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Szabó A, Orlandi F, Manuel P. Fragmented Spin Ice and Multi-k Ordering in Rare-Earth Antiperovskites. PHYSICAL REVIEW LETTERS 2022; 129:247201. [PMID: 36563278 DOI: 10.1103/physrevlett.129.247201] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/02/2022] [Accepted: 10/31/2022] [Indexed: 06/17/2023]
Abstract
We study near-neighbor and dipolar Ising models on a lattice of corner-sharing octahedra. In an extended parameter range of both models, frustration between antiferromagnetism and a spin-ice-like three-in-three-out rule stabilizes a Coulomb phase with correlated dipolar and quadrupolar spin textures, both yielding distinctive neutron-scattering signatures. Strong further-neighbor perturbations cause the two components to order independently, resulting in unusual multi-k orders. We propose experimental realizations of our model in rare-earth antiperovskites.
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Affiliation(s)
- Attila Szabó
- Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Oxford OX1 3PU, United Kingdom
- ISIS Facility, Rutherford Appleton Laboratory, Harwell Campus, Didcot OX11 0QX, United Kingdom
| | - Fabio Orlandi
- ISIS Facility, Rutherford Appleton Laboratory, Harwell Campus, Didcot OX11 0QX, United Kingdom
| | - Pascal Manuel
- ISIS Facility, Rutherford Appleton Laboratory, Harwell Campus, Didcot OX11 0QX, United Kingdom
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2
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Proton strings and rings in atypical nucleation of ferroelectricity in ice. Proc Natl Acad Sci U S A 2021; 118:2018837118. [PMID: 33443186 DOI: 10.1073/pnas.2018837118] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
Ordinary ice has a proton-disordered phase which is kinetically metastable, unable to reach, spontaneously, the ferroelectric (FE) ground state at low temperature where a residual Pauling entropy persists. Upon light doping with KOH at low temperature, the transition to FE ice takes place, but its microscopic mechanism still needs clarification. We introduce a lattice model based on dipolar interactions plus a competing, frustrating term that enforces the ice rule (IR). In the absence of IR-breaking defects, standard Monte Carlo (MC) simulation leaves this ice model stuck in a state of disordered proton ring configurations with the correct Pauling entropy. A replica exchange accelerated MC sampling strategy succeeds, without open path moves, interfaces, or off-lattice configurations, in equilibrating this defect-free ice, reaching its low-temperature FE order through a well-defined first-order phase transition. When proton vacancies mimicking the KOH impurities are planted into the IR-conserving lattice, they enable standard MC simulation to work, revealing the kinetics of evolution of ice from proton disorder to partial FE order below the transition temperature. Replacing ordinary nucleation, each impurity opens up a proton ring generating a linear string, an actual FE hydrogen bond wire that expands with time. Reminiscent of those described for spin ice, these impurity-induced strings are proposed to exist in doped water ice too, where IRs are even stronger. The emerging mechanism yields a dependence of the long-time FE order fraction upon dopant concentration, and upon quenching temperature, that compares favorably with that known in real-life KOH doped ice.
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Guruciaga PC, Pili L, Boyeras S, Slobinsky D, Grigera SA, Borzi RA. Anomalous out-of-equilibrium dynamics in the spin-ice material Dy 2Ti 2O 7under moderate magnetic fields. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2020; 32:425804. [PMID: 32604086 DOI: 10.1088/1361-648x/aba153] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/24/2020] [Accepted: 06/30/2020] [Indexed: 06/11/2023]
Abstract
We study experimentally and numerically the dynamics of the spin ice material Dy2Ti2O7in the low temperature (T) and moderate magnetic field (B) regime (T∈ [0.1, 1.7] K,B∈ [0, 0.3] T). Our objective is to understand the main physics shaping the out-of-equilibrium magnetisation vs temperature curves in two different regimes. Very far from equilibrium, turning on the magnetic field after having cooled the system in zero field (ZFC) can increase the concentration of magnetic monopoles (localised thermal excitations present in these systems); this accelerates the dynamics. Similarly to electrolytes, this occurs through dissociation of bound monopole pairs. However, for spin ices the polarisation of the vacuum out of which the monopole pairs are created is a key factor shaping the magnetisation curves, with no analog. We observe a threshold field near 0.2 T for this fast dynamics to take place, linked to the maximum magnetic force between the attracting pairs. Surprisingly, within a regime of low temperatures and moderate fields, an extended Ohm's law can be used to describe the ZFC magnetisation curve obtained with the dipolar spin-ice model. However, in real samples the acceleration of the dynamics appears even sharper than in simulations, possibly due to the presence of avalanches. On the other hand, the effect of the field nearer equilibrium can be just the opposite to that at very low temperatures. Single crystals, as noted before for powders, abandon equilibrium at a blocking temperatureTBwhich increases with field. Curiously, this behaviour is present in numerical simulations even within the nearest-neighbours interactions model. Simulations and experiments show that the increasing trend inTBis stronger forB‖[100]. This suggests that the field plays a part in the dynamical arrest through monopole suppression, which is quite manifest for this field orientation.
