Phase transitions in few-monolayer spin ice films

Kaiser V., Bloxsom J., Bovo L., Bramwell S.T., Holdsworth P.C., Moessner R.

The low-temperature picture of dipolar spin ice in terms of the Coulomb fluid of its fractionalised magnetic monopole excitations has allowed analytic and conceptual progress far beyond its original microscopic spin description. Here we develop its thermodynamic treatment as a `magnetolyte', a fluid of singly and doubly charged monopoles, an analogue of the electrochemical system ${\rm 2 H_2O = H_3O^+ +OH^- = H_4O^{2+} + O^{2-}}$, but with perfect symmetry between oppositely charged ions. For this lattice magnetolyte, we present an analysis based on Debye-H\"uckel theory, which is accurate at all temperatures and incorporates `Dirac strings' imposed by the microscopic ice rule constraints at the level of Pauling's approximation. Our results are in close agreement with the specific heat from numerical simulations as well as new experimental measurements with an improved lattice correction, which we present here, on the spin ice materials $\mathrm{Ho_2Ti_2O_7}$ and $\mathrm{Dy_2Ti_2O_7}$. Our study of the magnetolyte shows how electrochemistry can emerge in non-electrical systems. We also provide new experimental tests of Debye-H\"uckel theory and its extensions. The application of our results also yields insights into the electrochemical behaviour of water ice and liquid water, which are closely related to the spin ice magnetolyte.

Lantagne-Hurtubise É., Rau J.G., Gingras M.J.

We explore the physics of highly frustrated magnets in confined geometries, focusing on the Coulomb phase of pyrochlore spin ices. As a specific example, we investigate thin films of nearest-neighbor spin ice, using a combination of analytic large-N techniques and Monte Carlo simulations. In the simplest film geometry, with surfaces perpendicular to the [001] crystallographic direction, we observe pinch points in the spin-spin correlations characteristic of a two-dimensional Coulomb phase. We then consider the consequences of crystal symmetry breaking on the surfaces of the film through the inclusion of orphan bonds. We find that when these bonds are ferromagnetic, the Coulomb phase is destroyed by the presence of fluctuating surface magnetic charges, leading to a classical Z_2 spin liquid. Building on this understanding, we discuss other film geometries with surfaces perpendicular to the [110] or the [111] direction. We generically predict the appearance of surface magnetic charges and discuss their implications for the physics of such films, including the possibility of an unusual Z_3 classical spin liquid. Finally, we comment on open questions and promising avenues for future research.

Östman E., Stopfel H., Chioar I., Arnalds U.B., Stein A., Kapaklis V., Hjörvarsson B.

The modification of geometry and interactions in two-dimensional magnetic nanosystems has enabled a range of studies addressing the magnetic order1–6, collective low-energy dynamics7,8 and emergent magnetic properties5, 9,10 in, for example, artificial spin-ice structures. The common denominator of all these investigations is the use of Ising-like mesospins as building blocks, in the form of elongated magnetic islands. Here, we introduce a new approach: single interaction modifiers, using slave mesospins in the form of discs, within which the mesospin is free to rotate in the disc plane 11 . We show that by placing these on the vertices of square artificial spin-ice arrays and varying their diameter, it is possible to tailor the strength and the ratio of the interaction energies. We demonstrate the existence of degenerate ice-rule-obeying states in square artificial spin-ice structures, enabling the exploration of thermal dynamics in a spin-liquid manifold. Furthermore, we even observe the emergence of flux lattices on larger length scales, when the energy landscape of the vertices is reversed. The work highlights the potential of a design strategy for two-dimensional magnetic nano-architectures, through which mixed dimensionality of mesospins can be used to promote thermally emergent mesoscale magnetic states. Coupling strengths differ between neighbours in square artificial spin ices, resulting in the loss of degeneracy. Introducing mesospins on vertices of the array alleviates this problem, by tuning the strength and ratio of the interaction energies.

