Artificial Kagome Spin Ice Research Articles

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.

Magnetic phase recognition of artificial kagome spin ice through initial magnetization curve

Magnetic phase recognition of artificial kagome spin ice through initial magnetization curve

Micromagnetic Simulations of Emergent Monopole Defects and Magnetization Reversal in Connected and Dipolar Kagome Artificial Spin Ice

Artificial spin ice (ASI) materials, created by lithographically patterning nanoscale magnets in desired geometries, have shown a number of interesting phenomena, such as emergent magnetic monopoles (monopole defects), collective dynamics and phase transitions. The control of monopole defects with external stimuli such as magnetic and electric fields, strain, electric currents etc. would be of much interest in fabrication of future devices. In this work, we investigate the magnetization reversal as a function of the connectivity of the Kagome ASI, using micromagnetic simulations. The domain wall motion is expected to play an important role in the connected spin ice, whereas the dipolar interactions dominate for the unconnected case. The magnetic microstate of each lattice is uniquely determined by the vertex configuration, with the Kagome lattice supporting a six-fold-degenerate vertex state, obeying either a two-in/one-out (vertex charge +q) or one-in/two-out (vertex charge q) ice rule. We analyze the fraction of each vertex type to highlight changes in the magnetic microstate as a function of applied magnetic field. Our results could be correlated with magneto-transport measurements and direct imaging of vertex states in ASI using magnetic force microscopy.

Crystallizing Kagome Artificial Spin Ice.

Artificial spin ices are engineered arrays of dipolarly coupled nanobar magnets. They enable direct investigations of fascinating collective phenomena from their diverse microstates. However, experimental access to ground states in the geometrically frustrated systems has proven difficult, limiting studies and applications of novel properties and functionalities from the low energy states. Here, we introduce a convenient approach to control the competing diploar interactions between the neighboring nanomagnets, allowing us to tailor the vertex degeneracy of the ground states. We achieve this by tuning the length of selected nanobar magnets in the spin ice lattice. We demonstrate the effectiveness of our method by realizing multiple low energy microstates in a kagome artificial spin ice, particularly the hardly accessible long range ordered ground state-the spin crystal state. Our strategy can be directly applied to other artificial spin systems to achieve exotic phases and explore new emergent collective behaviors.

Real-space imaging of phase transitions in bridged artificial kagome spin ice

In frustrated spin systems, magnetic phase transitions underpin the formation of exotic, frustration-driven magnetic phases. Of great importance is the ability to manipulate these transitions to access specific phases, which in turn provides a means to discover and control novel phenomena. Artificial spin systems incorporating lithographically fabricated arrays of dipolar-coupled nanomagnets that enable real-space observation of the magnetic configurations provide such an opportunity. In particular, the kagome spin ice is predicted to exhibit two phase transitions, one of which is to a low-temperature phase whose long-range ground-state order has not been observed experimentally. To achieve this ordered state, we change the global symmetry of the artificial kagome system by selectively tuning the near-field nanomagnet interactions through nanoscale bridges at the lattice vertices. By precisely tuning the interactions, we are able to quantify the influence of frustration on the phase transition, finding that the driving force for spin and charge ordering depends on the degeneracy strength at the vertex.

Artificial spin ice phase-change memory resistors

We present a proposal for realization of an electrical memory reminiscent of a memristor in connected Kagome artificial spin ice. We show that current flowing through the system alters the magnetic ensemble, which in turns controls the overall resistance thus leaving memory of current passage in the system. This introduces a current-dependent effect for a dynamic resistive state. We simulate a spin-induced thermal phase-change mechanism, and an athermal domain-wall spin inversion. In both cases we observe electrical memory behavior with an I–V hysteretic pinched loop, typical of memristors. These results can be extended to the more complex geometries in which artificial spin ice can be designed to engineer the hysteresis curve.

Angular-dependent dynamic response and magnetization reversal in Fibonacci-distorted kagome artificial spin ice

We have measured the angular dependence of ferromagnetic resonance (FMR) spectra for Fibonacci-distorted, kagome artificial spin ice. The number of strong modes in the FMR spectra depend on the orientation of the applied DC magnetic field. In addition, discontinuities observed in the FMR field-frequency dispersion curves also depend on DC field orientation, and signal a multistep DC magnetization reversal, which is caused by the reduced energy degeneracy of Fibonacci-distorted vertices. The results suggest that the orientation of applied magnetic field and severity of Fibonacci distortion constitute control variables for FMR modes and multistep reversal in future magnonic devices and magnetic switching systems.

Vertex dependent dynamic response of a connected Kagome artificial spin ice

We present experimental and numerical results for the dynamic response of a connected Kagome artificial spin ice. We explicitly consider the effect of the vertex magnetization configuration on the ferromagnetic resonance (FMR) mode characteristics using micromagnetic simulations. We show that the bulk mode frequencies of each single-domain thin-film segment not only depend on the direction of the segment's easy-axes with respect to the applied magnetic field but also depend on the vertex magnetization configurations of nearby vertices. Therefore, the FMR modes can be controlled by altering the vertex magnetization texture. Moreover, we distinguish between vertex center modes (VCMs) and localized domain wall (LDW) modes. We show that the LDW mode evolves during the nucleation process of domain walls and that VCMs and LDW modes can be controlled using specific field protocols, which have important implications for future design of magnonic and spintronic devices.

