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

Jaubert, Ludovic D. C.; Chalker, J. T.; Holdsworth, Peter; Moessner, Roderich

doi:10.1103/physrevlett.100.067207

Cited by 95 publications

(257 citation statements)

References 25 publications

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“…There are also close parallels with the floating phases found in systems of gases adsorbed onto a substrate 33 . The transition between the stripe and nematic phases has a lot in common with the Kasteleyn model of dimers on the honeycomb lattice 18 and with spin-ice in a [100] magnetic field, which displays a 3d Kasteleyn transition [34][35][36] . In particular the second-order transition that we find in the presence of a J 5 interaction is within the same Pokrovsky-Talapov universality class as Kasteleyn's model.…”

Section: Figmentioning

confidence: 99%

Topological Aspects of Symmetry Breaking in Triangular-Lattice Ising Antiferromagnets

2016

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Using a specially designed Monte Carlo algorithm with directed loops, we investigate the triangular lattice Ising antiferromagnet with coupling beyond nearest neighbour. We show that the first-order transition from the stripe state to the paramagnet can be split, giving rise to an intermediate nematic phase in which algebraic correlations coexist with a broken symmetry. Furthermore, we demonstrate the emergence of several properties of a more topological nature such as fractional edge excitations in the stripe state, the proliferation of double domain walls in the nematic phase, and the Kasteleyn transition between them. Experimental implications are briefly discussed.The triangular-lattice Ising antiferromagnet (TLIAF) is the archetypal model of frustration. Ground states of the nearest-neighbour (n.n.) model obey the local constraint that triangles cannot host three equivalent Ising spins, and it follows that there is an extensive entropy 1,2 . This results in a critical state, characterised by algebraic correlations between the spins 3,4 .In reality, interactions are rarely limited to n.n., and a more realistic Hamiltonian takes the form,where σ i = ±1 and J ij > 0. This model is experimentally relevant in a diverse range of systems, including artificial dipolar magnets 5 , materials such as Ba 3 CuSb 2 O 9 where electrically charged dumbbells act as Ising degrees of freedom 6,7 , trapped ions 8,9 , frustrated Coulomb liquids 10 , Josephson junction arrays 11 and absorbed monolayers 12 .In spite of its ubiquity, this model has received limited attention. The difficulty in analysing H Is [Eq. 1] arises from the critical nature of the n.n. ground-state manifold, which is very sensitive to perturbation, and in the presence of further-neighbour coupling the model is not amenable to an analytic solution. Besides, in the limit J 1 → ∞ as compared to the other characteristic energy scales of the problem (J 2 , J 3 , etc.), Monte Carlo (MC) simulations based on the Metropolis algorithm are unable to reach the ground state, and the problem of freezing remains even when this constraint is relaxed, for example in the case of dipolar interactions 13 .The current understanding of the properties of H Is is based on estimates of the energy and entropy of different types of extended defects. This results in the prediction that the broken Z 2 ×Z 3 symmetry of the low-temperature stripe state 14,16,17 can be restored either in a single firstorder transition, or via a pair of transitions, where the low-temperature, Z 2 -restoring transition is second order and the higher-temperature, Z 3 -restoring transition is * deceased FIG. 1:Representative phase diagrams of the TLIAF with J 1 → ∞, determined by MC simulation. All phase boundaries were determined from the winding number. first order 14 . When the transition is split, an intermediate phase of nematic type is revealed, and it is characterised by a set of fluctuating double domain walls 14 (ddw).In this letter, we show that the difficulty in simulating the TLIAF with MC arises...

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Section: Figmentioning

confidence: 99%

Topological Aspects of Symmetry Breaking in Triangular-Lattice Ising Antiferromagnets

2016

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“…In the "field-cooled" case the degeneracy is completely lifted and at T = 0 we should have S = 0. Then the increase of the value of the field results in the "pseudo-transition" [138,139] from the spin ice state to the "saturated" state. Indeed at B = B K = (3) ln(2)k B T /2gµ B | J z |, a Kasteleyn transition [140,141], first predicted for the model of dimers on a two-dimensional lattice, takes place from the spin ice phase with the Pauling residual entropy to the "saturated" state with zero entropy and the average effective spin moment a little larger than 1/2 of the nominal value.…”

