Artificial Square Research Articles

Crystallites of magnetic charges in artificial spin ice

Artificial spin ice is a class of lithographically created arrays of interacting ferromagnetic nanometre-scale islands. It was introduced to investigate many-body phenomena related to frustration and disorder in a material that could be tailored to precise specifications and imaged directly. Because of the large magnetic energy scales of these nanoscale islands, it has so far been impossible to thermally anneal artificial spin ice into desired thermodynamic ensembles; nearly all studies of artificial spin ice have either treated it as a granular material activated by alternating fields or focused on the as-grown state of the arrays. This limitation has prevented experimental investigation of novel phases that can emerge from the nominal ground states of frustrated lattices. For example, artificial kagome spin ice, in which the islands are arranged on the edges of a hexagonal net, is predicted to support states with monopolar charge order at entropies below that of the previously observed pseudo-ice manifold. Here we demonstrate a method for thermalizing artificial spin ices with square and kagome lattices by heating above the Curie temperature of the constituent material. In this manner, artificial square spin ice achieves unprecedented thermal ordering of the moments. In artificial kagome spin ice, we observe incipient crystallization of the magnetic charges embedded in pseudo-ice, with crystallites of magnetic charges whose size can be controlled by tuning the lattice constant. We find excellent agreement between experimental data and Monte Carlo simulations of emergent charge-charge interactions.

An artificial bee colony-least square algorithm for solving harmonic estimation problems

Solving harmonic estimation problems in power quality signals has attained significant importance in recent times. Stochastic optimization algorithms have been successfully employed to determine magnitude of this information in an unknown signal contaminated with noise or containing additive dc decaying components. The present paper shows how a recently proposed stochastic optimization algorithm, called artificial bee colony algorithm, can be hybridized with least square algorithm to solve these problems effectively. The proposed algorithm has been tested for a series of case studies employing different benchmark environment situations and our extensive simulation tests validate the usefulness of the proposed algorithm and it could largely outperform several competing simulation algorithms, proposed in the recent past. The effectiveness of the proposed algorithm is further demonstrated for those situations where the number of harmonics present in the signal is also not known, along with the magnitude and phase of each harmonic.

Nambu monopoles interacting with lattice defects in a two-dimensional artificial square spin ice

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 interaction between a pair of Nambu monopoles with the deformed island is a problem involving four magnetic charges (two pairs of opposite poles) and a string. We also sketch the configuration of the field lines of these four charges to confirm this picture. The influence of the string on this interaction decays rapidly with the string distance from the defect.

Real and effective thermal equilibrium in artificial square spin ices

We have studied the magnetic microstates arising from single-shot thermalization processes that occur during growth in artificial square spin ices. The populations of different vertex types can be controlled by the system's lattice constant, as well as by the deposition of different material underlayers. The statistics of these populations are well described by a simple model based on the canonical ensemble, which is used to infer an effective temperature for an arrested microstate. The normalized energy level spacings of the different magnetic vertex configurations are found to be very close to those predicted for a point-dipole model: this is shown to be a very good approximation to energy level spacings calculated for finite-sized cuboid magnetic bodies. States prepared with a rotating field (an athermal method commonly used to lower the energy of these systems) cannot be described by this model, showing that such a method does not induce a near-equilibrium state.

Linear field demagnetization of artificial magnetic square ice

We have studied experimentally the states formed in artificial square ice nanomagnet systems following demagnetisation in a rotating in-plane applied magnetic field that reduces to zero in a manner that is linear in time. The final states are found to be controlled via the system's lattice constant, which determines the strength of the magnetostatic interactions between the elements, as well as the field ramping rate. We understand these effects as a requirement that the system undergoes a sufficiently large number of active rotations within the critical field window in which elements may be reversed, such that the interactions are allowed to locally exert their influence if the ground state is to be approached. On the other hand, if quenched disorder is too strong when compared to the interaction strength, any close approach to the ground state is impossible. These results show that it is not necessary for there to be any ac component to the field amplitude that is applied to the system during demagnetisation, which is the method almost exclusively employed in field protocols reported to date. Furthermore, by optimising the parameters of our linear demagnetisation protocol, the largest field-generated ground state domains yet reported are found.

Hysteresis and return-point memory in colloidal artificial spin ice systems

Using computer simulations, we investigate hysteresis loops and return-point memory for artificial square and kagome spin ice systems by cycling an applied bias force and comparing microscopic effective spin configurations throughout the hysteresis cycle. Return-point memory loss is caused by motion of individual defects in kagome ice or of grain boundaries in square ice. In successive cycles, return-point memory is recovered rapidly in kagome ice. Memory is recovered more gradually in square ice due to the extended nature of the grain boundaries. Increasing the amount of quenched disorder increases the defect density but also enhances the return-point memory since the defects become trapped more easily.

