Artificial ‘spin ice’ in a geometrically frustrated lattice of nanoscale ferromagnetic islands

Genetically tunable frustration controls allostery in an intrinsically disordered transcription factor

Intrinsically disordered proteins (IDPs) present a functional paradox because they lack stable tertiary structure, but nonetheless play a central role in signaling, utilizing a process known as allostery. Historically, allostery in structured proteins has been interpreted in terms of propagated structural changes that are induced by effector binding. Thus, it is not clear how IDPs, lacking such well-defined structures, can allosterically affect function. Here, we show a mechanism by which an IDP can allosterically control function by simultaneously tuning transcriptional activation and repression, using a novel strategy that relies on the principle of ‘energetic frustration’. We demonstrate that human glucocorticoid receptor tunes this signaling in vivo by producing translational isoforms differing only in the length of the disordered region, which modulates the degree of frustration. We expect this frustration-based model of allostery will prove to be generally important in explaining signaling in other IDPs.

Proteins carry out most of the key tasks inside cells. To perform these roles, proteins must fold up to form complex three-dimensional structures. Researchers used to think that the useful parts of proteins all had set structures. However, we now know that ‘disordered’ proteins with variable structures are common and disordered parts of proteins can have vital roles.

In a process called allosteric regulation, regulator molecules can increase or decrease the activity of a protein by binding to it. This binding was thought to work by changing the structure of the protein, but it was not clear how this works in disordered proteins. To investigate, Li et al. studied a disordered protein called glucocorticoid receptor, and found that disordered regions can have opposing effects on other regions of the protein. This creates a ‘tug-of-war’ that Li et al. term “energetic frustration”, whereby the activity of the protein results from the combination of the opposing interactions.

Further investigation revealed that the glucorticoid receptor produces different versions of itself that have different degrees of energetic frustration, which alters how effectively the proteins perform their tasks. This means that the protein can regulate its own activity even in the absence of binding to regulator molecules.

The concept of energetic frustration could enhance our understanding of the many different proteins that contain disordered regions. Eventually, this knowledge could be used to develop drugs that alter the activity of these proteins and so could form part of treatments for a wide range of conditions including autoimmune diseases (such as rheumatoid arthritis and lupus), cancers, and organ rejection for transplant patients. The results presented by Li et al. suggest where more research is needed to achieve this goal. For example, we need to understand more about the stability of disordered protein regions, and to identify which surfaces of the proteins interact with each other.

Three-dimensional nanomagnetism

Magnetic nanostructures are being developed for use in many aspects of our daily life, spanning areas such as data storage, sensing and biomedicine. Whereas patterned nanomagnets are traditionally two-dimensional planar structures, recent work is expanding nanomagnetism into three dimensions; a move triggered by the advance of unconventional synthesis methods and the discovery of new magnetic effects. In three-dimensional nanomagnets more complex magnetic configurations become possible, many with unprecedented properties. Here we review the creation of these structures and their implications for the emergence of new physics, the development of instrumentation and computational methods, and exploitation in numerous applications.

Nanoscale magnetic devices play a key role in modern technologies but current applications involve only 2D structures like magnetic discs. Here the authors review recent progress in the fabrication and understanding of 3D magnetic nanostructures, enabling more diverse functionalities.

Attraction Controls the Inversion of Order by Disorder in Buckled Colloidal Monolayers

We show how including attraction in interparticle interactions reverses the effect of fluctuations in ordering of a prototypical artificial frustrated system. Buckled colloidal monolayers exhibit the same ground state as the Ising antiferromagnet on a deformable triangular lattice, but it is unclear if ordering in the two systems is driven by the same geometric mechanism. By a real-space expansion we find that, for buckled colloids, bent stripes constitute the stable phase, whereas in the Ising antiferromagnet straight stripes are favored. For generic pair potentials we show that attraction governs this selection mechanism, in a manner that is linked to local packing considerations. This supports the geometric origin of entropy in jammed sphere packings and provides a tool for designing self-assembled colloidal structures.