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Affiliation(s)
- P C Guruciaga
- Centro Atómico Bariloche, Comisión Nacional de Energía Atómica (CNEA), Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Av. E. Bustillo 9500, R8402AGP San Carlos de Bariloche, Río Negro, Argentina
| | - L Pili
- Instituto de Física de Líquidos y Sistemas Biológicos (IFLYSIB), UNLP-CONICET, B1900BTE La Plata, Argentina
- Departamento de Física, Facultad de Ciencias Exactas, Universidad Nacional de La Plata, c.c. 16 suc. 4, B1900AJL La Plata, Argentina
| | - S Boyeras
- Instituto de Física de Líquidos y Sistemas Biológicos (IFLYSIB), UNLP-CONICET, B1900BTE La Plata, Argentina
| | - D Slobinsky
- Instituto de Física de Líquidos y Sistemas Biológicos (IFLYSIB), UNLP-CONICET, B1900BTE La Plata, Argentina
- Departamento de Ingeniería Mecánica, Facultad Regional La Plata, Universidad Tecnológica Nacional, Av. 60 esq. 124, 1900 La Plata, Argentina
| | - S A Grigera
- Instituto de Física de Líquidos y Sistemas Biológicos (IFLYSIB), UNLP-CONICET, B1900BTE La Plata, Argentina
- Departamento de Física, Facultad de Ciencias Exactas, Universidad Nacional de La Plata, c.c. 16 suc. 4, B1900AJL La Plata, Argentina
- School of Physics and Astronomy, University of St. Andrews, St. Andrews KY16 9SS, United Kingdom
| | - R A Borzi
- Instituto de Física de Líquidos y Sistemas Biológicos (IFLYSIB), UNLP-CONICET, B1900BTE La Plata, Argentina
- Departamento de Física, Facultad de Ciencias Exactas, Universidad Nacional de La Plata, c.c. 16 suc. 4, B1900AJL La Plata, Argentina
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4
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Bramwell ST, Harris MJ. The history of spin ice. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2020; 32:374010. [PMID: 32554893 DOI: 10.1088/1361-648x/ab8423] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/29/2019] [Accepted: 03/27/2020] [Indexed: 06/11/2023]
Abstract
This review is a study of how the idea of spin ice has evolved over the years, with a focus on the scientific questions that have come to define the subject. Since our initial discovery of spin ice in 1997, there have been well over five thousand papers that discuss it, and in the face of such detail, it must be difficult for the curious observer to 'see the wood for the trees'. To help in this task, we go in search of the biggest insight to have emerged from the study of spin ice. On the way, we identify highlights and outstanding puzzles, and celebrate the inspirational role that Roger Cowley played in the early years.
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Affiliation(s)
- Steven T Bramwell
- London Centre for Nanotechnology and Department of Physics and Astronomy, University College London, London WC1H 0AH, United Kingdom
| | - Mark J Harris
- School of Divinity, University of Edinburgh, New College, Edinburgh, EH1 2LX, United Kingdom
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5
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Otsuka H, Okabe Y, Nefedev K. Husimi-cactus approximation study on the diluted spin ice. Phys Rev E 2018; 97:042132. [PMID: 29758667 DOI: 10.1103/physreve.97.042132] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/14/2018] [Indexed: 06/08/2023]
Abstract
We investigate dilution effects on the classical spin-ice materials such as Ho_{2}Ti_{2}O_{7} and Dy_{2}Ti_{2}O_{7}. In particular, we derive a formula of the thermodynamic quantities as functions of the temperature and a nonmagnetic ion concentration based on a Husimi-cactus approximation. We find that the formula predicts a dilution-induced crossover from the cooperative to the conventional paramagnets in a ground state, and that it also reproduces the "generalized Pauling's entropy" given by Ke et al. To verify the formula from a numerical viewpoint, we compare these results with Monte Carlo simulation calculation data, and then find good agreement for all parameter values.