Magnetic interactions and reversal of artificial square spin ices

Artificial spin ices are nanoscale geometrically engineered systems that mimic the behavior of bulk spin ices at room temperature. We describe the nanoscale magnetic interactions in a square spin ice lattice by an experimentally verified model that accounts for the correct shape of the magnetic islands. Magnetic force microscopy measurements on lithographically fabricated lattices are compared to Monte Carlo simulations of the reversal process of two lattices with different lattice spacings. Lattice node statistics and correlations show significant differences in the reversal mechanism for lattices with different spacings. The effect of structural variations is also compared for the two lattice reversals.

Magnetic hysteresis of an artificial square ice studied by in-plane Bragg x-ray resonant magnetic scattering

We report X-ray resonant magnetic scattering studies of a Permalloy artificial square ice nanomagnet array, focussing on the field-driven evolution of the sum Σ and difference Δ signals of left and right handed circularly polarized synchrotron X-rays at different lateral positions in reciprocal space Qx. We used X-rays tuned to the Fe L3 resonance energy, with the scattering plane aligned along a principal symmetry axis of the array. Details of the specular Δ hysteresis curve are discussed, following the system magnetization from an initial demagnetized state. The periodic structure gives rise to distinct peaks at in-plane reciprocal Bragg positions, as shown by fitting Σ(Qx) to a model based on a simple unit cell structure. Diffraction order-dependent hysteresis in Δ is observed, indicative of the reordering of magnetization on the system's two interpenetrating sublattices, which markedly deviates from an ideal Ising picture under strong applied fields.

Extending spin ice concepts to another geometry: The artificial triangular spin ice

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 behave as a kind of Nambu monopoles (two opposite monopoles connected by an energetic string). Indeed, our results suggest that the monopoles charge value may have a universal value while the string tension could be tuned by changing the system's geometry, probably allowing the design of systems with different string tensions. Our Monte Carlo results suggest a phase transition in the Ising universality class where the mean distance between monopoles and anti-monopoles increases considerably at the critical temperature. The differences on the vertices topologies seem to facilitate the experimental achievement of the system's ground-state, thereby allowing a more detailed experimental study of the system's properties.

Domain dynamics and fluctuations in artificial square ice at finite temperatures

The thermally driven formation and evolution of vertex domains is studied for square artificial spin ice. A self-consistent mean-field theory is used to show how domains of ground state ordering form spontaneously, and how these evolve in the presence of disorder. The role of fluctuations is studied using Monte Carlo simulations and analytical modelling. Domain wall dynamics are shown to be driven by a biasing of random fluctuations towards processes that shrink closed domains, and fluctuations within domains are shown to generate isolated small excitations, which may stabilize as the effective temperature is lowered. Domain dynamics and fluctuations are determined by interaction strengths, which are controlled by inter-element spacing. The role of interaction strength is studied via experiments and Monte Carlo simulations. Our mean-field model is applicable to ferroelectric ‘spin’ ice, and we show that features similar to those of magnetic spin ice can be expected, but with different characteristic temperatures and rates.

Melting artificial spin ice

Artificial spin ice arrays of micromagnetic islands are a means of engineering additional energy scales and frustration into magnetic materials. Here we demonstrate a magnetic phase transition in an artificial square spin ice and use the symmetry of the lattice to verify the presence of excitations far below the ordering temperature. We do this by measuring the temperature-dependent magnetization in different principal directions and comparing it with simulations of idealized statistical mechanical models. Our results confirm a dynamical pre-melting of the artificial spin ice structure at a temperature well below the intrinsic ordering temperature of the island material. We thus create a spin ice array that has the real thermal dynamics of artificial spins over an extended temperature range.

Intelligent Operation and Control of Refrigeration Craft in Cold Storage

In this paper, we discuss the difference between intelligent and non-intelligent system, and analyze some problems in the development and research of auto-control system in the cold storage. These problems involve engineering survey, predictive control of technical parameters, control reliability of machinery equipment, local control and global control. And the methods of artificial neural networks, genetic algorithm and least square are put forward to resolve them.

