Electric dipoles on magnetic monopoles in spin ice

Epitaxial Stabilization of a Pyrochlore Interface between Weyl Semimetal and Spin Ice

Pyrochlore materials are known for their exotic magnetic and topological phases arising from complex interactions among electron correlations, band topology, and geometric frustration. Interfaces between different pyrochlore crystals characterized by complex many-body ground states hold immense potential for novel interfacial phenomena due to the strong interactions between these phases. However, the realization of such interfaces has been severely hindered by limitations in material synthesis methods. In this study, we discover a robust synthesis method that produces the previously unexplored epitaxial pyrochlore interface between spin ice Dy2Ti2O7 and Weyl semimetal Eu2Ir2O7. The method relies on an ultrahigh supersaturation regime during deposition aided by directional IR-laser-driven thermal gradients, transforming amorphous covalent networks into nearly perfectly ordered, atomically sharp interfaces with a chemically ideal arrangement of ions. The novel pyrochlore interface enables the study of interactions between relativistic Weyl fermions and spin ice magnetic monopoles, opening a path to designing diverse pyrochlore interfaces.

Proximity effect of emergent field from spin ice in an oxide heterostructure

Geometrical frustration endows magnets with degenerate ground states, resulting in exotic spin structures and quantum phenomena. Such magnets, called quantum magnets, can display non-coplanar spin textures and be a viable platform for the topological Hall effect driven by "emergent field." However, most quantum magnets are insulators, making it challenging to electrically detect associated fluctuations and excitations. Here, we probe magnetic transitions in the spin ice insulator Dy2Ti2O7, a prototypical quantum magnet, as emergent magnetotransport phenomena at the heterointerface with the nonmagnetic metal Bi2Rh2O7. Angle-dependent longitudinal resistivity exhibits peaks at the magnetic phase boundaries of spin ice due to domain boundary scattering. In addition, the anomalous Hall resistivity undergoes a sign change with the magnetic transition in Dy2Ti2O7, reflecting the inversion of the emergent field. These findings, on the basis of epitaxial techniques, connect the fundamental research on insulating quantum magnets to their potential electronic applications, possibly leading to transformative innovations in quantum technologies.

Dynamical Axions in U(1) Quantum Spin Liquids

Since their proposal nearly half a century ago, physicists have sought axions in both high energy and condensed matter settings. Despite intense and growing efforts, to date, experimental success has been limited, with the most prominent results arising in the context of topological insulators. Here, we propose a novel mechanism whereby axions can be realized in quantum spin liquids. We discuss the necessary symmetry requirements and identify possible experimental realizations in candidate pyrochlore materials. In this context, the axions couple to both the external and the emergent electromagnetic fields. We show that the interaction between the axion and the emergent photon leads to a characteristic dynamical response, which can be measured experimentally in inelastic neutron scattering. This Letter sets the stage for studying axion electrodynamics in the highly tunable setting of frustrated magnets.

Magnetoelectric Classification of Skyrmions

We develop a general theory to classify magnetic skyrmions and related spin textures in terms of their magnetoelectric multipoles. Since magnetic skyrmions are now established in insulating materials, where the magnetoelectric multipoles govern the linear magnetoelectric response, our classification provides a recipe for manipulating the magnetic properties of skyrmions using applied electric fields. We apply our formalism to skyrmions and antiskyrmions of different helicities, as well as to magnetic bimerons, which are topologically, but not geometrically, equivalent to skyrmions. We show that the nonzero components of the magnetoelectric multipole and magnetoelectric response tensors are uniquely determined by the topology, helicity, and geometry of the spin texture. Therefore, we propose straightforward linear magnetoelectric response measurements as an alternative to Lorentz microscopy for characterizing insulating skyrmionic textures.

