Magnetic analogue of an isolated free electric charge, i.e., a magnet with a single north or south pole, is a long sought-after particle which remains elusive so far. In magnetically frustrated pyrochlore solids, a classical analogue of monopole was observed as a result of excitation of spin ice vertices. Direct visualization of such excitations were proposed and later confirmed in analogous artificial spin ice (ASI) systems of square as well as Kagome geometries. However, such charged vertices are randomly created as they are thermally driven and are always associated with corresponding emergent antimonopoles of equal and opposite charges connected by observable strings. Here, we demonstrate a controlled stabilisation of a robust isolated emergent monopole state in individual square ASI vertices by application of an external magnetic field. The excitation conserves the magnetic charge without the involvement of a corresponding antimonopole. Well supported by Monte Carlo simulations our experimental results enable, in absence of a true elemental magnetic monopole, creation of electron vortices and studying electrodynamics in presence of a monopole field in a solid state environment.
Micromagnetic properties of monopoles in artificial kagome spin ice systems are investigated using numerical simulations. We show that micromagnetics brings additional complexity into the physics of these monopoles that is, by essence, absent in spin models: besides a fractionalized classical magnetic charge, monopoles in the artificial kagome ice are chiral at remanence. Our simulations predict that the chirality of these monopoles can be controlled without altering their charge state. This chirality breaks the vertex symmetry and triggers a directional motion of the monopole under an applied…
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 …
The effect of the size of the system, aspect ratio and impurities concentration on the dynamic of emergent magnetic monopoles in artificial spin ice systems
Facultad de Ingeniería, Universidad Diego Portales（迭戈帕拉莱斯大学工程学院）
In this work we propose and study a realization of an artificial spin ice-like system, not based on any real material, in a triangular geometry. At each vertex of the lattice, the "ice-like rule" dictates that three spins must point inward while the other three must point outward. We have studied the system's ground-state and the lowest energy excitations as well as the thermodynamic properties of the system. Our results show that, despite fundamental differences in the vertices topologies as compared to the artificial square spin ice, in the triangular array the lowest energy excitations also…
Magnetic monopole unpairing as a function of external magnetic fields is presented as a fingerprint of this emergent quasiparticles freedom in a two-dimensional artificial spin ice system. Such freedom, required for example for further application in magnetricity, is only possible due to ground-state degeneracy, which causes a decreasing of the string energy in rectangular geometries, designed to allow highest equidistance among nanomagnets. We show by simulations that spin correlation in different rectangular artificial spin ices evolves from antiferromagnetic ordered magnetic structure to a …
Current research on artificial spin ice (ASI) systems has revealed unique hysteretic memory effects and mobile quasi-particle monopoles controlled by externally applied magnetic fields. Here, we numerically demonstrate a strain-mediated multiferroic approach to locally control the ASI monopoles. The magnetization of individual lattice elements is controlled by applying voltage pulses to the piezoelectric layer resulting in strain-induced magnetic precession timed for 180 degree reorientation. The model demonstrates localized voltage control to move the magnetic monopoles across lattice sites, …
We relate the anomalous noise found experimentally in spin ice to the subdiffusion of magnetic monopoles. Because monopoles are emergent particles, they do not move in a structureless vacuum. Rather, the underlying spin ensemble filters the thermal white noise, leading to non-trivial coevolution. Thus, monopoles can be considered as random walkers under the effect of stochastic forces only as long as those are not trivially white, but instead subsume the evolution of the spin vacuum. Via this conceptualization, we conjecture relations between the color of the noise and other observables, such …
Arrays of suitably patterned and arranged magnetic elements may display artificial spin-ice structures with topological defects in the magnetization, such as Dirac monopoles and Dirac strings. It is known that these defects strongly influence the quasi-static and equilibrium behavior of the spin-ice lattice. Here we study the eigenmode dynamics of such defects in a square lattice consisting of stadium-like thin film elements using micromagnetic simulations. We find that the topological defects display distinct signatures in the mode spectrum, providing a means to qualitatively and quantitative…
Magnetricity- the magnetic equivalent of electricity- was recently verified experimentally for the first time. Indeed, just as the stream of electric charges produces electric current, emergent magnetic monopoles have been observed to roam freely (generating magnetic current) in geometrically frustrated magnets known as spin ice. However, this is realized only by considering extreme physical conditions as a single crystal of spin ice has to be cooled to a temperature of $0.36 K$. Candidates to overcome this difficulty are artificial analogues of spin ice crystals, the so-called artificial spin…
We consider a pure square spin ice, that is a square ice where only nearest neighbors are coupled. A gauge-free duality between the perpendicular and collinear structure leads to a natural description in terms of topological currents and charges as the relevant degrees of freedom. That, in turn, can be expressed via a continuous field theory where the discrete spins are subsumed into entropic interactions among charges and currents. This approach produces structure factors, correlations, and susceptibilities for spins, monopoles, and currents. It also generalizes to non-zero temperature the he…
