Spin Ice Research Articles

Charge-neutral electronic excitations in quantum insulators.

Experiments on quantum materials have uncovered many interesting quantum phases ranging from superconductivity to a variety of topological quantum matter including the recently observed fractional quantum anomalous Hall insulators. The findings have come in parallel with the development of approaches to probe the rich excitations inherent in such systems. In contrast to observing electrically charged excitations, the detection of charge-neutral electronic excitations in condensed matter remains difficult, although they are essential to understanding a large class of strongly correlated phases. Low-energy neutral excitations are especially important in characterizing unconventional phases featuring electron fractionalization, such as quantum spin liquids, spin ices and insulators with neutral Fermi surfaces. In this Perspective, we discuss searches for neutral fermionic, bosonic or anyonic excitations in unconventional insulators, highlighting theoretical and experimental progress in probing excitonic insulators, new quantum spin liquid candidates and emergent correlated insulators based on two-dimensional layered crystals and moiré materials. We outline the promises and challenges in probing and using quantum insulators, and discuss exciting new opportunities for future advancements offered by ideas rooted in next-generation quantum materials, devices and experimental schemes.

Polar domain walls induced by sequential symmetry breaking in frustrated mechanical metamaterials

Frustration hinders ideal local interactions in systems ranging from artificial spin ices with ice rules to mechanical metamaterials featuring regular floppy modes. While geometric frustrations have been known to promote complex ordered patterns in tessellated lattice structures, there is growing interest in global frustrations due to the topologically nontrivial geometry of metamaterials. However, multiferroic orders in globally frustrated metamaterials have remained elusive. Here, we present polar domain walls constrained in flexible mechanical metamaterials with global frustration and sequential symmetry breaking. We showcase that under simple compressive loading, competing interactions in globally frustrated metamaterials give rise to mixed deformations with high-order buckling modes described by an emergent order parameter. Utilizing an elastic mechanism model, we unveil the process of sequential symmetry breaking and capture the formation of polar domain walls exhibiting a chiral distribution within a multi-well potential landscape. We further demonstrate how to eliminate frustration through torsional loading, leading to symmetry restoration. These results provide insights into the intricate interactions between order and frustration, inspiring the modulation of domain walls in macroscopic systems.

Magnetic interactions in the cooperative paramagnet Tb2Ti2O7

For about two decades, Tb2Ti2O7 has remained an enigma in condensed matter physics and frustrated magnetism. This material evades long-range order down to temperature as low as 20 mK, and, as in spin ice, its ground state exhibits puzzling diffuse magnetic scattering. To shed light on this issue, we present spin dynamics measurements by inelastic neutron scattering, which we confront with random phase approximation calculations (RPA) to determine exchange couplings capable of reproducing the dispersion of the first excited crystal electric field level. These couplings suggest that Tb2Ti2O7 lives at the boundary between several phases, in particular the spin ice and planar antiferromagnetic ones. Published by the American Physical Society 2024

Ferromagnetic resonance in three-dimensional tilted-square artificial spin ices

Ferromagnetic resonance in three-dimensional tilted-square artificial spin ices

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.

Exploring possible magnetic monopoles-induced magneto-electricity in spin ices

The possibilities of combining several degrees of freedom inside a unique material have recently been highlighted in their dynamics and proposed as information carriers in quantum devices where their cross-manipulation by external parameters such as electric and magnetic fields could enhance their functionalities. An emblematic example is that of electromagnons, spin-waves dressed with electric dipoles, that are fingerprints of multiferroics. Point-like objects have also been identified, which may take the form of excited quasiparticles. This is the case for magnetic monopoles, the exotic excitations of spin ices, that have been recently proposed to carry an electric dipole, although experimental evidences remain elusive. Presently, we investigate the electrical signature of a classical spin ice and a related compound that supports quantum fluctuations. Our in-depth study clearly attributes magneto-electricity to the correlated spin ice phase distinguishing it from extrinsic and single-ion effects. Our calculations show that the proposed model conferring magneto-electricity to monopoles is not sufficient, calling for higher-order contributions.

