We have investigated the spin wave modes of strongly dipolar coupled, highly anisotropic nanoislands forming square artificial spin ice system using micromagnetic simulation in MUMAX3 in combination with Matlab coding. Artificial spin ice is considered to be formed by the four square ring-type structure of elliptical cross-section nanoislands. Our results state the direct relation between the spin wave modes generated and the micro-states formed in the system. We have shown that single ring type structure can alone be adequately used to understand the spin wave modes of square artificial spin ice.
The spin-wave dynamics of the ferromagnetic nanoarrays termed artificial spin ice (ASI) are known to vary depending on their magnetic microstate. However, little work has been done to characterise this relationship. Recent advances in control over the magnetic configuration of ASI bring designs harnessing the interplay between spin-wave eigenmodes and the microstate within reach, offering diverse applications including reconfigurable magnonic crystals, microwave filters and microstate read-out probes. These designs hinge on a strong understanding of the underlying spin wave-microstate correspo…
In artificial spin ice systems, an interplay of defects and dipolar interactions is expected to play important roles in stabilizing different collective magnetic states. In this work, we investigated the magnetization reversal of individual defective square artificial spin ice vertices where defects break four-fold rotational symmetry of the system. By varying the angle between the applied field and the geometrical axis of the vertices, we observe a change in energy landscape of the system resulting into the stabilization of collective low-energy magnetic states. We also observe that by changi…
Strongly-interacting nanomagnetic arrays are finding increasing use as model host systems for reconfigurable magnonics. The strong inter-element coupling allows for stark spectral differences across a broad microstate space due to shifts in the dipolar field landscape. While these systems have yielded impressive initial results, developing rapid, scaleable means to access abroad range of spectrally-distinct microstates is an open research problem.We present a scheme whereby square artificial spin ice is modified by widening a 'staircase' subset of bars relative to the rest of the array, allowi…
We experimentally demonstrate that arrays of interacting nanoscale ferromagnetic islands, known as artificial spin ice, develop reproducible microstates upon cycling an applied magnetic field. The onset of this memory effect is determined by the strength of the applied field relative to the array coercivity. Specifically, when the applied field strength is almost exactly equal to the array coercivity, several training cycles are required before the array achieves a nearly completely repeatable microstate, whereas when the applied field strength is stronger or weaker than the array coercivity, …
Artificial spin ices are magnetic metamaterials comprising geometrically-tiled interacting nanomagnets. There is significant interest in these systems for reconfigurable magnonics due to their vast microstate landscape. Studies to-date have focused on the in-field GHz spin-wave response, convoluting effects from applied field, nanofabrication-imperfections ('quenched disorder') and microstate-dependent dipolar field landscapes. Here, we study artificial spin ices in pure and disordered microstates and evaluate their zero-field spectra. Removing the applied field allows us to deconvolute contri…
Nanomagnetic arrays are widespread in data storage and processing. As current technologies approach fundamental limits on size and thermal stability, extracting additional functionality from arrays is crucial to advancing technological progress. One design exploiting the enhanced magnetic interactions in dense arrays is the geometrically-frustrated metamaterial 'artificial spin ice' (ASI). Frustrated systems offer vast untapped potential arising from their unique microstate landscapes, presenting intriguing opportunities from reconfigurable logic to magnonic devices or hardware neural networks…
Artificial spin ices (ASIs) are designable arrays of interacting nanomagnets that span a wide range of magnetic phases associated with a number of spin lattice models. Here, we demonstrate that the phase of an artificial kagome spin ice can be determined from its initial magnetization curve. As a proof of concept, micromagnetic simulations of these curves were performed starting from representative microstates of different phases of the system. We show that the curves are characterized by phase-specific features in such a way that a pattern recognition algorithm predicts the phase of the initi…
