Multiferroicity in spin ice: towards a magnetic crystallography of Tb2Ti2O7 in a field

We combine two aspects of magnetic frustration, multiferroicity and emergent quasi-particles in spin liquids, by studying magneto-electric monopoles. Spin ice offers to couple these emergent topological defects to external fields, and to each other, in unusual ways, making possible to lift the degeneracy underpinning the spin liquid and to potentially stabilize novel forms of charge crystals, opening the path to a "magnetic crystallography". In developing the general phase diagram including nearest-neighbour coupling, Zeeman energy, electric and magnetic dipolar interactions, we uncover the emergence of a bi-layered crystal of singly-charged monopoles, whose stability, remarkably, is strengthened by an external [110] magnetic field. Our theory is able to account for the ordering process of Tb2Ti2O7 in large field for reasonably small electric energy scales.Comment: 10 pages, 10 figure

Spin ice under pressure: symmetry enhancement and infinite order multicriticality

We study the low-temperature behaviour of spin ice when uniaxial pressure induces a tetragonal distortion. There is a phase transition between a Coulomb liquid and a fully magnetised phase. Unusually, it combines features of discontinuous and continuous transitions: the order parameter exhibits a jump, but this is accompanied by a divergent susceptibility and vanishing domain wall tension. All these aspects can be understood as a consequence of an emergent SU(2) symmetry at the critical point. We map out a possible experimental realisation

A Three Dimensional Kasteleyn Transition: Spin Ice in a [100] Field

We examine the statistical mechanics of spin-ice materials with a [100] magnetic field. We show that the approach to saturated magnetisation is, in the low-temperature limit, an example of a 3D Kasteleyn transition, which is topological in the sense that magnetisation is changed only by excitations that span the entire system. We study the transition analytically and using a Monte Carlo cluster algorithm, and compare our results with recent data from experiments on Dy2Ti2O7.Comment: 4 pages, 5 figure

Are multiphase competition & order-by-disorder the keys to understanding Yb2Ti2O7?

If magnetic frustration is most commonly known for undermining long-range order, as famously illustrated by spin liquids, the ability of matter to develop new collective mechanisms in order to fight frustration is no less fascinating, providing an avenue for the exploration and discovery of unconventional properties of matter. Here we study an ideal minimal model of such mechanisms which, incidentally, pertains to the perplexing quantum spin ice candidate Yb2Ti2O7. Specifically, we explain how thermal and quantum fluctuations, optimized by order-by-disorder selection, conspire to expand the stability region of an accidentally degenerate continuous symmetry U(1) manifold against the classical splayed ferromagnetic ground state that is displayed by the sister compound Yb2Sn2O7. The resulting competition gives rise to multiple phase transitions, in striking similitude with recent experiments on Yb2Ti2O7 [Lhotel et al., Phys. Rev. B 89 224419 (2014)]. Considering the effective Hamiltonian determined for Yb2Ti2O7, we provide, by combining a gamut of numerical techniques, compelling evidence that such multiphase competition is the long-sought missing key to understanding the intrinsic properties of this material. As a corollary, our work offers a pertinent illustration of the influence of chemical pressure in rare-earth pyrochlores.Comment: 9 page

Analysis of a fully packed loop model arising in a magnetic Coulomb phase

The Coulomb phase of spin ice, and indeed the Ic phase of water ice, naturally realise a fully-packed two-colour loop model in three dimensions. We present a detailed analysis of the statistics of these loops, which avoid themselves and other loops of the same colour, and contrast their behaviour to an analogous two-dimensional model. The properties of another extended degree of freedom are also addressed, flux lines of the emergent gauge field of the Coulomb phase, which appear as "Dirac strings" in spin ice. We mention implications of these results for related models, and experiments.Comment: 5 pages, 4 figure

The design of CO2-based working fluids for high-temperature heat source power cycles