Metal-ion induced ferromagnetic polarization in a mixed-spin system

Three new 3d-3d heterometallic complexes, [CuM^II(hmb)₆(OH)]ClO₄·H₂O (M = Zn (1), Ni (2) and Co (3)) (Hhmb = 2-hydroxy-3-methoxy-benzaldehyde), have been synthesized. Structural analysis reveals that the three complexes are isostructural. Three Cu^II ions are in a perfect trigonal geometrical frustration and form a tetrahedral frustrated system with the introduced fourth ion Zn^II/Ni^II/Co^II. Magnetic studies indicate the antiferromagnetic coupling between metal ions in all 1, 2 and 3. Due to the geometrical frustration, spin-frustrated magnetism is also a typical feature of 1-3 and the magnetostructural correlation is far more complicated than their structures. The detailed magnetic investigation found that the ground state spin of 2 cannot be simply determined by the antiferromagnetically linear arrangement of spins, because the strong antiferromagnetic coupling between Cu^II and Ni^II ions quenches the spin frustration and ferromagnetically polarizes the spins of the [Cu] unit. Contrarily, the antiferromagnetic coupling between Cu^II and Co^II ions is not strong enough in 3, so there is no similar behaviour compared to 2.

Dynamic Control of Topological Defects in Artificial Colloidal Ice

We demonstrate the use of an external field to stabilize and control defect lines connecting topological monopoles in spin ice. For definiteness we perform Brownian dynamics simulations with realistic units mimicking experimentally realized artificial colloidal spin ice systems, and show how defect lines can grow, shrink or move under the action of direct and alternating fields. Asymmetric alternating biasing forces can cause the defect line to ratchet in either direction, making it possible to precisely position the line at a desired location. Such manipulation could be employed to achieve mobile information storage in these metamaterials.

Thermal transport in the Fermi-Pasta-Ulam model with long-range interactions

We study the thermal transport properties of the one-dimensional Fermi-Pasta-Ulam model (β type) with long-range interactions. The strength of the long-range interaction decreases with the (shortest) distance between the lattice sites as distance^{-δ}, where δ≥0. Two Langevin heat baths at unequal temperatures are connected to the ends of the one-dimensional lattice via short-range harmonic interactions that drive the system away from thermal equilibrium. In the nonequilibrium steady state the heat current, thermal conductivity, and temperature profiles are computed by solving the equations of motion numerically. It is found that the conductivity κ has an interesting nonmonotonic dependence with δ with a maximum at δ=2.0 for this model. Moreover, at δ=2.0,κ diverges almost linearly with system size N and the temperature profile has a negligible slope, as one expects in ballistic transport for an integrable system. We demonstrate that the nonmonotonic behavior of the conductivity and the nearly ballistic thermal transport at δ=2.0 obtained under nonequilibrium conditions can be explained consistently by studying the variation of largest Lyapunov exponent λ_{max} with δ, and excess energy diffusion in the equilibrium microcanonical system.

Emergent inequality and self-organized social classes in a network of power and frustration

We propose a simple agent-based model on a network to conceptualize the allocation of limited wealth among more abundant expectations at the interplay of power, frustration, and initiative. Concepts imported from the statistical physics of frustrated systems in and out of equilibrium allow us to compare subjective measures of frustration and satisfaction to collective measures of fairness in wealth distribution, such as the Lorenz curve and the Gini index. We find that a completely libertarian, law-of-the-jungle setting, where every agent can acquire wealth from or lose wealth to anybody else invariably leads to a complete polarization of the distribution of wealth vs. opportunity. This picture is however dramatically ameliorated when hard constraints are imposed over agents in the form of a limiting network of transactions. There, an out of equilibrium dynamics of the networks, based on a competition between power and frustration in the decision-making of agents, leads to network coevolution. The ratio of power and frustration controls different dynamical regimes separated by kinetic transitions and characterized by drastically different values of equality. It also leads, for proper values of social initiative, to the emergence of three self-organized social classes, lower, middle, and upper class. Their dynamics, which appears mostly controlled by the middle class, drives a cyclical regime of dramatic social changes.

Layer-by-layer epitaxial thin films of the pyrochlore Tb2Ti2O7

Layer-by-layer epitaxial growth of the pyrochlore magnet Tb₂Ti₂O₇ on the isostructural substrate Y₂Ti₂O₇ results in high-quality single crystal films of up to 60 nm thickness. Substrate-induced strain is shown to act as a strong and controlled perturbation to the exotic magnetism of Tb₂Ti₂O₇, opening up the general prospect of strain-engineering the diverse magnetic and electrical properties of pyrochlore oxides.

Programmability of Co-antidot lattices of optimized geometry

Programmability of stable magnetization configurations in a magnetic device is a highly desirable feature for a variety of applications, such as in magneto-transport and spin-wave logic. Periodic systems such as antidot lattices may exhibit programmability; however, to achieve multiple stable magnetization configurations the lattice geometry must be optimized. We consider the magnetization states in Co-antidot lattices of ≈50 nm thickness and ≈150 nm inter-antidot distance. Micromagnetic simulations were applied to investigate the magnetization states around individual antidots during the reversal process. The reversal processes predicted by micromagnetics were confirmed by experimental observations. Magnetization reversal in these antidots occurs via field driven transition between 3 elementary magnetization states – termed G, C and Q. These magnetization states can be described by vectors, and the reversal process proceeds via step-wise linear operations on these vector states. Rules governing the co-existence of the three magnetization states were empirically observed. It is shown that in an n × n antidot lattice, a variety of field switchable combinations of G, C and Q can occur, indicating programmability of the antidot lattices.

