Kibble-Zurek scenario and coarsening across nonequilibrium phase transitions in driven vortices and skyrmions

Reichhardt, C.; Reichhardt, C. J. O.

doi:10.1103/PhysRevResearch.5.033221

Title: Kibble-Zurek scenario and coarsening across nonequilibrium phase transitions in driven vortices and skyrmions

Journal Article · Wed Sep 27 00:00:00 EDT 2023 · Physical Review Research

DOI:https://doi.org/10.1103/PhysRevResearch.5.033221· OSTI ID:2006681

Reichhardt, C.;

We investigate the topological defect populations for superconducting vortices and magnetic skyrmions on random pinning substrates under driving amplitudes that are swept at different rates or suddenly quenched. When the substrate pinning is sufficiently strong, the system exhibits a nonequilibrium phase transition at a critical drive into a more topologically ordered state where there are few non-sixfold coordinated particles. We examine the number of topological defects that remain as we cross the ordering transition at different rates. In the vortex case, the system dynamically orders into a moving smectic, and the Kibble-Zurek scaling hypothesis gives exponents consistent with directed percolation. Due to their strong Magnus force, the skyrmions dynamically order into an isotropic crystal, producing different Kibble-Zurek scaling exponents that are more consistent with coarsening. We argue that, in the skyrmion crystal, the topological defects can both climb and glide, facilitating coarsening, whereas in the vortex smectic state, the defects cannot climb and coarsening is suppressed. We also examine pulsed driving across the ordering transition and find that the defect population on the ordered side of the transition decreases with time as a power law, indicating that coarsening can occur across nonequilibrium phase transitions. Our results should be general to a wide class of nonequilibrium systems driven over random disorder where there are well-defined topological defects.

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Research Organization:: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Sponsoring Organization:: USDOE Laboratory Directed Research and Development (LDRD) Program; USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: 892333218NCA000001; 89233218CNA000001

OSTI ID:: 2006681

Alternate ID(s):: OSTI ID: 2246847

Report Number(s):: LA-UR-23-27243; PPRHAI; 033221

Journal Information:: Physical Review Research, Journal Name: Physical Review Research Vol. 5 Journal Issue: 3; ISSN 2643-1564

Publisher:: American Physical SocietyCopyright Statement

Country of Publication:: United States

Language:: English

References (80)

