Magnetic Monopoles In Spin Ice Research Articles

Multiferroics and Beyond: Electric Properties of Different Magnetic Textures

This article presents a survey of many nontrivial effects connected with the coupling of electric and magnetic degrees of freedom in solids -- the field initiated by I.~E.~Dzyaloshinskii in 1959. I briefly consider the main physics of ultiferroic materials, and concentrate on different effects "beyond multiferroics", based on the same physical mechanisms which operate in multiferroics. In particular they lead to nontrivial electric properties of different magnetic textures -- such as the appearance of dipoles on magnetic monopoles in spin ice, dipoles on some domain walls in the usual ferromagnets, on skyrmions etc. The inverse effect, the appearance of magnetic monopoles on electric charges in magnetoelectrics, is also discussed. This nontrivial electric activity of different magnetic textures has manifestations in many experimental properties of these materials, and it can potentially lead to novel applications.

Fragmentation in Frustrated Magnets: A Review

Spin liquids are exotic phases of matter that often support emergent gauge fields and quasi-particle excitations. While spin liquids are commonly known for remaining disordered, their definition has been extended to include phases with broken symmetry corresponding to (partial) long-range order, such as chiral and nematic spin liquids for example. For Coulomb spin liquids, this ordering can be quantitatively understood via a Helmholtz decomposition between divergence-free and divergence-full terms. This phenomenon has been coined fragmentation, where spin degrees of freedom fragment into two components; the fluctuating disordered part and the ordered one. In this review, we will cover the theoretical and experimental aspects of this growing field, in particular its relation to magnetic monopoles in spin ice, its phase diagram and the possibility to observe it in solid-state crystal and artificial networks.

Memory effect and generation-recombination noise of magnetic monopoles in spin ice

We theoretically investigate the generation-recombination processes of magnetic monopoles in spin ices. We calculate the spectrum of the relative fluctuations of the numbers of pairs of magnetic monopoles, directly related to that measurable of the magnetic flux noise, using the Langevin approach, previously proposed. Measurements of spectral density of magnetic-flux noise, recently, gave an experimental confirmation of our theoretical results. The agreement with the experimental results is obtained by suggesting a model for the total spectrum of relative fluctuations, which consists in superimposing the spectra of a set of generation-recombination processes, characterized by different time constants and a given probability density function.

Nuclear spin assisted quantum tunnelling of magnetic monopoles in spin ice

Extensive work on single molecule magnets has identified a fundamental mode of relaxation arising from the nuclear-spin assisted quantum tunnelling of nearly independent and quasi-classical magnetic dipoles. Here we show that nuclear-spin assisted quantum tunnelling can also control the dynamics of purely emergent excitations: magnetic monopoles in spin ice. Our low temperature experiments were conducted on canonical spin ice materials with a broad range of nuclear spin values. By measuring the magnetic relaxation, or monopole current, we demonstrate strong evidence that dynamical coupling with the hyperfine fields bring the electronic spins associated with magnetic monopoles to resonance, allowing the monopoles to hop and transport magnetic charge. Our result shows how the coupling of electronic spins with nuclear spins may be used to control the monopole current. It broadens the relevance of the assisted quantum tunnelling mechanism from single molecular spins to emergent excitations in a strongly correlated system.

Proposal for the detection of magnetic monopoles in spin ice via nanoscale magnetometry

We present a proposal for applying nanoscale magnetometry to the search for magnetic monopoles in the spin ice materials holmium and dysprosium titanate. Employing Monte Carlo simulations of the dipolar spin ice model, we find that when cooled to below $1.5\,$K these materials exhibit a sufficiently low monopole density to enable the direct observation of magnetic fields from individual monopoles. At these temperatures we demonstrate that noise spectroscopy can capture the intrinsic fluctuations associated with monopole dynamics, allowing one to isolate the qualitative effects associated with both the Coulomb interaction between monopoles and the topological constraints implied by Dirac strings. We describe in detail three different nanoscale magnetometry platforms (muon spin rotation, nitrogen vacancy defects, and nanoSQUID arrays) that can be used to detect monopoles in these experiments, and analyze the advantages of each.

