1
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King AD, Coraux J, Canals B, Rougemaille N. Magnetic Arctic Circle in a Square Ice Qubit Lattice. PHYSICAL REVIEW LETTERS 2023; 131:166701. [PMID: 37925737 DOI: 10.1103/physrevlett.131.166701] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/16/2023] [Accepted: 09/15/2023] [Indexed: 11/07/2023]
Abstract
Under certain boundary conditions, the square ice model exhibits a phase separation in which the core of the system is disordered while its outer region remains ordered. This phenomenon, known as the "arctic circle," has been studied theoretically in combinatorial mathematics and statistical mechanics. Here, we realize the physics of the arctic circle experimentally for the first time, using a programmable lattice of superconducting qubits, and investigate its properties under the prism of a highly frustrated magnet. Our work reveals two unexpected properties. First, the disordered spin manifold confined within the arctic curve is a spin liquid whose average spin texture resembles that of an antivortex, i.e., it is a topologically charged Coulomb phase. Second, monopole quasiparticle excitations, which are totally absent in theoretical works, can be isolated in a phase-separated system. Remarkably, a monopole segregation mechanism is observed, in which the monopoles are sorted according to the magnetic charge and magnetic moment they carry, without the application of an external driving force.
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Affiliation(s)
- A D King
- D-Wave Systems, Burnaby, British Columbia V5G 4M9, Canada
| | - J Coraux
- Université Grenoble Alpes, CNRS, Grenoble INP, Institut Néel, Grenoble 38000, France
| | - B Canals
- Université Grenoble Alpes, CNRS, Grenoble INP, Institut Néel, Grenoble 38000, France
| | - N Rougemaille
- Université Grenoble Alpes, CNRS, Grenoble INP, Institut Néel, Grenoble 38000, France
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2
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Saccone M, Caravelli F, Hofhuis K, Dhuey S, Scholl A, Nisoli C, Farhan A. Real-space observation of ergodicity transitions in artificial spin ice. Nat Commun 2023; 14:5674. [PMID: 37704596 PMCID: PMC10499874 DOI: 10.1038/s41467-023-41235-4] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/30/2022] [Accepted: 08/23/2023] [Indexed: 09/15/2023] Open
Abstract
Ever since its introduction by Ludwig Boltzmann, the ergodic hypothesis became a cornerstone analytical concept of equilibrium thermodynamics and complex dynamic processes. Examples of its relevance range from modeling decision-making processes in brain science to economic predictions. In condensed matter physics, ergodicity remains a concept largely investigated via theoretical and computational models. Here, we demonstrate the direct real-space observation of ergodicity transitions in a vertex-frustrated artificial spin ice. Using synchrotron-based photoemission electron microscopy we record thermally-driven moment fluctuations as a function of temperature, allowing us to directly observe transitions between ergodicity-breaking dynamics to system freezing, standing in contrast to simple trends observed for the temperature-dependent vertex populations, all while the entropy features arise as a function of temperature. These results highlight how a geometrically frustrated system, with thermodynamics strictly adhering to local ice-rule constraints, runs back-and-forth through periods of ergodicity-breaking dynamics. Ergodicity breaking and the emergence of memory is important for emergent computation, particularly in physical reservoir computing. Our work serves as further evidence of how fundamental laws of thermodynamics can be experimentally explored via real-space imaging.
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Affiliation(s)
- Michael Saccone
- Center for Nonlinear Studies and Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM, 87545, USA.
| | - Francesco Caravelli
- Center for Nonlinear Studies and Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM, 87545, USA
| | - Kevin Hofhuis
- Laboratory for Mesoscopic Systems, Department of Materials, ETH Zurich, 8093, Zurich, Switzerland
- Laboratory for Multiscale Materials Experiments (LMX), Paul Scherrer Institute, 5232, Villigen PSI, Switzerland
| | - Scott Dhuey
- Molecular Foundry, Lawrence Berkeley National Laboratory, One Cyclotron Road, Berkeley, CA, 94720, USA
| | - Andreas Scholl
- Advanced Light Source, Lawrence Berkeley National Laboratory, One Cyclotron Road, Berkeley, CA, 94720, USA
| | - Cristiano Nisoli
- Center for Nonlinear Studies and Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM, 87545, USA
| | - Alan Farhan
- Department of Physics, Baylor University, Waco, TX, 76798, USA.
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3
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Bingham NS, Rooke S, Park J, Simon A, Zhu W, Zhang X, Batley J, Watts JD, Leighton C, Dahmen KA, Schiffer P. Experimental Realization of the 1D Random Field Ising Model. PHYSICAL REVIEW LETTERS 2021; 127:207203. [PMID: 34860045 DOI: 10.1103/physrevlett.127.207203] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/12/2021] [Accepted: 10/06/2021] [Indexed: 06/13/2023]
Abstract
We have measured magnetic-field-induced avalanches in a square artificial spin ice array of interacting nanomagnets. Starting from the ground state ordered configuration, we imaged the individual nanomagnet moments after each successive application of an incrementally increasing field. The statistics of the evolution of the moment configuration show good agreement with the canonical one-dimensional random field Ising model. We extract information about the microscopic structure of the arrays from our macroscopic measurements of their collective behavior, demonstrating a process that could be applied to other systems exhibiting avalanches.