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Affiliation(s)
- Hiromi Otsuka
- Department of Physics, Tokyo Metropolitan University, Tokyo 192-0397, Japan
| | - Yutaka Okabe
- Department of Physics, Tokyo Metropolitan University, Tokyo 192-0397, Japan
| | - Konstantin Nefedev
- School of Natural Sciences, Far Eastern Federal University, Vladivostok 690091, Russian Federation
- Institute of Applied Mathematics, Far Eastern Branch, Russian Academy of Science, Vladivostok 690041, Russian Federation
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6
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Jurčišinová E, Jurčišin M. Adiabatic cooling processes in frustrated magnetic systems with pyrochlore structure. Phys Rev E 2017; 96:052128. [PMID: 29347644 DOI: 10.1103/physreve.96.052128] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/24/2017] [Indexed: 06/07/2023]
Abstract
We investigate in detail the process of adiabatic cooling in the framework of the exactly solvable antiferromagnetic spin-1/2 Ising model in the presence of the external magnetic field on an approximate lattice with pyrochlore structure. The behavior of the entropy of the model is studied and exact values of the residual entropies of all ground states are found. The temperature variation of the system under adiabatic (de)magnetization is investigated and the central role of the macroscopically degenerated ground states in cooling processes is explicitly demonstrated. It is shown that the model parameter space of the studied geometrically frustrated system is divided into five disjunct regions with qualitatively different processes of the adiabatic cooling. The effectiveness of the adiabatic (de)magnetization cooling in the studied model is compared to the corresponding processes in paramagnetic salts. It is shown that the processes of the adiabatic cooling in the antiferromagnetic frustrated systems are much more effective especially in nonzero external magnetic fields. It means that the frustrated magnetic materials with pyrochlore structure can be considered as very promising refrigerants mainly in the situations with nonzero final values of the magnetic field.
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Affiliation(s)
- E Jurčišinová
- Institute of Experimental Physics, Slovak Academy of Sciences, Watsonova 47, 040 01 Košice, Slovakia
| | - M Jurčišin
- Institute of Experimental Physics, Slovak Academy of Sciences, Watsonova 47, 040 01 Košice, Slovakia
- Department of Theoretical Physics and Astrophysics, Faculty of Science, P.J. Šafárik University, Park Angelinum 9, 040 01 Košice, Slovakia
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7
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Abstract
The complexity embedded in condensed matter fertilizes the discovery of new states of matter, enriched by ingredients like frustration. Illustrating examples in magnetic systems are Kitaev spin liquids, skyrmions phases, or spin ices. These unconventional ground states support exotic excitations, for example the magnetic charges in spin ices, also called monopoles. Here, we propose a mechanism to inject monopoles in a spin ice at equilibrium through a staggered magnetic field. We show theoretically, and demonstrate experimentally in the Ho2Ir2O7 pyrochlore iridate, that it results in the stabilization of a monopole crystal, which exhibits magnetic fragmentation. In this new state of matter, the magnetic moment fragments into an ordered part and a persistently fluctuating one. Compared to conventional spin ices, the different nature of the excitations in this fragmented state opens the way to tunable field-induced and dynamical behaviors. Exploring unconventional magnetism facilities both fundamental understanding of materials and their real applications. Here the authors demonstrate that a magnetic monopole crystal is stabilized by a staggered magnetic field in the pyrochlore iridate Ho2Ir2O7, leading to a fragmented magnetization.
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8
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Jaubert LDC, Lin T, Opel TS, Holdsworth PCW, Gingras MJP. Spin ice Thin Film: Surface Ordering, Emergent Square ice, and Strain Effects. PHYSICAL REVIEW LETTERS 2017; 118:207206. [PMID: 28581768 DOI: 10.1103/physrevlett.118.207206] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/24/2016] [Indexed: 06/07/2023]
Abstract
Motivated by recent realizations of Dy_{2}Ti_{2}O_{7} and Ho_{2}Ti_{2}O_{7} spin ice thin films, and more generally by the physics of confined gauge fields, we study a model spin ice thin film with surfaces perpendicular to the [001] cubic axis. The resulting open boundaries make half of the bonds on the interfaces inequivalent. By tuning the strength of these inequivalent "orphan" bonds, dipolar interactions induce a surface ordering equivalent to a two-dimensional crystallization of magnetic surface charges. This surface ordering may also be expected on the surfaces of bulk crystals. For ultrathin films made of one cubic unit cell, once the surfaces have ordered, a square ice phase is stabilized over a finite temperature window. The square ice degeneracy is lifted at lower temperature and the system orders in analogy with the well-known F transition of the 6-vertex model. To conclude, we consider the addition of strain effects, a possible consequence of interface mismatches at the film-substrate interface. Our simulations qualitatively confirm that strain can lead to a smooth loss of Pauling entropy upon cooling, as observed in recent experiments on Dy_{2}Ti_{2}O_{7} films.