Brillouin light scattering spectral fingerprinting of magnetic microstates in artificial spin ice

The family of nanomagnetic arrays termed artificial spin ice (ASI) possess a vast range of metastable microstates. These states exhibit both exotic fundamental physics and more recently applied functionality, garnering attention as reconfigurable magnonic circuits and neuromorphic computing platforms. However, open questions remain on the role of microstate imperfections or angular disorder – particularly in the GHz response of the system. We report a study on the GHz dynamics of a series of five carefully prepared microstates in the same ASI sample, with both coexistence of vortex and uniformly magnetized macrospins, and disorder in the orientation of the macrospins at different vertices. We observe microstate-specific mode frequency shifting, mode creation and mode crossing. This versatility of characteristic spin-wave (SW) peaks for specific magnetic microstates in ASI enables identification of microstate configurations via SW spectral characterization. The wide reconfigurability of microstate-specific SW dynamics also opens avenues for developing rich magnonic devices operating in the GHz frequency regime and advances the understanding of ASI physics.

Competing gauge fields and entropically driven spin liquid to spin liquid transition in non-Kramers pyrochlores.

Gauge theories are powerful theoretical physics tools that allow complex phenomena to be reduced to simple principles and are used in both high-energy and condensed matter physics. In the latter context, gauge theories are becoming increasingly popular for capturing the intricate spin correlations in spin liquids, exotic states of matter in which the dynamics of quantum spins never ceases, even at absolute zero temperature. We consider a spin system on a three-dimensional pyrochlore lattice where emergent gauge fields not only describe the spin liquid behavior at zero temperature but crucially determine the system's temperature evolution, with distinct gauge fields giving rise to different spin liquid phases in separate temperature regimes. Focusing first on classical spins, in an intermediate temperature regime, the system shows an unusual coexistence of emergent vector and tensor gauge fields where the former is known from classical spin ice systems while the latter has been associated with fractonic quasiparticles, a peculiar type of excitation with restricted mobility. Upon cooling, the system transitions into a low-temperature phase where an entropic selection mechanism depopulates the degrees of freedom associated with the tensor gauge field, rendering the system spin-ice-like. We further provide numerical evidence that in the corresponding quantum model, a spin liquid with coexisting vector and tensor gauge fields has a finite window of stability in the parameter space of spin interactions down to zero temperature. Finally, we discuss the relevance of our findings for non-Kramers magnetic pyrochlore materials.

Entropy-stabilized materials as a platform to explore terbium-based pyrochlore frustrated magnets

Two decades of work have shown that the physics of Tb-based pyrochlores is controlled by a subtle equilibrium between quadrupole-quadrupole and dipolar-dipolar magnetic interactions, as exemplified by the ordered spin ice Tb2Sn2O7 and the quantum spin liquid candidate Tb2Ti2O7. The high-entropy approach is thus quite promising, as it offers the possibility of a delicate tuning of chemical disorder. In this work, we investigate the entropy-stabilized pyrochlore compound Tb2(TiZrHfGeSn)2O7. We report the lack of long range magnetic order, yet the observed magnetic diffuse scattering is characteristic of antiferromagnetic first-neighbor correlations. The crystal field excitation spectrum, with broaden levels, visibly reflects the smooth environmental disorder of the Tb environment. The low energy dynamics are characterized by a narrow mode at about 0.4 meV, consistent with specific heat. Remarkably, as illustrated by a model of random isotropic shifts of oxygen atoms around Tb ions, the spectral weight of this mode is a direct consequence of deviations from the D3d symmetry at Tb sites. In the light of these results, quadrupolar interactions are also discussed.

Local Excitation of Kagome Spin Ice Magnetism Seen by Scanning Tunneling Microscopy.

The kagome spin ice can host frustrated magnetic excitations by flipping its local spin. Under an inelastic tunneling condition, the tip in a scanning tunneling microscope can flip the local spin, and we apply this technique to kagome metal HoAgGe with a long-range ordered spin ice ground state. Away from defects, we discover a pair of pronounced dips in the local tunneling spectrum at symmetrical bias voltages with negative intensity values, serving as a striking inelastic tunneling signal. This signal disappears above the spin ice formation temperature and has a dependence on the magnetic fields, demonstrating its intimate relation with the spin ice magnetism. We provide a two-level spin-flip model to explain the tunneling dips considering the spin ice magnetism under spin-orbit coupling. Our results uncover a local emergent excitation of spin ice magnetism in a kagome metal, suggesting that local electrical field induced spin flip climbs over a barrier caused by spin-orbital locking.