Topological frustration of artificial spin ice

Frustrated systems, typically characterized by competing interactions that cannot all be simultaneously satisfied, display rich behaviours not found elsewhere in nature. Artificial spin ice takes a materials-by-design approach to studying frustration, where lithographically patterned bar magnets mimic the frustrated interactions in real materials but are also amenable to direct characterization. Here, we introduce controlled topological defects into square artificial spin ice lattices in the form of lattice edge dislocations and directly observe the resulting spin configurations. We find the presence of a topological defect produces extended frustration within the system caused by a domain wall with indeterminate configuration. Away from the dislocation, the magnets are locally unfrustrated, but frustration of the lattice persists due to its topology. Our results demonstrate the non-trivial nature of topological defects in a new context, with implications for many real systems in which a typical density of dislocations could fully frustrate a canonically unfrustrated system.

Frustrated systems display rich behaviour due to unsatisfied competing interactions. Here, the authors report extended frustration by introducing controlled topological defects into square artificial spin ice lattices, demonstrating the potential of lattice topology to induce frustration.

Thermally induced magnetic relaxation in square artificial spin ice

The properties of natural and artificial assemblies of interacting elements, ranging from Quarks to Galaxies, are at the heart of Physics. The collective response and dynamics of such assemblies are dictated by the intrinsic dynamical properties of the building blocks, the nature of their interactions and topological constraints. Here we report on the relaxation dynamics of the magnetization of artificial assemblies of mesoscopic spins. In our model nano-magnetic system - square artificial spin ice – we are able to control the geometrical arrangement and interaction strength between the magnetically interacting building blocks by means of nano-lithography. Using time resolved magnetometry we show that the relaxation process can be described using the Kohlrausch law and that the extracted temperature dependent relaxation times of the assemblies follow the Vogel-Fulcher law. The results provide insight into the relaxation dynamics of mesoscopic nano-magnetic model systems, with adjustable energy and time scales, and demonstrates that these can serve as an ideal playground for the studies of collective dynamics and relaxations.

Defect Dynamics in Artificial Colloidal Ice: Real-Time Observation, Manipulation, and Logic Gate

We study the defect dynamics in a colloidal spin ice system realized by filling a square lattice of topographic double well islands with repulsively interacting magnetic colloids. We focus on the contraction of defects in the ground state, and contraction or expansion in a metastable biased state. Combining real-time experiments with simulations, we prove that these defects behave like emergent topological monopoles obeying a Coulomb law with an additional line tension. We further show how to realize a completely resettable "nor" gate, which provides guidelines for fabrication of nanoscale logic devices based on the motion of topological magnetic monopoles.

Energy rectification in quantum graded spin chains: Analysis of the XXZ model

In this work, with focus on the energy-transport properties in quantum, low-dimensional, graded materials, we address the investigation of the energy (and spin) current in XXZ open chains with graded inner structures and driven out of equilibrium by magnetization pumping applied at the ends. We study several types of graded structures in different situations in order to show a ubiquitous occurrence of energy rectification, even for the system under a homogeneous magnetic field. Due to technical difficulties, we carry out the computation for small chains, but we present arguments that indicate the extension of some results to larger systems. Recalling the generic existence of energy rectification in classical, graded materials, which are described by anharmonic chains of oscillators, and recalling also the anharmonicity of these XXZ models, which involve quartic terms in more transparent representation in terms of fermionic creation and annihilation operators, we may say that our results extend the ubiquity of energy rectification occurrence in classical graded materials to the case of quantum systems.

Magnetic Yoking and Tunable Interactions in FePt-Based Hard/Soft Bilayers

Magnetic interactions in magnetic nanostructures are critical to nanomagnetic and spintronic explorations. Here we demonstrate an extremely sensitive magnetic yoking effect and tunable interactions in FePt based hard/soft bilayers mediated by the soft layer. Below the exchange length, a thin soft layer strongly exchange couples to the perpendicular moments of the hard layer; above the exchange length, just a few nanometers thicker, the soft layer moments turn in-plane and act to yoke the dipolar fields from the adjacent hard layer perpendicular domains. The evolution from exchange to dipolar-dominated interactions is experimentally captured by first-order reversal curves, the ΔM method, and polarized neutron reflectometry, and confirmed by micromagnetic simulations. These findings demonstrate an effective yoking approach to design and control magnetic interactions in wide varieties of magnetic nanostructures and devices.