She J., Kim C.H., Fennie C.J., Lawler M.J., Kim E.

We propose a strategy to achieve an unconventional superconductor in a heterostructure: use a quantum paramagnet (QPM) as a substrate for heterostructure growth of metallic films to design exotic superconductors. The proposed setup allows us to “customize” electron–electron interaction imprinted on the metallic layer. The QPM material of our choice is quantum spin ice. Assuming the metallic layer forms a single isotropic Fermi pocket, we predict its coupling to spin fluctuations in quantum spin ice will drive topological odd-parity pairing. We further present guiding principles for materializing the suitable heterostructure using ab initio calculations and describe the band structure we predict for the case of Y2Sn2−x Sb x O7 grown on the (111) surface of Pr2Zr2O7. Using this microscopic information, we predict topological odd-parity superconductivity at a few Kelvin in this heterostructure, which is comparable to the T c of the only other confirmed odd-parity superconductor Sr2RuO4. A new strategy for using quantum spin ices to drive superconductivity is proposed. Quantum spin ices are materials in which quantum fluctuations prevent long-range magnetic ordering. It has long been though that such materials could become superconducting if some of the spins could be removed, but experimental evidence for this is scarce. A team of researchers from Cornell and Binghamton Universities, led by Eun-Ah Kim, now suggest an alternative approach, which could enable not just conventional but exotic superconducting states to be created. Their proposal is to grow a heterostructure with metallic films using the quantum spin ice as a substrate. They predict that a coupling between spin fluctuations and electrons in the metallic layer could drive an exotic form of pairing that would give rise to a new class of topological superconductors.

Jaubert L. ., Lin T., Opel T. ., Holdsworth P. ., Gingras M. .

Motivated by recent realizations of Dy$_{2}$Ti$_{2}$O$_{7}$ and Ho$_{2}$Ti$_{2}$O$_{7}$ spin ice thin films, and more generally by the physics of confined gauge fields, we study a model of spin ice thin film with surfaces perpendicular to the $[001]$ cubic axis. The resulting open boundaries make half of the bonds on the interfaces inequivalent. By tuning the strength of these inequivalent "orphan" bonds, dipolar interactions induce a surface ordering equivalent to a two-dimensional crystallization of magnetic surface charges. This surface ordering can also be expected on the surfaces of bulk crystals. In analogy with partial wetting in soft matter, spins just below the surface are more correlated than in the bulk, but \emph{not} ordered. For ultrathin films made of one cubic unit cell, once the surfaces are ordered, a square ice phase is stabilized over a finite temperature window, as confirmed by its entropy and the presence of pinch points in the structure factor. Ultimately, the square ice degeneracy is lifted at lower temperature and the system orders in analogy with the well-known $F$-transition of the $6$-vertex model.

Cugliandolo L.F.

In classical and quantum frustrated magnets the interactions in combination with the lattice structure impede the spins to order in optimal configurations at zero temperature. The theoretical interest in their classical realisations has been boosted by the artificial manufacture of materials with these properties, that are of flexible design. This note summarises work on the use of vertex models to study bidimensional spin-ices samples, done in collaboration with R. A. Borzi, M. V. Ferreyra, L. Foini, G. Gonnella, S. A. Grigera, P. Guruciaga, D. Levis, A. Pelizzola and M. Tarzia, in recent years. It is an invited contribution to a J. Stat. Mech. special issue dedicated to the memory of Leo P. Kadanoff.

Bovo L., Rouleau C.M., Prabhakaran D., Bramwell S.T.

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.

Perrin Y., Canals B., Rougemaille N.

