Emergent Monopoles Research Articles

Slow Equilibrium Relaxation in a Chiral Magnet Mediated by Topological Defects.

We performed a pump-probe experiment on the chiral magnet Cu_{2}OSeO_{3} to study the relaxation dynamics of its noncollinear magnetic orders, employing a millisecond magnetic field pulse as the pump and resonant elastic x-ray scattering as the probe. Our findings reveal that the system requires ∼0.2 s to stabilize after the perturbation applied to both the conical and skyrmion lattice phase, which is significantly slower than the typical nanosecond timescale observed in micromagnetics. This prolonged relaxation is attributed to the formation and slow dissipation of local topological defects, such as emergent monopoles. By unveiling the experimental lifetime of these emergent singularities in a noncollinear magnetic system, our study highlights a universal relaxation mechanism in solitonic textures within the slow dynamics regime, offering new insights into topological physics and advanced information storage solutions.

Stochastic hexagonal injectors in artificial spin ice

Artificial spin ice (ASI) systems have emerged as powerful platforms for exploring the fundamental aspects of magnetic frustration and topological phenomena in condensed matter physics. In this study, we investigate the bountiful effects that result from introducing hexagonal magnetic defects into an ASI lattice. The stochastic stabilisation of a plethora of metastable states in the hexagonal defects are explored, as well as harnessing the defect magnetisation state for the selective injection of emergent monopoles of different polarities and proximities within the lattice. We demonstrate a mechanism for tailoring the ASI behaviour using the magnetic state of the defect, which is of interest to applications including magnetic memory devices and spin-based logic.

Theory of Collective Excitations in the Quadruple-Q Magnetic Hedgehog Lattices.

Hedgehog and antihedgehog spin textures in magnets behave as emergent monopoles and antimonopoles, which give rise to astonishing transport and electromagnetic phenomena. Using the Kondo-lattice model in three dimensions, we theoretically study collective spin-wave excitation modes of magnetic hedgehog lattices which have recently been discovered in itinerant magnets such as MnSi_{1-x}Ge_{x} and SrFeO_{3}. It is revealed that the spin-wave modes, which appear in the subterahertz regime, have dominant amplitudes localized at Dirac strings connecting hedgehog-antihedgehog pairs and are characterized by their translational oscillations. It is found that their spectral features sensitively depend on the number and configuration of the Dirac strings and, thus, can be exploited for identifying the topological phase transitions associated with the monopole-antimonopole pair annihilations.

Magnetoresistive Evidence of Degeneracy in Nanomagnets Obtained by Electrodeposition Technique

Inspired in pyrochlore materials presenting residual entropy and featuring collective excitation behaving like emergent monopoles, geometrically frustrated arrays of nanomagnets, denominated artificial spin ices (ASIs), were proposed as an interesting platform to investigate such excitation at room temperature. However, in such artificial systems, emergent magnetic monopoles lack the same freedom present their natural counterpart, once energetic strings connecting opposite magnetic charges arise. In this work, we aim to experimentally investigate the proposed degeneracy obtained in connected square arrays of ASIs, a characteristic that allows a reduction in the string connecting monopole–antimonopole pairs in regular non-connected ASIs and could represent an important development for technological applications of connected nanomagnets. As in general those systems are developed by nanofabrication processes involving expensive and time-consuming physical vapour deposition techniques, we also present a new nanofabrication route using an electrodeposition technique for permalloy growth in different lattice geometries as an alternative for fast and low-cost ASI system production.

Micromagnetic simulations of emergent monopole defects and magnetization reversal in connected and dipolar Square Artificial Spin Ice

Artificial spin ice (ASI) structures have garnered significant attention due to their unique properties including emergent magnetic monopoles, phase transitions, and collective switching dynamics. In this study, we employ micromagnetic simulations to investigate the magnetic microstates and magnetization reversal dynamics of square ASI with varying connectivity. In particular, we explore an intermediate or a quasi-connected system where the connectivity is altered without significantly changing the strength of dipolar interactions through the introduction of narrow gaps at the vertices. Our results reveal distinct differences in the populations of different vertex types during magnetic reversal for lattices with varying connectivity. These results suggest the possibility of engineering ASI systems in which specific vertex types can be repeatably accessed through adjustments in lattice connectivity.

Field-controlled dynamics of skyrmions and monopoles.

