Magnetic monopoles have eluded experimental detection since their prediction nearly a century ago by Dirac. Recently it has been shown that classical analogues of these enigmatic particles occur as excitations out of the topological ground state of a model magnetic system, dipolar spin ice. These quasi-particle excitations do not require a modification of Maxwell's equations, but they do interact via Coulombs law and are of magnetic origin. In this paper we present an experimentally measurable signature of monopole dynamics and show that magnetic relaxation measurements in the spin ice material $Dy_{2}Ti_{2}O_{7}$ can be interpreted entirely in terms of the diffusive motion of monopoles in the grand canonical ensemble, constrained by a network of "Dirac strings" filling the quasi-particle vacuum. In a magnetic field the topology of the network prevents charge flow in the steady state, but there is a monopole density gradient near the surface of an open system

The Coulomb phase, with its dipolar correlations and pinch-point-scattering patterns, is central to discussions of geometrically frustrated systems, from water ice to binary and mixed-valence alloys, as well as numerous examples of frustrated magnets. The emergent Coulomb phase of lattice-based systems has been associated with divergence-free fields and the absence of long-range order. Here, we go beyond this paradigm, demonstrating that a Coulomb phase can emerge naturally as a persistent fluctuating background in an otherwise ordered system. To explain this behavior, we introduce the concept of the fragmentation of the field of magnetic moments into two parts, one giving rise to a magnetic monopole crystal, the other a magnetic fluid with all the characteristics of an emergent Coulomb phase. Our theory is backed up by numerical simulations, and we discuss its importance with regard to the interpretation of a number of experimental results

We examine the statistical mechanics of spin-ice materials with a [100] magnetic field. We show that the approach to saturated magnetization is, in the low-temperature limit, an example of a 3D Kasteleyn transition, which is topological in the sense that magnetization 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.

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 2008 Nature 451 42-5). 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 the 'quantum tunnelling' regime is modelled 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.

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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 perhaps no less fascinating, providing an avenue for the exploration and discovery of unconventional behaviors. Here we study a realistic minimal model where a number of such mechanisms converge and which, incidentally, pertain to the perplexing quantum spin ice candidate Yb2Ti2O7. Specifically, we explain how thermal and quantum fluctuations, optimized by order-bydisorder selection, conspire to expand the stability region of a degenerate continuous 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)]. By combining a gamut of numerical techniques, we obtain compelling evidence that such multiphase competition is a natural engine for the substantial sample-to-sample variability observed in Yb2Ti2O7 and is the missing key to ultimately understand 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.The vast interest in magnetic frustration largely stems from the diversity of unconventional phenomena it begets, ranging from anomalous Hall effect [1] to multiferroicity [2], to name only a few. The reason for this diversity is the indecisiveness of frustrated magnets towards ordering which opens an avenue for exotic mechanisms to control their low-temperature properties.This diversity of ordering processes is vividly illustrated within the family of rare-earth pyrochlore compounds [3][4][5][6][7]. In Er 2 Ti 2 O 7 [8-12], soft modes of excitations are claimed to lift a ground-state degeneracy whose symmetry is U(1), i.e. generated by a continuous rotation of all spins. This order-by-disorder (ObD) mechanism [13] selects the so-called ψ 2 over the ψ 3 configurations depicted in Fig. 1(b-c) Under such circumstances, we believe that in order to make progress in understanding Yb 2 Ti 2 O 7 , it is necessary to search for unifying patterns. Recent bulk measurements [18] are particularly enlightening in that respect, as they provide compelling evidence for multi-step ordering in putative disorder-free Yb 2 Ti 2 O 7 , common to both powder and single crystals. Our motivation here is twofold. Firstly, we present a thorough analysis of multiphase competition for a range of parameters near those found to describe Yb 2 Ti 2 O 7 [14]. We show how both thermal and quantum fluctuations enhance the stability of the degenerate U(1) manifold previously observed in Er 2 Ti 2 O 7 , to the detriment of a splayed ferromagnetic (SFM) phase displayed in Fig. 1(d). Then, we apply our theory to Yb 2 Ti 2 O 7 , successfully accounting for the unusual multi-step ordering process and fie...

International audienceAt low temperatures, a spin ice enters a Coulomb phase—a state with algebraic correlations and topologically constrained spin configurations. We show how analytical and numerical approaches for model spin-ice systems reveal a crossover between two Curie laws. One of these laws characterizes the high-temperature paramagnetic regime, while the other, which we call the “spin-liquid Curie law,” characterizes the low-temperature Coulomb-phase regime, which provides implicit evidence that the topological sector fluctuates. We compare our theory with experiment for Ho2Ti2O7, where this process leads to a nonstandard temperature evolution of the bulk susceptibility and the wave-vector-dependent magnetic susceptibility, as measured by neutron scattering. Theory and experiment agree for bulk quantities and at large scattering wave vectors, but differences at small wave vectors indicate that the classical spin-ice states are not equally populated at low temperatures. More generally, the crossover appears to be a generic property of the emergent gauge field for a classical spin liquid, and it sheds light on the experimental difficulty of measuring a precise Curie-Weiss temperature in frustrated materials. The susceptibility at finite wave vectors is shown to be a local probe of fluctuations among topological sectors on varying length scales

The Coulomb phase of spin ice, and indeed the Ic phase of water ice, naturally realise a fullypacked 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.