Tailoring magnon modes by extending square, kagome, and trigonal spin ice lattices vertically via interlayer coupling of trilayer nanomagnets

In this work high-frequency magnetization dynamics and statics of artificial spin-ice lattices with different geometric nanostructure array configurations are studied where the individual nanostructures are composed of ferromagnetic/non-magnetic/ferromagnetic trilayers with different non-magnetic thicknesses. These thickness variations enable additional control over the magnetic interactions within the spin-ice lattice that directly impacts the resulting magnetization dynamics and the associated magnonic modes. Specifically the geometric arrangements studied are square, kagome and trigonal spin ice configurations, where the individual lithographically patterned nanomagnets (NMs) are trilayers, made up of two magnetic layers of Ni81Fe19 of 30 nm and 70 nm thickness respectively, separated by a non-magnetic copper layer of either 2 nm or 40 nm. We show that coupling via the magnetostatic interactions between the ferromagnetic layers of the NMs within square, kagome and trigonal spin-ice lattices offers fine-control over magnetization states and magnetic resonant modes. In particular, the kagome and trigonal lattices allow tuning of an additional mode and the spacing between multiple resonance modes, increasing functionality beyond square lattices. These results demonstrate the ability to move beyond quasi-2D single magnetic layer nanomagnetics via control of the vertical interlayer interactions in spin ice arrays. This additional control enables multi-mode magnonic programmability of the resonance spectra, which has potential for magnetic metamaterials for microwave or information processing applications.

An improved artificial spin ice structure for restoring ice degeneracy

It is known that rare-earth-based pyrochlore oxide may accommodate the well-defined two-in-two-out spin ice state with its tetrahedral unit. Low-energy excitation is argued to favor the highly concerned monopole state which attracts essential attention. However, such an excitation cannot be directly tracked and imaged using advanced characterizations, raising challenges to our understanding of the physics of monopoles. In this work, we propose an improved two-dimensional artificial spin ice structure on the Shastry–Sutherland lattice to restore the degeneracy of realistic pyrochlore systems. Such a structure avoids the deficiency of inequivalent nearest and next-nearest exchanges in the planar quadrate unit, which, however, is equivalent to the tetrahedral unit of realistic pyrochlore oxides. Therefore, this spin ice model restores state degeneracy that is lost in conventional planar artificial spin ice structures, representing an improved simulator of real spin ice systems. Our careful investigations of such improved structures reveal the rich physics of spin ice excitations, including the phase diagram, which allows different ordered phases and interesting critical phase transitions between spin ice phase I and phase II. Energy spectrum analysis suggests that restoration of state degeneracy substantially reduces monopole excitation energy, resulting in a striking monopole emergency at the critical point. Furthermore, the emergent spin dimer phase in this improved model allows high-density monopole excitations and exhibits high-correlated monopole fluid states.

Strain-tuned incompatible magnetic exchange-interaction in La2NiO4

Magnetic frustration is a route for novel ground states, including spin liquids and spin ices. Such frustration can be introduced through either lattice geometry or incompatible exchange interactions. Here, we find that epitaxial strain is an effective tool for tuning antiferromagnetic exchange interactions in a square-lattice system. By studying the magnon excitations in La2NiO4 films using resonant inelastic x-ray scattering, we show that the magnon displays substantial dispersion along the antiferromagnetic zone boundary, at energies that depend on the lattice of the film’s substrate. Using first principles simulations and an effective spin model, we demonstrate that the antiferromagnetic next-nearest neighbour coupling is a consequence of the two-orbital nature of La2NiO4. Altogether, we illustrate that compressive epitaxial strain enhances this coupling and, as a result, increases the level of incompatibility between exchange interactions within a model square-lattice system.