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Affiliation(s)
- L D C Jaubert
- Okinawa Institute of Science and Technology Graduate University, Onna-son, Okinawa 904-0495, Japan
- Université de Bordeaux, CNRS, LOMA, UMR 5798, F-33405 Talence, France
| | - T Lin
- Department of Physics and Astronomy, University of Waterloo, 200 University Avenue West, Waterloo, Ontario N2L 3G1, Canada
| | - T S Opel
- Department of Physics and Astronomy, University of Waterloo, 200 University Avenue West, Waterloo, Ontario N2L 3G1, Canada
| | - P C W Holdsworth
- Université de Lyon, Laboratoire de Physique, École normale supérieure de Lyon, CNRS, UMR5672, 46 Allée d'Italie, 69364 Lyon, France
| | - M J P Gingras
- Department of Physics and Astronomy, University of Waterloo, 200 University Avenue West, Waterloo, Ontario N2L 3G1, Canada
- Perimeter Institute for Theoretical Physics, 31 Caroline North, Waterloo, Ontario N2L 2Y5, Canada
- Canadian Institute for Advanced Research, Toronto, Ontario M5G 1Z8, Canada
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9
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Baez ML, Borzi RA. The 3D Kasteleyn transition in dipolar spin ice: a numerical study with the conserved monopoles algorithm. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2017; 29:055806. [PMID: 27941225 DOI: 10.1088/1361-648x/aa4e6a] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
We study the three-dimensional Kasteleyn transition in both nearest neighbours and dipolar spin ice models using an algorithm that conserves the number of excitations. We first limit the interactions range to nearest neighbours to test the method in the presence of a field applied along [Formula: see text], and then focus on the dipolar spin ice model. The effect of dipolar interactions, which is known to be greatly self screened at zero field, is particularly strong near full polarization. It shifts the Kasteleyn transition to lower temperatures, which decreases ≈0.4 K for the parameters corresponding to the best known spin ice materials, [Formula: see text] and [Formula: see text]. This shift implies effective dipolar fields as big as 0.05 T opposing the applied field, and thus favouring the creation of 'strings' of reversed spins. We compare the reduction in the transition temperature with results in previous experiments, and study the phenomenon quantitatively using a simple molecular field approach. Finally, we relate the presence of the effective residual field to the appearance of string-ordered phases at low fields and temperatures, and we check numerically that for fields applied along [Formula: see text] there are only three different stable phases at zero temperature.
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Affiliation(s)
- M L Baez
- Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas (INIFTA), UNLP-CONICET, La Plata, Argentina
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10
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Rehn J, Moessner R. Maxwell electromagnetism as an emergent phenomenon in condensed matter. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2016; 374:rsta.2016.0093. [PMID: 27458263 DOI: 10.1098/rsta.2016.0093] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 04/25/2016] [Indexed: 06/06/2023]
Abstract
The formulation of a complete theory of classical electromagnetism by Maxwell is one of the milestones of science. The capacity of many-body systems to provide emergent mini-universes with vacua quite distinct from the one we inhabit was only recognized much later. Here, we provide an account of how simple systems of localized spins manage to emulate Maxwell electromagnetism in their low-energy behaviour. They are much less constrained by symmetry considerations than the relativistically invariant electromagnetic vacuum, as their substrate provides a non-relativistic background with even translational invariance broken. They can exhibit rich behaviour not encountered in conventional electromagnetism. This includes the existence of magnetic monopole excitations arising from fractionalization of magnetic dipoles; as well as the capacity of disorder, by generating defects on the lattice scale, to produce novel physics, as exemplified by topological spin glassiness or random Coulomb magnetism.This article is part of the themed issue 'Unifying physics and technology in light of Maxwell's equations'.