All of the characteristics of the square-ice model are observed in an artificial square-ice system in which the two sublattices of nanomagnets are slightly vertically separated. Geometric frustration in atomic lattices, such as those in water ice and magnetic materials called spin ice, leads to rich physical behaviour. So-called artificial spin ice, consisting of two-dimensional lattices of nanomagnets, was developed as a means of modelling these systems. Magnetic ordering, where neighbouring magnets try to align such that one is spin-up and the other spin-down, cannot be optimized owing to geometric frustration in these systems, which can be directly imaged. Until now it has not been possible to realize a fundamental 'square ice' model in these artificial systems that is of direct relevance to real materials. Nicolas Rougemaille and colleagues have solved this problem by designing a square lattice in which one of the two sublattices of nanomagnets is slightly vertically displaced. This enables them to directly observe the predicted spin-liquid state. Artificial spin-ice systems are lithographically patterned arrangements of interacting magnetic nanostructures that were introduced as way of investigating the effects of geometric frustration in a controlled manner1,2,3,4. This approach has enabled unconventional states of matter to be visualized directly in real space5,6,7,8,9,10,11,12,13,14,15,16,17,18, and has triggered research at the frontier between nanomagnetism, statistical thermodynamics and condensed matter physics. Despite efforts to create an artificial realization of the square-ice model—a two-dimensional geometrically frustrated spin-ice system defined on a square lattice—no simple geometry based on arrays of nanomagnets has successfully captured the macroscopically degenerate ground-state manifold of the model19. Instead, square lattices of nanomagnets are characterized by a magnetically ordered ground state that consists of local loop configurations with alternating chirality1,20,21,22,23,24,25,26. Here we show that all of the characteristics of the square-ice model are observed in an artificial square-ice system that consists of two sublattices of nanomagnets that are vertically separated by a small distance. The spin configurations we image after demagnetizing our arrays reveal unambiguous signatures of a Coulomb phase and algebraic spin-spin correlations, which are characterized by the presence of ‘pinch’ points in the associated magnetic structure factor. Local excitations—the classical analogues of magnetic monopoles27—are free to evolve in an extensively degenerate, divergence-free vacuum. We thus provide a protocol that could be used to investigate collective magnetic phenomena, including Coulomb phases28 and the physics of ice-like materials.

Benton O., Sikora O., Shannon N.

It has been known since the pioneering work of Bernal, Fowler and Pauling that common, hexagonal (Ih) water ice is the archetype of a frustrated material : a proton-bonded network in which protons satisfy strong local constraints - the "ice rules" - but do not order. While this proton disorder is well established, there is now a growing body of evidence that quantum effects may also have a role to play in the physics of ice at low temperatures. In this Article we use a combination of numerical and analytic techniques to explore the nature of proton correlations in both classical and quantum models of ice Ih. In the case of classical ice Ih, we find that the ice rules have two, distinct, consequences for scattering experiments - singular "pinch points", reflecting a zero-divergence condition on the uniform polarization of the crystal, and broad, asymmetric features, coming from its staggered polarisation. In the case of the quantum model, we find that the collective quantum tunnelling of groups of protons can convert states obeying the ice rules into a quantum liquid, whose excitations are birefringent, emergent photons. We make explicit predictions for scattering experiments on both classical and quantum ice Ih, and show how the quantum theory can explain the "wings" of incoherent inelastic scattering observed in recent neutron scattering experiments [Bove et al., Phys. Rev. Lett. 103, 165901 (2009)]. These results raise the intriguing possibility that the protons in ice Ih could form a quantum liquid at low temperatures, in which protons are not merely disordered, but continually fluctuate between different configurations obeying the ice rules.

Paulsen C., Giblin S.R., Lhotel E., Prabhakaran D., Balakrishnan G., Matsuhira K., Bramwell S.T.