Constructing coarse-grained skyrmion potentials from experimental data with Iterative Boltzmann Inversion Ge, Yuqing; Rothörl, Jan; Brems, Maarten A. Communications Physics, Vol. 6, Issue 1 https://doi.org/10.1038/s42005-023-01145-9	journal	February 2023
Dynamical Phases of Driven Vortex Systems Moon, Kyungsun; Scalettar, Richard T.; Zimányi, Gergely T. Physical Review Letters, Vol. 77, Issue 13 https://doi.org/10.1103/PhysRevLett.77.2778	journal	September 1996
Nonequilibrium Dynamic Phase Diagram for Vortex Lattices Olson, C. J.; Reichhardt, C.; Nori, Franco Physical Review Letters, Vol. 81, Issue 17 https://doi.org/10.1103/PhysRevLett.81.3757	journal	October 1998
Spin Transfer Torques in MnSi at Ultralow Current Densities Jonietz, F.; Muhlbauer, S.; Pfleiderer, C. Science, Vol. 330, Issue 6011 https://doi.org/10.1126/science.1195709	journal	December 2010
Defect structures in the growth kinetics of the Swift-Hohenberg model Qian, Hai; Mazenko, Gene F. Physical Review E, Vol. 67, Issue 3 https://doi.org/10.1103/PhysRevE.67.036102	journal	March 2003
Dynamic phases of active matter systems with quenched disorder Sándor, Cs.; Libál, A.; Reichhardt, C. Physical Review E, Vol. 95, Issue 3 https://doi.org/10.1103/PhysRevE.95.032606	journal	March 2017
Fluctuations and noise signatures of driven magnetic skyrmions Díaz, Sebastián A.; Reichhardt, C. J. O.; Arovas, Daniel P. Physical Review B, Vol. 96, Issue 8 https://doi.org/10.1103/PhysRevB.96.085106	journal	August 2017
Particle model for skyrmions in metallic chiral magnets: Dynamics, pinning, and creep Lin, Shi-Zeng; Reichhardt, Charles; Batista, Cristian D. Physical Review B, Vol. 87, Issue 21 https://doi.org/10.1103/PhysRevB.87.214419	journal	June 2013
Driven Skyrmions and Dynamical Transitions in Chiral Magnets Lin, Shi-Zeng; Reichhardt, Charles; Batista, Cristian D. Physical Review Letters, Vol. 110, Issue 20 https://doi.org/10.1103/PhysRevLett.110.207202	journal	May 2013
Ordering Dynamics in the Two-Dimensional Stochastic Swift-Hohenberg Equation Elder, K. R.; Viñals, Jorge; Grant, Martin Physical Review Letters, Vol. 68, Issue 20 https://doi.org/10.1103/PhysRevLett.68.3024	journal	May 1992
Cosmological experiments in condensed matter systems Zurek, W. H. Physics Reports, Vol. 276, Issue 4 https://doi.org/10.1016/S0370-1573(96)00009-9	journal	November 1996
The Cosmological Kibble Mechanism in the Laboratory: String Formation in Liquid Crystals Bowick, M. J.; Chandar, L.; Schiff, E. A. Science, Vol. 263, Issue 5149 https://doi.org/10.1126/science.263.5149.943	journal	February 1994
Vortices in high-temperature superconductors Blatter, G.; Feigel'man, M. V.; Geshkenbein, V. B. Reviews of Modern Physics, Vol. 66, Issue 4 https://doi.org/10.1103/RevModPhys.66.1125	journal	October 1994
Structural evidence for a two-step process in the depinning of the superconducting flux-line lattice Yaron, U.; Gammel, P. L.; Huse, D. A. Nature, Vol. 376, Issue 6543 https://doi.org/10.1038/376753a0	journal	August 1995
Collective Transport Properties of Driven Skyrmions with Random Disorder Reichhardt, C.; Ray, D.; Reichhardt, C. J. Olson Physical Review Letters, Vol. 114, Issue 21 https://doi.org/10.1103/PhysRevLett.114.217202	journal	May 2015
Directed percolation phase transition to sustained turbulence in Couette flow Lemoult, Grégoire; Shi, Liang; Avila, Kerstin Nature Physics, Vol. 12, Issue 3 https://doi.org/10.1038/nphys3675	journal	February 2016
Moving Wigner Glasses and Smectics: Dynamics of Disordered Wigner Crystals Reichhardt, C.; Olson, C. J.; Grønbech-Jensen, N. Physical Review Letters, Vol. 86, Issue 19 https://doi.org/10.1103/PhysRevLett.86.4354	journal	May 2001
Current-Driven Skyrmion Dynamics and Drive-Dependent Skyrmion Hall Effect in an Ultrathin Film Juge, Roméo; Je, Soong-Geun; Chaves, Dayane de Souza Physical Review Applied, Vol. 12, Issue 4 https://doi.org/10.1103/PhysRevApplied.12.044007	journal	October 2019
Depinning and Collective Dynamics of Magnetically Driven Colloidal Monolayers Tierno, Pietro Physical Review Letters, Vol. 109, Issue 19 https://doi.org/10.1103/PhysRevLett.109.198304	journal	November 2012