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Affiliation(s)
- N S Bingham
- Department of Applied Physics, Yale University, New Haven, Connecticut 06511, USA
| | - S Rooke
- Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
| | - J Park
- Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
| | - A Simon
- Department of Applied Physics, Yale University, New Haven, Connecticut 06511, USA
| | - W Zhu
- Department of Applied Physics, Yale University, New Haven, Connecticut 06511, USA
| | - X Zhang
- Department of Applied Physics, Yale University, New Haven, Connecticut 06511, USA
- Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
| | - J Batley
- Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, Minnesota 55455, USA
| | - J D Watts
- Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, Minnesota 55455, USA
- School of Physics and Astronomy, University of Minnesota, Minneapolis, Minnesota 55455, USA
| | - C Leighton
- Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, Minnesota 55455, USA
| | - K A Dahmen
- Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
| | - P Schiffer
- Department of Applied Physics, Yale University, New Haven, Connecticut 06511, USA
- Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
- Department of Physics, Yale University, New Haven, Connecticut 06511, USA
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4
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Caravelli F, Saccone M, Nisoli C. On the degeneracy of spin ice graphs, and its estimate via the Bethe permanent. Proc Math Phys Eng Sci 2021. [DOI: 10.1098/rspa.2021.0108] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/20/2023] Open
Abstract
The concept of spin ice can be extended to a general graph. We study the degeneracy of spin ice graph on arbitrary interaction structures via graph theory. We map spin ice graphs to the Ising model on a graph and clarify whether the inverse mapping is possible via a modified Krausz construction. From the gauge freedom of frustrated Ising systems, we derive exact, general results about frustration and degeneracy. We demonstrate for the first time that every spin ice graph, with the exception of the one-dimensional Ising model, is degenerate. We then study how degeneracy scales in size, using the mapping between Eulerian trails and spin ice manifolds, and a permanental identity for the number of Eulerian orientations. We show that the Bethe permanent technique provides both an estimate and a lower bound to the frustration of spin ices on arbitrary graphs of even degree. While such a technique can also be used to obtain an upper bound, we find that in all finite degree examples we studied, another upper bound based on Schrijver inequality is tighter.
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Affiliation(s)
- Francesco Caravelli
- Theoretical Division (T4), Los Alamos National Laboratory, Los Alamos, NM 87545, USA
| | - Michael Saccone
- Theoretical Division (T4), Los Alamos National Laboratory, Los Alamos, NM 87545, USA
- Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, NM 87545, USA
| | - Cristiano Nisoli
- Theoretical Division (T4), Los Alamos National Laboratory, Los Alamos, NM 87545, USA
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5
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Paterson GW, Macauley GM, Macêdo R. Field‐Driven Reversal Models in Artificial Spin Ice. ADVANCED THEORY AND SIMULATIONS 2021. [DOI: 10.1002/adts.202100109] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
Affiliation(s)
- Gary W. Paterson
- SUPA, School of Physics and Astronomy University of Glasgow Glasgow G12 8QQ UK
- James Watt School of Engineering Electronics and Nanoscale Engineering Division University of Glasgow Glasgow G12 8QQ UK
| | - Gavin M. Macauley
- SUPA, School of Physics and Astronomy University of Glasgow Glasgow G12 8QQ UK
| | - Rair Macêdo
- James Watt School of Engineering Electronics and Nanoscale Engineering Division University of Glasgow Glasgow G12 8QQ UK
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6
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Duzgun A, Nisoli C. Skyrmion Spin Ice in Liquid Crystals. PHYSICAL REVIEW LETTERS 2021; 126:047801. [PMID: 33576672 DOI: 10.1103/physrevlett.126.047801] [Citation(s) in RCA: 11] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/21/2019] [Revised: 10/17/2020] [Accepted: 12/23/2020] [Indexed: 06/12/2023]
Abstract
We propose the first skyrmion spin ice, realized via confined, interacting liquid crystal skyrmions. Skyrmions in a chiral nematic liquid crystal behave as quasiparticles that can be dynamically confined, bound, and created or annihilated individually with ease and precision. We show that these quasiparticles can be employed to realize binary variables that interact to form ice-rule states. Because of their unique versatility, liquid crystal skyrmions can open entirely novel avenues in the field of frustrated systems. More broadly, our findings also demonstrate the viability of liquid crystal skyrmions as elementary degrees of freedom in the design of collective complex behaviors.