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Affiliation(s)
- J Rehn
- Max Planck Institut für Physik komplexer Systeme, 01187 Dresden, Germany
| | - R Moessner
- Max Planck Institut für Physik komplexer Systeme, 01187 Dresden, Germany
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11
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Borzi RA, Gómez Albarracín FA, Rosales HD, Rossini GL, Steppke A, Prabhakaran D, Mackenzie AP, Cabra DC, Grigera SA. Intermediate magnetization state and competing orders in Dy2Ti2O7 and Ho2Ti2O7. Nat Commun 2016; 7:12592. [PMID: 27558021 PMCID: PMC5007346 DOI: 10.1038/ncomms12592] [Citation(s) in RCA: 24] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/18/2015] [Accepted: 07/15/2016] [Indexed: 12/03/2022] Open
Abstract
Among the frustrated magnetic materials, spin-ice stands out as a particularly interesting system. Residual entropy, freezing and glassiness, Kasteleyn transitions and fractionalization of excitations in three dimensions all stem from a simple classical Hamiltonian. But is the usual spin-ice Hamiltonian a correct description of the experimental systems? Here we address this issue by measuring magnetic susceptibility in the two most studied spin-ice compounds, Dy2Ti2O7 and Ho2Ti2O7, using a vector magnet. Using these results, and guided by a theoretical analysis of possible distortions to the pyrochlore lattice, we construct an effective Hamiltonian and explore it using Monte Carlo simulations. We show how this Hamiltonian reproduces the experimental results, including the formation of a phase of intermediate polarization, and gives important information about the possible ground state of real spin-ice systems. Our work suggests an unusual situation in which distortions might contribute to the preservation rather than relief of the effects of frustration. A classical Hamiltonian captures key properties of spin ice materials such as residual entropy and fractionalized excitations. Here, the authors present experimental results of the polarization transition that motivate a Hamiltonian with lattice distortions, which predicts an intermediate magnetization state and competing ground state orders.
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Affiliation(s)
- R A Borzi
- Instituto de Física de Líquidos y Sistemas Biológicos (IFLYSIB), UNLP-CONICET, La Plata 1900, Argentina.,Departamento de Física, Facultad de Ciencias Exactas,Universidad Nacional de La Plata, 1900 La Plata, Argentina
| | - F A Gómez Albarracín
- Departamento de Física, Facultad de Ciencias Exactas,Universidad Nacional de La Plata, 1900 La Plata, Argentina.,Instituto de Física de La Plata, UNLP-CONICET, 1900 La Plata, Argentina
| | - H D Rosales
- Departamento de Física, Facultad de Ciencias Exactas,Universidad Nacional de La Plata, 1900 La Plata, Argentina.,Instituto de Física de La Plata, UNLP-CONICET, 1900 La Plata, Argentina
| | - G L Rossini
- Departamento de Física, Facultad de Ciencias Exactas,Universidad Nacional de La Plata, 1900 La Plata, Argentina.,Instituto de Física de La Plata, UNLP-CONICET, 1900 La Plata, Argentina
| | - A Steppke
- School of Physics and Astronomy, University of St. Andrews, St. Andrews KY16 9SS, UK.,Max Planck Institute for Chemical Physics of Solids, Nöthnitzer Str. 40, Dresden, Germany
| | - D Prabhakaran
- Department of Physics, Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, UK
| | - A P Mackenzie
- School of Physics and Astronomy, University of St. Andrews, St. Andrews KY16 9SS, UK.,Max Planck Institute for Chemical Physics of Solids, Nöthnitzer Str. 40, Dresden, Germany
| | - D C Cabra
- Departamento de Física, Facultad de Ciencias Exactas,Universidad Nacional de La Plata, 1900 La Plata, Argentina.,Instituto de Física de La Plata, UNLP-CONICET, 1900 La Plata, Argentina
| | - S A Grigera
- Instituto de Física de Líquidos y Sistemas Biológicos (IFLYSIB), UNLP-CONICET, La Plata 1900, Argentina.,Departamento de Física, Facultad de Ciencias Exactas,Universidad Nacional de La Plata, 1900 La Plata, Argentina.,School of Physics and Astronomy, University of St. Andrews, St. Andrews KY16 9SS, UK
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12
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Smerald A, Korshunov S, Mila F. Topological Aspects of Symmetry Breaking in Triangular-Lattice Ising Antiferromagnets. PHYSICAL REVIEW LETTERS 2016; 116:197201. [PMID: 27232039 DOI: 10.1103/physrevlett.116.197201] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/04/2016] [Indexed: 06/05/2023]
Abstract
Using a specially designed Monte Carlo algorithm with directed loops, we investigate the triangular lattice Ising antiferromagnet with coupling beyond the nearest neighbors. 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.