In this work we study demagnetization protocols for an artificial spin ice in a triangular geometry. Our results show that a simple hysteresis-like process is very efficient in driving the system to its ground state, even for a relatively strong disorder in the system, confirming previous expectations. In addition, transitions between the magnetized state and the ground state were observed to be mediated by the creation and propagation of vertices that behave like magnetic monopoles pseudo-particles. This is an important step towards a more detailed experimental study of monopole-like excitati…
Proceeding from the more general to the more concrete, we propose an equilibrium field theory describing spin ice systems in terms of topological charges and magnetic monopoles. We show that for a spin ice on a graph, the entropic interaction in a Gaussian approximation is the inverse of the graph Laplacian matrix, while the screening function for external charges is the inverse of the screened laplacian. We particularize the treatment to square and pyrochlore ice. For square ice we highlight the gauge-free duality between direct and perpendicular structure in terms of symmetry between charges…
We describe degenerate square spin as an ensemble of magnetic monopoles coupled via an emergent entropic field that subsumes the effect of the underlying spin vacuum. We compute their effective free energy, entropic interaction, correlations, screening, and structure factors that coincide with the experimental ones. Unlike in pyrochlore ices, a dimensional mismatch between real and entropic interactions leads to weak singularities at the pinch points and algebraic correlations at long distance. This algebraic screening can be, however, camouflaged by a pseudo-screening regime.
Artificial spin ice offers the possibility to investigate a variety of dipolar orderings, spin frustrations and ground states. However, the most fascinating aspect is the realization that magnetic charge order can be established without spin order. We have investigated magnetic dipoles arranged on a honeycomb lattice as a function of applied field, using magnetic force microscopy. For the easy direction with the field parallel to one of the three dipole sublattices we observe at coercivity a maximum of spin frustration and simultaneously a maximum of charge order of magnetic monopoles with alt…
We report here the results of micromagnetic simulations of square artificial spin ice (ASI) systems with defects. The defects are introduced by misaligning of a nanomagnet at the vertex. In these defective systems, we are able to stabilize emergent monopole-like state by applying a small external field. We observe a systematic change of dipolar energies of the systems with varying misalignment angle. The fields at which the emergent monopoles are created vary linearly with the dipolar energies of the systems. Our results clearly show that the magnetization reversal of the ASI systems is intric…
We investigate the thermodynamics of artificial square spin ice systems assuming only dipolar interactions among the islands that compose the array. The emphasis is given on the effects of the temperature on the elementary excitations (magnetic monopoles and their Dirac strings). By using Monte Carlo techniques we calculate the specific heat, the density of poles and their average separation as functions of temperature. The specific heat and average separation between monopoles and antimonopoles exhibit a sharp peak and a local maximum, respectively, at the same temperature, $T_{p}\approx 7.2D…
We study a frustrated two-dimensional array of dipoles forming an artificial rectangular spin ice with horizontal and vertical lattice parameters given by $a$ and $b$ respectively. We show that the ice regime could be stabilized by appropriate choices for the ratio $γ\equiv a/b$. Our results show that for $γ\approx \sqrt{3}$, i.e., when the center of the islands form a triangular lattice, the ground state becomes degenerate. Therefore, while the magnetic charges (monopoles) are excitations connected by an energetic string for general rectangular lattices (including the particular case of a squ…
The interactions between an excitation (similar to a pair of Nambu monopoles) and a lattice defect are studied in an artificial two-dimensional square spin ice. This is done by considering a square array of islands containing only one island different from all others. This difference is incorporated in the magnetic moment (spin) of the "imperfect" island and several cases are studied, including the special situation in which this distinct spin is zero (vacancy). We have shown that the two extreme points of a malformed island behave like two opposite magnetic charges. Then, the effective intera…
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…
We show that in colloidal models of artificial kagome and modified square ice systems, a variety of ordering and disordering regimes occur as a function of biasing field, temperature, and colloid-colloid interaction strength, including ordered monopole crystals, biased ice rule states, thermally induced ice rule ground states, biased triple states, and disordered states. We describe the lattice geometries and biasing field protocols that create the different states and explain the formation of the states in terms of sublattice switching thresholds. For a system prepared in a monopole lattice s…
We introduce FePd$_{3}$ as a new material for studying thermally active artificial spin ice (ASI) systems and use it to investigate both the square and kagome ice geometries. We readily achieve perfect ground state ordering in the square lattice and demonstrate the highest yet degree of monopole charge-ordering in the kagome lattice. We find that smaller lattice constants in the kagome system generally produce larger domains of charge order. Monte Carlo simulations show excellent agreement with our data when a small amount of disorder is included in the simulation.