Thermodynamics of elementary excitations in artificial magnetic square ice

We investigate the thermodynamics of artificial square spin ice systems assuming only dipolar interactions among the islands that compose the array. Emphasis is given to the effects of temperature on elementary excitations (magnetic monopoles and their 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 with opposite charges exhibit a sharp peak and a local maximum, respectively, at the same temperature, Tp ≈ 7.2D/kB (here, D is the strength of the dipolar interaction and kB the Boltzmann constant). When the lattice size is increased, the amplitude of these features also increases but very slowly. Really, the specific heat and the maximum of the average separation dmax between oppositely charged monopoles increase logarithmically with system size, indicating that completely isolated charges could be found only at the thermodynamic limit. In general, the results obtained here suggest that, for temperatures T ⩾ Tp, these systems may exhibit a phase with separated monopoles, although the quantity dmax should not be larger than a few lattice spacings for viable artificial materials.

Magneto-optical Kerr effect studies of square artificial spin ice

We report a magneto-optical Kerr effect study of the collective magnetic response of artificial square spin ice, a lithographically defined array of single-domain ferromagnetic islands. We find that the anisotropic interisland interactions lead to a nonmonotonic angular dependence of the array coercive field. Comparisons with micromagnetic simulations indicate that the two perpendicular sublattices exhibit distinct responses to island edge roughness, which clearly influence the magnetization reversal process. Furthermore, such comparisons demonstrate that disorder associated with roughness in the island edges plays a hitherto unrecognized but essential role in the collective behavior of these systems.

Magnetic reversal of an artificial square ice: dipolar correlation and charge ordering

Magnetic reversal of an artificial square ice pattern subject to a sequence of magnetic fields applied slightly off the diagonal axis is investigated via magnetic force microscopy of the remanent states that result. Sublattice independent reversal is observed via correlated incrementally pinned flip cascades along parallel dipolar chains, as evident from analysis of vertex populations and dipolar correlation functions. Weak dipolar interactions between adjacent chains favour antialignment and give rise to weak charge ordering of ‘monopole’ vertices during the reversal process.

Thermal ground-state ordering and elementary excitations in artificial magnetic square ice

Simply cooling down an artificial spin-ice does not necessarily lead to ground-state magnetic order. But as-grown artificial square ice reaches a thermodynamic ground state, with monopole dynamics possibly involved in the thermalization.

Resolving land subsidence within the Venice Lagoon by persistent scatterer SAR interferometry

Land subsidence is a severe geologic hazard threatening the lowlying transitional coastal areas worldwide. Monitoring land subsidence has been significantly improved over the last decade by space borne earth observation techniques based on Synthetic Aperture Radar (SAR) interferometry. Within the INLET Project, funded by Magistrato alle Acque di Venezia – Venice Water Authority (VWA) and Consorzio Venezia Nuova (CVN), we use Interferometric Point Target Analysis (IPTA) to characterize the ground displacements within the Venice Lagoon. IPTA measures the movement of backscattering point targets (PTs) at the ground surface that persistently reflect radar signals emitted by the SAR system at different passes. For this study 80 ERS-1/2 and 44 ENVISAT SAR scenes recorded from 1992 to 2005 and from 2003 to 2007, respectively, have been processed. Highly reliable displacement measurements have been detected for thousands of PTs located on the lagoon margins, along the littorals, in major and small islands, and on single structures scattered within the lagoon. On the average, land subsidence ranges from less than 1mm/year to 5mm/year, with some PTs that exhibit values also larger than 10mm/year depending on both the local geologic conditions and the anthropic activities. A network of a few tens of artificial square trihedral corner reflectors (TCRs) has been established before summer 2007 in order to monitor land subsidence in the inner lagoon areas where “natural” reflectors completely lack (e.g., on the salt marshes). The first interferometric results on the TCRs appear very promising.

Artificial Square Ice and Related Dipolar Nanoarrays

We study a frustrated dipolar array recently manufactured lithographically by Wang in order to realize the square ice model in an artificial structure. We discuss models for thermodynamics and dynamics of this system. We show that an ice regime can be stabilized by small changes in the array geometry; a different magnetic state, kagome ice, can similarly be constructed. At low temperatures, the square ice regime is terminated by a thermodynamic ordering transition, which can be chosen to be ferro- or antiferromagnetic. We show that the arrays do not fully equilibrate experimentally, and identify a likely dynamical bottleneck.

Calculating a Standard Error for the Gini Coefficient: Some Further Results*

AbstractSeveral authors have suggested using the jackknife technique to approximate a standard error for the Gini coefficient. It has also been shown that the Gini measure can be obtained simply from an artificial ordinary least square (OLS) regression based on the data and their ranks. We show that obtaining an exact analytical expression for the standard error is actually a trivial matter. Further, by extending the regression framework to one involving seemingly unrelated regressions (SUR), several interesting hypotheses regarding the sensitivity of the Gini coefficient to changes in the data are readily tested in a formal manner.