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Affiliation(s)
- Ayhan Duzgun
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - Cristiano Nisoli
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
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7
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Parakkat VM, Macauley GM, Stamps RL, Krishnan KM. Configurable Artificial Spin Ice with Site-Specific Local Magnetic Fields. PHYSICAL REVIEW LETTERS 2021; 126:017203. [PMID: 33480755 DOI: 10.1103/physrevlett.126.017203] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/18/2020] [Accepted: 12/18/2020] [Indexed: 06/12/2023]
Abstract
We demonstrate ground state tunability for a hybrid artificial spin ice composed of Fe nanomagnets which are subject to site-specific exchange-bias fields, applied in integer multiples of the lattice along one sublattice of the classic square artificial spin ice. By varying this period, three distinct magnetic textures are identified: a striped ferromagnetic phase; an antiferromagnetic phase attainable through an external field protocol alone; and an unconventional ground state with magnetically charged pairs embedded in an antiferromagnetic matrix. Monte Carlo simulations support the results of field protocols and demonstrate that the pinning tunes relaxation timescales and their critical behavior.
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Affiliation(s)
- Vineeth Mohanan Parakkat
- Department of Materials Science and Engineering, 323 Roberts Hall, University of Washington, Seattle, Washington 98195, USA
| | - Gavin M Macauley
- SUPA, School of Physics and Astronomy, University of Glasgow, Glasgow G12 8QQ, United Kingdom
| | - Robert L Stamps
- Department of Physics and Astronomy, University of Manitoba, Winnipeg, Manitoba R3T 2N2, Canada
| | - Kannan M Krishnan
- Department of Materials Science and Engineering, 323 Roberts Hall, University of Washington, Seattle, Washington 98195, USA
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8
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Schánilec V, Canals B, Uhlíř V, Flajšman L, Sadílek J, Šikola T, Rougemaille N. Bypassing Dynamical Freezing in Artificial Kagome Ice. PHYSICAL REVIEW LETTERS 2020; 125:057203. [PMID: 32794868 DOI: 10.1103/physrevlett.125.057203] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/21/2020] [Revised: 07/01/2020] [Accepted: 07/10/2020] [Indexed: 06/11/2023]
Abstract
Spin liquids are correlated, disordered states of matter that fluctuate even at low temperatures. Experimentally, the extensive degeneracy characterizing their low-energy manifold is expected to be lifted, for example, because of dipolar interactions, leading to an ordered ground state at absolute zero. However, this is not what is usually observed, and many systems, whether they are chemically synthesized or nanofabricated, dynamically freeze before magnetic ordering sets in. In artificial realizations of highly frustrated magnets, ground state configurations, and even low-energy manifolds, thus remain out of reach for practical reasons. Here, we show how dynamical freezing can be bypassed in an artificial kagome ice. We illustrate the efficiency of our method by demonstrating that the a priori dynamically inaccessible ordered ground state and fragmented spin liquid configurations can be obtained reproducibly, imaged in real space at room temperature, and studied conveniently. We then identify the mechanism by which dynamical freezing occurs in the dipolar kagome ice.
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Affiliation(s)
- V Schánilec
- Univ. Grenoble Alpes, CNRS, Grenoble INP, Institut NEEL, 38000 Grenoble, France
- Central European Institute of Technology, CEITEC BUT, Brno University of Technology, Purkyňova 123, Brno 612 00, Czech Republic
| | - B Canals
- Univ. Grenoble Alpes, CNRS, Grenoble INP, Institut NEEL, 38000 Grenoble, France
| | - V Uhlíř
- Central European Institute of Technology, CEITEC BUT, Brno University of Technology, Purkyňova 123, Brno 612 00, Czech Republic
| | - L Flajšman
- Central European Institute of Technology, CEITEC BUT, Brno University of Technology, Purkyňova 123, Brno 612 00, Czech Republic
| | - J Sadílek
- Central European Institute of Technology, CEITEC BUT, Brno University of Technology, Purkyňova 123, Brno 612 00, Czech Republic
| | - T Šikola
- Central European Institute of Technology, CEITEC BUT, Brno University of Technology, Purkyňova 123, Brno 612 00, Czech Republic
- Institute of Physical Engineering, Faculty of Mechanical Engineering, Brno University of Technology, Technická 2, Brno, 616 69, Czech Republic
| | - N Rougemaille
- Univ. Grenoble Alpes, CNRS, Grenoble INP, Institut NEEL, 38000 Grenoble, France
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9
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Di Pietro Martínez M, Buceta RC. Energetic analysis of disorder effects in an artificial spin ice with dipolar interactions. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2020; 32:285801. [PMID: 32155604 DOI: 10.1088/1361-648x/ab7e58] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
We study the effect of quenched disorder in square artificial spin ice by means of numerical simulations. We introduce disorder in the length of magnetic islands using two kinds of distributions: Gaussian and uniform. As the system behavior depends on its geometrical parameters, we focus on studying it in the proximity of the ice regime which is quite difficult to thermalize both in experiments and simulations. We show how length disorder affect the antiferromagnetic and (locally) ferromagnetic ordering, by inducing the system, in the case of weak disorder, to intermediate or mix states. Moreover, in the case of strong disorder, ferromagnetic plaquettes prevail regardless of whether the mean length of the islands corresponds to an antiferromagnetic ordering.
