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Title: Vogel-Fulcher-Tammann freezing of a thermally fluctuating artificial spin ice probed by x-ray photon correlation spectroscopy

Abstract

We report on the crossover from the thermal to the athermal regime of an artificial spin ice formed from a square array of magnetic islands whose lateral size, 30 nm × 70 nm, is small enough that they are dynamic at room temperature.We used resonant magnetic soft x-ray photon correlation spectroscopy as a method to observe the time-time correlations of the fluctuating magnetic configurations of spin ice during cooling, which are found to slow abruptly as a freezing temperature of T 0 = 178 ± 5 K is approached. This slowing is well described by a Vogel-Fulcher-Tammann law, implying that the frozen state is glassy, with the freezing temperature being commensurate with the strength of magnetostatic interaction energies in the array. The activation temperature, T A = 40 ± 10 K, is much less than that expected from a Stoner-Wohlfarth coherent rotation model. Zerofield- cooled/field-cooled magnetometry reveals a freeing up of fluctuations of states within islands above this temperature, caused by variation in the local anisotropy axes at the oxidised edges. This Vogel-Fulcher-Tammann behavior implies that the system enters a glassy state upon freezing, which is unexpected for a system with a well-defined ground state.

Authors:
 [1];  [2];  [2];  [1];  [3];  [4];  [5];  [2];  [1]
  1. Univ. of Leeds (United Kingdom)
  2. Science and Technology Facilities Council (STFC), Oxford (United Kingdom). Rutherford Appleton Lab., ISIS Neutron Source
  3. Brookhaven National Lab. (BNL), Upton, NY (United States)
  4. Science and Technology Facilities Council (STFC), Harwell Campus, Oxford (United Kingdom). Diamond Light Source, Ltd.
  5. Univ. of Glasgow, Scotland (United Kingdom)
Publication Date:
Research Org.:
Brookhaven National Lab. (BNL), Upton, NY (United States). Center for Functional Nanomaterials (CFN)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)
OSTI Identifier:
1389248
Alternate Identifier(s):
OSTI ID: 1347265
Report Number(s):
BNL-114268-2017-JA
Journal ID: ISSN 2469-9950; PRBMDO; KC0403020; TRN: US1702699
Grant/Contract Number:  
SC0012704; AC02-98CH10886
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review B
Additional Journal Information:
Journal Volume: 95; Journal Issue: 10; Journal ID: ISSN 2469-9950
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
77 NANOSCIENCE AND NANOTECHNOLOGY; Center for Functional Nanomaterials

Citation Formats

Morley, S. A., Alba Venero, D., Porro, J. M., Riley, S. T., Stein, A., Steadman, P., Stamps, R. L., Langridge, S., and Marrows, C. H. Vogel-Fulcher-Tammann freezing of a thermally fluctuating artificial spin ice probed by x-ray photon correlation spectroscopy. United States: N. p., 2017. Web. doi:10.1103/PhysRevB.95.104422.
Morley, S. A., Alba Venero, D., Porro, J. M., Riley, S. T., Stein, A., Steadman, P., Stamps, R. L., Langridge, S., & Marrows, C. H. Vogel-Fulcher-Tammann freezing of a thermally fluctuating artificial spin ice probed by x-ray photon correlation spectroscopy. United States. doi:10.1103/PhysRevB.95.104422.
Morley, S. A., Alba Venero, D., Porro, J. M., Riley, S. T., Stein, A., Steadman, P., Stamps, R. L., Langridge, S., and Marrows, C. H. Thu . "Vogel-Fulcher-Tammann freezing of a thermally fluctuating artificial spin ice probed by x-ray photon correlation spectroscopy". United States. doi:10.1103/PhysRevB.95.104422. https://www.osti.gov/servlets/purl/1389248.
@article{osti_1389248,
title = {Vogel-Fulcher-Tammann freezing of a thermally fluctuating artificial spin ice probed by x-ray photon correlation spectroscopy},
author = {Morley, S. A. and Alba Venero, D. and Porro, J. M. and Riley, S. T. and Stein, A. and Steadman, P. and Stamps, R. L. and Langridge, S. and Marrows, C. H.},
abstractNote = {We report on the crossover from the thermal to the athermal regime of an artificial spin ice formed from a square array of magnetic islands whose lateral size, 30 nm × 70 nm, is small enough that they are dynamic at room temperature.We used resonant magnetic soft x-ray photon correlation spectroscopy as a method to observe the time-time correlations of the fluctuating magnetic configurations of spin ice during cooling, which are found to slow abruptly as a freezing temperature of T0 = 178 ± 5 K is approached. This slowing is well described by a Vogel-Fulcher-Tammann law, implying that the frozen state is glassy, with the freezing temperature being commensurate with the strength of magnetostatic interaction energies in the array. The activation temperature, TA = 40 ± 10 K, is much less than that expected from a Stoner-Wohlfarth coherent rotation model. Zerofield- cooled/field-cooled magnetometry reveals a freeing up of fluctuations of states within islands above this temperature, caused by variation in the local anisotropy axes at the oxidised edges. This Vogel-Fulcher-Tammann behavior implies that the system enters a glassy state upon freezing, which is unexpected for a system with a well-defined ground state.},
doi = {10.1103/PhysRevB.95.104422},
journal = {Physical Review B},
number = 10,
volume = 95,
place = {United States},
year = {2017},
month = {3}
}