Magnetic monopoles, despite their ongoing experimental search as elementary particles, have inspired the discovery of analogous excitations in condensed matter systems. In chiral condensed matter systems, emergent monopoles are responsible for the onset of transitions between topologically distinct states and phases, such as in the case of transitions from helical and conical phase to A-phase comprising periodic arrays of skyrmions. By combining numerical modeling and optical characterizations, we describe how different geometrical configurations of skyrmions terminating at monopoles can be realized in liquid crystals and liquid crystal ferromagnets. We demonstrate how these complex structures can be effectively manipulated by external magnetic and electric fields. Furthermore, we discuss how our findings may hint at similar dynamics in other physical systems and their potential applications.

Exploring the phase diagram of 3D artificial spin-ice

Artificial spin-ices consist of lithographic arrays of single-domain magnetic nanowires organised into frustrated lattices. These geometries are usually two-dimensional, allowing a direct exploration of physics associated with frustration, topology and emergence. Recently, three-dimensional geometries have been realised, in which transport of emergent monopoles can be directly visualised upon the surface. Here we carry out an exploration of the three-dimensional artificial spin-ice phase diagram, whereby dipoles are placed within a diamond-bond lattice geometry. We find a rich phase diagram, consisting of a double-charged monopole crystal, a single-charged monopole crystal and conventional spin-ice with pinch points associated with a Coulomb phase. In experimental demagnetised systems, broken symmetry forces formation of ferromagnetic stripes upon the surface, forbidding the lower energy double-charged monopole crystal. Instead, we observe crystallites of single magnetic charge, superimposed upon an ice background. The crystallites are found to form due to the distribution of magnetic charge around the 3D vertex, which locally favours monopole formation.

Three-dimensional neutron far-field tomography of a bulk skyrmion lattice

AbstractMagnetic skyrmions are localized non-collinear spin textures, characterized by an integer topological charge. Commonly observed in thin systems as two-dimensional sheets, in three dimensions skyrmions form tubes that are thought to nucleate and annihilate along their depth on points of vanishing magnetization. However, a lack of techniques that can probe the bulk of the material has made it difficult to perform experimental visualizations of skyrmion lattices and their stabilization through defects. Here we present three-dimensional visualizations of a bulk Co8Zn8Mn4 skyrmion lattice through a tomographic algorithm applied to multiprojection small-angle neutron scattering measurements. Reconstructions of the sample show a disordered skyrmion lattice exhibiting three-dimensional topological transitions through emergent (anti)monopole branching and segmentation defect pathways. Our technique provides insights into skyrmion stabilization and topological transition pathways in a bulk skyrmion lattice, guiding the future development and manipulation of skyrmion materials for spintronic applications.

Evolution of Emergent Monopoles into Magnetic Skyrmion Strings.

Topological defects are fundamental concepts in physics, but little is known about the transition between distinct types across different dimensionalities. In topological magnetism, as in field theory, the transition between 1D strings and 0D monopoles is a key process whose observation has remained elusive. Here, we introduce a novel mechanism that allows for the controlled stabilization of emergent monopoles and show that magnetic skyrmion strings can be folded into monopoles. Conversely, they act as seeds out of which the entire string structure can unfold, containing its complete information. In chiral magnets, this process can be observed by resonant elastic X-ray scattering when the objects are in proximity to a polarized ferromagnet, whereby a pure monopole lattice is emerging on the surface. Our experimental proof of the reversible evolution from monopole to string sheds new light on topological defects and establishes the emergent monopole lattice as a new 3D topological phase.

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

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

Formation of magnetic biskyrmions mediated by an intrinsic emergent monopole-antimonopole pair

Various properties and potential technological applications of magnetic skyrmions have stimulated a flourishing interest in topological spin textures. Among them, biskyrmions with a rare topological charge of two are observed but their existence is still under debate. In this work, we present the formation of biskyrmion bubbles mediated by emergent monopoles via micromagnetic simulations. We find that biskyrmion bubbles and trivial bubbles share a unified three-dimensional structure, in which the relative position of an intrinsic emergent monopole-antimonopole pair dominates the two-dimensional topological property at the middle plane of magnetic uniaxial films. Biskyrmion bubbles can be transformed from trivial bubbles by the motion of emergent monopoles in confined geometry, paving the way for developing devices. These results highlight the three-dimensional aspect of skyrmion-related nanostructures and the versatile roles of emergent monopoles in topological spin textures.