Magnetization dynamics of a Fibonacci-distorted kagome artificial spin ice

We present results of ferromagnetic resonance (FMR) experiments and micromagnetic simulations for a distorted, 2D Kagome artificial spin ice. The distorted structure is created by continuously modulating the 2D primitive lattice translation vectors of a periodic honeycomb lattice, according to an aperiodic Fibonacci sequence used to generate 1D quasicrystals. Experimental data and micromagnetic simulations show the Fibonacci distortion causes broadening and splitting of FMR modes into multiple branches, which accompany the increasing number of segment lengths and orientations that develop with increasing distortion. When the applied field is increased in the opposite direction to the net magnetization of a segment, spin wave modes appear, disappear or suddenly shift, to signal segment magnetization reversal events. These results show the complex behavior of reversal events, as well as well-defined frequencies and frequency-field slopes of FMR modes, can be precisely tuned by varying the severity of the aperiodic lattice distortion. This type of distorted structure could therefore provide a new tool for the design of complicated magnonic systems.

Micromagnetic simulations of magnetization reversal in kagome artificial spin ice

This work reports micromagnetic simulations used to study magnetization reversal in kagome artificial spin ice, taking into account the actual edge imperfections presented by the magnetic nanoislands as a source of disorder. An important advantage of the micromagnetic approach is to discretize a magnetic element in nanometric domains, allowing access to the sample magnetic moments distribution in detail. The limit case of zero disorder is accessed considering a system composed of perfect magnetic islands. The main result is the prediction of a critical angle between the applied magnetic field and the direction of one of the sublattices, above which Dirac strings emerge. For lower values, the reversal occurs through a bidimensional fashion, being smooth or abrupt depending on whether or not roughness is present, respectively. Finally, our simulations open the question of how the contour imperfections really influence the magnetic response of artificial spin ice.

Thermally superactive artificial kagome spin ice structures obtained with the interfacial Dzyaloshinskii-Moriya interaction

Artificial kagome spin ice exhibits exotic magnetic correlations driven by a combination of geometric frustration and dipolar interactions that, at low-enough temperature, can result in ordered phases. This order, whether it is the ground state of several kagome rings, or the theoretically predicted long-range order of an extended array, has yet to be experimentally observed. By introducing an interfacial Dzyaloshinskii-Moriya interaction, we are able to reduce the blocking temperature of the individual nanomagnets, allowing a system of 30 kagome nanomagnets to explore its vast manifold of microstates and find its ground state. Furthermore, the extracted magnetic correlations in an extended artificial kagome spin ice are found to exhibit quantitative signatures of long-range charge order, providing evidence of the theoretically predicted continuous phase transition to the charge-ordered state. The significant lowering of the blocking temperature in nanomagnets is important for the exploitation of superparamagnetism in artificial spin systems and devices.

Magnon Modes of Microstates and Microwave-Induced Avalanche in Kagome Artificial Spin Ice with Topological Defects.

We investigate spin dynamics of microstates in artificial spin ice (ASI) in Ni_{81}Fe_{19} nanomagnets arranged in an interconnected kagome lattice using microfocus Brillouin light scattering, broadband ferromagnetic resonance, magnetic force microscopy, x-ray photoemission electron microscopy, and simulations. We experimentally reconfigure microstates in ASI using a 2D vector field protocol and apply microwave-assisted switching to intentionally trigger reversal. Our work is key for the creation of avalanches inside the kagome ASI and reprogrammable magnonics based on ASIs.

Influence of the Vertex Region on Spin Dynamics in Artificial Kagome Spin Ice

Stuck in the middle with you: The spin-wave mode localized in the contact area among macrospins in an artificial spin ice (ASI) is interesting for magnonic devices and applications. Detection and characterization of this mode is difficult, though. This study uses carefully designed lattices of individual macrospins with the right aspect ratio of individual nanoelements, the right geometry of macrospins on an ASI vertex, and the right configuration for clear detection of the spin dynamics. The localized mode is found to exhibit a peculiar sensitivity to the applied field's direction, which could impact applications such as magnonic position transducers.

Kerr microscopy real-time imaging of the magnetization reversal process in kagome artificial spin ice

The magnetization reversal process in an interconnected kagome artificial spin ice has been investigated using high-resolution Kerr microscopy. The magnetization switching with two-dimensional system-size avalanches has been directly imaged for the applied field parallel to one of the sublattice branches, suggesting very low disorder in our sample. The discrete one-dimensional Dirac-string-like magnetization reversal is found for the field with a certain angle. The real-time imaging under the field suggests that the reversal of the third bars next to the reversed Dirac string can mediate the reversal of the neighboring Dirac string. The observed reversal behaviors can be understood by the ice rule, consistent with the micromagnetic simulation results. Our studies demonstrate that Kerr microscopy can be applied to study the magnetization reversal process in artificial spin ice structures in real space and real time under an external magnetic field.