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10
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Li Y, Paterson GW, Macauley GM, Nascimento FS, Ferguson C, Morley SA, Rosamond MC, Linfield EH, MacLaren DA, Macêdo R, Marrows CH, McVitie S, Stamps RL. Superferromagnetism and Domain-Wall Topologies in Artificial "Pinwheel" Spin Ice. ACS NANO 2019; 13:2213-2222. [PMID: 30588800 DOI: 10.1021/acsnano.8b08884] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
For over ten years, arrays of interacting single-domain nanomagnets, referred to as artificial spin ices, have been engineered with the aim to study frustration in model spin systems. Here, we use Fresnel imaging to study the reversal process in "pinwheel" artificial spin ice, a modified square ASI structure obtained by rotating each island by some angle about its midpoint. Our results demonstrate that a simple 45° rotation changes the magnetic ordering from antiferromagnetic to ferromagnetic, creating a superferromagnet which exhibits mesoscopic domain growth mediated by domain wall nucleation and coherent domain propagation. We observe several domain-wall configurations, most of which are direct analogues to those seen in continuous ferromagnetic films. However, charged walls also appear due to the geometric constraints of the system. Changing the orientation of the external magnetic field allows control of the nature of the spin reversal with the emergence of either one- or two-dimensional avalanches. This property of pinwheel ASI could be employed to tune devices based on magnetotransport phenomena such as Hall circuits.
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Affiliation(s)
- Yue Li
- SUPA, School of Physics and Astronomy , University of Glasgow , Glasgow G12 8QQ , United Kingdom
| | - Gary W Paterson
- SUPA, School of Physics and Astronomy , University of Glasgow , Glasgow G12 8QQ , United Kingdom
| | - Gavin M Macauley
- SUPA, School of Physics and Astronomy , University of Glasgow , Glasgow G12 8QQ , United Kingdom
| | - Fabio S Nascimento
- Departamento de Física , Universidade Federal de Viçosa , Viçosa 36570-900 , Minas Gerais , Brazil
| | - Ciaran Ferguson
- SUPA, School of Physics and Astronomy , University of Glasgow , Glasgow G12 8QQ , United Kingdom
| | - Sophie A Morley
- School of Physics and Astronomy , University of Leeds , Leeds LS2 9JT , United Kingdom
- Department of Physics , University of California , Santa Cruz , California 95064 , United States
| | - Mark C Rosamond
- School of Electronic and Electrical Engineering , University of Leeds , Leeds LS2 9JT , United Kingdom
| | - Edmund H Linfield
- School of Electronic and Electrical Engineering , University of Leeds , Leeds LS2 9JT , United Kingdom
| | - Donald A MacLaren
- SUPA, School of Physics and Astronomy , University of Glasgow , Glasgow G12 8QQ , United Kingdom
| | - Rair Macêdo
- SUPA, School of Physics and Astronomy , University of Glasgow , Glasgow G12 8QQ , United Kingdom
| | - Christopher H Marrows
- School of Physics and Astronomy , University of Leeds , Leeds LS2 9JT , United Kingdom
| | - Stephen McVitie
- SUPA, School of Physics and Astronomy , University of Glasgow , Glasgow G12 8QQ , United Kingdom
| | - Robert L Stamps
- SUPA, School of Physics and Astronomy , University of Glasgow , Glasgow G12 8QQ , United Kingdom
- Department of Physics and Astronomy , University of Manitoba , Manitoba R3T 2N2 , Canada
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11
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Tunable and switchable magnetic dipole patterns in nanostructured superconductors. Nat Commun 2018; 9:2576. [PMID: 29968732 PMCID: PMC6030140 DOI: 10.1038/s41467-018-05045-3] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/17/2017] [Accepted: 06/08/2018] [Indexed: 11/08/2022] Open
Abstract
Design and manipulation of magnetic moment arrays have been at the focus of studying the interesting cooperative physical phenomena in various magnetic systems. However, long-range ordered magnetic moments are rather difficult to achieve due to the excited states arising from the relatively weak exchange interactions between the localized moments. Here, using a nanostructured superconductor, we investigate a perfectly ordered magnetic dipole pattern with the magnetic poles having the same distribution as the magnetic charges in an artificial spin ice. The magnetic states can simply be switched on/off by applying a current flowing through nanopatterned area. Moreover, by coupling magnetic dipoles with the pinned vortex lattice, we are able to erase the positive/negative poles, resulting in a magnetic dipole pattern of only one polarity, analogous to the recently predicted vortex ice. These switchable and tunable magnetic dipole patterns open pathways for the study of exotic ordering phenomena in magnetic systems.