We study an artificial spin ice system consisting of two identical layers separated by a height offset $h$. For small separation, the layers are shown to attract each other, provided the whole system is in the ground state. Such an attraction comes about by means of a power-law force that we compare to van der Waals forces. When magnetic monopoles occur in one (or both) layers, the scenario becomes even more interesting and these layers may also repel each other. By tuning parameters like $h$ and monopole distance, switching between attraction and repulsion may be accomplished in a feasible wa…
We report broadband spin-wave spectroscopy on kagome artificial spin ice (ASI) made of large arrays of interconnected Ni$_{80}$Fe$_{20}$ nanobars. Spectra taken in saturated and disordered states exhibit a series of resonances with characteristic magnetic field dependencies. Making use of micromagnetic simulations, we identify resonances that reflect the spin-solid-state and monopole-antimonopole pairs on Dirac strings. The latter resonances allow for the generation of highly-charged vertices in ASIs via microwave assisted switching. Our findings open further perspectives for fundamental studi…
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 …
We investigate spin dynamics of artificial spin ice (ASI) where topological defects confine magnon modes in Ni$_{81}$Fe$_{19}$ nanomagnets arranged on an interconnected kagome lattice. Brillouin light scattering microscopy performed on magnetically disordered states exhibit a series of magnon resonances which depend on topological defect configurations detected by magnetic force microscopy. Nanomagnets on a Dirac string and between a monopole-antimonopole pair show pronounced modifications in magnon frequencies both in experiments and simulations. Our work is key for the creation and annihilat…
Designing and constructing model systems that embody the statistical mechanics of frustration is now possible using nanotechnology. We have arranged nanomagnets on a two-dimensional square lattice to form an artificial spin ice, and studied its fractional excitations, emergent magnetic monopoles, and how they respond to a driving field using X-ray magnetic microscopy. We observe a regime in which the monopole drift velocity is linear in field above a critical field for the onset of motion. The temperature dependence of the critical field can be described by introducing an interaction term into…
In this letter, we have constructed and experimentally investigated frustrated arrays of dipoles forming two-dimensional artificial spin ices with different lattice parameters (rectangular arrays with horizontal and vertical lattice spacings denoted by $a$ and $b$ respectively). Arrays with three different ratios $γ=a/b = \sqrt{2}$, $\sqrt{3}$ and $\sqrt{4}$ are studied. Theoretical calculations of low-energy demagnetized configurations for these same parameters are also presented. Experimental data for demagnetized samples confirm most of the theoretical results. However, the highest energy t…
We report on a theoretical investigation of artificial spin-ice dipolar arrays, using a nanoisland geometry adopted from recent experiments [A. Farhan \textit{et al.}, Nature Phys.\ \textbf{9} (2013) 375]. The number of thermal magnetic string excitations in the square lattice is drastically increased by a vertical displacement of rows and columns. We find large increments especially for low temperatures and for string excitations with quasi-monopoles of charges $\pm 4$. By kinetic Monte Carlo simulations we address the thermal stability of such excitations, thereby providing time scales for t…
Artificial ices enable the study of geometrical frustration by design and through direct observation. However, it has proven difficult to achieve tailored long-range ordering of their diverse configurations, limiting both fundamental and applied research directions. We designed an artificial spin structure that produces a magnetic charge ice with tunable long-range ordering of eight different configurations. We also developed a technique to precisely manipulate the local magnetic charge states and demonstrate write-read-erase multifunctionality at room temperature. This globally reconfigurable…
Artificial spin ice is a frustrated magnetic two-dimensional nano-material, recently employed to study variety of tailor-designed unusual collective behaviours. Recently proposed extensions to three dimensions are based on self-assembly techniques and allow little control over geometry and disorder. We present a viable design for the realization of a three-dimensional artificial spin ice with the same level of precision and control allowed by lithographic nano-fabrication of the popular two-dimensional case. Our geometry is based on layering already available two-dimensional artificial spin ic…
Artificial spin ices are frustrated spin systems that can be engineered, wherein fine tuning of geometry and topology has allowed the design and characterization of exotic emergent phenomena at the constituent level. Here we report a realization of spin ice in a lattice of superconducting qubits. Unlike conventional artificial spin ice, our system is disordered by both quantum and thermal fluctuations. The ground state is classically described by the ice rule, and we achieve control over a fragile degeneracy point leading to a Coulomb phase. The ability to pin individual spins allows us to dem…