Defect-induced monopole injection and manipulation in artificial spin ice

Lithographically defined arrays of nanomagnets are well placed for application in areas such as probabilistic computing or reconfigurable magnonics due to their emergent collective dynamics and writable magnetic order. Among them are artificial spin ice (ASI), which are arrays of binary in-plane macrospins exhibiting geometric frustration at the vertex interfaces. Macrospin flips in the arrays create topologically protected magnetic charges, or emergent monopoles, which are bound to an antimonopole to conserve charge. In the absence of controllable pinning, it is difficult to manipulate individual monopoles in the array without also influencing other monopole excitations or the counter-monopole charge. Here, we tailor the local magnetic order of a classic ASI lattice by introducing a ferromagnetic defect with shape anisotropy into the array. This creates monopole injection sites at nucleation fields below the critical lattice switching field. Once formed, the high energy monopoles are fixed to the defect site and may controllably propagate through the lattice under stimulation. Defect programing of bound monopoles within the array allows fine control of the pathways of inverted macrospins. Such control is a necessary prerequisite for the realization of functional devices, e. g. reconfigurable waveguide in nanomagnonic applications.

Superposition of Emergent Monopole and Antimonopole in CoTb Thin Films.

A three-dimensional singular point that consists of two oppositely aligned emergent monopoles is identified in continuous CoTb thin films, as confirmed by complementary techniques of resonant elastic x-ray scattering, Lorentz transmission electron microscopy, and scanning transmission x-ray microscopy. This new type of topological defect can be regarded as a superposition of an emergent magnetic monopole and an antimonopole, around which the source and drain of the magnetic flux overlap in space. We experimentally prove that the observed spin twist seen in Lorentz transmission electron microscopy reveals the cross section of the superimposed three-dimensional structure, providing a straightforward strategy for the observation of magnetic singularities. Such a quasiparticle provides an excellent platform for studying the rich physics of emergent electromagnetism.

Topological magnetic textures and long-range orders in terbium-based quasicrystal and approximant

The quasicrystal (QC) possesses a unique lattice structure with rotational symmetry forbidden in periodic crystals. The electric property is far from complete understanding. It has been a long-standing issue whether magnetic long-range order is realized in the QC. Here, we report our theoretical discovery of the ferromagnetic long-range order in the Tb-based QC. The difficulty in past theoretical studies on the QC was lack of the microscopic theory of the crystalline electric field (CEF), which is crucially important in the rare earth systems. By analyzing the CEF in the Tb-based QC, we clarify that magnetic anisotropy plays a key role in realizing unique magnetic textures in the Tb-based QC and approximant crystal (AC). By constructing the minimal model, we show that various magnetic textures on the icosahedron, at whose vertices Tb atoms are located, are realized. We find that the hedgehog state is characterized by the topological charge of one and the whirling-moment state is characterized by an unusually large topological charge of three. The hedgehog and whirling-moment states are shown to be realized as antiferromagnetic orders transcribed as the emergent monopole and antimonopole in the 1/1 AC. We find that these states exhibit the topological Hall effect under applied magnetic field accompanied by the topological as well as metamagnetic transition. Our model and the determined phase diagram are expected to be relevant to the broad range of the rare earth-based QCs and ACs with strong magnetic anisotropy, which are useful not only to understand magnetism but also, to explore topological properties.

Control of emergent magnetic monopole currents in artificial spin ice

The control of emergent magnetic monopoles for the generation of monopole currents in artificial spin ice is essential for their use in nanomagnet-based device applications. Here we present a scheme to inject monopole currents into an artificial square ice at specific locations, which provides a means to control the propagation of the generated emergent monopole currents. Specifically, we modify an artificial square ice by populating two of its edges with different vertex configurations consisting of two, three, and four nanomagnets meeting at a common point. After setting an initial state with a global magnetic field, injection of monopoles occurs at one of the edges where the vertices have higher switching probability. We experimentally observe this vertex-specific nucleation of emergent magnetic monopoles using x-ray photoemission electron microscopy. Additionally, we demonstrate that a lateral shift in the reversal of the magnets, leading to the formation of large domains, is consistent with theoretical simulations incorporating higher-order contributions in the magnetic Hamiltonian. Finally, we find a strong correlation between the location of emergent monopole injection and the film thickness, which is a result of the switching probability associated with the different vertex configurations.