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12
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Libál A, Nisoli C, Reichhardt CJO, Reichhardt C. Inner Phases of Colloidal Hexagonal Spin Ice. PHYSICAL REVIEW LETTERS 2018; 120:027204. [PMID: 29376707 DOI: 10.1103/physrevlett.120.027204] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/14/2017] [Indexed: 06/07/2023]
Abstract
Using numerical simulations that mimic recent experiments on hexagonal colloidal ice, we show that colloidal hexagonal artificial spin ice exhibits an inner phase within its ice state that has not been observed previously. Under increasing colloid-colloid repulsion, the initially paramagnetic system crosses into a disordered ice regime, then forms a topologically charge ordered state with disordered colloids, and finally reaches a threefold degenerate, ordered ferromagnetic state. This is reminiscent of, yet distinct from, the inner phases of the magnetic kagome spin ice analog. The difference in the inner phases of the two systems is explained by their difference in energetics and frustration.
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Affiliation(s)
- A Libál
- Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
- Mathematics and Computer Science Department, Babeş-Bolyai University, Cluj 400084, Romania
| | - C Nisoli
- Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - C J O Reichhardt
- Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - C Reichhardt
- Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
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13
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Loehr J, Ortiz-Ambriz A, Tierno P. Defect Dynamics in Artificial Colloidal Ice: Real-Time Observation, Manipulation, and Logic Gate. PHYSICAL REVIEW LETTERS 2016; 117:168001. [PMID: 27792372 DOI: 10.1103/physrevlett.117.168001] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/02/2016] [Indexed: 06/06/2023]
Abstract
We study the defect dynamics in a colloidal spin ice system realized by filling a square lattice of topographic double well islands with repulsively interacting magnetic colloids. We focus on the contraction of defects in the ground state, and contraction or expansion in a metastable biased state. Combining real-time experiments with simulations, we prove that these defects behave like emergent topological monopoles obeying a Coulomb law with an additional line tension. We further show how to realize a completely resettable "nor" gate, which provides guidelines for fabrication of nanoscale logic devices based on the motion of topological magnetic monopoles.
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Affiliation(s)
- Johannes Loehr
- Departament de Física de la Matèria Condensada, Universitat de Barcelona, Barcelona 08028, Spain
- Physikalisches Institut, Universität Bayreuth, 95440 Bayreuth, Germany
| | - Antonio Ortiz-Ambriz
- Departament de Física de la Matèria Condensada, Universitat de Barcelona, Barcelona 08028, Spain
- Institut de Nanociència i Nanotecnologia, IN2UB, Universitat de Barcelona, Barcelona 08028, Spain
| | - Pietro Tierno
- Departament de Física de la Matèria Condensada, Universitat de Barcelona, Barcelona 08028, Spain
- Institut de Nanociència i Nanotecnologia, IN2UB, Universitat de Barcelona, Barcelona 08028, Spain
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14
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Wang YL, Xiao ZL, Snezhko A, Xu J, Ocola LE, Divan R, Pearson JE, Crabtree GW, Kwok WK. Rewritable artificial magnetic charge ice. Science 2016; 352:962-6. [DOI: 10.1126/science.aad8037] [Citation(s) in RCA: 106] [Impact Index Per Article: 13.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/03/2015] [Accepted: 04/13/2016] [Indexed: 11/02/2022]
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15
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Farmer B, Bhat VS, Balk A, Teipel E, Smith N, Unguris J, Keavney DJ, Hastings JT, De Long LE. Direct imaging of coexisting ordered and frustrated sublattices in artificial ferromagnetic quasicrystals. PHYSICAL REVIEW. B 2016; 93:134428. [PMID: 28691109 PMCID: PMC5497597 DOI: 10.1103/physrevb.93.134428] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
We have used scanning electron microscopy with polarization analysis and photoemission electron microscopy to image the two-dimensional magnetization of permalloy films patterned into Penrose P2 tilings (P2T). The interplay of exchange interactions in asymmetrically coordinated vertices and short-range dipole interactions among connected film segments stabilize magnetically ordered, spatially distinct sublattices that coexist with frustrated sublattices at room temperature. Numerical simulations that include long-range dipole interactions between sublattices agree with images of as-grown P2T samples and predict a magnetically ordered ground state for a two-dimensional quasicrystal lattice of classical Ising spins.
