Pauling Entropy, Metastability, and Equilibrium in Dy_{2}Ti_{2}O_{7} Spin Ice.

Determining the fate of the Pauling entropy in the classical spin ice material Dy_{2}Ti_{2}O_{7} with respect to the third law of thermodynamics has become an important test case for understanding the existence and stability of ice-rule states in general. The standard model of spin ice-the dipolar spin ice model-predicts an ordering transition at T≈0.15 K, but recent experiments by Pomaranski et al. suggest an entropy recovery over long timescales at temperatures as high as 0.5 K, much too high to be compatible with the theory. Using neutron scattering and specific heat measurements at low temperatures and with long timescales (0.35 K/10^{6} s and 0.5 K/10^{5} s, respectively) on several isotopically enriched samples, we find no evidence of a reduction of ice-rule correlations or spin entropy. High-resolution simulations of the neutron structure factor show that the spin correlations remain well described by the dipolar spin ice model at all temperatures. Furthermore, by careful consideration of hyperfine contributions, we conclude that the original entropy measurements of Ramirez et al. are, after all, essentially correct: The short-time relaxation method used in that study gives a reasonably accurate estimate of the equilibrium spin ice entropy due to a cancellation of contributions.

ac Wien Effect in Spin Ice, Manifest in Nonlinear, Nonequilibrium Susceptibility.

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.

Measurement of the charge and current of magnetic monopoles in spin ice.

The transport of electrically charged quasiparticles (based on electrons or ions) plays a pivotal role in modern technology as well as in determining the essential functions of biological organisms. In contrast, the transport of magnetic charges has barely been explored experimentally, mainly because magnetic charges, in contrast to electric ones, are generally considered at best to be convenient macroscopic parameters, rather than well-defined quasiparticles. However, it was recently proposed that magnetic charges can exist in certain materials in the form of emergent excitations that manifest like point charges, or magnetic monopoles. Here we address the question of whether such magnetic charges and their associated currents-'magnetricity'-can be measured directly in experiment, without recourse to any material-specific theory. By mapping the problem onto Onsager's theory of electrolytes, we show that this is indeed possible, and devise an appropriate method for the measurement of magnetic charges and their dynamics. Using muon spin rotation as a suitable local probe, we apply the method to a real material, the 'spin ice' Dy(2)Ti(2)O(7) (refs 5-8). Our experimental measurements prove that magnetic charges exist in this material, interact via a Coulomb potential, and have measurable currents. We further characterize deviations from Ohm's law, and determine the elementary unit of magnetic charge to be 5 mu(B) A(-1), which is equal to that recently predicted using the microscopic theory of spin ice. Our measurement of magnetic charge and magnetic current establishes an instance of a perfect symmetry between electricity and magnetism.

Onsager's Wien effect on a lattice.

The second Wien effect describes the nonlinear, non-equilibrium response of a weak electrolyte in moderate to high electric fields. Onsager's 1934 electrodiffusion theory, along with various extensions, has been invoked for systems and phenomena as diverse as solar cells, surfactant solutions, water splitting reactions, dielectric liquids, electrohydrodynamic flow, water and ice physics, electrical double layers, non-ohmic conduction in semiconductors and oxide glasses, biochemical nerve response and magnetic monopoles in spin ice. In view of this technological importance and the experimental ubiquity of such phenomena, it is surprising that Onsager's Wien effect has never been studied by numerical simulation. Here we present simulations of a lattice Coulomb gas, treating the widely applicable case of a double equilibrium for free charge generation. We obtain detailed characterization of the Wien effect and confirm the accuracy of the analytical theories as regards the field evolution of the free charge density and correlations. We also demonstrate that simulations can uncover further corrections, such as how the field-dependent conductivity may be influenced by details of microscopic dynamics. We conclude that lattice simulation offers a powerful means by which to model and investigate system-specific corrections to the Onsager theory, and thus constitutes a valuable tool for detailed theoretical studies of the numerous practical applications of the second Wien effect.

Spin ice state in frustrated magnetic pyrochlore materials.