Soliton motion in skyrmion chains: Stabilization and guidance by nanoengineered pinning Vizarim, N. P.; Souza, J. C. Bellizotti; Reichhardt, C. J. O. Physical Review B, Vol. 105, Issue 22 https://doi.org/10.1103/PhysRevB.105.224409	journal	June 2022
Quenched dynamics of artificial colloidal spin ice Libál, A.; del Campo, A.; Nisoli, C. Physical Review Research, Vol. 2, Issue 3 https://doi.org/10.1103/PhysRevResearch.2.033433	journal	September 2020
Skyrmion Hall effect revealed by direct time-resolved X-ray microscopy Litzius, Kai; Lemesh, Ivan; Krüger, Benjamin Nature Physics, Vol. 13, Issue 2 https://doi.org/10.1038/nphys4000	journal	December 2016
Defect-mediated dynamics of coherent structures in active nematics Serra, Mattia; Lemma, Linnea; Giomi, Luca Nature Physics, Vol. 19, Issue 9 https://doi.org/10.1038/s41567-023-02062-y	journal	May 2023
Spontaneous vortices in the formation of Bose–Einstein condensates Weiler, Chad N.; Neely, Tyler W.; Scherer, David R. Nature, Vol. 455, Issue 7215 https://doi.org/10.1038/nature07334	journal	October 2008
Deformation of the moving magnetic skyrmion lattice in MnSi under electric current flow Okuyama, D.; Bleuel, M.; White, J. S. Communications Physics, Vol. 2, Issue 1 https://doi.org/10.1038/s42005-019-0175-z	journal	July 2019
Directed Percolation Criticality in Turbulent Liquid Crystals Takeuchi, Kazumasa A.; Kuroda, Masafumi; Chaté, Hugues Physical Review Letters, Vol. 99, Issue 23 https://doi.org/10.1103/PhysRevLett.99.234503	journal	December 2007
Order-disorder transition of vortex matter in $a {-Mo}_{x} {Ge}_{1 - x}$ films probed by noise Okuma, S.; Kashiro, K.; Suzuki, Y. Physical Review B, Vol. 77, Issue 21 https://doi.org/10.1103/PhysRevB.77.212505	journal	June 2008
Dynamics of a disordered flux line lattice Bhattacharya, S.; Higgins, M. J. Physical Review Letters, Vol. 70, Issue 17 https://doi.org/10.1103/PhysRevLett.70.2617	journal	April 1993
Glassy phases and driven response of the phase-field-crystal model with random pinning Granato, E.; Ramos, J. A. P.; Achim, C. V. Physical Review E, Vol. 84, Issue 3 https://doi.org/10.1103/PhysRevE.84.031102	journal	September 2011
Dynamical Ordering of Driven Stripe Phases in Quenched Disorder Reichhardt, C.; Reichhardt, C. J. Olson; Martin, I. Physical Review Letters, Vol. 90, Issue 2 https://doi.org/10.1103/PhysRevLett.90.026401	journal	January 2003
Non-reciprocal phase transitions Fruchart, Michel; Hanai, Ryo; Littlewood, Peter B. Nature, Vol. 592, Issue 7854 https://doi.org/10.1038/s41586-021-03375-9	journal	April 2021
Dynamic ordering transitions in charged solid Sun, Jian; Niu, Jiasen; Li, Yifan Fundamental Research, Vol. 2, Issue 2 https://doi.org/10.1016/j.fmre.2021.07.006	journal	March 2022
Universality of phase transition dynamics: Topological defects from symmetry breaking del Campo, Adolfo; Zurek, Wojciech H. International Journal of Modern Physics A, Vol. 29, Issue 08 https://doi.org/10.1142/S0217751X1430018X	journal	March 2014
Dynamics of Skyrmion Crystals in Metallic Thin Films Zang, Jiadong; Mostovoy, Maxim; Han, Jung Hoon Physical Review Letters, Vol. 107, Issue 13 https://doi.org/10.1103/PhysRevLett.107.136804	journal	September 2011
Skyrmion relaxation dynamics in the presence of quenched disorder Brown, Barton L.; Täuber, Uwe C.; Pleimling, Michel Physical Review B, Vol. 100, Issue 2 https://doi.org/10.1103/PhysRevB.100.024410	journal	July 2019
Topological properties and dynamics of magnetic skyrmions Nagaosa, Naoto; Tokura, Yoshinori Nature Nanotechnology, Vol. 8, Issue 12 https://doi.org/10.1038/nnano.2013.243	journal	December 2013
Ecological collapse and the emergence of travelling waves at the onset of shear turbulence Shih, Hong-Yan; Hsieh, Tsung-Lin; Goldenfeld, Nigel Nature Physics, Vol. 12, Issue 3 https://doi.org/10.1038/nphys3548	journal	November 2015
Testing the Kibble-Zurek mechanism in Rayleigh-Bénard convection Casado, S.; González-Viñas, W.; Mancini, H. Physical Review E, Vol. 74, Issue 4 https://doi.org/10.1103/PhysRevE.74.047101	journal	October 2006