Direct Observation of the Statics and Dynamics of Emergent Magnetic Monopoles in a Chiral Magnet.

In the three-dimensional (3D) Heisenberg model, topological point defects known as spin hedgehogs behave as emergent magnetic monopoles, i.e., quantized sources and sinks of gauge fields that couple strongly to conduction electrons, and cause unconventional transport responses such as the gigantic Hall effect. We observe a dramatic change in the Hall effect upon the transformation of a spin hedgehog crystal in a chiral magnet MnGe through combined measurements of magnetotransport and small-angle neutron scattering (SANS). At low temperatures, well-defined SANS peaks and a negative Hall signal are each consistent with expectations for a static hedgehog lattice. In contrast, a positive Hall signal takes over when the hedgehog lattice fluctuates at higher temperatures, with a diffuse SANS signal observed upon decomposition of the hedgehog lattice. Our approach provides a simple way to both distinguish and disentangle the roles of static and dynamic emergent monopoles on the augmented Hall motion of conduction electrons.

On the micromagnetic behavior of dipolar-coupled nanomagnets in defective square artificial spin ice systems

We report here the results of micromagnetic simulations of square artificial spin ice (ASI) systems with defects. The defects are introduced by the misaligning of a nanomagnet at the vertex. In these defective systems, we are able to stabilize emergent monopolelike 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 intricately related to the interplay of defects and dipolar interactions.

Spin-lattice coupling in U(1) quantum spin liquids

Quantum spin liquids (QSLs) are exotic phases with intrinsic massive entanglements. Instead of microscopic spins, fractionalized particles and gauge fluctuations are emergent, revealing QSLs' exotic natures. Quantum spins with strong spin-orbit coupling on a pyrochlore lattice, for example ${\mathrm{Pr}}_{2}{\mathrm{Zr}}_{2}{\mathrm{O}}_{7}$, are suggested to host a U(1) QSL with emergent photons, gapless excitations, as well as emergent monopoles. One of the key issues in QSLs is an interplay between emergent degrees of freedom of QSLs and conventional degrees of freedom, and we investigate the interplay by constructing a general theory of spin-lattice coupling in U(1) QSLs. We find that the coupling induces characteristic interplay between phonons and photons. For example, photons become qualitatively more stable than phonons at low temperature. We also propose mechanisms to detect emergent photons in experiments such as sound attenuation and thermal transport relying on spin-lattice coupling in U(1) QSLs.

Discovery of Emergent Photon and Monopoles in a Quantum Spin Liquid

Quantum spin liquid (QSL) is an exotic quantum phase of matter whose ground state is quantum-mechanically entangled without any magnetic ordering. A central issue concerns emergent excitations that characterize QSLs, which are hypothetically associated with quasiparticle fractionalization and topological order. Here we report highly unusual heat conduction generated by the spin degrees of freedom in a QSL state of the pyrochlore magnet Pr$_2$Zr$_2$O$_7$, which hosts spin-ice correlations with strong quantum fluctuations. The thermal conductivity in high temperature regime exhibits a two-gap behavior, which is consistent with the gapped excitations of magnetic ($M$-) and electric monopoles ($E$-particles). At very low temperatures below 200\,mK, the thermal conductivity unexpectedly shows a dramatic enhancement, which well exceeds purely phononic conductivity, demonstrating the presence of highly mobile spin excitations. This new type of excitations can be attributed to emergent photons ($\nu$-particle), coherent gapless spin excitations in a spin-ice manifold.

Semiclassical theory of anomalous transport in type-II topological Weyl semimetals

Weyl semimetals possess low energy excitations which act as monopoles of Berry curvature in momentum space. These emergent monopoles are at the heart of the extensive novel transport properties that Weyl semimetals exhibit. The singular nature of the Berry curvature around the nodal points in Weyl semimetals allows for the possibility of large anomalous transport coefficients in zero applied magnetic field. Recently a new class, termed type-II Weyl semimetals, has been demonstrated in a variety of materials, where the Weyl nodes are tilted. We present here a study of anomalous transport in this new class of Weyl semimetals. We find that the parameter governing the tilt of these type-II Weyl points is intimately related to the zero field transverse transport properties. We also find that the temperature dependence of the chemical potential plays an important role in determining how the transport coefficients can effectively probe the Berry curvature of the type-II Weyl points. We also discuss the experimental implications of our work for time-reversal breaking type-II Weyl semimetals.