Thermodynamics of emergent magnetic charge screening in artificial spin ice

Electric charge screening is a fundamental principle governing the behaviour in a variety of systems in nature. Through reconfiguration of the local environment, the Coulomb attraction between electric charges is decreased, leading, for example, to the creation of polaron states in solids or hydration shells around proteins in water. Here, we directly visualize the real-time creation and decay of screened magnetic charge configurations in a two-dimensional artificial spin ice system, the dipolar dice lattice. By comparing the temperature dependent occurrence of screened and unscreened emergent magnetic charge defects, we determine that screened magnetic charges are indeed a result of local energy reduction and appear as a transient minimum energy state before the system relaxes towards the predicted ground state. These results highlight the important role of emergent magnetic charges in artificial spin ice, giving rise to screened charge excitations and the emergence of exotic low-temperature configurations.

Inspired by the physics of bulk frustrated materials, arrays of coupled nanomagnets have been widely explored for the study of collective ordering and emergent behaviour. Here, the authors demonstrate interaction-driven charge screening in a thermally active artificial spin ice lattice.

Combinatorial design of textured mechanical metamaterials

The structural complexity of metamaterials is limitless, but, in practice, most designs comprise periodic architectures that lead to materials with spatially homogeneous features. More advanced applications in soft robotics, prosthetics and wearable technology involve spatially textured mechanical functionality, which requires aperiodic architectures. However, a naive implementation of such structural complexity invariably leads to geometrical frustration (whereby local constraints cannot be satisfied everywhere), which prevents coherent operation and impedes functionality. Here we introduce a combinatorial strategy for the design of aperiodic, yet frustration-free, mechanical metamaterials that exhibit spatially textured functionalities. We implement this strategy using cubic building blocks-voxels-that deform anisotropically, a local stacking rule that allows cooperative shape changes by guaranteeing that deformed building blocks fit together as in a three-dimensional jigsaw puzzle, and three-dimensional printing. These aperiodic metamaterials exhibit long-range holographic order, whereby the two-dimensional pixelated surface texture dictates the three-dimensional interior voxel arrangement. They also act as programmable shape-shifters, morphing into spatially complex, but predictable and designable, shapes when uniaxially compressed. Finally, their mechanical response to compression by a textured surface reveals their ability to perform sensing and pattern analysis. Combinatorial design thus opens up a new avenue towards mechanical metamaterials with unusual order and machine-like functionalities.

Magnetostatic Interactions in Self-Assembled CoxNi1-xFe2O4/BiFeO3 Multiferroic Nanocomposites

Self-assembled vertically aligned oxide nanocomposites consisting of magnetic pillars embedded in a ferroelectric matrix have been proposed for logic devices made from arrays of magnetostatically interacting pillars. To control the ratio between the nearest neighbor interaction field and the switching field of the pillars, the pillar composition CoxNi1-xFe2O4 was varied over the range 0 ≤ x ≤ 1, which alters the magnetoelastic and magnetocrystalline anisotropy and the saturation magnetization. Nanocomposites were templated into square arrays of pillars in which the formation of a "checkerboard" ground state after ac-demagnetization indicated dominant magnetostatic interactions. The effect of switching field distribution in disrupting the antiparallel nearest neighbor configuration was analyzed using an Ising model and compared with experimental results.

Nano- and micro-patterning biotemplated magnetic CoPt arrays

Patterned thin-films of magnetic nanoparticles (MNPs) can be used to make: surfaces for manipulating and sorting cells, sensors, 2D spin-ices and high-density data storage devices. Conventional manufacture of patterned magnetic thin-films is not environmentally friendly because it uses high temperatures (hundreds of degrees Celsius) and high vacuum, which requires expensive specialised equipment. To tackle these issues, we have taken inspiration from nature to create environmentally friendly patterns of ferromagnetic CoPt using a biotemplating peptide under mild conditions and simple apparatus. Nano-patterning via interference lithography (IL) and micro-patterning using micro-contact printing (μCP) were used to create a peptide resistant mask onto a gold surface under ambient conditions. We redesigned a biotemplating peptide (CGSGKTHEIHSPLLHK) to self-assemble onto gold surfaces, and mineralised the patterns with CoPt at 18 °C in water. Ferromagnetic CoPt is biotemplated by the immobilised peptides, and the patterned MNPs maintain stable magnetic domains. This bioinspired study offers an ecological route towards developing biotemplated magnetic thin-films for use in applications such as sensing, cell manipulation and data storage.