Magnetic monopole density and antiferromagnetic domain control in spin-ice iridates

Magnetically frustrated systems provide fertile ground for complex behaviour, including unconventional ground states with emergent symmetries, topological properties, and exotic excitations. A canonical example is the emergence of magnetic-charge-carrying quasiparticles in spin-ice compounds. Despite extensive work, a reliable experimental indicator of the density of these magnetic monopoles is yet to be found. Using measurements on single crystals of Ho2Ir2O7 combined with dipolar Monte Carlo simulations, we show that the isothermal magnetoresistance is highly sensitive to the monopole density. Moreover, we uncover an unexpected and strong coupling between the monopoles on the holmium sublattice and the antiferromagnetically ordered iridium ions. These results pave the way towards a quantitative experimental measure of monopole density and demonstrate the ability to control antiferromagnetic domain walls using a uniform external magnetic field, a key goal in the design of next-generation spintronic devices.

Electric activity at magnetic moment fragmentation in spin ice

Spin ice systems display a variety of very nontrivial properties, the most striking being the existence in them of magnetic monopoles. Such monopole states can also have nontrivial electric properties: there exist electric dipoles attached to each monopole. A novel situation is encountered in the moment fragmentation (MF) state, in which monopoles and antimonopoles are perfectly ordered, whereas spins themselves remain disordered. We show that such partial ordering strongly modifies the electric activity of such systems: the electric dipoles, which are usually random and dynamic, become paired in the MF state in (d, -d) pairs, thus strongly reducing their electric activity. The electric currents existing in systems with noncoplanar spins are also strongly influenced by MF. We also consider modifications in dipole and current patterns in magnetic textures (domain walls, local defects) and at excitations with nontrivial dynamics in a MF state, which show very rich behaviour and which could in principle allow to control them by electric field.

Spin-ice physics in cadmium cyanide

Spin-ices are frustrated magnets that support a particularly rich variety of emergent physics. Typically, it is the interplay of magnetic dipole interactions, spin anisotropy, and geometric frustration on the pyrochlore lattice that drives spin-ice formation. The relevant physics occurs at temperatures commensurate with the magnetic interaction strength, which for most systems is 1-5 K. Here, we show that non-magnetic cadmium cyanide, Cd(CN)2, exhibits analogous behaviour to magnetic spin-ices, but does so on a temperature scale that is nearly two orders of magnitude greater. The electric dipole moments of cyanide ions in Cd(CN)2 assume the role of magnetic pseudospins, with the difference in energy scale reflecting the increased strength of electric vs magnetic dipolar interactions. As a result, spin-ice physics influences the structural behaviour of Cd(CN)2 even at room temperature.

Proximate Quantum Spin Liquid on Designer Lattice

Complementary to bulk synthesis, here we propose a designer lattice with extremely high magnetic frustration and demonstrate the possible realization of a quantum spin liquid state from both experiments and theoretical calculations. In an ultrathin (111) CoCr₂O₄ slice composed of three triangular and one kagome cation planes, the absence of a spin ordering or freezing transition is demonstrated down to 0.03 K, in the presence of strong antiferromagnetic correlations in the energy scale of 30 K between Co and Cr sublattices, leading to the frustration factor of ∼1000. Persisting spin fluctuations are observed at low temperatures via low-energy muon spin relaxation. Our calculations further demonstrate the emergence of highly degenerate magnetic ground states at the 0 K limit, due to the competition among multiply altered exchange interactions. These results collectively indicate the realization of a proximate quantum spin liquid state on the synthetic lattice.

Electromagnetic control of spin ordered Mn3 qubits: a density functional study

[Mn3O(O2CMe)(dpd3/2)]2 is composed of two monomers each of which contain three Mn atoms at the vertices of an equilateral triangle. A full analysis of the electronic and magnetic structure of the dimer shows that each Mn atom carries a local spin of S = 2 while other spin states are energetically much higher. This result suggests application for conventional as well as quantum tasks. A detailed analysis of the electronic and magnetic structure of the monomer, on the other hand, suggests that there are three spin states of S = 1, S = 3/2 and S = 2 per monomer which are energetically competitive. We found that while monomer-monomer interactions are very weak, the coupling of monomers via covalent linkers affects both the magnetization and electronic energy levels of monomers. In particular, the isolated monomers prefer a ground state with local spin of S = 1 on Mn atoms and an antiferromagnetically ordered structure while the dimers possess a ground state with local spin of S = 2 on Mn atoms and a ferromagnetically ordered structure. The investigation of the polarizability of both monomer and dimer is examined for antiferromagnetically ordered structures which induces a high dipole moment of 0.08 (a.u.) and 0.16 (a.u.) for monomer and dimer, respectively. The energy of the antiferromagnetic structure is also high compared to other spin-electric molecules.