Dynamics of self-organized driven particles with competing range interaction Zhao, H. J.; Misko, V. R.; Peeters, F. M. Physical Review E, Vol. 88, Issue 2 https://doi.org/10.1103/PhysRevE.88.022914	journal	August 2013
Kibble-Zurek Mechanism in Driven Dissipative Systems Crossing a Nonequilibrium Phase Transition Zamora, A.; Dagvadorj, G.; Comaron, P. Physical Review Letters, Vol. 125, Issue 9 https://doi.org/10.1103/PhysRevLett.125.095301	journal	August 2020
Theory of current-driven skyrmions in disordered magnets Koshibae, Wataru; Nagaosa, Naoto Scientific Reports, Vol. 8, Issue 1 https://doi.org/10.1038/s41598-018-24693-5	journal	April 2018
Moving glass theory of driven lattices with disorder Le Doussal, Pierre; Giamarchi, Thierry Physical Review B, Vol. 57, Issue 18 https://doi.org/10.1103/PhysRevB.57.11356	journal	May 1998
Real-space observation of a two-dimensional skyrmion crystal Yu, X. Z.; Onose, Y.; Kanazawa, N. Nature, Vol. 465, Issue 7300 https://doi.org/10.1038/nature09124	journal	June 2010
Moving smectic phase and transverse mode locking in driven vortex matter Maegochi, S.; Ienaga, K.; Okuma, S. Physical Review Research, Vol. 4, Issue 3 https://doi.org/10.1103/PhysRevResearch.4.033085	journal	July 2022
Cosmological experiments in superfluid helium? Zurek, W. H. Nature, Vol. 317, Issue 6037 https://doi.org/10.1038/317505a0	journal	October 1985
Colloquium : Modeling friction: From nanoscale to mesoscale Vanossi, Andrea; Manini, Nicola; Urbakh, Michael Reviews of Modern Physics, Vol. 85, Issue 2 https://doi.org/10.1103/RevModPhys.85.529	journal	April 2013
Collective transport in random media: from superconductors to earthquakes Fisher, Daniel S. Physics Reports, Vol. 301, Issue 1-3 https://doi.org/10.1016/S0370-1573(98)00008-8	journal	July 1998
Experimental Observation of Directional Locking and Dynamical Ordering of Colloidal Monolayers Driven across Quasiperiodic Substrates Bohlein, Thomas; Bechinger, Clemens Physical Review Letters, Vol. 109, Issue 5 https://doi.org/10.1103/PhysRevLett.109.058301	journal	July 2012
Flux Flow Noise and Dynamical Transitions in a Flux Line Lattice Marley, A. C.; Higgins, M. J.; Bhattacharya, S. Physical Review Letters, Vol. 74, Issue 15 https://doi.org/10.1103/PhysRevLett.74.3029	journal	April 1995
Kibble–Zurek mechanism in colloidal monolayers Deutschländer, Sven; Dillmann, Patrick; Maret, Georg Proceedings of the National Academy of Sciences, Vol. 112, Issue 22 https://doi.org/10.1073/pnas.1500763112	journal	April 2015
Geometry and Topology of Turbulence in Active Nematics Giomi, Luca Physical Review X, Vol. 5, Issue 3 https://doi.org/10.1103/PhysRevX.5.031003	journal	July 2015
Theory of dynamic critical phenomena Hohenberg, P. C.; Halperin, B. I. Reviews of Modern Physics, Vol. 49, Issue 3 https://doi.org/10.1103/RevModPhys.49.435	journal	July 1977
Dynamic Melting of the Vortex Lattice Koshelev, A. E.; Vinokur, V. M. Physical Review Letters, Vol. 73, Issue 26 https://doi.org/10.1103/PhysRevLett.73.3580	journal	December 1994
Skyrmion Lattice in a Chiral Magnet Muhlbauer, S.; Binz, B.; Jonietz, F. Science, Vol. 323, Issue 5916 https://doi.org/10.1126/science.1166767	journal	February 2009
Ising Model with Second-Neighbor Interaction. I. Some Exact Results and an Approximate Solution Fan, Chungpeng; Wu, F. Y. Physical Review, Vol. 179, Issue 2 https://doi.org/10.1103/PhysRev.179.560	journal	March 1969
A universal transition to turbulence in channel flow Sano, Masaki; Tamai, Keiichi Nature Physics, Vol. 12, Issue 3 https://doi.org/10.1038/nphys3659	journal	February 2016
Random organization in periodically driven systems Corté, Laurent; Chaikin, P. M.; Gollub, J. P. Nature Physics, Vol. 4, Issue 5 https://doi.org/10.1038/nphys891	journal	March 2008
Nonequilibrium steady states of driven periodic media Balents, Leon; Marchetti, M. Cristina; Radzihovsky, Leo Physical Review B, Vol. 57, Issue 13 https://doi.org/10.1103/PhysRevB.57.7705	journal	April 1998