A frustrated system is one whose symmetry precludes the possibility that every pairwise interaction ("bond") in the system can be satisfied at the same time. Such systems are common in all areas of physical and biological science. In the most extreme cases, they can have a disordered ground state with "macroscopic" degeneracy; that is, one that comprises a huge number of equivalent states of the same energy. Pauling's description of the low-temperature proton disorder in water ice was perhaps the first recognition of this phenomenon and remains the paradigm. In recent years, a new class of magnetic substance has been characterized, in which the disorder of the magnetic moments at low temperatures is precisely analogous to the proton disorder in water ice. These substances, known as spin ice materials, are perhaps the "cleanest" examples of such highly frustrated systems yet discovered. They offer an unparalleled opportunity for the study of frustration in magnetic systems at both an experimental and a theoretical level. This article describes the essential physics of spin ice, as it is currently understood, and identifies new avenues for future research on related materials and models.

Phase transitions in few-monolayer spin ice films.

Vertex models are an important class of statistical mechanical system that admit exact solutions and exotic physics. Applications include water ice, ferro- and antiferro-electrics, spin ice and artificial spin ice. Here we show that it is possible to engineer spin ice films with atomic-layer precision down to the monolayer limit. Specific heat measurements show that these films, which have a fundamentally different symmetry to bulk spin ice, realise systems close to the two-dimensional F-model, with exotic phase transitions on topologically-constrained configurational manifolds. Our results show how spin ice thin films can release the celebrated Pauling entropy of spin ice without an anomaly in the specific heat. They also significantly expand the class of vertex models available to experiment.

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.

Universal window for two-dimensional critical exponents.

Two-dimensional condensed matter is realized in increasingly diverse forms that are accessible to experiment and of potential technological value. The properties of these systems are influenced by many length scales and reflect both generic physics and chemical detail. To unify their physical description is therefore a complex and important challenge. Here we investigate the distribution of experimentally estimated critical exponents, ß, that characterize the evolution of the order parameter through the ordering transition. The distribution is found to be bimodal and bounded within a window ∼0.1≤ß≤0.25, facts that are only in partial agreement with the established theory of critical phenomena. In particular, the bounded nature of the distribution is impossible to reconcile with the existing theory for one of the major universality classes of two-dimensional behaviour-the XY model with four-fold crystal field-which predicts a spectrum of non-universal exponents bounded only from below. Through a combination of numerical and renormalization group arguments we resolve the contradiction between theory and experiment and demonstrate how the 'universal window' for critical exponents observed in experiment arises from a competition between marginal operators.

Special temperatures in frustrated ferromagnets.

The description and detection of unconventional magnetic states, such as spin liquids, is a recurring topic in condensed matter physics. While much of the efforts have traditionally been directed at geometrically frustrated antiferromagnets, recent studies reveal that systems featuring competing antiferromagnetic and ferromagnetic interactions are also promising candidate materials. We find that this competition leads to the notion of special temperatures, analogous to those of gases, at which the competing interactions balance, and the system is quasi-ideal. Although induced by weak perturbing interactions, these special temperatures are surprisingly high and constitute an accessible experimental diagnostic of eventual order or spin-liquid properties. The well characterised Hamiltonian and extended low-temperature susceptibility measurement of the canonical frustrated ferromagnet Dy2Ti2O7 enables us to formulate both a phenomenological and microscopic theory of special temperatures for magnets. Other members of this class of magnets include kapellasite Cu3Zn(OH)6Cl2 and the spinel GeCo2O4.

Universal magnetic fluctuations with a field-induced length scale.

We calculate the probability density function for the order-parameter fluctuations in the low-temperature phase of the two-dimensional XY model of magnetism near the line of critical points. A finite correlation length xi, is introduced with a small magnetic field h, and an expression for xi(h) is developed by treating nonlinear contributions to the field energy using a Hartree approximation. We find analytically a series of universal non-Gaussian distributions of the finite-size scaling form P(m,L,xi) approximately L(beta/nu)P(L)(mL(beta/nu),xi/L) and present a function of the form P(x) approximately [exp[x-exp(x)]](a(h)) that gives the probability density functions to an excellent approximation. We propose a(h) as an indirect measure of the length scale of correlations in a wide range of complex systems.

Magnetic fluctuations in the classical XY model: the origin of an exponential tail in a complex system.