Fragmentation of magnetism in artificial kagome dipolar spin ice

Geometrical frustration in magnetic materials often gives rise to exotic, low-temperature states of matter, such as the ones observed in spin ices. Here we report the imaging of the magnetic states of a thermally active artificial magnetic ice that reveal the fingerprints of a spin fragmentation process. This fragmentation corresponds to a splitting of the magnetic degree of freedom into two channels and is evidenced in both real and reciprocal space. Furthermore, the internal organization of both channels is interpreted within the framework of a hybrid spin–charge model that directly emerges from the parent spin model of the kagome dipolar spin ice. Our experimental and theoretical results provide insights into the physics of frustrated magnets and deepen our understanding of emergent fields through the use of tailor-made magnetism.

By nanofabricating arrays of dipolar-coupled bistable single-domain nanomagnets, artificial model systems exhibiting collective ordering may be realized. Here, the authors present signatures of spin fragmentation in low-energy states of an artificial kagome ice.

Direct imaging of coexisting ordered and frustrated sublattices in artificial ferromagnetic quasicrystals

We have used scanning electron microscopy with polarization analysis and photoemission electron microscopy to image the two-dimensional magnetization of permalloy films patterned into Penrose P2 tilings (P2T). The interplay of exchange interactions in asymmetrically coordinated vertices and short-range dipole interactions among connected film segments stabilize magnetically ordered, spatially distinct sublattices that coexist with frustrated sublattices at room temperature. Numerical simulations that include long-range dipole interactions between sublattices agree with images of as-grown P2T samples and predict a magnetically ordered ground state for a two-dimensional quasicrystal lattice of classical Ising spins.

Dynamics of Bound Monopoles in Artificial Spin Ice: How to Store Energy in Dirac Strings

Dirac strings in spin ices are lines of reversed dipoles joining two quasiparticle excitations. These excitations behave as unbound emergent monopoles if the tension of Dirac strings vanishes. In this Letter, analytical and numerical analysis are used to study the dynamics of two-dimensional dipolar spin ices, artificially created analogs of bulk spin ice, in the regime of bound monopoles. It is shown that, in this regime, strings, rather than monopoles, are effective degrees of freedom explaining the finite-width band of Pauling states. A measurable prediction of path-time dependence of endpoints of a stretched and, then, released Dirac string is made and verified via simulations. It is shown that string dynamics is defined by the characteristic tension-to-mass ratio, which is determined by the fine structure constant and lattice dependent parameter. It is proposed to use string tension to achieve spontaneous magnetic currents. A concept of an energy storing device on the basis of this principle is proposed and illustrated by an experimental demonstration. A scheme of independent measurement at the nanoscale is proposed.

Engineering of frustration in colloidal artificial ices realized on microfeatured grooved lattices

Artificial spin ice systems, namely lattices of interacting single domain ferromagnetic islands, have been used to date as microscopic models of frustration induced by lattice topology, allowing for the direct visualization of spin arrangements and textures. However, the engineering of frustrated ice states in which individual spins can be manipulated in situ and the real-time observation of their collective dynamics remain both challenging tasks. Inspired by recent theoretical advances, here we realize a colloidal version of an artificial spin ice system using interacting polarizable particles confined to lattices of bistable gravitational traps. We show quantitatively that ice-selection rules emerge in this frustrated soft matter system by tuning the strength of the pair interactions between the microscopic units. Via independent control of particle positioning and dipolar coupling, we introduce monopole-like defects and strings and use loops with defined chirality as an elementary unit to store binary information.

Visualizing the dynamics of electron spins in frustrated systems is a challenging task, which may require an alternative way at the microscale. Here, the authors realize an artificial system composed of interacting colloidal particles to mimick frustrated spins, which is potentially helpful in information storage.

Geometric Frustration of Colloidal Dimers on a Honeycomb Magnetic Lattice

We study the phase behavior and the collective dynamics of interacting paramagnetic colloids assembled above a honeycomb lattice of triangular shaped magnetic minima. A frustrated colloidal molecular crystal is realized when filling these potential minima with exactly two particles per pinning site. External in-plane rotating fields are used to anneal the system into different phases, including long range ordered stripes, random fully packed loops, labyrinth and disordered states. At a higher amplitude of the annealing field, the dimer lattice displays a two-step melting transition where the initially immobile dimers perform first localized rotations and later break up by exchanging particles across consecutive lattice minima.

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.