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Affiliation(s)
- Andrew Smerald
- Institute of Physics, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
| | - Sergey Korshunov
- L. D. Landau Institute for Theoretical Physics, Kosygina 2, Moscow 119334, Russia
| | - Frédéric Mila
- Institute of Physics, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
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13
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Oakes T, Garrahan JP, Powell S. Emergence of cooperative dynamics in fully packed classical dimers. Phys Rev E 2016; 93:032129. [PMID: 27078314 DOI: 10.1103/physreve.93.032129] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/12/2015] [Indexed: 11/07/2022]
Abstract
The classical dimer model on the square lattice is a paradigmatic example of a system subject to strong local constraints. We study its behavior under local stochastic dynamics, by means of Monte Carlo simulations and theoretical arguments. We observe clear signatures of correlated dynamics in both global and local observables and over a broad range of time scales, indicating a breakdown of the simple continuum description that approximates well the statics. We show that this collective dynamics can be understood in terms of one-dimensional "strings" of high mobility, which govern both local and long-wavelength dynamical properties. We introduce a coarse-grained description of the strings, based on the Edwards-Wilkinson model, which leads to exact results in the limit of low string density and provides a detailed qualitative understanding of the dynamics in all flux sectors. We discuss the implications of our results for the dynamics of constrained systems more generally.
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Affiliation(s)
- Tom Oakes
- School of Physics and Astronomy, The University of Nottingham, Nottingham NG7 2RD, United Kingdom
| | - Juan P Garrahan
- School of Physics and Astronomy, The University of Nottingham, Nottingham NG7 2RD, United Kingdom
| | - Stephen Powell
- School of Physics and Astronomy, The University of Nottingham, Nottingham NG7 2RD, United Kingdom
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14
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Bovo L, Jaubert LDC, Holdsworth PCW, Bramwell ST. Crystal shape-dependent magnetic susceptibility and Curie law crossover in the spin ices Dy2Ti2O7 and Ho2Ti2O7. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2013; 25:386002. [PMID: 23988470 DOI: 10.1088/0953-8984/25/38/386002] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/02/2023]
Abstract
We present an experimental determination of the isothermal magnetic susceptibility of the spin ice materials Dy2Ti2O7 and Ho2Ti2O7 in the temperature range 1.8-300 K. The use of spherical crystals has allowed accurate correction for demagnetizing fields and allowed the true bulk isothermal susceptibility χT(T) to be estimated. This has been compared against a theoretical expression based on a Husimi tree approximation to the spin ice model. Agreement between experiment and theory is excellent at T > 10 K, but systematic deviations occur below that temperature. Our results largely resolve an apparent disagreement between neutron scattering and bulk measurements that has been previously noted. They also show that the use of non-spherical crystals in magnetization studies of spin ice may introduce very significant systematic errors, although we note some interesting--and possibly new--systematics concerning the demagnetizing factor in cuboidal samples. Finally, our results show how experimental susceptibility measurements on spin ices may be used to extract the characteristic energy scale of the system and the corresponding chemical potential for emergent magnetic monopoles.
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Affiliation(s)
- L Bovo
- London Centre for Nanotechnology and Department of Physics and Astronomy, University College London, 17-19 Gordon Street, London WC1H 0AJ, UK.
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15
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Levis D, Cugliandolo LF, Foini L, Tarzia M. Thermal phase transitions in artificial spin ice. PHYSICAL REVIEW LETTERS 2013; 110:207206. [PMID: 25167447 DOI: 10.1103/physrevlett.110.207206] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/15/2013] [Indexed: 06/03/2023]
Abstract
We use the sixteen-vertex model to describe bidimensional artificial spin ice. We find excellent agreement between vertex densities in 15 differently grown samples and the predictions of the model. Our results demonstrate that the samples are in usual thermal equilibrium away from a critical point separating a disordered and an antiferromagnetic phase in the model. The second-order phase transition that we predict suggests that the spatial arrangement of vertices in near-critical artificial spin ice should be studied in more detail in order to verify whether they show the expected space and time long-range correlations.
