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

Topological Sector Fluctuations and Curie Law Crossover in Spin Ice

At low temperatures, a spin ice enters a Coulomb phase - a state with algebraic correlations and topologically constrained spin configurations. In Ho2Ti2O7, we have observed experimentally that this process is accompanied by a non-standard temperature evolution of the wave vector dependent magnetic susceptibility, as measured by neutron scattering. Analytical and numerical approaches reveal signatures of a crossover between two Curie laws, one characterizing the high temperature paramagnetic regime, and the other the low temperature topologically constrained regime, which we call the spin liquid Curie law. The theory is shown to be in excellent agreement with neutron scattering experiments. On a more general footing, i) the existence of two Curie laws appears to be a general property of the emergent gauge field for a classical spin liquid, and ii) sheds light on the experimental difficulty of measuring a precise Curie-Weiss temperature in frustrated materials; iii) the mapping between gauge and spin degrees of freedom means that the susceptibility at finite wave vector can be used as a local probe of fluctuations among topological sectors.Comment: 10 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

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

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

Growth of a dynamical correlation length in an aging superspin glass

We report on zero field cooled magnetization relaxation experiments on a concen- trated frozen ferrofluid exhibiting a low temperature superspin glass transition. With a method initially developed for spin glasses, we investigate the field dependence of the relaxations that take place after different aging times. We extract the typical number of correlated spins involved in the aging dynamics. This brings important insights into the dynamical correlation length and its time growth. Our results, consistent with expressions obtained for spin glasses, extend the generality of these behaviours to the class of superspin glasses. Since the typical flipping time is much larger for superspins than for atomic spins, our experiments probe a time regime much closer to that of numerical simulations

Spin ice in a field: quasi-phases and pseudo-transitions

Thermodynamics of the short-range model of spin ice magnets in a field is considered in the Bethe - Peierls approximation. The results obtained for [111], [100] and [011] fields agrees reasonably well with the existing Monte-Carlo simulations and some experiments. In this approximation all extremely sharp field-induced anomalies are described by the analytical functions of temperature and applied field. In spite of the absence of true phase transitions the analysis of the entropy and specific heat reliefs over H-T plane allows to discern the "pseudo-phases" with specific character of spin fluctuations and define the lines of more or less sharp "pseudo-transitions" between them.Comment: 18 pages, 16 figure

Fluctuations of two-time quantities and time-reparametrization invariance in spin-glasses

This article is a contribution to the understanding of fluctuations in the out of equilibrium dynamics of glassy systems. By extending theoretical ideas based on the assumption that time-reparametrization invariance develops asymptotically we deduce the scaling properties of diverse high-order correlation functions. We examine these predictions with numerical tests in a standard glassy model, the 3d Edwards-Anderson spin-glass, and in a system where time-reparametrization invariance is not expected to hold, the 2d ferromagnetic Ising model, both at low temperatures. Our results enlighten a qualitative difference between the fluctuation properties of the two models and show that scaling properties conform to the time-reparametrization invariance scenario in the former but not in the latter.Comment: 17 pages, 5 figure

Spin Dynamics at Very Low Temperature in Spin Ice Dy2_2Ti2_2O7_7

We have performed AC susceptibility and DC magnetic relaxation measurements on the spin ice system Dy$_2$Ti$_2$O$_7$ down to 0.08 K. The relaxation time of the magnetization has been estimated below 2 K down to 0.08 K. The spin dynamics of Dy$_2$Ti$_2$O$_7$ is well described by using two relaxation times ($\tau_{\rm S}$ (short time) and $\tau_{\rm L}$ (long time)). Both $\tau_{\rm S}$ and $\tau_{\rm L}$ increase on cooling. Assuming the Arrhenius law in the temperature range 0.5-1 K, we obtained an energy barrier of 9 K. Below 0.5 K, both $\tau_{\rm S}$ and $\tau_{\rm L}$ show a clear deviation from the thermal activated dynamics toward temperature independent relaxation, suggesting a quantum dynamics.Comment: 4 page

Low-temperature muon spin rotation studies of the monopole charges and currents in Y doped Ho2Ti2O7

In the ground state of Ho2Ti2O7 spin ice, the disorder of the magnetic moments follows the same rules as the proton disorder in water ice. Excitations take the form of magnetic monopoles that interact via a magnetic Coulomb interaction. Muon spin rotation has been used to probe the low-temperature magnetic behaviour in single crystal Ho2−xYxTi2O7 (x = 0, 0.1, 1, 1.6 and 2). At very low temperatures, a linear field dependence for the relaxation rate of the muon precession λ(B), that in some previous experiments on Dy2Ti2O7 spin ice has been associated with monopole currents, is observed in samples with x = 0, and 0.1. A signal from the magnetic fields penetrating into the silver sample plate due to the magnetization of the crystals is observed for all the samples containing Ho allowing us to study the unusual magnetic dynamics of Y doped spin ice