Specific Heat of Square Spin Ice in Finite Point Ising-Like Dipoles Model

In the model of finite number (up to 24) of point Ising-like magnetic dipoles with magnetostatic interaction on square 2D lattice within the framework of statistical physics, with using Gibbs formalism and by the means of Metropolis algorithm the heating dependence of temperature has been evaluated. The temperature dependence of the heat capacity on finite number of point dipoles has the finite value of maximum. Together with increase of the system in size the heating peak grows and moves to the area with higher temperature. The obtained results are useful in experimental verification of statistical models, as well as in development and testing of approximate calculation methods of systems with great number of particles.

Emergence and mobility of monopoles in a unidirectional arrangement of magnetic nanoislands

Magnetricity, the magnetic equivalent of electricity, was recently verified experimentally for the first time. Indeed, like the stream of electric charges that produces electric current, emergent magnetic monopoles have been observed to roam freely in geometrically frustrated magnets known as spin ice. However, such phenomena demand extreme physical conditions, say, a single spin ice crystal has to be cooled to very low temperature, around 0.36 K. Candidates to overcome this difficulty are their artificial analogues, the so-called artificial spin ices. Here, we demonstrate that a specific unidirectional arrangement of nanoislands yields a peculiar system where magnetic monopoles emerge and are constrained to move along aligned dipoles, providing an ordered flow of magnetic charges at room temperature.

Topological solitons in helical strings

The low-energy physics of (quasi)degenerate one-dimensional systems is typically understood as the particle-like dynamics of kinks between stable, ordered structures. Such dynamics, we show, becomes highly nontrivial when the ground states are topologically constrained: a dynamics of the domains rather than on the domains which the kinks separate. Motivated by recently reported observations of charged polymers physio-adsorbed on nanotubes, we study kinks between helical structures of a string wrapping around a cylinder. While their motion cannot be disentangled from domain dynamics, and energy and momentum is not concentrated in the solitons, the dynamics of the domains can be folded back into a particle-like description of the local excitations.

Unique atom hyper-kagome order in Na4Ir3O8and in low-symmetry spinel modifications

Group-theoretical and thermodynamic methods of the Landau theory of phase transitions are used to investigate the hyper-kagome atomic order in structures of ordered spinels and a spinel-like Na4Ir3O8crystal. The formation of an atom hyper-kagome sublattice in Na4Ir3O8is described theoretically on the basis of the archetype (hypothetical parent structure/phase) concept. The archetype structure of Na4Ir3O8has a spinel-like structure (space group Fd\bar 3m) and composition [Na1/2Ir3/2]16d[Na3/2]16cO32e4. The critical order parameter which induces hypothetical phase transition has been stated. It is shown that the derived structure of Na4Ir3O8is formed as a result of the displacements of Na, Ir and O atoms, and ordering of Na, Ir and O atoms, orderingdxy,dxz,dyzorbitals as well. Ordering of all atoms takes place according to the type 1:3. Ir and Na atoms form an intriguing atom order: a network of corner-shared Ir triangles called a hyper-kagome lattice. The Ir atoms form nanoclusters which are named decagons. The existence of hyper-kagome lattices in six types of ordered spinel structures is predicted theoretically. The structure mechanisms of the formation of the predicted hyper-kagome atom order in some ordered spinel phases are established. For a number of cases typical diagrams of possible crystal phase states are built in the framework of the Landau theory of phase transitions. Thermodynamical conditions of hyper-kagome order formation are discussed by means of these diagrams. The proposed theory is in accordance with experimental data.

Order and thermalized dynamics in Heisenberg-like square and Kagomé spin ices

Thermodynamic properties of a spin ice model on a Kagomé lattice are obtained from dynamic simulations and compared with properties in square lattice spin ice. The model assumes three-component Heisenberg-like dipoles of an array of planar magnetic islands situated on a Kagomé lattice. Ising variables are avoided. The island dipoles interact via long-range dipolar interactions and are restricted in their motion due to local shape anisotropies. We define various order parameters and obtain them and thermodynamic properties from the dynamics of the system via a Langevin equation, solved by the Heun algorithm. Generally, a slow cooling from high to low temperature does not lead to a particular state of order, even for a set of coupling parameters that gives well thermalized states and dynamics. At very low temperature, however, square ice is more likely to reach states near the ground state than Kagomé ice, for the same island coupling parameters.

Configuration and conformation of poly(3-carbazolylacetylene) including cis and trans radicals revealed by ESR spectroscopy

π-Conjugated cis and trans radicals of poly(N-isobutyl-3-carbazolylacetylene) were stereospecifically prepared using the [Rh(norbornadiene)Cl]₂-NEt₃ catalyst, and their geometric structures were determined using the electron spin resonance (ESR) method.

