Out-of-equilibrium dynamics and extended textures of topological defects in spin ice

Fractionalization is a ubiquitous phenomenon in topological states of matter. In this work, we study the collective behavior of fractionalized topological charges and their instabilities, through the J 1 -J 2 -J 3 Ising model on a kagome lattice. This model can be mapped onto a Hamiltonian of interacting topological charges under the constraint of Gauss' law. We find that the recombination of topological charges gives rise to a yet unexplored classical spin liquid. This spin liquid is characterized by an extensive residual entropy, as well as the formation of hexamers of same-sign topological charges. The emergence of hexamers is reflected by a half-moon signal in the magnetic structure factor, which provides a signature of this new spin liquid in elastic neutron-scattering experiments. To study this phase, a worm algorithm has been developed which does not require the usual divergence-free condition.PACS numbers: 75.10.KtFractionalization is a hallmark of topological states of matter. In these systems, an excitation with a unit quantum number, such as a charge and a spin, is fractionalized into several constituents. These excitations can then condense into exotic topological phases [1]. The nature of fractionalized excitations have been studied through a number of systems, such as quasi-one-dimensional conducting polymers [2], fractional quantum Hall systems [3,4], and quantum spin liquids (QSLs) in one and higher dimensions [5].Among the systems showing fractionalization, QSLs are of special interest. QSL is a long-range-entangled quantum ground state without spontaneous symmetry breaking; the ground state is expressed as a superposition of a macroscopic number of product states. The realization of QSL has been intensively sought in frustrated magnets, and a number of candidate materials have been explored actively [6][7][8][9][10][11][12][13].Quantum spin ice [14,15] is one of the most promising systems in this context. Its classical counterpart, spin ice, is a classical spin liquid (CSL) with macroscopically degenerate ground states. CSL often serves as a constituting source of QSL, thanks to quantum fluctuations inducing a superposition between the degenerate ground states. This is why the parent CSL phase reflects several important properties of its descendant QSL state. In the case of quantum spin ice, a fractional excitation, called monopole, can be found in its classical counterpart, in which a flipped spin from the ground state is fractionalized into two half-unit charges [16,17]. CSL, due to its simplicity in comparison with QSL, enables us to study rather intractable aspects of fractional excitations.In this work, we study the cooperative phenomena of fractionalized topological charges in the kagome CSL [18-21] of the J 1 -J 2 -J 3 Ising model. The nearest neighbor (NN) interactions (J 1 ) alone lead to a CSL phase, composed of the constrained configurations of topological charges, analogous to the fractional monopole excitations in spin ice. The furtherneighbor interactions (J 2 , J 3 ) introduce a ...

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“…3(e)]. Similar patterns are observed on a fine-tuned point of the J 1 -J 2 -J 3 model on pyrochlores [28,29].…”

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confidence: 70%

Clustering of Topological Charges in a Kagome Classical Spin Liquid

2017

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“…The qualitative difference of patterns between region (II) with half-moons and region (III) with stars indicates that different types of clusters evolve in these two regions. For region (III) the positive NN correlation is surrounded by the negative correlations, which is reminiscent of the crystalization of double-and triple-charge clusters in the Ising models 15,20 .…”

Section: B Conserved-spin Correlatormentioning

confidence: 90%

“…Their proliferation leads to unconventional classical spin liquids. Accompanying the clustering, the magnetic correlations display a noticeable evolution, characterized by half-moon patterns in S(q), which replace the pinch point singularities 15,16,20,47 .…”

Section: Introductionmentioning

confidence: 99%

Magnetic clustering, half-moons, and shadow pinch points as signals of a proximate Coulomb phase in frustrated Heisenberg magnets

et al. 2018

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We study the formation of magnetic clusters in frustrated magnets in their cooperative paramagnetic regime. For this purpose, we consider the J1-J2-J3 classical Heisenberg model on kagome and pyrochlore lattices with J2 = J3 = J. In the absence of farther-neighbor couplings, J = 0, the system is in the Coulomb phase with magnetic correlations well characterized by pinch-point singularities. Farther-neighbor couplings lead to the formation of magnetic clusters, which can be interpreted as a counterpart of topological-charge clusters in Ising frustrated magnets [T. Mizoguchi, L. D. C. Jaubert and M. Udagawa, Phys. Rev. Lett. 119, 077207 (2017)]. The concomitant static and dynamical magnetic structure factors, respectively S(q) and S(q, ω), develop half-moon patterns. As J increases, the continuous nature of the Heisenberg spins enables the half-moons to coalesce into connected "star" structures spreading across multiple Brillouin zones. These characteristic patterns are a dispersive complement of the pinch point singularities, and signal the proximity to a Coulomb phase. Shadows of the pinch points remain visible at finite energy, ω. This opens the way to observe these clusters through (in)elastic neutron scattering experiments. The origin of these features are clarified by complementary methods: large-N calculations, semi-classical dynamics of the Landau-Lifshitz equation, and Monte Carlo simulations. As promising candidates to observe the clustering states, we revisit the origin of "spin molecules" observed in a family of spinel oxides AB2O4 (A = Zn, Hg, Mg, B = Cr, Fe). PACS numbers: 75.10.Kt FIG. 6. The energy minima in the Brillouin zone for (a) J = 0.26 and (b) J = 1.1 in the kagome system. B. From pinch points to half-moons, near J1cThe flat bands form the ground-state manifold up to J = J 1c = 1/5 for kagome 36 and 1/6 for pyrochlore. This FIG. 7. The energy minima in the Brillouin zone on a hhlplane for (a) J = 0.22 and (b) J = 1 in the pyrochlore system.

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“…More generally, singlycharged monopoles may be favored by quantum fluctuations in the context of Yb 2 Ti 2 O 7 44 and magneto-electric coupling 45,46 . However, our goal in this paper is not to focus on a given Hamiltonian or to propose a mechanism to stabilize the FCSL phase, which will be investigated elsewhere 47 . Our goal is to describe and understand how the co-existence of order and spin liquid, mediated by dipolar interactions, affect the emergence of topological defects and eventually the ordering of the spin liquid phase itself.…”

Section: Fig 2 Thementioning

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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Out-of-equilibrium dynamics and extended textures of topological defects in spin ice

Cited by 38 publications

References 89 publications

Clustering of Topological Charges in a Kagome Classical Spin Liquid

Clustering of Topological Charges in a Kagome Classical Spin Liquid

Magnetic clustering, half-moons, and shadow pinch points as signals of a proximate Coulomb phase in frustrated Heisenberg magnets

Monopole Holes in a Partially Ordered Spin Liquid

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