Modelling nanomagnet vertex dynamics through Coulomb charges

We investigate the magnetization dynamics in nanomagnet vertices often found in artificial spin ices. Our analysis involves creating a simplified model that depicts edge magnetization using magnetic charges. We utilize the model to explore the energy landscape, its associated curvatures, and the fundamental modes. Our study uncovers specific magnonic regimes and transitions between magnetization states, marked by zero-modes, which can be understood within the framework of Landau theory. To verify our model, we compare it with micromagnetic simulations, demonstrating a noteworthy agreement.

Polyamorphism gets a magnetic boost

Four decades since the concept of polyamorphism was introduced by [L. S. Palatnik (1909–1994), Fiz. Nizk. Temp. 25, 400 (1909)], numerous investigations proved its presence in a broad variety of nonmagnetic short-range ordered materials, like structural, metallic, a-metallic, inorganic molecule, orientational, electron glasses, water, ice, carbons, and others. It was manifested by phase transitions between amorphous states as a function of the quench condition and under compression, mediated by long-wave fluctuations of an order parameter. There has been much recent discussion given to the phenomenon of polyamorphism where distinct, different states of amorphous liquids and solids are observed as a function of density. The outstanding contribution of the recently late [A. Sella, et al. (1956–2022), Nat. Mater. 21, 490 (2022)],2 in the field should be recognized here. Underlying this phenomenon is the possibility of a first-order liquid-liquid phase transition driven by the density and entropy differences between the two amorphous phases. Magnetic boost of multilayer graphene under pressure was also recently discovered. Their famous spin counterparts, such as spin liquid, spin ice, and spin glass have been less studied at this end despite numerous similarities, registered so far. Taking that in mind, for further polyamorphism platform development, we demonstrate the signatures of phase transition in spin glass, driven by a magnetic field, and eventually, a novel type of polyamorphism, the spin-glass one.

Partial magnetic order in kagome spin ice

Partial magnetic order in kagome spin ice

Pyrochlore-type lanthanide titanates and zirconates: Synthesis, structural peculiarities, and properties

This contribution provides a thorough examination of the structural characteristics of pyrochlore-type lanthanide titanates and zirconates Ln2Ti2O7 and Ln2Zr2O7, across various length scales. This paper also examines their processing, interesting physical properties (electrical, magnetic, and thermal characteristics), and responses to high pressure and ion irradiation. Brief sections on the elemental oxides' crystal chemistry, pertinent phase diagrams, and energetics of defect formation are also provided. Pyrochlore-type Ln2Ti2O7 and Ln2Zr2O7 stand out as truly multifunctional materials. Moreover, they have emerged as fascinating materials due to magnetic geometrical frustration, arising from the ordering of magnetic Ln3+ and non-magnetic Ti4+ (or Zr4+) cations into separate, interpenetrating lattices of corner-sharing tetrahedra. This results in a diverse array of exotic magnetic ground states, such as spin-ice (e.g., Dy2Ti2O7 or Ho2Ti2O7) or quantum spin ice (e.g., Tb2Ti2O7), observed at both low and room temperatures. They also exhibit varied electrical and electrochemical characteristics. Some members such as Gd2Zr2O7, function as fast ion conductors with a conductivity (σ) of ≈10−2 S·cm−1 at 800 °C and activation energy (Ea) ranging from 0.85 to 1.52 eV, depending on the degree of structural disorder. Others, such as Gd2TiMoO7, are mixed ionic-electronic conductors with σ ≈ 25 S·cm−1 at 1000 °C, making them promising candidate materials for applications in energy conversion and storage devices and oxygen separation membranes. Their exceptionally low thermal conductivity (e.g., κ ∼ 1.1–1.7 W·m−1·K−1 between 700 and 1200 °C for Ln2Zr2O7), close to the glass-like lower limit of highly disordered solids, positions them as valuable materials for thermal barrier coatings. They can also effectively accommodate actinides (e.g., Pu, Np, Cm, Am) in solid solutions and sustain prolonged exposure to radiation due to alpha-decay events, while preserving the integrity of the periodic atomic structure. Proposed as major components in actinide-bearing ceramics, they contribute to the long-term immobilization and disposal of long-lived waste radionuclides from nuclear programs. Some of these properties are displayed simultaneously, opening avenues for new applications. Despite the wealth of data available in the literature, this review highlights the need for a better understanding of order/disorder processes in pyrochlore-type materials and the influence of the structural length scale on their physical and chemical properties. Recent experimental evidence has revealed that pyrochlore short-range structure is far more complex than originally thought. Moreover, pyrochlore local structure is now believed to include short-range, lower symmetry, ordered domains, such as the orthorhombic weberite-type of structure. Notably, short- and long-range structures appear decoupled across different length scales and temperature regimes, and these differences persist even in well-ordered samples. We believe that the pyrochlore structure offers a unique opportunity for examining the interplay between chemical composition, defect chemistry, and properties. In Memoriam: Rodney C. Ewing, Fondly Remembered.