Tunable magnetization dynamics in artificial spin ice via shape anisotropy modification

Ferromagnetic resonance (FMR) is performed on kagome artificial spin ice (ASI) formed of disconnected ${\mathrm{Ni}}_{80}{\mathrm{Fe}}_{20}$ nanowires. Here we break the threefold angular symmetry of the kagome lattice by altering the coercive field of each sublattice via shape anisotropy modification. This allows for distinct high-frequency responses when a magnetic field is aligned along each sublattice and additionally enables simultaneous spin-wave resonances to be excited in all nanowire sublattices, unachievable in conventional kagome ASI. The different coercive field of each sublattice allows selective magnetic switching via global field, unlocking novel microstates inaccessible in homogeneous-nanowire ASI. The distinct spin-wave spectra of these states are detected experimentally via FMR and linked to underlying microstates using micromagnetic simulation.

Influence of cutoff dipole interaction radius and dilution on phase transition in kagome artificial spin ice

The investigations carried out in this paper show the influence of cutoff dipole interaction radius and dilution on the basic thermodynamic characteristics of the kagome artificial spin ice with free boundary conditions. The phase transition disappearance at the dipole interaction radius limitation was shown in our previous study by Shevchenko {\it et al.} [JETP {\bf 124}(6), 982-993 (2017)]. This work continues this study and answers the question of the coordination spheres numbers that must be taken into account, in order not to lose the basic collective phenomena. The answer is at least three coordination spheres with 14 nearest neighbors must be taken into account for kagome artificial spin ice. Restriction to a smaller cutoff radius leads to significant changes in the thermodynamic behavior of the main characteristics of the system. An increase of the interaction radius shifts the phase transition temperature to the low-temperature area. The effects of dilution on kagome artificial spin ice were also investigated. It is shown that the phase transition occurs up to $p_c\approx0.35$ dilution concentrations, that well coincides with the Sykes and Essam theory. Further dilution leads to the phase transition disappearance.

Balanced Magnetic Logic Gates in a Kagome Spin Ice

Nanomagnetic logic (NML) is a promising candidate to replace or complement traditional charged-based logic devices. Single NML gates such as the three-input majority gate are well studied, and their functionality has been verified experimentally. However, such gates suffer from a problem in that they sometimes produce erroneous output when integrated into circuits. A fundamental solution is offered by using balanced logic gates: gates for which the ground states corresponding to all possible input states have the same energy. We investigate how balanced gates can be created from kagome spin ice elements. We present a balanced NAND (and NOR) gate consisting of 19 dipole-coupled uniaxially anisotropic magnets. This gate can be either driven by an external clocking field or thermally driven. In the latter case, we numerically show that the gate has a reliability of at least 96%, a number which is shown to be robust against disorder. The presented gate provides a proof of concept for an artificial kagome spin ice NML gate.

Coupled macrospins: Mode dynamics in symmetric and asymmetric vertices

We report the microwave response of symmetric and asymmetric threefold clusters with nearly contacting segments that can serve as the node in a Kagome artificial spin ice lattice. The structures are patterned on a coplanar waveguide and consist of elongated and nearly-contacting ellipses with uniform thickness. Branches of the ferromagnetic resonance spectra display mode softening that correlates well with the calculations, whereas agreement between the measured and simulated static magnetization is more qualitative.

Magnetotransport in Artificial Kagome Spin Ice

Magnetic nanoarray with special geometries exhibits nontrivial collective behaviors similar to those observed in the spin ice materials. Here we present a novel circuit model to describe the complex magnetotransport phenomena in artificial kagome spin ice. In this picture, the system can be viewed as a resistor network driven by voltage sources that are located at vertices of the honeycomb array. The differential voltages across different terminals of these sources are related to the ice-rules that govern the local magnetization ordering. The circuit model relates the transverse Hall voltage of kagome ice to the underlying spin correlations. Treating the magnetic nanoarray as metamaterials, we present a mesoscopic constitutive equation relating the Hall resistance to magnetization components of the system. We further show that the Hall signal is significantly enhanced when the kagome ice undergoes a magnetic-charge ordering transition. Our analysis can be readily generalized to other lattice geometry, providing a quantitative method for the design of magnetoresistance devices based on artificial spin ices.

Realization of ground state in artificial kagome spin ice via topological defect-driven magnetic writing.

Arrays of non-interacting nanomagnets are widespread in data storage and processing. As current technologies approach fundamental limits on size and thermal stability, enhancing functionality through embracing the strong interactions present at high array densities becomes attractive. In this respect, artificial spin ices are geometrically frustrated magnetic metamaterials that offervast untapped potential due to their unique microstate landscapes, with intriguing prospects in applications from reconfigurable logic to magnonic devices or hardware neural networks. However, progress in such systems is impeded by the inability to access more than a fraction of the total microstate space. Here, we demonstrate that topological defect-driven magnetic writing-a scanning probe technique-provides access to all of the possible microstates in artificial spin ices and related arrays of nanomagnets. We create previously elusive configurations such as the spin-crystal ground state of artificial kagome dipolar spin ices and high-energy, low-entropy 'monopole-chain' states that exhibit negative effective temperatures.