A magnetic analogue of the Poole–Frenkel effect shows that magnetic monopole quasiparticles in a spin ice behave similar to electrons in a semiconductor, with an attractive Coulomb force acting between positive and negative monopoles. A non-Ohmic current that grows exponentially with the square root of applied electric field is well known from thermionic field emission (the Schottky effect)1, electrolytes (the second Wien effect)2 and semiconductors (the Poole–Frenkel effect)3. It is a universal signature of the attractive Coulomb force between positive and negative electrical charges, which is revealed as the charges are driven in opposite directions by the force of an applied electric field. Here we apply thermal quenches4 to spin ice5,6,7,8,9,10,11 to prepare metastable populations of bound pairs of positive and negative emergent magnetic monopoles12,13,14,15,16 at millikelvin temperatures. We find that the application of a magnetic field results in a universal exponential-root field growth of magnetic current, thus confirming the microscopic Coulomb force between the magnetic monopole quasiparticles and establishing a magnetic analogue of the Poole–Frenkel effect. At temperatures above 300 mK, gradual restoration of kinetic monopole equilibria causes the non-Ohmic current to smoothly evolve into the high-field Wien effect2 for magnetic monopoles, as confirmed by comparison to a recent and rigorous theory of the Wien effect in spin ice17,18. Our results extend the universality of the exponential-root field form into magnetism and illustrate the power of emergent particle kinetics to describe far-from-equilibrium response in complex systems.

Kaiser V., Bramwell S. ., Holdsworth P. ., Moessner R.

The Wien effect is a model process for field-induced charge creation. Here it is derived for a nonelectrical system: the spin ice "magnetolyte"-a unique system showing perfect charge symmetry. An entropic reaction field, analogous to the Jaccard field in ice, opposes direct current, but a frequency window exists in which the Wien effect for magnetolyte and electrolyte are indistinguishable. The universal enhancement of monopole density speeds up the magnetization dynamics, which manifests in the nonlinear, nonequilibrium ac susceptibility. This is a rare instance where such effects may be calculated, providing new insights for electrolytes. Experimental predictions are made for Dy2Ti2O7 spin ice.

Sasaki T., Imai E., Kanazawa I.

We propose that there might be emergent quasiparticles with fractional electronic charge such dyons on the domain wall between topological insulators and spin ice compounds through the Witten effect and interaction between the Dirac fermions and excited magnetic monopoles.

Sala G., Gutmann M.J., Prabhakaran D., Pomaranski D., Mitchelitis C., Kycia J.B., Porter D.G., Castelnovo C., Goff J.P.

The idea of magnetic monopoles in spin ice has enjoyed much success at intermediate temperatures, but at low temperatures a description in terms of monopole dynamics alone is insufficient. Recently, numerical simulations were used to argue that magnetic impurities account for this discrepancy by introducing a magnetic equivalent of residual resistance in the system. Here we propose that oxygen deficiency is the leading cause of magnetic impurities in as-grown samples, and we determine the defect structure and magnetism in Y2Ti2O7−δ using diffuse neutron scattering and magnetization measurements. These defects are eliminated by oxygen annealing. The introduction of oxygen vacancies causes Ti4+ to transform to magnetic Ti3+ with quenched orbital magnetism, but the concentration is anomalously low. In the spin-ice material Dy2Ti2O7 we find that the same oxygen-vacancy defects suppress moments on neighbouring rare-earth sites, and that these magnetic distortions markedly slow down the long-time monopole dynamics at sub-Kelvin temperatures. A number of rare-earth pyrochlore materials are experimental realizations of spin ice, a magnetic state that shares a number of similarities with conventional water ice. Diffuse neutron scattering experiments now show that oxygen vacancies strongly affect the dynamics of monopole excitations in the spin-ice material Y2Ti2O7−δ.

Bovo L., Moya X., Prabhakaran D., Soh Y., Boothroyd A.T., Mathur N.D., Aeppli G., Bramwell S.T.

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 Dy2Ti2O7a zero entropy state is induced at 0.4 K, plausibly by lattice strain.

Leusink D.P., Coneri F., Hoek M., Turner S., Idrissi H., Van Tendeloo G., Hilgenkamp H.