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Affiliation(s)
- B Farmer
- Department of Physics and Astronomy, University of Kentucky, 505 Rose Street, Lexington, Kentucky 40506-0055, USA
| | - V S Bhat
- Department of Physics and Astronomy, University of Kentucky, 505 Rose Street, Lexington, Kentucky 40506-0055, USA
| | - A Balk
- Center for Nanoscale Science and Technology, National Institute of Standards and Technology, 100 Bureau Dr., Gaithersburg, Maryland 20899, USA
- Maryland Nanocenter, University of Maryland, College Park, Maryland 20742, USA
| | - E Teipel
- Department of Physics and Astronomy, University of Kentucky, 505 Rose Street, Lexington, Kentucky 40506-0055, USA
| | - N Smith
- Department of Physics and Astronomy, University of Kentucky, 505 Rose Street, Lexington, Kentucky 40506-0055, USA
| | - J Unguris
- Center for Nanoscale Science and Technology, National Institute of Standards and Technology, 100 Bureau Dr., Gaithersburg, Maryland 20899, USA
| | - D J Keavney
- Advanced Photon Source 431-E007, Argonne National Laboratory, 9700 S. Cass Ave., Argonne, Illinois 60439, USA
| | - J T Hastings
- Department of Electrical and Computer Engineering, University of Kentucky, 453F Paul Anderson Tower, Lexington, Kentucky 40506-0046, USA
| | - L E De Long
- Department of Physics and Astronomy, University of Kentucky, 505 Rose Street, Lexington, Kentucky 40506-0055, USA
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16
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Modeling of nanoparticular magnetoresistive systems and the impact on molecular recognition. SENSORS 2015; 15:9251-64. [PMID: 25903554 PMCID: PMC4431232 DOI: 10.3390/s150409251] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 02/27/2015] [Revised: 04/07/2015] [Accepted: 04/14/2015] [Indexed: 11/26/2022]
Abstract
The formation of magnetic bead or nanoparticle superstructures due to magnetic dipole dipole interactions can be used as configurable matter in order to realize low-cost magnetoresistive sensors with very high GMR-effect amplitudes. Experimentally, this can be realized by immersing magnetic beads or nanoparticles in conductive liquid gels and rearranging them by applying suitable external magnetic fields. After gelatinization of the gel matrix the bead or nanoparticle positions are fixed and the resulting system can be used as a magnetoresistive sensor. In order to optimize such sensor structures we have developed a simulation tool chain that allows us not only to study the structuring process in the liquid state but also to rigorously calculate the magnetoresistive characteristic curves for arbitrary nanoparticle arrangements. As an application, we discuss the role of magnetoresistive sensors in finding answers to molecular recognition.
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Montaigne F, Lacour D, Chioar IA, Rougemaille N, Louis D, Mc Murtry S, Riahi H, Burgos BS, Menteş TO, Locatelli A, Canals B, Hehn M. Size distribution of magnetic charge domains in thermally activated but out-of-equilibrium artificial spin ice. Sci Rep 2014; 4:5702. [PMID: 25029620 PMCID: PMC4100542 DOI: 10.1038/srep05702] [Citation(s) in RCA: 25] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/18/2014] [Accepted: 06/26/2014] [Indexed: 11/09/2022] Open
Abstract
A crystal of emerging magnetic charges is expected in the phase diagram of the dipolar kagomé spin ice. An observation of charge crystallites in thermally demagnetized artificial spin ice arrays has been recently reported by S. Zhang and coworkers and explained through the thermodynamics of the system as it approaches a charge-ordered state. Following a similar approach, we have generated a partial order of magnetic charges in an artificial kagomé spin ice lattice made out of ferrimagnetic material having a Curie temperature of 475 K. A statistical study of the size of the charge domains reveals an unconventional sawtooth distribution. This distribution is in disagreement with the predictions of the thermodynamic model and is shown to be a signature of the kinetic process governing the remagnetization.
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Affiliation(s)
- F Montaigne
- Institut Jean Lamour, Université de Lorraine and CNRS, Vandoeuvre lès Nancy, F-54506, France
| | - D Lacour
- Institut Jean Lamour, Université de Lorraine and CNRS, Vandoeuvre lès Nancy, F-54506, France
| | - I A Chioar
- 1] CNRS, Institut NEEL, F-38042 Grenoble, France [2] Univ. Grenoble Alpes, Institut NEEL, F-38042 Grenoble, France
| | - N Rougemaille
- 1] CNRS, Institut NEEL, F-38042 Grenoble, France [2] Univ. Grenoble Alpes, Institut NEEL, F-38042 Grenoble, France
| | - D Louis
- Institut Jean Lamour, Université de Lorraine and CNRS, Vandoeuvre lès Nancy, F-54506, France
| | - S Mc Murtry
- Institut Jean Lamour, Université de Lorraine and CNRS, Vandoeuvre lès Nancy, F-54506, France
| | - H Riahi
- Institut Jean Lamour, Université de Lorraine and CNRS, Vandoeuvre lès Nancy, F-54506, France
| | - B Santos Burgos
- Elettra-Sincrotrone Trieste S.C.p.A. S.S. 14 - km 163,5 in AREA Science Park, 34149 Basovizza, Trieste, Italy
| | - T O Menteş
- Elettra-Sincrotrone Trieste S.C.p.A. S.S. 14 - km 163,5 in AREA Science Park, 34149 Basovizza, Trieste, Italy
| | - A Locatelli
- Elettra-Sincrotrone Trieste S.C.p.A. S.S. 14 - km 163,5 in AREA Science Park, 34149 Basovizza, Trieste, Italy
| | - B Canals
- 1] CNRS, Institut NEEL, F-38042 Grenoble, France [2] Univ. Grenoble Alpes, Institut NEEL, F-38042 Grenoble, France
| | - M Hehn
- Institut Jean Lamour, Université de Lorraine and CNRS, Vandoeuvre lès Nancy, F-54506, France
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18
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Kapaklis V, Arnalds UB, Farhan A, Chopdekar RV, Balan A, Scholl A, Heyderman LJ, Hjörvarsson B. Thermal fluctuations in artificial spin ice. NATURE NANOTECHNOLOGY 2014; 9:514-519. [PMID: 24908258 DOI: 10.1038/nnano.2014.104] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/27/2014] [Accepted: 05/02/2014] [Indexed: 06/03/2023]
Abstract
Artificial spin ice systems have been proposed as a playground for the study of monopole-like magnetic excitations, similar to those observed in pyrochlore spin ice materials. Currents of magnetic monopole excitations have been observed, demonstrating the possibility for the realization of magnetic-charge-based circuitry. Artificial spin ice systems that support thermal fluctuations can serve as an ideal setting for observing dynamical effects such as monopole propagation and as a potential medium for magnetricity investigations. Here, we report on the transition from a frozen to a dynamic state in artificial spin ice with a square lattice. Magnetic imaging is used to determine the magnetic state of the islands in thermal equilibrium. The temperature-induced onset of magnetic fluctuations and excitation populations are shown to depend on the lattice spacing and related interaction strength between islands. The excitations are described by Boltzmann distributions with their factors in the frozen state relating to the blocking temperatures of the array. Our results provide insight into the design of thermal artificial spin ice arrays where the magnetic charge density and response to external fields can be studied in thermal equilibrium.