Strong ferromagnetism beyond the mechanism of uncompensated surface spins in nanocrystalline GaCMn3

Bulk antiperovskite compound GaCMn₃ has an antiferromagnetic ground state. However, in nanocrystalline GaCMn₃, strong ferromagnetism with large coercive field beyond the scenario of uncompensated surface spins was observed.

Freezing and thawing of artificial ice by thermal switching of geometric frustration in magnetic flux lattices

The problem of an ensemble of repulsive particles on a potential-energy landscape is common to many physical systems and has been studied in multiple artificial playgrounds. However, the latter usually involve fixed energy landscapes, thereby impeding in situ investigations of the particles' collective response to controlled changes in the landscape geometry. Here, we experimentally realize a system in which the geometry of the potential-energy landscape can be switched using temperature as the control knob. This realization is based on a high-temperature superconductor in which we engineer a nanoscale spatial modulation of the superconducting condensate. Depending on the temperature, the flux quanta induced by an applied magnetic field see either a geometrically frustrated energy landscape that favours an ice-like flux ordering, or an unfrustrated landscape that yields a periodic flux distribution. This effect is reflected in a dramatic change in the superconductor's magneto-transport. The thermal switching of the energy landscape geometry opens new opportunities for the study of ordering and reorganization in repulsive particle manifolds.

Thermal string excitations in artificial spin-ice square dipolar array

We report on a theoretical investigation of artificial spin-ice dipolar arrays using a nanoisland shape adopted from recent experiments (Farhan et al 2013 Nature Phys. 9 375). 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 ± 4. By kinetic Monte Carlo simulations we address the thermal stability of such excitations, thereby providing time scales for their experimental observation.

Diffraction by a frustrated system: the triangular Ising antiferromagnet

Expressions are derived for diffraction by the triangular Ising antiferromagnet, a disordered lattice system consisting of two kinds of scatterer and exhibiting geometric frustration. Analysis of the expressions shows characteristics of the diffraction patterns, including the presence of Bragg and diffuse diffraction, superlattice reflections, and their behavior with temperature. These characteristics are illustrated by numerical simulations. The results have application to diffraction imaging of disordered systems.

Thermal fluctuations in artificial spin ice

Artificial spin ice systems have been proposed as a playground for the study of monopole-like magnetic excitations, similar to those observed in pyrochlore spin ice materials. Currents of magnetic monopole excitations have been observed, demonstrating the possibility for the realization of magnetic-charge-based circuitry. Artificial spin ice systems that support thermal fluctuations can serve as an ideal setting for observing dynamical effects such as monopole propagation and as a potential medium for magnetricity investigations. Here, we report on the transition from a frozen to a dynamic state in artificial spin ice with a square lattice. Magnetic imaging is used to determine the magnetic state of the islands in thermal equilibrium. The temperature-induced onset of magnetic fluctuations and excitation populations are shown to depend on the lattice spacing and related interaction strength between islands. The excitations are described by Boltzmann distributions with their factors in the frozen state relating to the blocking temperatures of the array. Our results provide insight into the design of thermal artificial spin ice arrays where the magnetic charge density and response to external fields can be studied in thermal equilibrium.

Templated self-assembly of functional oxide nanocomposites

In perovskite/spinel self-assembled oxide nanocomposites, the substrate surface plays a dominant role in determining the final morphology. Topgraphic features, such as pits and trenches, are written in the substrate using either Focused Ion Beam or wet etching through a block co-polymer mask. These features are effective at templating the self-assembly, resulting in a wide range of attainable nano-assemblies.

Magnetometry with nitrogen-vacancy defects in diamond

The isolated electronic spin system of the nitrogen-vacancy (NV) centre in diamond offers unique possibilities to be employed as a nanoscale sensor for detection and imaging of weak magnetic fields. Magnetic imaging with nanometric resolution and field detection capabilities in the nanotesla range are enabled by the atomic-size and exceptionally long spin-coherence times of this naturally occurring defect. The exciting perspectives that ensue from these characteristics have triggered vivid experimental activities in the emerging field of 'NV magnetometry'. It is the purpose of this article to review the recent progress in high-sensitivity nanoscale NV magnetometry, generate an overview of the most pertinent results of the last years and highlight perspectives for future developments. We will present the physical principles that allow for magnetic field detection with NV centres and discuss first applications of NV magnetometers that have been demonstrated in the context of nano magnetism, mesoscopic physics and the life sciences.