Statistics of Fluctuations of Magnetic Monopole Concentration in Spin Ice

In this paper, we theoretically investigate the fluctuations in the number of emergent magnetic monopoles in spin ice. The Langevin equation for these fluctuations is deduced. This allows us to calculate the spectrum of relative fluctuations, which can be measured experimentally.

Observation of magnetic fragmentation in spin ice

Fractionalised excitations that emerge from a many body system have revealed rich physics and concepts, from composite fermions in two-dimensional electron systems, revealed through the fractional quantum Hall effect, to spinons in antiferromagnetic chains and, more recently, fractionalisation of Dirac electrons in graphene and magnetic monopoles in spin ice. Even more surprising is the fragmentation of the degrees of freedom themselves, leading to coexisting and a priori independent ground states. This puzzling phenomenon was recently put forward in the context of spin ice, in which the magnetic moment field can fragment, resulting in a dual ground state consisting of a fluctuating spin liquid, a so-called Coulomb phase, on top of a magnetic monopole crystal. Here we show, by means of neutron scattering measurements, that such fragmentation occurs in the spin ice candidate Nd$_2$Zr$_2$O$_7$. We observe the spectacular coexistence of an antiferromagnetic order induced by the monopole crystallisation and a fluctuating state with ferromagnetic correlations. Experimentally, this fragmentation manifests itself via the superposition of magnetic Bragg peaks, characteristic of the ordered phase, and a pinch point pattern, characteristic of the Coulomb phase. These results highlight the relevance of the fragmentation concept to describe the physics of systems that are simultaneously ordered and fluctuating.

Experimental signature of the attractive Coulomb force between positive and negative magnetic monopoles in spin ice

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), electrolytes (the second Wien effect) and semiconductors (the Poole-Frenkel effect). 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 quenches to spin ice to prepare metastable populations of bound pairs of positive and negative emergent magnetic monopoles 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 effect for magnetic monopoles, as confirmed by comparison to a recent and rigorous theory of the Wien effect in spin ice. 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.

Dynamics of electrically polarized magnetic monopoles in spin ice

We propose a simple mechanism through which elementary excitations in spin ice, namely, magnetic monopoles, lead to spontaneous macroscopic electric polarization by breaking the space inversion symmetry in the spin configuration. We show that while the magnetic monopole charge is conserved in hopping, the corresponding electric dipole moment cannot be a constant of motion. The possibilities as well as the limitations involved in electrical manipulation of the monopole dynamics are also discussed.

Vacancy defects and monopole dynamics in oxygen-deficient pyrochlores.

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 Ti(4+) to transform to magnetic Ti(3+) 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.

Far-from-equilibrium monopole dynamics in spin ice

Condensed matter in the low temperature limit reveals much exotic physics associated with unusual orders and excitations, examples ranging from helium superfluidity to magnetic monopoles in spin ice. The far-from-equilibrium physics of such low temperature states may be even more exotic, yet to access it in the laboratory remains a challenge. Here we demonstrate a simple and robust technique, the 'magnetothermal avalanche quench', and its use in the controlled creation of nonequilibrium populations of magnetic monopoles in spin ice at millikelvin temperatures. These populations are found to exhibit spontaneous dynamical effects that typify far-from-equilibrium systems, yet are captured by simple models. Our method thus opens the door to the study of far-from-equilibrium states in spin ice and other exotic magnets.

Determination of the entropy via measurement of the magnetization: application to the spin ice Dy2Ti2O7

The residual entropy of spin ice and other frustrated magnets is a property of considerable interest, yet the usual way of determining it, by integrating the heat capacity, is generally ambiguous. Here we note that a straightforward alternative method based on Maxwell’s thermodynamic relations can yield the residual entropy on an absolute scale. The method utilizes magnetization measurements only and hence is a useful alternative to calorimetry. We confirm that it works for the spin ice Dy2Ti2O7, which recommends its application to other systems. The analysis described here also gives an insight into the dependence of entropy on magnetic moment, which plays an important role in the theory of magnetic monopoles in spin ice. Finally, we present evidence of a field-induced crossover from correlated spin ice behaviour to ordinary paramagnetic behaviour with increasing applied field, as signalled by a change in the effective Curie constant.

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.

Generalized longitudinal susceptibility for magnetic monopoles in spin ice.