The history of spin ice

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.

Splitting of the magnetic monopole pair-creation energy in spin ice

The thermodynamics in spin-ice systems are governed by emergent magnetic monopole excitations and, until now, the creation of a pair of these topological defects was associated with one specific pair-creation energy. Here, we show that the electric dipole moments inherent to the magnetic monopoles lift the degeneracy of their creation process and lead to a splitting of the pair-creation energy. We consider this finding to extend the model of magnetic relaxation in spin-ice systems and show that an electric dipole interaction in the theoretically estimated order of magnitude leads to a splitting which can explain the controversially discussed discrepancies between the measured temperature dependence of the magnetic relaxation times and previous theory. By applying our extended model to experimental data of, various spin-ice systems, we show its universal applicability and determine a dependence of the electric dipole interaction on the system parameters, which is in accordance with the theoretical model of electric dipole formation.

Two-dimensional magnetic monopole gas in an oxide heterostructure

Magnetic monopoles have been proposed as emergent quasiparticles in pyrochlore spin ice compounds. However, unlike semiconductors and two-dimensional electron gases where the charge degree of freedom can be actively controlled by chemical doping, interface modulation, and electrostatic gating, there is as of yet no analogue of these effects for emergent magnetic monopoles. To date, all experimental investigations have been limited to large ensembles comprised of equal numbers of monopoles and antimonopoles in bulk crystals. To address these issues, we propose the formation of a two-dimensional magnetic monopole gas (2DMG) with a net magnetic charge, confined at the interface between a spin ice and an isostructural antiferromagnetic pyrochlore iridate and whose monopole density can be controlled by an external field. Our proposal is based on Monte Carlo simulations of the thermodynamic and transport properties. This proposed 2DMG should enable experiments and devices which can be performed on magnetic monopoles, akin to two-dimensional electron gases in semiconductor heterostructures.

Heterostructure interfaces have physical properties distinct from bulk materials, providing the basis for many electronic devices. Miao et al. propose a spin ice heterostructure that can host a two-dimensional gas of emergent magnetic monopoles with a net magnetic charge.

Experimental Identification of Electric Dipoles Induced by Magnetic Monopoles in Tb_{2}Ti_{2}O_{7}

The fundamental principles of electrodynamics allow an electron carrying both electric monopole (charge) and magnetic dipole (spin) but prohibit its magnetic counterpart. Recently, it was predicted that the magnetic "monopoles" carrying emergent magnetic charges in spin ice systems can induce electric dipoles. The inspiring prediction offers a novel way to study magnetic monopole excitations and magnetoelectric coupling. However, no clear example has been identified up to now. Here, we report the experimental evidence for electric dipoles induced by magnetic monopoles in spin frustrated Tb_{2}Ti_{2}O_{7}. The magnetic field applied to pyrochlore Tb_{2}Ti_{2}O_{7} along the [111] direction, brings out a "3-in-1-out" magnetic monopole configuration, and then induces a subtle structural phase transition at H_{c}∼2.3  T. The transition is made evident by the nonlinear phonon splitting under magnetic fields and the anomalous crystal-field excitations of Tb^{3+} ions. The observations consistently point to the displacement of the oxygen O^{''} anions along the [111] axis which gives rise to the formation of electric dipoles. The finding demonstrates that the scenario of magnetic monopole having both magnetic charge and electric dipole is realized in Tb_{2}Ti_{2}O_{7} and sheds light into the coupling between electricity and magnetism of magnetic monopoles in spin frustrated systems.