The pyrochlore compounds Ho 2 Ti 2 O 7 and Dy 2 Ti 2 O 7 show an exotic form of magnetism called the spin ice state, resulting from the interplay between geometrical frustration and ferromagnetic coupling. A fascinating feature of this state is the appearance of magnetic monopoles as emergent excitations above the degenerate ground state. Over the past years, strong effort has been devoted to the investigation of these monopoles and other properties of the spin ice state in bulk crystals. Here, we report the fabrication of Ho 2 Ti 2 O 7 thin films using pulsed laser deposition on yttria-stabilized ZrO 2 substrates. We investigated the structural properties of these films by X-ray diffraction, scanning transmission electron microscopy, and atomic force microscopy, and the magnetic properties by vibrating sample magnetometry at 2 K. The films not only show a high crystalline quality, but also exhibit the hallmarks of a spin ice: a pronounced magnetic anisotropy and an intermediate plateau in the magnetization along the [111] crystal direction. © 2014 Author(s).

Smirnov A., Anisimkin V., Ageykin N., Datsuk E., Kuznetsova I.

An important technical task is to develop methods for recording the phase transitions of water to ice. At present, many sensors based on various types of acoustic waves are suggested for solving this challenge. This paper focuses on the theoretical and experimental study of the effect of water-to-ice phase transition on the properties of Lamb and quasi shear horizontal (QSH) acoustic waves of a higher order propagating in different directions in piezoelectric plates with strong anisotropy. Y-cut LiNbO3, 128Y-cut LiNbO3, and 36Y-cut LiTaO3 plates with a thickness of 500 μm and 350 μm were used as piezoelectric substrates. It was shown that the amplitude of the waves under study can decrease, increase, or remain relatively stable due to the water-to-ice phase transition, depending on the propagation direction and mode order. The greatest decrease in amplitude (42.1 dB) due to glaciation occurred for Lamb waves with a frequency of 40.53 MHz and propagating in the YX+30° LiNbO3 plate. The smallest change in the amplitude (0.9 dB) due to glaciation was observed for QSH waves at 56.5 MHz propagating in the YX+60° LiNbO3 plate. Additionally, it was also found that, in the YX+30° LiNbO3 plate, the water-to-ice transition results in the complete absorption of all acoustic waves within the specified frequency range (10–60 MHz), with the exception of one. The phase velocities, electromechanical coupling coefficients, elastic polarizations, and attenuation of the waves under study were calculated. The structures “air–piezoelectric plate–air”, “air–piezoelectric plate–liquid”, and “air–piezoelectric plate–ice” were considered. The results obtained can be used to develop methods for detecting ice formation and measuring its parameters.

Berchialla L., Macauley G.M., Heyderman L.J.

Artificial spin ices are arrays of coupled single domain nanomagnets that have mainly been explored in two dimensions. They display a number of intriguing phenomena arising from the collective behavior of the magnets including vertex frustration, emergent magnetic monopoles, and phase transitions. Escaping this flat paradigm into the third dimension is now possible, thanks to advances in fabrication and characterization of three-dimensional mesoscopic magnetic systems, which have magnetic elements with dimensions between a few 10's and a few 100's nanometers. By exploiting the extra degrees of freedom inherent to fully three-dimensional structures, it will be possible to harness the dipolar and other interactions between magnetic elements in a way that cannot be achieved in planar systems. This will offer an unparalleled opportunity to produce three-dimensional mesoscopic magnetic structures exhibiting true spin ice physics and also, more broadly, to engineer exotic magnetic states and cooperative phenomena in a range of three-dimensional artificial spin ices that may have no direct analog in natural materials. In this perspective, we review the development of research into three-dimensional artificial spin ice, highlighting the main routes by which such structures can be created and measured. We discuss some new frontiers for the field, both in terms of realizing 3D model systems, and exciting opportunities for applications, such as sensing and computing.

Lu Z., Schäfer R., Hallén J.N., Laumann C.R.

Smirnov A., Anisimkin V., Voronova N., Kashin V., Kuznetsova I.