Muon spin relaxation and emergence of disorder-induced unconventional dynamic magnetic fluctuations in Dy2Zr2O7

The disordered pyrochlore oxide Dy2Zr2O7 shows the signatures of field-induced spin freezing with remnant zero-point spin-ice entropy at 5 kOe magnetic field. We have performed zero-field and longitudinal field Muon spin relaxation (µSR) studies on Dy2Zr2O7. Our zero field studies reveal the absence of both long-range ordering and spin freezing down to 62 mK. The µSR relaxation rate exhibits a temperature-independent plateau below 4 K, indicating a dynamic ground state of fluctuating spins similar to the well-known spin ice system Dy2Ti2O7. The low-temperature spin fluctuations persist in the longitudinal field of 20 kOe as well and show unusual field dependence of the relaxation rate, which is uncommon for a spin-liquid system. Our results, combined with the previous studies do not show any evidence of spin ice or spin glass ground state, rather point to a disorder-induced dynamic magnetic ground state in the Dy2Zr2O7 material.

Emergent disorder and mechanical memory in periodic metamaterials

Ordered mechanical systems typically have one or only a few stable rest configurations, and hence are not considered useful for encoding memory. Multistable and history-dependent responses usually emerge from quenched disorder, for example in amorphous solids or crumpled sheets. In contrast, due to geometric frustration, periodic magnetic systems can create their own disorder and espouse an extensive manifold of quasi-degenerate configurations. Inspired by the topological structure of frustrated artificial spin ices, we introduce an approach to design ordered, periodic mechanical metamaterials that exhibit an extensive set of spatially disordered states. While our design exploits the correspondence between frustration in magnetism and incompatibility in meta-mechanics, our mechanical systems encompass continuous degrees of freedom, and thus generalize their magnetic counterparts. We show how such systems exhibit non-Abelian and history-dependent responses, as their state can depend on the order in which external manipulations were applied. We demonstrate how this richness of the dynamics enables to recognize, from a static measurement of the final state, the sequence of operations that an extended system underwent. Thus, multistability and potential to perform computation emerge from geometric frustration in ordered mechanical lattices that create their own disorder.

Ultrastrong magnon-magnon coupling and chiral spin-texture control in a dipolar 3D multilayered artificial spin-vortex ice

Strongly-interacting nanomagnetic arrays are ideal systems for exploring reconfigurable magnonics. They provide huge microstate spaces and integrated solutions for storage and neuromorphic computing alongside GHz functionality. These systems may be broadly assessed by their range of reliably accessible states and the strength of magnon coupling phenomena and nonlinearities. Increasingly, nanomagnetic systems are expanding into three-dimensional architectures. This has enhanced the range of available magnetic microstates and functional behaviours, but engineering control over 3D states and dynamics remains challenging. Here, we introduce a 3D magnonic metamaterial composed from multilayered artificial spin ice nanoarrays. Comprising two magnetic layers separated by a non-magnetic spacer, each nanoisland may assume four macrospin or vortex states per magnetic layer. This creates a system with a rich 16N microstate space and intense static and dynamic dipolar magnetic coupling. The system exhibits a broad range of emergent phenomena driven by the strong inter-layer dipolar interaction, including ultrastrong magnon-magnon coupling with normalised coupling rates of Δfν=0.57\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\frac{\\Delta f}{\ u }=0.57$$\\end{document}, GHz mode shifts in zero applied field and chirality-control of magnetic vortex microstates with corresponding magnonic spectra.