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dataset, June 2017

  • Morley, S.A.; Alba-Venero, D.; Porro, J. M.
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  • DOI: 10.5518/59

Susceptibility phenomena in a fine particle system
journal, August 1992

  • El-Hilo, M.; O'Grady, K.; Chantrell, R. W.
  • Journal of Magnetism and Magnetic Materials, Vol. 114, Issue 3
  • DOI: 10.1016/0304-8853(92)90272-p

    Works referencing / citing this record:

    X-ray Photon Correlation Spectroscopy Studies of Surfaces and Thin Films
    journal, September 2014

    • Sinha, Sunil K.; Jiang, Zhang; Lurio, Laurence B.
    • Advanced Materials, Vol. 26, Issue 46
    • DOI: 10.1002/adma.201401094

    Theorie des elektrischen Rückstandes in der Leidener Flasche
    journal, January 1854


    Die Abhängigkeit der Viscosität von der Temperatur bie unterkühlten Flüssigkeiten
    journal, October 1926

    • Tammann, G.; Hesse, W.
    • Zeitschrift für anorganische und allgemeine Chemie, Vol. 156, Issue 1
    • DOI: 10.1002/zaac.19261560121

    The theory of the Vogel-Fulcher law of spin glasses
    journal, October 1981


    A possible origin for the Vogel-Fulcher law
    journal, June 1981


    A review of X-ray intensity fluctuation spectroscopy
    journal, June 2008


    Heterodyne and homodyne detection in fluctuating smectic membranes by photon correlation spectroscopy at X-ray and visible wavelengths
    journal, February 2005

    • de Jeu, Wim H.; Madsen, Anders; Sikharulidze, Irakli
    • Physica B: Condensed Matter, Vol. 357, Issue 1-2
    • DOI: 10.1016/j.physb.2004.11.016

    Zero-point entropy in ‘spin ice’
    journal, May 1999

    • Ramirez, A. P.; Hayashi, A.; Cava, R. J.
    • Nature, Vol. 399, Issue 6734
    • DOI: 10.1038/20619

    How ‘spin ice’ freezes
    journal, September 2001

    • Snyder, J.; Slusky, J. S.; Cava, R. J.
    • Nature, Vol. 413, Issue 6851
    • DOI: 10.1038/35092516

    Observation of speckle by diffraction with coherent X-rays
    journal, August 1991

    • Sutton, M.; Mochrie, S. G. J.; Greytak, T.
    • Nature, Vol. 352, Issue 6336
    • DOI: 10.1038/352608a0

    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

    Direct measurement of antiferromagnetic domain fluctuations
    journal, May 2007

    • Shpyrko, O. G.; Isaacs, E. D.; Logan, J. M.
    • Nature, Vol. 447, Issue 7140
    • DOI: 10.1038/nature05776

    Magnetic monopoles in spin ice
    journal, January 2008

    • Castelnovo, C.; Moessner, R.; Sondhi, S. L.
    • Nature, Vol. 451, Issue 7174
    • DOI: 10.1038/nature06433

    Crystallites of magnetic charges in artificial spin ice
    journal, August 2013

    • Zhang, Sheng; Gilbert, Ian; Nisoli, Cristiano
    • Nature, Vol. 500, Issue 7464
    • DOI: 10.1038/nature12399

    Sidewall oxide effects on spin-torque- and magnetic-field-induced reversal characteristics of thin-film nanomagnets
    journal, June 2008

    • Ozatay, O.; Gowtham, P. G.; Tan, K. W.
    • Nature Materials, Vol. 7, Issue 7
    • DOI: 10.1038/nmat2204