The detection of the liquid-to-ice transition is an important challenge for many applications. In this paper, a method for multi-parameter characterization of the liquid-to-ice phase transition is proposed and tested. The method is based on the fundamental properties of bulk acoustic waves (BAWs). BAWs with shear vertical (SV) or shear horizontal (SH) polarization cannot propagate in liquids, only in solids such as ice. BAWs with longitudinal (L) polarization, however, can propagate in both liquids and solids, but with different velocities and attenuations. Velocities and attenuations for L-BAWs and SV-BAWs are measured in ice using parameters such as time delay and wave amplitude at a frequency range of 1–37 MHz. Based on these measurements, relevant parameters for Rayleigh surface acoustic waves and Poisson’s modulus for ice are determined. The homogeneity of the ice sample is also detected along its length. A dual sensor has been developed and tested to analyze two-phase transitions in two liquids simultaneously. Distilled water and a 0.9% solution of NaCl in water were used as examples.

Ohno M., Fujita T.C., Kawasaki M.

We present an epitaxial stabilization of pyrochlore Bi2Rh2O7 on the Y-stabilized ZrO2 (YSZ) (111) substrate by inserting a pyrochlore Eu2Ti2O7 template layer, otherwise Bi-based layered structures being formed directly on the YSZ (111) substrate. This result reveals that “iso-structural crystal phase” plays an important role in the interfacial phase control. The Bi2Rh2O7 film exhibits p-type electrical conduction with the lowest longitudinal resistivity (ρxx) among the reported Rh pyrochlore oxides. Such parameters as ρxx, carrier density, and mobility show almost no temperature dependence in the measured range of 2–300 K.

Szabó A., Orlandi F., Manuel P.

We study near-neighbor and dipolar Ising models on a lattice of corner-sharing octahedra. In an extended parameter range of both models, frustration between antiferromagnetism and a spin-ice-like three-in-three-out rule stabilizes a Coulomb phase with correlated dipolar and quadrupolar spin textures, both yielding distinctive neutron-scattering signatures. Strong further-neighbor perturbations cause the two components to order independently, resulting in unusual multi-$k$ orders. We propose experimental realizations of our model in rare-earth antiperovskites.

Hafez M.A., Zayed M.K., Elsayed-Ali H.E.

Reflection high-energy electron diffraction (RHEED) is widely used to characterize the surface structure of single crystals. Moreover, RHEED has become a standard tool to monitor thin film growth in molecular beam epitaxy and is used to monitor other vapor deposition techniques including evaporation, sputtering, and pulsed laser deposition. With the rapid development of the fabrication methods and use of nanoparticles, RHEED operating in the transmission mode is being applied to characterize nanoparticles on surfaces. In this review, the fundamentals needed to interpret RHEED patterns from the top few atomic layers, in its reflection mode, and from nanoparticles and nanofeatures, in its transmission mode, are discussed based on the geometric kinematic approximation. Examples are provided on the interpretation of RHEED patterns from unreconstructed and 2 × 1-reconstructed Si(100), InP(100), highly oriented pyrolytic graphite, indium nanoparticles, and indium growth on Si(100)- 2 × 1.

Bonbien V., Zhuo F., Salimath A., Ly O., Abbout A., Manchon A.

AbstractThe long fascination that antiferromagnetic materials has exerted on the scientific community over about a century has been entirely renewed recently with the discovery of several unexpected phenomena, including various classes of anomalous spin and charge Hall effects and unconventional magnonic transport, and also homochiral magnetic entities such as skyrmions. With these breakthroughs, antiferromagnets stand out as a rich playground for the investigation of novel topological behavior, and as promising candidate materials for disruptive low-power microelectronic applications. Remarkably, the newly discovered phenomena are all related to the topology of the magnetic, electronic or magnonic ground state of the antiferromagnets. This review exposes how non-trivial topology emerges at different levels in antiferromagnets and explores the novel mechanisms that have been discovered recently. We also discuss how novel classes of quantum magnets could enrich the currently expanding field of antiferromagnetic spintronics and how spin transport can in turn favor a better understanding of exotic quantum excitations.