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Affiliation(s)
- Demian Levis
- Université Pierre et Marie Curie-Paris 6, Laboratoire de Physique Théorique et Hautes Energies, 4, Place Jussieu, Tour 13, 5ème étage, 75252 Paris Cedex 05, France
| | - Leticia F Cugliandolo
- Université Pierre et Marie Curie-Paris 6, Laboratoire de Physique Théorique et Hautes Energies, 4, Place Jussieu, Tour 13, 5ème étage, 75252 Paris Cedex 05, France
| | - Laura Foini
- Université Pierre et Marie Curie-Paris 6, Laboratoire de Physique Théorique et Hautes Energies, 4, Place Jussieu, Tour 13, 5ème étage, 75252 Paris Cedex 05, France
| | - Marco Tarzia
- Université Pierre et Marie Curie-Paris 6, Laboratoire de Physique Théorique de la Matière Condensée, 4, Place Jussieu, Tour 12, 5ème étage, 75252 Paris Cedex 05, France
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16
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Powell S. Universal monopole scaling near transitions from the Coulomb phase. PHYSICAL REVIEW LETTERS 2012; 109:065701. [PMID: 23006280 DOI: 10.1103/physrevlett.109.065701] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/26/2012] [Revised: 05/22/2012] [Indexed: 06/01/2023]
Abstract
Certain frustrated systems, including spin ice and dimer models, exhibit a Coulomb phase at low temperatures, with power-law correlations and fractionalized monopole excitations. Transitions out of this phase, at which the effective gauge theory becomes confining, provide examples of unconventional criticality. This Letter studies the behavior at nonzero monopole density near such transitions, using scaling theory to arrive at universal expressions for the crossover phenomena. For a particular transition in spin ice, quantitative predictions are made by mapping to the XY model and confirmed using Monte Carlo simulations.
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Affiliation(s)
- Stephen Powell
- Joint Quantum Institute and Condensed Matter Theory Center, Department of Physics, University of Maryland, College Park, Maryland 20742, USA
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17
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Wan Y, Tchernyshyov O. Quantum strings in quantum spin ice. PHYSICAL REVIEW LETTERS 2012; 108:247210. [PMID: 23004322 DOI: 10.1103/physrevlett.108.247210] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/26/2012] [Indexed: 06/01/2023]
Abstract
We study quantum spin ice in an external magnetic field applied along a <100> direction. When quantum spin fluctuations are weak, elementary excitations are quantum strings with monopoles at their ends manifested as multiple spin wave branches in the dynamical structure factor. Strong quantum fluctuations make the string tension negative and give rise to the deconfinement of monopoles. We discuss our results in the light of recent neutron scattering experiments in Yb2Ti2O7.
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Affiliation(s)
- Yuan Wan
- Department of Physics and Astronomy, Johns Hopkins University, Baltimore, Massachusetts 21218, USA
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18
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Wang Y, De Sterck H, Melko RG. Generalized Monte Carlo loop algorithm for two-dimensional frustrated Ising models. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 85:036704. [PMID: 22587206 DOI: 10.1103/physreve.85.036704] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/02/2011] [Indexed: 05/31/2023]
Abstract
We introduce a generalized loop move (GLM) update for Monte Carlo simulations of frustrated Ising models on two-dimensional lattices with bond-sharing plaquettes. The GLM updates are designed to enhance Monte Carlo sampling efficiency when the system's low-energy states consist of an extensive number of degenerate or near-degenerate spin configurations, separated by large energy barriers to single spin flips. Through implementation on several frustrated Ising models, we demonstrate the effectiveness of the GLM updates in cases where both degenerate and near-degenerate sets of configurations are favored at low temperatures. The GLM update's potential to be straightforwardly extended to different lattices and spin interactions allows it to be readily adopted on many other frustrated Ising models of physical relevance.
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Affiliation(s)
- Yuan Wang
- Department of Applied Mathematics, University of Waterloo, Ontario, N2L 3G1, Canada
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19
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Chalker JT. Geometrically Frustrated Antiferromagnets: Statistical Mechanics and Dynamics. INTRODUCTION TO FRUSTRATED MAGNETISM 2011. [DOI: 10.1007/978-3-642-10589-0_1] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/12/2023]
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21
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Jaubert LDC, Chalker JT, Holdsworth PCW, Moessner R. Spin ice under pressure: symmetry enhancement and infinite order multicriticality. PHYSICAL REVIEW LETTERS 2010; 105:087201. [PMID: 20868127 DOI: 10.1103/physrevlett.105.087201] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/10/2010] [Revised: 07/14/2010] [Indexed: 05/29/2023]
Abstract
We study the low-temperature behavior of spin ice when uniaxial pressure induces a tetragonal distortion. There is a phase transition between a Coulomb liquid and a fully magnetized 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 realization.