Correlated Quantum Tunneling of Monopoles in Spin Ice

The spin ice materials Ho_{2}Ti_{2}O_{7} and Dy_{2}Ti_{2}O_{7} are by now perhaps the best-studied classical frustrated magnets. A crucial step towards the understanding of their low temperature behavior-both regarding their unusual dynamical properties and the possibility of observing their quantum coherent time evolution-is a quantitative understanding of the spin-flip processes which underpin the hopping of magnetic monopoles. We attack this problem in the framework of a quantum treatment of a single-ion subject to the crystal, exchange, and dipolar fields from neighboring ions. By studying the fundamental quantum mechanical mechanisms, we discover a bimodal distribution of hopping rates that depends on the local spin configuration, in broad agreement with rates extracted from experiment. Applying the same analysis to Pr_{2}Sn_{2}O_{7} and Pr_{2}Zr_{2}O_{7}, we find an even more pronounced separation of timescales signaling the likelihood of coherent many-body dynamics.

Giant Magnetoelastic-Coupling Driven Spin-Lattice Liquid State in Molybdate Pyrochlores

We propose the idea of a spin-lattice liquid, in which spin and lattice degrees of freedom are strongly coupled and remain disordered and fluctuating down to low temperatures. We show that such a state arises naturally from a microscopic analysis of a class of molybdate pyrochlore compounds, and is driven by a giant magnetoelastic effect. Finally, we argue that this could explain some of the experimental features of Y_{2}Mo_{2}O_{7}.

Quantum spin liquids: a review

Quantum spin liquids may be considered 'quantum disordered' ground states of spin systems, in which zero-point fluctuations are so strong that they prevent conventional magnetic long-range order. More interestingly, quantum spin liquids are prototypical examples of ground states with massive many-body entanglement, which is of a degree sufficient to render these states distinct phases of matter. Their highly entangled nature imbues quantum spin liquids with unique physical aspects, such as non-local excitations, topological properties, and more. In this review, we discuss the nature of such phases and their properties based on paradigmatic models and general arguments, and introduce theoretical technology such as gauge theory and partons, which are conveniently used in the study of quantum spin liquids. An overview is given of the different types of quantum spin liquids and the models and theories used to describe them. We also provide a guide to the current status of experiments in relation to study quantum spin liquids, and to the diverse probes used therein.

Emergent spin-valley-orbital physics by spontaneous parity breaking

The spin-orbit coupling in the absence of spatial inversion symmetry plays an important role in realizing intriguing electronic states in solids, such as topological insulators and unconventional superconductivity. Usually, the inversion symmetry breaking is inherent in the lattice structures, and hence, it is not easy to control these interesting properties by external parameters. We here theoretically investigate the possibility of generating the spin-orbital entanglement by spontaneous electronic ordering caused by electron correlations. In particular, we focus on the centrosymmetric lattices with local asymmetry at the lattice sites, e.g. zigzag, honeycomb, and diamond structures. In such systems, conventional staggered orders, such as charge order and antiferromagnetic order, break the inversion symmetry and activate the antisymmetric spin-orbit coupling, which is hidden in a sublattice-dependent form in the paramagnetic state. Considering a minimal two-orbital model on a honeycomb structure, we scrutinize the explicit form of the antisymmetric spin-orbit coupling for all the possible staggered charge, spin, orbital, and spin-orbital orders. We show that the complete table is useful for understanding of spin-valley-orbital physics, such as spin and valley splitting in the electronic band structure and generalized magnetoelectric responses in not only spin but also orbital and spin-orbital channels, reflecting in peculiar magnetic, elastic, and optical properties in solids.

Magnetoelectric effect in organic molecular solids

The Magnetoelectric (ME) effect in solids is a prominent cross correlation phenomenon, in which the electric field (E) controls the magnetization (M) and the magnetic field (H) controls the electric polarization (P). A rich variety of ME effects and their potential in practical applications have been investigated so far within the transition-metal compounds. Here, we report a possible way to realize the ME effect in organic molecular solids, in which two molecules build a dimer unit aligned on a lattice site. The linear ME effect is predicted in a long-range ordered state of spins and electric dipoles, as well as in a disordered state. One key of the ME effect is a hidden ferroic order of the spin-charge composite object. We provide a new guiding principle of the ME effect in materials without transition-metal elements, which may lead to flexible and lightweight multifunctional materials.

