simple and flexible techniques to access exotic magnetisation states without convoluted fabrication and application processes. 360° domain walls (metastable twists in magnetisation separating two domains with parallel magnetisation) are one such state, which is currently of great interest in data storage and magnonics. Here, we demonstrate a straightforward and powerful process whereby a moving magnetic charge, provided experimentally by a magnetic force microscope tip, can write and manipulate magnetic charge states in ferromagnetic nanowires. The method is applicable to a wide range of nanowire architectures with considerable benefits over existing techniques. We confirm the method’s efficacy via the injection and spatial manipulation of 360° domain walls in Py and Co nanowires. Experimental results are supported by micromagnetic simulations of the tip-nanowire interaction.

Low temperature and high field regimes of connected kagome artificial spin ice: the role of domain wall topology

Artificial spin ices are frustrated magnetic nanostructures where single domain nanobars act as macrosized spins. In connected kagome artificial spin ice arrays, reversal occurs along one-dimensional chains by propagation of ferromagnetic domain walls through Y-shaped vertices. Both the vertices and the walls are complex chiral objects with well-defined topological edge-charges. At room temperature, it is established that the topological edge-charges determine the exact switching reversal path taken. However, magnetic reversal at low temperatures has received much less attention and how these chiral objects interact at reduced temperature is unknown. In this study we use magnetic force microscopy to image the magnetic reversal process at low temperatures revealing the formation of quite remarkable high energy remanence states and a change in the dynamics of the reversal process. The implication is the breakdown of the artificial spin ice regime in these connected structures at low temperatures.

Nanofaceting as a stamp for periodic graphene charge carrier modulations

The exceptional electronic properties of monatomic thin graphene sheets triggered numerous original transport concepts, pushing quantum physics into the realm of device technology for electronics, optoelectronics and thermoelectrics. At the conceptual pivot point is the particular two-dimensional massless Dirac fermion character of graphene charge carriers and its volitional modification by intrinsic or extrinsic means. Here, interfaces between different electronic and structural graphene modifications promise exciting physics and functionality, in particular when fabricated with atomic precision. In this study we show that quasiperiodic modulations of doping levels can be imprinted down to the nanoscale in monolayer graphene sheets. Vicinal copper surfaces allow to alternate graphene carrier densities by several 10(13) carriers per cm(2) along a specific copper high-symmetry direction. The process is triggered by a self-assembled copper faceting process during high-temperature graphene chemical vapor deposition, which defines interfaces between different graphene doping levels at the atomic level.

Reconfigurable logic via gate controlled domain wall trajectory in magnetic network structure

An all-magnetic logic scheme has the advantages of being non-volatile and energy efficient over the conventional transistor based logic devices. In this work, we present a reconfigurable magnetic logic device which is capable of performing all basic logic operations in a single device. The device exploits the deterministic trajectory of domain wall (DW) in ferromagnetic asymmetric branch structure for obtaining different output combinations. The programmability of the device is achieved by using a current-controlled magnetic gate, which generates a local Oersted field. The field generated at the magnetic gate influences the trajectory of the DW within the structure by exploiting its inherent transverse charge distribution. DW transformation from vortex to transverse configuration close to the output branch plays a pivotal role in governing the DW chirality and hence the output. By simply switching the current direction through the magnetic gate, two universal logic gate functionalities can be obtained in this device. Using magnetic force microscopy imaging and magnetoresistance measurements, all basic logic functionalities are demonstrated.

Direct observation of deterministic domain wall trajectory in magnetic network structures

Controlling the domain wall (DW) trajectory in magnetic network structures is crucial for spin-based device related applications. The understanding of DW dynamics in network structures is also important for study of fundamental properties like observation of magnetic monopoles at room temperature in artificial spin ice lattice. The trajectory of DW in magnetic network structures has been shown to be chirality dependent. However, the DW chirality periodically oscillates as it propagates a distance longer than its fidelity length due to Walker breakdown phenomenon. This leads to a stochastic behavior in the DW propagation through the network structure. In this study, we show that the DW trajectory can be deterministically controlled in the magnetic network structures irrespective of its chirality by introducing a potential barrier. The DW propagation in the network structure is governed by the geometrically induced potential barrier and pinning strength against the propagation. This technique can be extended for controlling the trajectory of magnetic charge carriers in an artificial spin ice lattice.

Magnetic-charge ordering and phase transitions in monopole-conserved square spin ice

Magnetic-charge ordering and corresponding magnetic/monopole phase transitions in spin ices are the emergent topics of condensed matter physics. In this work, we investigate a series of magnetic-charge (monopole) phase transitions in artificial square spin ice model using the conserved monopole density algorithm. It is revealed that the dynamics of low monopole density lattices is controlled by the effective Coulomb interaction and the Dirac string tension, leading to the monopole dimerization which is quite different from the dynamics of three-dimensional pyrochlore spin ice. The condensation of the monopole dimers into monopole crystals with staggered magnetic-charge order can be predicted clearly. For the high monopole density cases, the lattice undergoes two consecutive phase transitions from high-temperature paramagnetic/charge-disordered phase into staggered charge-ordered phase before eventually toward the long-range magnetically-ordered phase as the ground state which is of staggered charge order too. A phase diagram over the whole temperature-monopole density space, which exhibits a series of emergent spin and monopole ordered states, is presented.

Artificial ferroic systems: novel functionality from structure, interactions and dynamics

Lithographic processing and film growth technologies are continuing to advance, so that it is now possible to create patterned ferroic materials consisting of arrays of sub-1 μm elements with high definition. Some of the most fascinating behaviour of these arrays can be realised by exploiting interactions between the individual elements to create new functionality. The properties of these artificial ferroic systems differ strikingly from those of their constituent components, with novel emergent behaviour arising from the collective dynamics of the interacting elements, which are arranged in specific designs and can be activated by applying magnetic or electric fields. We first focus on artificial spin systems consisting of arrays of dipolar-coupled nanomagnets and, in particular, review the field of artificial spin ice, which demonstrates a wide range of fascinating phenomena arising from the frustration inherent in particular arrangements of nanomagnets, including emergent magnetic monopoles, domains of ordered macrospins, and novel avalanche behaviour. We outline how demagnetisation protocols have been employed as an effective thermal anneal in an attempt to reach the ground state, comment on phenomena that arise in thermally activated systems and discuss strategies for selectively generating specific configurations using applied magnetic fields. We then move on from slow field and temperature driven dynamics to high frequency phenomena, discussing spinwave excitations in the context of magnonic crystals constructed from arrays of patterned magnetic elements. At high frequencies, these arrays are studied in terms of potential applications including magnetic logic, linear and non-linear microwave optics, and fast, efficient switching, and we consider the possibility to create tunable magnonic crystals with artificial spin ice. Finally, we discuss how functional ferroic composites can be incorporated to realise magnetoelectric effects. Specifically, we discuss artificial multiferroics (or multiferroic composites), which hold promise for new applications that involve electric field control of magnetism, or electric and magnetic field responsive devices for high frequency integrated circuit design in microwave and terahertz signal processing. We close with comments on how enhanced functionality can be realised through engineering of nanostructures with interacting ferroic components, creating opportunities for novel spin electronic devices that, for example, make use of the transport of magnetic charges, thermally activated elements, and reprogrammable nanomagnet systems.