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Affiliation(s)
- Vassilios Kapaklis
- Department of Physics and Astronomy, Uppsala University, Box 516, SE-75120, Uppsala, Sweden
| | - Unnar B Arnalds
- Department of Physics and Astronomy, Uppsala University, Box 516, SE-75120, Uppsala, Sweden
| | - Alan Farhan
- 1] Laboratory for Micro- and Nanotechnology, Paul Scherrer Institute, CH-5232 Villigen PSI, Switzerland [2] Laboratory for Mesoscopic Systems, Department of Materials, ETH Zurich, CH-8093 Zurich, Switzerland
| | - Rajesh V Chopdekar
- 1] Laboratory for Micro- and Nanotechnology, Paul Scherrer Institute, CH-5232 Villigen PSI, Switzerland [2] Swiss Light Source, Paul Scherrer Institute, CH-5232 Villigen PSI, Switzerland
| | - Ana Balan
- Swiss Light Source, Paul Scherrer Institute, CH-5232 Villigen PSI, Switzerland
| | - Andreas Scholl
- Lawrence Berkeley National Laboratory (LBNL), 1 Cyclotron Road, Berkeley, California 94720, USA
| | - Laura J Heyderman
- 1] Laboratory for Micro- and Nanotechnology, Paul Scherrer Institute, CH-5232 Villigen PSI, Switzerland [2] Laboratory for Mesoscopic Systems, Department of Materials, ETH Zurich, CH-8093 Zurich, Switzerland
| | - Björgvin Hjörvarsson
- Department of Physics and Astronomy, Uppsala University, Box 516, SE-75120, Uppsala, Sweden
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19
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Krawczyk M, Grundler D. Review and prospects of magnonic crystals and devices with reprogrammable band structure. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2014; 26:123202. [PMID: 24599025 DOI: 10.1088/0953-8984/26/12/123202] [Citation(s) in RCA: 47] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/26/2023]
Abstract
Research efforts addressing spin waves (magnons) in microand nanostructured ferromagnetic materials have increased tremendously in recent years. Corresponding experimental and theoretical work in magnonics faces significant challenges in that spinwave dispersion relations are highly anisotropic and different magnetic states might be realized via, for example, the magnetic field history. At the same time, these features offer novel opportunities for wave control in solids going beyond photonics and plasmonics. In this topical review we address materials with a periodic modulation of magnetic parameters that give rise to artificially tailored band structures and allow unprecedented control of spin waves. In particular, we discuss recent achievements and perspectives of reconfigurable magnonic devices for which band structures can be reprogrammed during operation. Such characteristics might be useful for multifunctional microwave and logic devices operating over a broad frequency regime on either the macroor nanoscale.