Section: Spin Ices In An External Magnetic Fieldmentioning

confidence: 99%

New physics in frustrated magnets: Spin ices, monopoles, etc. (Review Article)

Zvyagin

2013

Low Temperature Physics

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During recent years the interest to frustrated magnets has grown considerably. Such systems reveal very peculiar properties which distinguish them from standard paramagnets, magnetically ordered regular systems (like ferro-, ferri-, and antiferromagnets), or spin glasses. In particular great amount of attention has been devoted to the socalled spin ices, in which magnetic frustration together with the large value of the single-ion magnetic anisotropy of a special kind, yield peculiar behavior. One of the most exciting features of spin ices is related to low-energy emergent excitations, which, from many viewpoints can be considered as analogies of Dirac's monopoles. In this article we review the main achievements of theory and experiment in this field of physics.

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“…The semiconductor analogy is able to catch a surprising number of characteristic features of the FCSL. There are of course limitations to this analogy, which we believe are good places to look for exotic physics, such as the possibility of domain walls separating domains with opposite time-reversal symmetry or the inherent topological nature of the FCSL which would probably lead to phase transitions beyond the standard Landau-GinzburgWilson paradigm [73][74][75][76][77] .…”

Section: Semiconductor Analogy a Monopole Holesmentioning

confidence: 99%

Monopole Holes in a Partially Ordered Spin Liquid

Jaubert

2015

SPIN

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If spin liquids have been famously defined by what they are not, i.e. ordered, the past years have seen the frontier between order and spin liquid starting to fade, with a growing number of materials whose low-temperature physics cannot be explained without co-existence of (partial) magnetic order and spin fluctuations. Here we study an example of such co-existence in the presence of magnetic dipolar interactions, related to spin ice, where the order is long range and the fluctuations support a Coulomb gauge field. Topological defects are effectively coupled via energetic and entropic Coulomb interactions, the latter one being stronger than for the spin-ice ground state. Depending on whether these defects break the divergence-free condition of the Coulomb gauge field or the long-range order, they are respectively categorized as monopoles -as in spin ice -or monopole holes, in analogy with electron holes in semiconductors. The long-range order plays the role of a fully-occupied valence band, while the Coulomb spin liquid can be seen as an empty conducting band. These results are discussed in the context of other lattices and models which support a similar co-existence of Coulomb gauge field and long-range order. We conclude this work by explaining how dipolar interactions lift the spin liquid degeneracy at very low energy scale by maximizing the number of flippable plaquettes, in light of the equivalent quantum dimer model.The possibility to recast the collective behavior of electrons and atoms as elegant emergent phenomena is probably one of the most fascinating aspect of condensed matter. The emergence of quasi-particles does not only allow for a deeper understanding of the problem at hand but has also often led to surprising connections across physics, as recently illustrated by photon-like magnetic excitations in quantum spin ice 1-4 . Such approach takes an enhanced flavor when the particle has not yet been observed at high energy, or may not exist. This is for example the case for Majorana fermions observed in nanowires coupled to superconductors 5 , and for magnetic monopoles and their underlying Coulomb gauge field 6 .Coulomb gauge theories have emerged from a variety of discrete models, on the kagome lattice 7 , in fully-packed loop models 8 , itinerant-electron systems at partial-filling 9-11 and chemically disordered materials such as CsNiCrF 6 12 . We refer the interested reader to the excellent review by Chris Henley on this topic 13 . But its most famous experimental realization has probably been observed in the classical spin liquid ground state of spin ice materials Dy 2 Ti 2 O 7 and Ho 2 Ti 2 O 7 , where topological excitations take the form of magnetic monopoles effectively interacting via long-range Coulomb interactions.Interestingly, a Coulomb phase is not incompatible with partial magnetic order. For example, the stability of a Coulomb ferromagnet has been discussed in the context of the generalized Quantum Spin Ice model 14,15 and observed over a finite temperature window in a classical spin...

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

Cited by 95 publications

References 25 publications

Topological Aspects of Symmetry Breaking in Triangular-Lattice Ising Antiferromagnets

Topological Aspects of Symmetry Breaking in Triangular-Lattice Ising Antiferromagnets

New physics in frustrated magnets: Spin ices, monopoles, etc. (Review Article)

Monopole Holes in a Partially Ordered Spin Liquid

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