Physics in ordered and disordered colloidal matter composed of poly(N-isopropylacrylamide) microgel particles

This review collects and describes experiments that employ colloidal suspensions to probe physics in ordered and disordered solids and related complex fluids. The unifying feature of this body of work is its clever usage of poly(N-isopropylacrylamide) (PNIPAM) microgel particles. These temperature-sensitive colloidal particles provide experimenters with a 'knob' for in situ control of particle size, particle interaction and particle packing fraction that, in turn, influence the structural and dynamical behavior of the complex fluids and solids. A brief summary of PNIPAM particle synthesis and properties is given, followed by a synopsis of current activity in the field. The latter discussion describes a variety of soft matter investigations including those that explore formation and melting of crystals and clusters, and those that probe structure, rearrangement and rheology of disordered (jammed/glassy) and partially ordered matter. The review, therefore, provides a snapshot of a broad range of physics phenomenology which benefits from the unique properties of responsive microgel particles.

Review and prospects of magnonic crystals and devices with reprogrammable band structure

Research efforts addressing spin waves (magnons) in microand nanostructured ferromagnetic materials have increased tremendously in recent years. Corresponding experimental and theoretical work in magnonics faces significant challenges in that spinwave dispersion relations are highly anisotropic and different magnetic states might be realized via, for example, the magnetic field history. At the same time, these features offer novel opportunities for wave control in solids going beyond photonics and plasmonics. In this topical review we address materials with a periodic modulation of magnetic parameters that give rise to artificially tailored band structures and allow unprecedented control of spin waves. In particular, we discuss recent achievements and perspectives of reconfigurable magnonic devices for which band structures can be reprogrammed during operation. Such characteristics might be useful for multifunctional microwave and logic devices operating over a broad frequency regime on either the macroor nanoscale.

Restoration of the third law in spin ice thin films

A characteristic feature of spin ice is its apparent violation of the third law of thermodynamics. This leads to a number of interesting properties including the emergence of an effective vacuum for magnetic monopoles and their currents – magnetricity. Here we add a new dimension to the experimental study of spin ice by fabricating thin epitaxial films of Dy₂Ti₂O₇, varying between 5 and 60 monolayers on an inert substrate. The films show the distinctive characteristics of spin ice at temperatures >2 K, but at lower temperature we find evidence of a zero entropy state. This restoration of the third law in spin ice thin films is consistent with a predicted strain-induced ordering of a very unusual type, previously discussed for analogous electrical systems. Our results show how the physics of frustrated pyrochlore magnets such as spin ice may be significantly modified in thin-film samples.

In bulk, the spin ice Dy₂Ti₂O₇ has posed an enigma because – due to its slow dynamics – it is unclear whether and how the material will reach a zero entropy state at zero temperature. Here, the authors show that in thin films of Dy₂Ti₂O₇ a zero entropy state is induced at 0.4 K, plausibly by lattice strain.

Complex ordered patterns in mechanical instability induced geometrically frustrated triangular cellular structures

Geometrical frustration arises when a local order cannot propagate throughout the space because of geometrical constraints. This phenomenon plays a major role in many systems leading to disordered ground-state configurations. Here, we report a theoretical and experimental study on the behavior of buckling-induced geometrically frustrated triangular cellular structures. To our surprise, we find that buckling induces complex ordered patterns which can be tuned by controlling the porosity of the structures. Our analysis reveals that the connected geometry of the cellular structure plays a crucial role in the generation of ordered states in this frustrated system.

Quantitative decoding of interactions in tunable nanomagnet arrays using first order reversal curves

To develop a full understanding of interactions in nanomagnet arrays is a persistent challenge, critically impacting their technological acceptance. This paper reports the experimental, numerical and analytical investigation of interactions in arrays of Co nanoellipses using the first-order reversal curve (FORC) technique. A mean-field analysis has revealed the physical mechanisms giving rise to all of the observed features: a shift of the non-interacting FORC-ridge at the low-H_C end off the local coercivity H_C axis; a stretch of the FORC-ridge at the high-H_C end without shifting it off the H_C axis; and a formation of a tilted edge connected to the ridge at the low-H_C end. Changing from flat to Gaussian coercivity distribution produces a negative feature, bends the ridge, and broadens the edge. Finally, nearest neighbor interactions segment the FORC-ridge. These results demonstrate that the FORC approach provides a comprehensive framework to qualitatively and quantitatively decode interactions in nanomagnet arrays.

A bilayer triangular lattice with crown-like Co7 spin cluster SBUs exhibiting high spin frustration

An unprecedented crown-like Co₇(OH)₆ spin cluster is assembled in a bilayer triangular lattice, showing high spin frustration.