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20
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Heyderman LJ, Stamps RL. Artificial ferroic systems: novel functionality from structure, interactions and dynamics. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2013; 25:363201. [PMID: 23948652 DOI: 10.1088/0953-8984/25/36/363201] [Citation(s) in RCA: 24] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/02/2023]
Abstract
Lithographic processing and film growth technologies are continuing to advance, so that it is now possible to create patterned ferroic materials consisting of arrays of sub-1 μm elements with high definition. Some of the most fascinating behaviour of these arrays can be realised by exploiting interactions between the individual elements to create new functionality. The properties of these artificial ferroic systems differ strikingly from those of their constituent components, with novel emergent behaviour arising from the collective dynamics of the interacting elements, which are arranged in specific designs and can be activated by applying magnetic or electric fields. We first focus on artificial spin systems consisting of arrays of dipolar-coupled nanomagnets and, in particular, review the field of artificial spin ice, which demonstrates a wide range of fascinating phenomena arising from the frustration inherent in particular arrangements of nanomagnets, including emergent magnetic monopoles, domains of ordered macrospins, and novel avalanche behaviour. We outline how demagnetisation protocols have been employed as an effective thermal anneal in an attempt to reach the ground state, comment on phenomena that arise in thermally activated systems and discuss strategies for selectively generating specific configurations using applied magnetic fields. We then move on from slow field and temperature driven dynamics to high frequency phenomena, discussing spinwave excitations in the context of magnonic crystals constructed from arrays of patterned magnetic elements. At high frequencies, these arrays are studied in terms of potential applications including magnetic logic, linear and non-linear microwave optics, and fast, efficient switching, and we consider the possibility to create tunable magnonic crystals with artificial spin ice. Finally, we discuss how functional ferroic composites can be incorporated to realise magnetoelectric effects. Specifically, we discuss artificial multiferroics (or multiferroic composites), which hold promise for new applications that involve electric field control of magnetism, or electric and magnetic field responsive devices for high frequency integrated circuit design in microwave and terahertz signal processing. We close with comments on how enhanced functionality can be realised through engineering of nanostructures with interacting ferroic components, creating opportunities for novel spin electronic devices that, for example, make use of the transport of magnetic charges, thermally activated elements, and reprogrammable nanomagnet systems.
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Affiliation(s)
- L J Heyderman
- Laboratory for Mesoscopic Systems, Department of Materials, ETH Zurich, 8093 Zurich, Switzerland.
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21
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Latimer ML, Berdiyorov GR, Xiao ZL, Peeters FM, Kwok WK. Realization of artificial ice systems for magnetic vortices in a superconducting MoGe thin film with patterned nanostructures. PHYSICAL REVIEW LETTERS 2013; 111:067001. [PMID: 23971602 DOI: 10.1103/physrevlett.111.067001] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/25/2013] [Indexed: 06/02/2023]
Abstract
We report an anomalous matching effect in MoGe thin films containing pairs of circular holes arranged in such a way that four of those pairs meet at each vertex point of a square lattice. A remarkably pronounced fractional matching was observed in the magnetic field dependences of both the resistance and the critical current. At the half matching field the critical current can be even higher than that at zero field. This has never been observed before for vortices in superconductors with pinning arrays. Numerical simulations within the nonlinear Ginzburg-Landau theory reveal a square vortex ice configuration in the ground state at the half matching field and demonstrate similar characteristic features in the field dependence of the critical current, confirming the experimental realization of an artificial ice system for vortices for the first time.
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Affiliation(s)
- M L Latimer
- Materials Science Division, Argonne National Laboratory, Argonne, Illinois 60439, USA
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22
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Chern GW, Reichhardt C, Olson Reichhardt CJ. Frustrated colloidal ordering and fully packed loops in arrays of optical traps. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 87:062305. [PMID: 23848673 DOI: 10.1103/physreve.87.062305] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/12/2013] [Indexed: 06/02/2023]
Abstract
We propose that a system of colloidal particles interacting with a honeycomb array of optical traps that each contain three wells can be used to realize a fully packed loop model. One of the phases in this system can be mapped to Baxter's three-coloring problem, offering an easily accessible physical realization of this problem. As a function of temperature and interaction strength, we find a series of phases, including long range ordered loop or stripe states, stripes with sliding symmetries, random packed loop states, and disordered states in which the loops break apart. Our geometry could be constructed using ion trap arrays, BEC vortices in optical traps, or magnetic vortices in nanostructured superconductors.
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Affiliation(s)
- Gia-Wei Chern
- Center for Nonlinear Studies and Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
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23
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Pollard SD, Zhu Y. The Aharanov-Bohm effect, magnetic monopoles and reversal in spin-ice lattices. Microscopy (Oxf) 2013; 62 Suppl 1:S55-64. [PMID: 23549453 DOI: 10.1093/jmicro/dft017] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/13/2022] Open
Abstract
The proof of the Aharonov-Bohm (AB) effect has been one of the most important experiments of the last century and used as essential evidence for the theory of gauge fields. In this article, we look at its fundamental relation to the Dirac monopole and string. Despite the Dirac string being invisible to the AB effect, it can be used to study emergent quasiparticles in condensed matter settings that behave similar to the fundamental monopoles and strings between them. We utilize phase-imaging method based on the AB effect to study the ordering in a one-model system - that of frustrated spin ice - to understand the ordering processes that occur during a magnetic field reversal cycle. The reversal is linked to the propagation of monopole defects linked by flux channels, reminiscent of Dirac strings. Monopole interactions govern the defect densities within the lattice. Furthermore, we exploit these interactions to propose a new ordering method in which high degrees of ground-state ordering can be achieved in a frustrated system.
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Affiliation(s)
- Shawn D Pollard
- Department of Condensed Matter Physics, Brookhaven National Laboratory, Upton, NY 11973, USA
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