May A., Saccone M., van den Berg A., Askey J., Hunt M., Ladak S.

Magnetic charge propagation in spin-ice materials has yielded a paradigm-shift in science, allowing the symmetry between electricity and magnetism to be studied. Recent work is now suggesting the spin-ice surface may be important in mediating the ordering and associated phase space in such materials. Here, we detail a 3D artificial spin-ice, which captures the exact geometry of bulk systems, allowing magnetic charge dynamics to be directly visualized upon the surface. Using magnetic force microscopy, we observe vastly different magnetic charge dynamics along two principal directions. For a field applied along the surface termination, local energetics force magnetic charges to nucleate over a larger characteristic distance, reducing their magnetic Coulomb interaction and producing uncorrelated monopoles. In contrast, applying a field transverse to the surface termination yields highly correlated monopole-antimonopole pairs. Detailed simulations suggest it is the difference in effective chemical potential as well as the energy landscape experienced during dynamics that yields the striking differences in monopole transport. Two-dimensional artificial spin-ice systems have been studied for over 15 years but do not capture the detailed geometry of their bulk counterparts. Here, the authors fabricate a three-dimensional artificial spin-ice and show that the surface termination plays a crucial role in dictating the magnetic charge transport.

Philathong H., Akshay V., Samburskaya K., Biamonte J.

Abstract While there are various approaches to benchmark physical processors, recent findings have focused on computational phase transitions. This is due to several factors. Importantly, the hardest instances appear to be well-concentrated in a narrow region, with a control parameter allowing uniform random distributions of problem instances with similar computational challenge. It has been established that one could observe a computational phase transition in a distribution produced from coherent Ising machine(s). In terms of quantum approximate optimisation, the ability for the quantum algorithm to function depends critically on the ratio of a problems constraint to variable ratio (called density). The critical density dependence on performance resulted in what was called, reachability deficits. In this perspective we recall the background needed to understand how to apply computational phase transitions in various bench-marking tasks and we survey several such contemporary findings.

Anisimkin V., Kolesov V., Kuznetsova A., Shamsutdinova E., Kuznetsova I.

It is shown that, in spite of the wave radiation into the adjacent liquid, a large group of Lamb waves are able to propagate along piezoelectric plates (quartz, LiNbO3, LiTaO3) coated with a liquid layer (distilled water H2O). When the layer freezes, most of the group’s waves increase their losses, essentially forming an acoustic response towards water-to-ice transformation. Partial contributions to the responses originating from wave propagation, electro-mechanical transduction, and wave scattering were estimated and compared with the coupling constants, and the vertical displacements of the waves were calculated numerically at the water–plate and ice–plate interfaces. The maximum values of the responses (20–30 dB at 10–100 MHz) are attributed to the total water-to-ice transformation. Time variations in the responses at intermediate temperatures were interpreted in terms of a two-phase system containing both water and ice simultaneously. The results of the paper may turn out to be useful for some applications where the control of ice formation is an important problem (aircraft wings, ship bodies, car roads, etc.).

Arroo D.M., Bramwell S.T.

