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Title: Classical topological order in the kinetics of artificial spin ice

Abstract

Systems of interacting nanomagnets known as artificial spin ice have allowed the design, realization and study of geometrically frustrated exotic collective states that are absent in natural magnets. We have experimentally measured the thermally induced moment fluctuations in the Shakti geometry of artificial spin ice. We show that its disordered moment configuration is a topological phase described by an emergent dimer-cover model with excitations that can be characterized as topologically charged defects. Examination of the low-energy dynamics of the system confirms that these effective topological charges have long lifetimes associated with their topological protection, that is, they can be created and annihilated only as charge pairs with opposite sign and are kinetically constrained. Here, this manifestation of classical topological order demonstrates that geometrical design in nanomagnetic systems can lead to emergent, topologically protected kinetics that can limit pathways to equilibration and ergodicity.

Authors:
 [1]; ORCiD logo [2];  [3];  [1]; ORCiD logo [1];  [4];  [5];  [6];  [3]; ORCiD logo [3];  [1]
  1. Univ. of Illinois, Urbana-Champaign, IL (United States). Dept. of Physics, and Frederick Seitz Materials Research Lab.
  2. Los Alamos National Lab. (LANL), Los Alamos, NM (United States). Theoretical Division, Inst. for Materials Science, and Center for Nonlinear Studies
  3. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
  4. Univ. of Minnesota, Minneapolis, MN (United States). Dept. of Chemical Engineering and Materials Science; Univ. of Minnesota, Minneapolis, MN (United States). School of Physics and Astronomy
  5. Univ. of Minnesota, Minneapolis, MN (United States). Dept. of Chemical Engineering and Materials Science
  6. Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
Publication Date:
Research Org.:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Univ. of Illinois at Urbana-Champaign, IL (United States)
Sponsoring Org.:
USDOE Laboratory Directed Research and Development (LDRD) Program; USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22). Materials Sciences & Engineering Division
OSTI Identifier:
1479948
Alternate Identifier(s):
OSTI ID: 1485098; OSTI ID: 1594859
Report Number(s):
LA-UR-17-29552
Journal ID: ISSN 1745-2473
Grant/Contract Number:  
AC52-06NA25396; AC02-05CH11231; SC0010778
Resource Type:
Accepted Manuscript
Journal Name:
Nature Physics
Additional Journal Information:
Journal Volume: 14; Journal Issue: 7; Journal ID: ISSN 1745-2473
Publisher:
Nature Publishing Group (NPG)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS

Citation Formats

Lao, Yuyang, Caravelli, Francesco, Sheikh, Mohammed, Sklenar, Joseph, Gardeazabal, Daniel, Watts, Justin D., Albrecht, Alan M., Scholl, Andreas, Dahmen, Karin, Nisoli, Cristiano, and Schiffer, Peter. Classical topological order in the kinetics of artificial spin ice. United States: N. p., 2018. Web. doi:10.1038/s41567-018-0077-0.
Lao, Yuyang, Caravelli, Francesco, Sheikh, Mohammed, Sklenar, Joseph, Gardeazabal, Daniel, Watts, Justin D., Albrecht, Alan M., Scholl, Andreas, Dahmen, Karin, Nisoli, Cristiano, & Schiffer, Peter. Classical topological order in the kinetics of artificial spin ice. United States. doi:10.1038/s41567-018-0077-0.
Lao, Yuyang, Caravelli, Francesco, Sheikh, Mohammed, Sklenar, Joseph, Gardeazabal, Daniel, Watts, Justin D., Albrecht, Alan M., Scholl, Andreas, Dahmen, Karin, Nisoli, Cristiano, and Schiffer, Peter. Mon . "Classical topological order in the kinetics of artificial spin ice". United States. doi:10.1038/s41567-018-0077-0. https://www.osti.gov/servlets/purl/1479948.
@article{osti_1479948,
title = {Classical topological order in the kinetics of artificial spin ice},
author = {Lao, Yuyang and Caravelli, Francesco and Sheikh, Mohammed and Sklenar, Joseph and Gardeazabal, Daniel and Watts, Justin D. and Albrecht, Alan M. and Scholl, Andreas and Dahmen, Karin and Nisoli, Cristiano and Schiffer, Peter},
abstractNote = {Systems of interacting nanomagnets known as artificial spin ice have allowed the design, realization and study of geometrically frustrated exotic collective states that are absent in natural magnets. We have experimentally measured the thermally induced moment fluctuations in the Shakti geometry of artificial spin ice. We show that its disordered moment configuration is a topological phase described by an emergent dimer-cover model with excitations that can be characterized as topologically charged defects. Examination of the low-energy dynamics of the system confirms that these effective topological charges have long lifetimes associated with their topological protection, that is, they can be created and annihilated only as charge pairs with opposite sign and are kinetically constrained. Here, this manifestation of classical topological order demonstrates that geometrical design in nanomagnetic systems can lead to emergent, topologically protected kinetics that can limit pathways to equilibration and ergodicity.},
doi = {10.1038/s41567-018-0077-0},
journal = {Nature Physics},
number = 7,
volume = 14,
place = {United States},
year = {2018},
month = {4}
}

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Works referenced in this record:

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Emergent ice rule and magnetic charge screening from vertex frustration in artificial spin ice
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The Structure and Entropy of Ice and of Other Crystals with Some Randomness of Atomic Arrangement
journal, December 1935