Critical speeding-up in the magnetoelectric response of spin-ice near its monopole liquid-gas transition

Competing interactions in the so-called spin-ice compounds stabilize a frustrated ground state with finite zero-point entropy and, interestingly, emergent magnetic monopole excitations. The properties of these monopoles are at the focus of recent research with particular emphasis on their quantum dynamics. It is predicted that each monopole also possesses an electric dipole moment, which allows to investigate their dynamics via the dielectric function ε(ν). Here we report on broadband spectroscopic measurements of ε(ν) in Dy2Ti2O7 down to temperatures of 200 mK with a specific focus on the critical end point present for a magnetic field along the crystallographic [111] direction. Clear critical signatures are revealed in the dielectric response when, similarly as in the liquid-gas transition, the density of monopoles changes in a critical manner. The dielectric relaxation time τ exhibits a critical speeding-up with a significant enhancement of 1/τ as the temperature is lowered towards the critical temperature. Besides demonstrating the magnetoelectric character of the emergent monopole excitations, our results corroborate the unique critical dynamics near the monopole condensation transition.

Multiferroics of spin origin

Multiferroics, compounds with both magnetic and ferroelectric orders, are believed to be a key material system to achieve cross-control between magnetism and electricity in a solid with minute energy dissipation. Such a colossal magnetoelectric (ME) effect has been an issue of keen interest for a long time in condensed matter physics as well as a most desired function in the emerging spin-related electronics. Here we begin with the basic mechanisms to realize multiferroicity or spin-driven ferroelectricity in magnetic materials, which have recently been clarified and proved both theoretically and experimentally. According to the proposed mechanisms, many families of multiferroics have been explored, found (re-discovered), and newly developed, realizing a variety of colossal ME controls. We overview versatile multiferroics from the viewpoints of their multiferroicity mechanisms and their fundamental ME characteristics on the basis of the recent advances in exploratory materials. One of the new directions in multiferroic science is the dynamical ME effect, namely the dynamical and/or fast cross-control between electric and magnetic dipoles in a solid. We argue here that the dynamics of multiferroic domain walls significantly contributes to the amplification of ME response, which has been revealed through the dielectric spectroscopy. Another related issue is the electric-dipole-active magnetic resonance, called electromagnons. The electromagnons can provide a new stage of ME optics via resonant coupling with the external electromagnetic wave (light). Finally, we give concluding remarks on multiferroics physics in the light of a broader perspective from the emergent electromagnetism in a solid as well as from the possible application toward future dissipationless electronics.

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.

Orbital magnetism induced by heat currents in Mott insulators

We derive the effective heat current density operator for the strong-coupling regime of Mott insulators. Similarly to the case of the electric current density, the leading contribution to this effective operator is proportional to the local scalar spin chirality χ(jkl)=S(l)·(S(j)×S(k)). This common form of the effective heat and electric current density operators leads to a novel cross response in Mott insulators. A heat current induces a distribution of orbital magnetic moments in systems containing loops of an odd number of hopping terms. The relative orientation of the orbital moments depends on the particular lattice of magnetic ions. This subtle effect arises from the symmetries that the heat and electric currents have in common.

Brownian motion and quantum dynamics of magnetic monopoles in spin ice

Spin ice illustrates many unusual magnetic properties, including zero point entropy, emergent monopoles and a quasi liquid–gas transition. To reveal the quantum spin dynamics that underpin these phenomena is an experimental challenge. Here we show how crucial information is contained in the frequency dependence of the magnetic susceptibility and in its high frequency or adiabatic limit. The typical response of Dy₂Ti₂O₇ spin ice indicates that monopole diffusion is Brownian but is underpinned by spin tunnelling and is influenced by collective monopole interactions. The adiabatic response reveals evidence of driven monopole plasma oscillations in weak applied field, and unconventional critical behaviour in strong applied field. Our results clarify the origin of the relatively high frequency response in spin ice. They disclose unexpected physics and establish adiabatic susceptibility as a revealing characteristic of exotic spin systems.

Isolated magnetic monopoles are usually forbidden, but can arise as quasiparticles in magnetically frustrated spin-ice materials. Bovo et al. explore the classical and quantum natures of these excitations through their influence on the high frequency magnetic susceptibility of dysprosium titanate.