    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

    Direct entropy determination and application to artificial spin ice
    journal, July 2010

    • Lammert, Paul E.; Ke, Xianglin; Li, Jie
    • Nature Physics, Vol. 6, Issue 10
    • DOI: 10.1038/nphys1728

    Thermal ground-state ordering and elementary excitations in artificial magnetic square ice
    journal, November 2010

    • Morgan, Jason P.; Stein, Aaron; Langridge, Sean
    • Nature Physics, Vol. 7, Issue 1
    • DOI: 10.1038/nphys1853

    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 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

    Classical topological order in the kinetics of artificial spin ice
    journal, April 2018


    Thermally induced magnetic relaxation in square artificial spin ice
    journal, November 2016

    • Andersson, M. S.; Pappas, S. D.; Stopfel, H.
    • Scientific Reports, Vol. 6, Issue 1
    • DOI: 10.1038/srep37097

    Universal non-diffusive slow dynamics in aging soft matter
    journal, September 2002

    • Cipelletti, Luca; Ramos, Laurence; Manley, S.
    • Faraday Discussions, Vol. 123
    • DOI: 10.1039/b204495a

    Non-symmetrical dielectric relaxation behaviour arising from a simple empirical decay function
    journal, January 1970

    • Williams, Graham; Watts, David C.
    • Transactions of the Faraday Society, Vol. 66
    • DOI: 10.1039/tf9706600080

    On a Dynamical Model of Glasses
    journal, December 1995

    • Bouchaud, Jean-Philippe; Comtet, Alain; Monthus, C�cile
    • Journal de Physique I, Vol. 5, Issue 12
    • DOI: 10.1051/jp1:1995104

    Superparamagnetism
    journal, April 1959

    • Bean, C. P.; Livingston, J. D.
    • Journal of Applied Physics, Vol. 30, Issue 4
    • DOI: 10.1063/1.2185850

    Soft x-ray coherent scattering: Instrument and methods at ESRF ID08
    journal, September 2007

    • Beutier, Guillaume; Marty, Alain; Livet, Frédéric
    • Review of Scientific Instruments, Vol. 78, Issue 9
    • DOI: 10.1063/1.2779218

    Time dependence of switching fields in magnetic recording media (invited)
    journal, November 1994

    • Sharrock, M. P.
    • Journal of Applied Physics, Vol. 76, Issue 10
    • DOI: 10.1063/1.358282

    Magnetic hysteresis of an artificial square ice studied by in-plane Bragg x-ray resonant magnetic scattering
    journal, June 2012

    • Morgan, J. P.; Kinane, C. J.; Charlton, T. R.
    • AIP Advances, Vol. 2, Issue 2
    • DOI: 10.1063/1.4732147

    Supercooled spin liquid state in the frustrated pyrochlore Dy 2 Ti 2 O 7
    journal, June 2015

    • Kassner, Ethan R.; Eyvazov, Azar B.; Pichler, Benjamin
    • Proceedings of the National Academy of Sciences, Vol. 112, Issue 28
    • DOI: 10.1073/pnas.1511006112

    Novel dynamical magnetic properties in the spin ice compound Dy 2 Ti 2 O 7
    journal, July 2001


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


    Melting artificial spin ice
    journal, March 2012


    Exploring thermally induced states in square artificial spin-ice arrays
    journal, May 2013


    Effects of exchange bias on magnetotransport in permalloy kagome artificial spin ice
    journal, February 2015


    Analysis of Recent Measurements of the Viscosity of Glasses
    journal, June 1925


    Temperature and magnetic-field driven dynamics in artificial magnetic square ice
    conference, September 2015

    • Morley, Sophie A.; Stein, Aaron; Rosamond, Mark C.
    • SPIE Nanoscience + Engineering, SPIE Proceedings
    • DOI: 10.1117/12.2189320

    Spin Ice State in Frustrated Magnetic Pyrochlore Materials
    journal, November 2001


    Formation of Glasses from Liquids and Biopolymers
    journal, March 1995


    Thermally and field-driven mobility of emergent magnetic charges in square artificial spin ice
    journal, November 2019


    Classical topological order in the kinetics of artificial spin ice
    journal, April 2018


    Thermally and field-driven mobility of emergent magnetic charges in square artificial spin ice
    journal, November 2019


    Frustration and thermalization in an artificial magnetic quasicrystal
    journal, December 2017