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Affiliation(s)
- L D C Jaubert
- Max-Planck-Institut für Physik komplexer Systeme, 01187 Dresden, Germany
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22
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Morris DJP, Tennant DA, Grigera SA, Klemke B, Castelnovo C, Moessner R, Czternasty C, Meissner M, Rule KC, Hoffmann JU, Kiefer K, Gerischer S, Slobinsky D, Perry RS. Dirac Strings and Magnetic Monopoles in the Spin Ice Dy
2
Ti
2
O
7. Science 2009; 326:411-4. [DOI: 10.1126/science.1178868] [Citation(s) in RCA: 447] [Impact Index Per Article: 29.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
Affiliation(s)
- D. J. P. Morris
- Helmholtz-Zentrum Berlin für Materialien und Energie, Glienicker Str. 100, D-14109 Berlin, Germany
| | - D. A. Tennant
- Helmholtz-Zentrum Berlin für Materialien und Energie, Glienicker Str. 100, D-14109 Berlin, Germany
- Institut für Festkörperphysik, Technische Universität Berlin, Hardenbergstr. 36, D-10623 Berlin, Germany
| | - S. A. Grigera
- School of Physics and Astronomy, North Haugh, St. Andrews, Fife KY15 9SS, UK
- Instituto de Física de Líquidos y Sistemas Biológicos, CONICET, UNLP, La Plata, Argentina
| | - B. Klemke
- Helmholtz-Zentrum Berlin für Materialien und Energie, Glienicker Str. 100, D-14109 Berlin, Germany
- Institut für Festkörperphysik, Technische Universität Berlin, Hardenbergstr. 36, D-10623 Berlin, Germany
| | - C. Castelnovo
- Rudolf Peierls Centre for Theoretical Physics, 1 Keble Road, Oxford OX1 3NP, UK
| | - R. Moessner
- Max-Planck-Institut für Physik Komplexer Systeme, Nöthnitzer Str. 38, D-01187 Dresden, Germany
| | - C. Czternasty
- Helmholtz-Zentrum Berlin für Materialien und Energie, Glienicker Str. 100, D-14109 Berlin, Germany
| | - M. Meissner
- Helmholtz-Zentrum Berlin für Materialien und Energie, Glienicker Str. 100, D-14109 Berlin, Germany
| | - K. C. Rule
- Helmholtz-Zentrum Berlin für Materialien und Energie, Glienicker Str. 100, D-14109 Berlin, Germany
| | - J.-U. Hoffmann
- Helmholtz-Zentrum Berlin für Materialien und Energie, Glienicker Str. 100, D-14109 Berlin, Germany
| | - K. Kiefer
- Helmholtz-Zentrum Berlin für Materialien und Energie, Glienicker Str. 100, D-14109 Berlin, Germany
| | - S. Gerischer
- Helmholtz-Zentrum Berlin für Materialien und Energie, Glienicker Str. 100, D-14109 Berlin, Germany
| | - D. Slobinsky
- School of Physics and Astronomy, North Haugh, St. Andrews, Fife KY15 9SS, UK
| | - R. S. Perry
- School of Physics, University of Edinburgh, Mayfield Road, Edinburgh EH9 3JZ, UK
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23
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Jaubert LDC, Chalker JT, Holdsworth PCW, Moessner R. The Kasteleyn transition in three dimensions: Spin ice in a [100] field. ACTA ACUST UNITED AC 2009. [DOI: 10.1088/1742-6596/145/1/012024] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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Cao H, Gukasov A, Mirebeau I, Bonville P, Dhalenne G. Field-induced spin-ice-like orders in spin liquid Tb2Ti2O7. PHYSICAL REVIEW LETTERS 2008; 101:196402. [PMID: 19113288 DOI: 10.1103/physrevlett.101.196402] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/07/2008] [Indexed: 05/27/2023]
Abstract
We have studied the field-induced magnetic structures in Tb2Ti2O7, in a wide temperature (0.3 < T < 270 K) and field (0 < H < 7 T) range, by single crystal polarized and unpolarized neutron diffraction, with H parallel[110] axis. A ferromagneticlike structure with k = 0 propagation vector is induced, whose local order at low field and low temperature is akin to spin ice. The four Tb ions separate in alpha and beta chains having different values of the magnetic moments, which is quantitatively explained by taking the crystal field anisotropy into account. Above 2 T and below 2 K, an antiferromagneticlike structure with k = (0,0,1) is induced besides the k = 0 structure. It shows a reentrant behavior and extends over a finite length scale. It occurs together with a broadening of the nuclear peaks, which suggests a field-induced distortion and magnetostriction effect.
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Affiliation(s)
- H Cao
- Laboratoire Léon Brillouin, CEA-CNRS, CE-Saclay, 91191 Gif-sur-Yvette, France
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