The generalized longitudinal susceptibility χ(q,ω) affords a sensitive measure of the spatial and temporal correlations of magnetic monopoles in spin ice. Starting with the monopole model, a mean field expression for χ(q,ω) is derived as well as expressions for the mean square longitudinal field and induction at a point. Monopole motion is shown to be strongly correlated, and both spatial and temporal correlations are controlled by the dimensionless monopole density x which defines the ratio of the magnetization relaxation rate and the monopole hop rate. Thermal effects and spin-lattice relaxation are also considered. The derived equations are applicable in the temperature range where the Wien effect for magnetic monopoles is negligible. They are discussed in the context of existing theories of spin ice and the following experimental techniques: DC and AC magnetization, neutron scattering, neutron spin echo and longitudinal and transverse field μSR. The monopole theory is found to unify diverse experimental results, but several discrepancies between theory and experiment are identified. One of these, concerning the neutron scattering line shape, is explained by means of a phenomenological modification to the theory.

Emergent magnetic monopoles in frustrated magnetic systems

Emergent magnetic monopoles in frustrated magnetic systems

A classification of spin frustration in molecular magnets from a physical study of large odd-numbered-metal, odd electron rings

The term "frustration" in the context of magnetism was originally used by P. W. Anderson and quickly adopted for application to the description of spin glasses and later to very special lattice types, such as the kagomé. The original use of the term was to describe systems with competing antiferromagnetic interactions and is important in current condensed matter physics in areas such as the description of emergent magnetic monopoles in spin ice. Within molecular magnetism, at least two very different definitions of frustration are used. Here we report the synthesis and characterization of unusual nine-metal rings, using magnetic measurements and inelastic neutron scattering, supported by density functional theory calculations. These compounds show different electronic/magnetic structures caused by frustration, and the findings lead us to propose a classification for frustration within molecular magnets that encompasses and clarifies all previous definitions.

Stability of the Coulomb phase in spin ice at finite temperature

The temperature dependence of the concentration of magnetic monopoles in spin ice has been analyzed. It has been shown that magnetic Coulomb interaction between monopoles can lead to a temperature-induced stepwise increase in their concentration by several orders of magnitude. This first-order phase transition is also accompanied by a decrease in the relaxation time by several orders of magnitude and can be considered as the melting of the Coulomb phase of spin ice. The phase diagram, as well as the critical point, has been determined.

Electric dipoles on magnetic monopoles in spin ice

The close connection of electricity and magnetism is one of the cornerstones of modern physics. This connection has a crucial role from a fundamental point of view and in practical applications, including spintronics and multiferroic materials. A breakthrough was a recent proposal that in magnetic materials called spin ice the elementary excitations have a magnetic charge and behave as magnetic monopoles. I show that, besides magnetic charge, there should be an electric dipole attached to each magnetic monopole. This opens new possibilities to study and control such monopoles using an electric field. Thus, the electric-magnetic analogy goes even further than usually assumed: whereas electrons have electric charge and magnetic dipole (spin), magnetic monopoles in spin ice, while having magnetic charge, also have an electric dipole.

High pressure route to generate magnetic monopole dimers in spin ice

The gas of magnetic monopoles in spin ice is governed by one key parameter: the monopole chemical potential. A significant variation of this parameter could access hitherto undiscovered magnetic phenomena arising from monopole correlations, as observed in the analogous electrical Coulomb gas, like monopole dimerization, critical phase separation, or charge ordering. However, all known spin ices have values of chemical potential imposed by their structure and chemistry that place them deeply within the weakly correlated regime, where none of these interesting phenomena occur. Here we use high-pressure synthesis to create a new monopole host, Dy2Ge2O7, with a radically altered chemical potential that stabilizes a large fraction of monopole dimers. The system is found to be ideally described by the classic Debye–Huckel–Bjerrum theory of charge correlations. We thus show how to tune the monopole chemical potential in spin ice and how to access the diverse collective properties of magnetic monopoles.

Screening of the magnetic field by magnetic monopoles in spin ice

The screening of the external magnetic field by magnetic monopoles in spin ice has been considered. The polarization of the magnetic system with moving monopoles has been shown to result in the incomplete screening of the external magnetic field. The static permeability of spin ice and the magnetic-field screening length have been calculated and numerically estimated and the physical meaning of introducing monopoles is discussed.