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Magnetic charge and moment dynamics in artificial kagome spin ice
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Diversity Enabling Equilibration: Disorder and the Ground State in Artificial Spin Ice
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Artificial ‘spin ice’ in a geometrically frustrated lattice of nanoscale ferromagnetic islands
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Thermodynamic phase transitions in a frustrated magnetic metamaterial
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Thermal fluctuations in artificial spin ice
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Near-edge X-ray absorption fine-structure microscopy of organic and magnetic materials
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Classical Topological Order in Abelian and Non-Abelian Generalized Height Models
journal, December 2013

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Frustration by design
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Glassy dynamics of kinetically constrained models
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Exploring hyper-cubic energy landscapes in thermally active finite artificial spin-ice systems
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Topological frustration of artificial spin ice
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Artificial ferroic systems: novel functionality from structure, interactions and dynamics
journal, August 2013


Direct Observation of Thermal Relaxation in Artificial Spin Ice
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Deliberate exotic magnetism via frustration and topology
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Thermal Quenches in Spin Ice
journal, March 2010


Emergent reduced dimensionality by vertex frustration in artificial spin ice
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  • Nature Physics, Vol. 12, Issue 2
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Unhappy vertices in artificial spin ice: new degeneracies from vertex frustration
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Classical height models with topological order
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The “Coulomb Phase” in Frustrated Systems
journal, August 2010


Entanglement and topological entropy of the toric code at finite temperature
journal, November 2007


    Works referencing / citing this record:

    The statistics of dimers on a lattice
    journal, December 1961


    The Structure and Entropy of Ice and of Other Crystals with Some Randomness of Atomic Arrangement
    journal, December 1935

    • Pauling, Linus
    • Journal of the American Chemical Society, Vol. 57, Issue 12
    • DOI: 10.1021/ja01315a102

    Artificial ‘spin ice’ in a geometrically frustrated lattice of nanoscale ferromagnetic islands
    journal, January 2006

    • Wang, R. F.; Nisoli, C.; Freitas, R. S.
    • Nature, Vol. 439, Issue 7074
    • DOI: 10.1038/nature04447

    Extensive degeneracy, Coulomb phase and magnetic monopoles in artificial square ice
    journal, November 2016

    • Perrin, Yann; Canals, Benjamin; Rougemaille, Nicolas
    • Nature, Vol. 540, Issue 7633
    • DOI: 10.1038/nature20155

    Thermodynamics of emergent magnetic charge screening in artificial spin ice
    journal, September 2016

    • Farhan, Alan; Scholl, Andreas; Petersen, Charlotte F.
    • Nature Communications, Vol. 7, Issue 1
    • DOI: 10.1038/ncomms12635

    Topological frustration of artificial spin ice
    journal, January 2017

    • Drisko, Jasper; Marsh, Thomas; Cumings, John
    • Nature Communications, Vol. 8, Issue 1
    • DOI: 10.1038/ncomms14009

    Thermodynamic phase transitions in a frustrated magnetic metamaterial
    journal, September 2015

    • Anghinolfi, L.; Luetkens, H.; Perron, J.
    • Nature Communications, Vol. 6, Issue 1
    • DOI: 10.1038/ncomms9278

    Near-edge X-ray absorption fine-structure microscopy of organic and magnetic materials
    journal, April 2009

    • Ade, Harald; Stoll, Herman
    • Nature Materials, Vol. 8, Issue 4
    • DOI: 10.1038/nmat2399

    Thermal fluctuations in artificial spin ice
    journal, June 2014

    • Kapaklis, Vassilios; Arnalds, Unnar B.; Farhan, Alan
    • Nature Nanotechnology, Vol. 9, Issue 7, p. 514-519
    • DOI: 10.1038/nnano.2014.104

    Exploring hyper-cubic energy landscapes in thermally active finite artificial spin-ice systems
    journal, May 2013

    • Farhan, A.; Derlet, P. M.; Kleibert, A.
    • Nature Physics, Vol. 9, Issue 6
    • DOI: 10.1038/nphys2613

    Emergent ice rule and magnetic charge screening from vertex frustration in artificial spin ice
    journal, August 2014

    • Gilbert, Ian; Chern, Gia-Wei; Zhang, Sheng
    • Nature Physics, Vol. 10, Issue 9
    • DOI: 10.1038/nphys3037

    The unhappy wanderer
    journal, August 2014


    Emergent reduced dimensionality by vertex frustration in artificial spin ice
    journal, October 2015

    • Gilbert, Ian; Lao, Yuyang; Carrasquillo, Isaac
    • Nature Physics, Vol. 12, Issue 2
    • DOI: 10.1038/nphys3520

    Deliberate exotic magnetism via frustration and topology
    journal, March 2017

    • Nisoli, Cristiano; Kapaklis, Vassilios; Schiffer, Peter
    • Nature Physics, Vol. 13, Issue 3
    • DOI: 10.1038/nphys4059

    Tunable nonequilibrium dynamics of field quenches in spin ice
    journal, December 2013

    • Mostame, S.; Castelnovo, C.; Moessner, R.
    • Proceedings of the National Academy of Sciences, Vol. 111, Issue 2
    • DOI: 10.1073/pnas.1317631111

    Glassy dynamics of kinetically constrained models
    journal, June 2003


    Studies of nanomagnetism using synchrotron-based x-ray photoemission electron microscopy (X-PEEM)
    journal, January 2012


    Classical height models with topological order
    journal, April 2011


    Artificial ferroic systems: novel functionality from structure, interactions and dynamics
    journal, August 2013


    Unhappy vertices in artificial spin ice: new degeneracies from vertex frustration
    journal, April 2013


    Spin Ice, Fractionalization, and Topological Order
    journal, March 2012


    The “Coulomb Phase” in Frustrated Systems
    journal, August 2010