We study the probability density function for the fluctuations of the magnetic order parameter in the low-temperature phase of the XY model of finite size. In two dimensions, this system is critical over the whole of the low-temperature phase. It is shown analytically and without recourse to the scaling hypothesis that, in this case, the distribution is non-Gaussian and of universal form, independent of both system size and critical exponent eta. An exact expression for the generating function of the distribution is obtained, which is transformed and compared with numerical data from high-resolution molecular dynamics and Monte Carlo simulations. The asymptotes of the distribution are calculated and found to be of exponential and double exponential form. The calculated distribution is fitted to three standard functions: a generalization of Gumbel's first asymptote distribution from the theory of extremal statistics, a generalized log-normal distribution, and a chi(2) distribution. The calculation is extended to general dimension and an exponential tail is found in all dimensions less than 4, despite the fact that critical fluctuations are limited to D=2. These results are discussed in the light of similar behavior observed in models of interface growth and for dissipative systems driven into a nonequilibrium steady state.

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.

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 Dy(2)Ti(2)O(7) 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.

Crystal shape-dependent magnetic susceptibility and Curie law crossover in the spin ices Dy2Ti2O7 and Ho2Ti2O7.

We present an experimental determination of the isothermal magnetic susceptibility of the spin ice materials Dy2Ti2O7 and Ho2Ti2O7 in the temperature range 1.8-300 K. The use of spherical crystals has allowed accurate correction for demagnetizing fields and allowed the true bulk isothermal susceptibility χT(T) to be estimated. This has been compared against a theoretical expression based on a Husimi tree approximation to the spin ice model. Agreement between experiment and theory is excellent at T > 10 K, but systematic deviations occur below that temperature. Our results largely resolve an apparent disagreement between neutron scattering and bulk measurements that has been previously noted. They also show that the use of non-spherical crystals in magnetization studies of spin ice may introduce very significant systematic errors, although we note some interesting--and possibly new--systematics concerning the demagnetizing factor in cuboidal samples. Finally, our results show how experimental susceptibility measurements on spin ices may be used to extract the characteristic energy scale of the system and the corresponding chemical potential for emergent magnetic monopoles.

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, Dy(2)Ge(2)O(7), 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.

Neutron scattering and crystal field studies of the rare earth double perovskite Ba2ErSbO6.

The rare earth double perovskite Ba(2)ErSbO(6) contains an ordered face-centred cubic lattice of Er(3+) ions, suggesting that this material is a candidate for showing the effects of geometric magnetic frustration. Crystal field effects have also been shown to be important in this series. We report a systematic experimental study involving neutron scattering and bulk measurements that show no evidence of long ranged magnetic order or spin glass freezing down to 70 mK. A description of the system in terms of a crystal field scheme is established from inelastic neutron scattering. These measurements rule out significant magnetic coupling and show that all observed properties are fully explained by a model of uncoupled magnetic Er(3+) ions.

Magnetic Coulomb phase in the spin ice Ho2Ti2O7.

Spin-ice materials are magnetic substances in which the spin directions map onto hydrogen positions in water ice. Their low-temperature magnetic state has been predicted to be a phase that obeys a Gauss' law and supports magnetic monopole excitations: in short, a Coulomb phase. We used polarized neutron scattering to show that the spin-ice material Ho2Ti2O7 exhibits an almost perfect Coulomb phase. Our result proves the existence of such phases in magnetic materials and strongly supports the magnetic monopole theory of spin ice.

Static magnetic order in Tb2Sn2O7 revealed by muon spin relaxation with exterior muon implantation.

Tb2Sn2O7 has been proposed as an ordered spin ice, but the precise nature of the low temperature magnetic state remains uncertain. Recent independent muon spin relaxation (microSR) investigations suggest the possibility of exotic ground states with static order precluded on time scales longer than 10(-6) s. Here the more conventional hypothesis of canted ferromagnetism is tested by means of microSR with the muons stopped outside the sample, as well as ultralow field bulk magnetization measurements. The field cooled state shows conventional static order, while the zero field cooled state may be interpreted in terms of conventional closed domains. These results rule out purely dynamical ground states and illustrate the value of exterior muon implantation as a complement to the conventional technique.

Psychosocial factors in athletic injuries: development and application of the social and athletic readjustment rating scale (SARRS).

The possible role of psychosocial factors in athletics, namely football injuries, is examined. Initially Holmes and Rahe's Social Readjustment Rating Scale (SRRS) was modified to the Social and Athletic Readjustment Scale (SARRS). Additions to the scale and differences in football players from the general population are discussed. Life change scores over one- and two-year intervals were obtained for college varsity football players. Players suffering major time loss injuries had significantly higher predictive scores than noninjured players.