We use spatially resolved magneto-optical Kerr microscopy to track the complete microstates of arrays of perpendicular anisotropy nanomagnets during magnetization hysteresis cycles. These measurements allow us to disentangle the intertwined effects of nearest neighbor interaction, disorder, and stochasticity on magnetization switching. We find that the nearest neighbor correlations depend on both interaction strength and disorder. We also find that although the global characteristics of the hysteretic switching are repeatable, the exact microstate sampled is stochastic with the behavior of ind…
Strongly-interacting artificial spin systems are moving beyond mimicking naturally-occurring materials to emerge as versatile functional platforms, from reconfigurable magnonics to neuromorphic computing. Typically artificial spin systems comprise nanomagnets with a single magnetisation texture: collinear macrospins or chiral vortices. By tuning nanoarray dimensions we achieve macrospin/vortex bistability and demonstrate a four-state metamaterial spin-system 'Artificial Spin-Vortex Ice' (ASVI). ASVI can host Ising-like macrospins with strong ice-like vertex interactions, and weakly-coupled vor…
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 b…
We report the experimental and theoretical characterization of the angular-dependent spin dynamics in arrays of ferromagnetic nanodisks arranged on a honeycomb lattice. The magnetic field and microwave frequency dependence, measured by broadband ferromagnetic resonance, reveal a rich spectrum of modes that is strongly affected by the microstate of the network. Based on symmetry arguments with respect to the external field, we show that certain parts of the ferromagnetic network contribute to the detected signal. A comparison of the experimental data with micromagnetic simulations reveals that …
Dipolar magnon-magnon coupling has long been predicted in nano-patterned artificial spin systems. However, observation of such phenomena and related collective spin-wave signatures have until recently proved elusive or limited to low-power edge-modes which are difficult to measure experimentally. Here we describe the requisite conditions for dipolar mode-hybridisation, how it may be controlled, why it was not observed earlier and how strong coupling may occur between nanomagnet bulk-modes. We experimentally investigate four nano-patterned artificial spin system geometries: `chevron' arrays, `s…
In this paper we conduct Monte Carlo simulations to investigate the thermodynamic properties of a geometry of artificial spin ice recently proposed in the literature that had been termed "rewritable" spin ice, for its experimental realization allows total control over the microstates of the system. Our results show that in the thermodynamic limit a single phase transition between a fully magnetized state and a paramagnetic state exists, whereas for finite systems an intermediate phase also emerges, engendering a low temperature pseudo phase transition. This intermediate phase is characterized …
Using extensive numerical simulations, we probe the magnetization switching in two-dimensional artificial spin ice (ASI) system consisting of peanut-shaped nanomagnets. We also investigated the effect of the external magnetic field on the degeneracy of the magnetic states in such a system. The switching field is found to be one order smaller in the proposed ASI system with peanut-shaped nanomagnets as compared to the conventionally used highly-anisotropic nanoisland such as elliptically shaped nanomagnets. The metastable 2-in/2-out (Type II) magnetic state is robust at the remanence. We are al…
Artificial spin ice systems have been introduced as a possible mean to investigate frustration effects in a well-controlled manner by fabricating lithographically-patterned two-dimensional arrangements of interacting magnetic nanostructures. This approach offers the opportunity to visualize unconventional states of matter, directly in real space, and triggered a wealth of studies at the frontier between nanomagnetism, statistical thermodynamics and condensed matter physics. Despite the strong efforts made these last ten years to provide an artificial realization of the celebrated square ice mo…
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…
Excitation caging in a vertex-frustrated quasiperiodic Einstein artificial spin ice
ETH Zurich（苏黎世联邦理工学院）；PSI Center for Neutron and Muon Sciences（保罗谢尔研究所中子与μ子科学中心）；Institut Néel, CNRS UPR2940（内勒研究所，法国国家科学研究中心）；School of Physics, University of Bristol（布里斯托大学物理学院）；PSI Center for Scientific Computing, Theory and Data（保罗谢尔研究所科学计算、理论与数据中心）