The two-dimensional F-model is an ice-rule-obeying model, with a low-temperature antiferroelectric state and high-temperature critical Coulomb phase. Polarization in the system is associated with topological defects in the form of system-spanning windings which makes it an ideal system on which to observe topological sector fluctuations, as have been discussed in the context of spin ice and Berezinskii-Kosterlitz-Thouless (BKT) systems. In particular, the F-model offers a useful counterpoint to the BKT transition in that winding defects are energetically suppressed in the ordered state, rather than dynamically suppressed in the critical phase. In this paper we develop Lieb and Baxter's historic solutions of the F-model to exactly calculate relevant properties, several apparently for the first time. We further calculate properties not amenable to exact solution by an approximate cavity method and by referring to established scaling results. Of particular relevance to topological sector fluctuations are the exact results for the applied field polarization and the ``energetic susceptibility.'' The latter is a both a measure of topological sector fluctuations and, surprisingly, in this case, a measure of the order parameter correlation exponent. In the high-temperature phase, the temperature tunes the density of topological defects and algebraic correlations, with the energetic susceptibility undergoing a jump to zero at the antiferroelectric ordering temperature, analogous to the ``universal jump'' in BKT systems. We discuss how these results are relevant to experimental systems, including to spin-ice thin films, and, unexpectedly, to three-dimensional dipolar spin ice and water ice, where we find that an analogous ``universal jump'' has previously been established in numerical studies. This unexpected result suggests a universal limit on the stability of perturbed Coulomb phases that is independent of dimension and of the order of the transition. Experimental results on water ice Ih are not inconsistent with this proposition. We complete the paper by relating our new results to experimental studies of artificial spin-ice arrays.

Nisoli C.

Abstract Both the Rys F-model and antiferromagnetic square ice possess the same ordered, antiferromagnetic ground state, but the ordering transition is of second order in the latter, and of infinite order in the former. To tie this difference to topological properties and their breakdown, we introduce a Faraday lines representation where loops carry the energy and magnetization of the system. Because the F-model does not admit monopoles, its Faraday loops have distinct topological properties, absent in square ice, and which allow for a natural partition of its phase space into topological sectors. Then, the Néel temperature corresponds to a transition from topologically trivial to non-trivial Faraday loops. Because magnetization is a homotopy invariant of the Faraday loops, and it is zero for topologically trivial ones, the susceptibility is zero below a critical field. In square spin ice, instead, monopoles destroy the homotopy invariance and the parity distinction among loops, thus erasing this rich topological structure. Consequently, even trivial loops can be magnetized in square ice, and their susceptibility is never zero.

Miura K., Fujiwara K., Nakayama K., Ishikawa R., Shibata N., Tsukazaki A.

In quantum spin liquid research, thin films are an attractive arena that enables the control of magnetic interactions via epitaxial strain and two-dimensionality, which are absent in bulk crystals. Here, as a promising candidate for the development of quantum spin liquids in thin films, we propose a robust ilmenite-type oxide with a honeycomb lattice of edge-sharing IrO6 octahedra artificially stabilised by superlattice formation using the ilmenite-type antiferromagnetic oxide MnTiO3. Stabilised sub-unit-cell-thick Mn–Ir–O layers are isostructural to MnTiO3 and have an atomic arrangement corresponding to ilmenite-type MnIrO3. By performing spin Hall magnetoresistance measurements, we observe that antiferromagnetic ordering in the ilmenite Mn sublattice is suppressed by modified magnetic interactions in the MnO6 planes via the IrO6 planes. These findings contribute to the development of two-dimensional Kitaev candidate materials, accelerating the discovery of exotic physics and applications specific to quantum spin liquids. Atomically thin films are ideal candidate materials for realizing clean, long sought-after, Kitaev spin liquids. Here, a two-dimensional IrO6 honeycomb lattice is stabilized within a MnTiO3 ilmenite superlattice, inducing a suppression of antiferromagnetic order that suggests potential spin-liquid behavior.

Bramwell S.T., Harris M.J.

Abstract This review is a study of how the idea of spin ice has evolved over the years, with a focus on the scientific questions that have come to define the subject. Since our initial discovery of spin ice in 1997, there have been well over five thousand papers that discuss it, and in the face of such detail, it must be difficult for the curious observer to ‘see the wood for the trees’. To help in this task, we go in search of the biggest insight to have emerged from the study of spin ice. On the way, we identify highlights and outstanding puzzles, and celebrate the inspirational role that Roger Cowley played in the early years.