The application of CO2power cycles is advantageous to exploit high-temperature sources (500-800°C) in the case of available low-temperature heat sinks (15-25°C). However, their efficiency is strongly reduced for higher heat sink temperatures. At these temperatures, due to the low-critical temperature of CO2(about 31°C), CO2is in fact compressed in the supercritical vapor phase rather than in the liquid phase, thus increasing energetic demand for compression. One of the solutions envisaged to overcome this problem is the addition of one or more chemicals that allow having a mixture with a higher critical temperature than the one of pure CO2. This preserve the working fluid compression in its liquid phase, even in the case of heat sinks with temperatures greater than 25°C. This research shows that the addition to CO2of a properly selected chemical component enables to increase the critical temperature up to 45°C with relevant improvements of cycle efficiency with respect to pure-CO2power cycles. In particular, it summarizes the most relevant criteria to be accounted for when selecting CO2-additives. Moreover, the paper warns of the thermodynamic effects deriving from adding to CO2a second characterized by a much more high critical temperature, such as the occurrence of infinite-pressure critical points and multiple-phase liquid-liquid and vapor-liquid critical points. Finally, the paper analyses the thermodynamic properties of a high-critical temperature CO2-based mixture, suitable for these applications, that presents multiple phase critical points. In this regard, it is specified that the paper also aims at filling a knowledge gap in the study of thermodynamic properties of mixtures presenting how do enthalpy and specific volume change in response to pressure variations in the event of liquid-liquid and vapour-liquid critical points. Finally, we present the comparison between performances of power cycles which use, as working fluid, either pure CO2or the novel designed higher temperature CO2-based mixture

The Kasteleyn transition in three dimensions: spin ice in a [100] field

We discuss the nearest neighbour spin ice model in the presence of a magnetic field placed along the cubic [100] direction. As recently shown in Phys. Rev. Lett. 100, 067207, 2008, the symmetry sustaining ordering transition observed at low temperature is a three dimensional Kasteleyn transition. We confirm this with numerical data using a non-local algorithm that conserves the topological constraints at low temperature and from analytic calculations from a Bethe lattice of corner sharing tetrahedra . We present a thermodynamic description of the Kasteleyn transition and discuss the relevance of our results to recent neutron scattering experiments on spin ice materials

Classical Topological Order in Kagome Ice

We examine the onset of classical topological order in a nearest-neighbor kagome ice model. Using Monte Carlo simulations, we characterize the topological sectors of the groundstate using a non-local cut measure which circumscribes the toroidal geometry of the simulation cell. We demonstrate that simulations which employ global loop updates that are allowed to wind around the periodic boundaries cause the topological sector to fluctuate, while restricted local loop updates freeze the simulation into one topological sector. The freezing into one topological sector can also be observed in the susceptibility of the real magnetic spin vectors projected onto the kagome plane. The ability of the susceptibility to distinguish between fluctuating and non-fluctuating topological sectors should motivate its use as a local probe of topological order in a variety of related model and experimental systems.Comment: 17 pages, 9 figure

Random site dilution properties of frustrated magnets on a hierarchical lattice

We present a method to analyze magnetic properties of frustrated Ising spin models on specific hierarchical lattices with random dilution. Disorder is induced by dilution and geometrical frustration rather than randomness in the internal couplings of the original Hamiltonian. The two-dimensional model presented here possesses a macroscopic entropy at zero temperature in the large size limit, very close to the Pauling estimate for spin-ice on pyrochlore lattice, and a crossover towards a paramagnetic phase. The disorder due to dilution is taken into account by considering a replicated version of the recursion equations between partition functions at different lattice sizes. An analysis at first order in replica number allows for a systematic reorganization of the disorder configurations, leading to a recurrence scheme. This method is numerically implemented to evaluate the thermodynamical quantities such as specific heat and susceptibility in an external field.Comment: 26 pages, 11 figure

Magnetic Monopole Dynamics in Spin Ice

One of the most remarkable examples of emergent quasi-particles, is that of the "fractionalization" of magnetic dipoles in the low energy configurations of materials known as "spin ice", into free and unconfined magnetic monopoles interacting via Coulomb's 1/r law [Castelnovo et. al., Nature, 451, 42-45 (2008)]. Recent experiments have shown that a Coulomb gas of magnetic charges really does exist at low temperature in these materials and this discovery provides a new perspective on otherwise largely inaccessible phenomenology. In this paper, after a review of the different spin ice models, we present detailed results describing the diffusive dynamics of monopole particles starting both from the dipolar spin ice model and directly from a Coulomb gas within the grand canonical ensemble. The diffusive quasi-particle dynamics of real spin ice materials within "quantum tunneling" regime is modeled with Metropolis dynamics, with the particles constrained to move along an underlying network of oriented paths, which are classical analogues of the Dirac strings connecting pairs of Dirac monopoles.Comment: 26 pages, 12 figure