Universal current-velocity relation of skyrmion motion in chiral magnets Iwasaki, Junichi; Mochizuki, Masahito; Nagaosa, Naoto Nature Communications, Vol. 4, Issue 1 https://doi.org/10.1038/ncomms2442	journal	February 2013
Quantum Kibble–Zurek mechanism and critical dynamics on a programmable Rydberg simulator Keesling, Alexander; Omran, Ahmed; Levine, Harry Nature, Vol. 568, Issue 7751 https://doi.org/10.1038/s41586-019-1070-1	journal	April 2019
Deriving the skyrmion Hall angle from skyrmion lattice dynamics Brearton, R.; Turnbull, L. A.; Verezhak, J. A. T. Nature Communications, Vol. 12, Issue 1 https://doi.org/10.1038/s41467-021-22857-y	journal	May 2021
Critical behavior of plastic depinning of vortex lattices in two dimensions: Molecular dynamics simulations Fily, Y.; Olive, E.; Di Scala, N. Physical Review B, Vol. 82, Issue 13 https://doi.org/10.1103/PhysRevB.82.134519	journal	October 2010
Topology of cosmic domains and strings Kibble, T. W. B. Journal of Physics A: Mathematical and General, Vol. 9, Issue 8 https://doi.org/10.1088/0305-4470/9/8/029	journal	August 1976
Observation of smectic and moving-Bragg-glass phases in flowing vortex lattices Pardo, F.; de la Cruz, F.; Gammel, P. L. Nature, Vol. 396, Issue 6709 https://doi.org/10.1038/24581	journal	November 1998
Topological defect formation and spontaneous symmetry breaking in ion Coulomb crystals Pyka, K.; Keller, J.; Partner, H. L. Nature Communications, Vol. 4, Issue 1 https://doi.org/10.1038/ncomms3291	journal	August 2013
Observation of the Kibble–Zurek scaling law for defect formation in ion crystals Ulm, S.; Roßnagel, J.; Jacob, G. Nature Communications, Vol. 4, Issue 1 https://doi.org/10.1038/ncomms3290	journal	August 2013
Noise fluctuations and drive dependence of the skyrmion Hall effect in disordered systems Reichhardt, C.; Olson Reichhardt, C. J. New Journal of Physics, Vol. 18, Issue 9 https://doi.org/10.1088/1367-2630/18/9/095005	journal	September 2016
Current-driven dynamics of skyrmions stabilized in MnSi nanowires revealed by topological Hall effect Liang, Dong; DeGrave, John P.; Stolt, Matthew J. Nature Communications, Vol. 6, Issue 1 https://doi.org/10.1038/ncomms9217	journal	September 2015
Depinning and nonequilibrium dynamic phases of particle assemblies driven over random and ordered substrates: a review Reichhardt, C.; Olson Reichhardt, C. J. Reports on Progress in Physics, Vol. 80, Issue 2 https://doi.org/10.1088/1361-6633/80/2/026501	journal	December 2016
Mechanisms of Ordering in Striped Patterns Harrison, C. Science, Vol. 290, Issue 5496 https://doi.org/10.1126/science.290.5496.1558	journal	November 2000
Statics and dynamics of skyrmions interacting with disorder and nanostructures Reichhardt, C.; Reichhardt, C. J. O.; Milošević, M. V. Reviews of Modern Physics, Vol. 94, Issue 3 https://doi.org/10.1103/RevModPhys.94.035005	journal	September 2022
Vortex Dynamics in Two-Dimensional Amorphous M $o_{77}$ G $e_{23}$ Films Hellerqvist, M. C.; Ephron, D.; White, W. R. Physical Review Letters, Vol. 76, Issue 21 https://doi.org/10.1103/PhysRevLett.76.4022	journal	May 1996
Perspective: Magnetic skyrmions—Overview of recent progress in an active research field Everschor-Sitte, K.; Masell, J.; Reeve, R. M. Journal of Applied Physics, Vol. 124, Issue 24 https://doi.org/10.1063/1.5048972	journal	December 2018
Diameter-independent skyrmion Hall angle observed in chiral magnetic multilayers Zeissler, Katharina; Finizio, Simone; Barton, Craig Nature Communications, Vol. 11, Issue 1 https://doi.org/10.1038/s41467-019-14232-9	journal	January 2020
Non-equilibrium critical phenomena and phase transitions into absorbing states Hinrichsen, Haye Advances in Physics, Vol. 49, Issue 7 https://doi.org/10.1080/00018730050198152	journal	November 2000
Domain Coarsening in Electroconvection Purvis, Lynne; Dennin, Michael Physical Review Letters, Vol. 86, Issue 26 https://doi.org/10.1103/PhysRevLett.86.5898	journal	June 2001
Nonlinear transport, dynamic ordering, and clustering for driven skyrmions on random pinning Reichhardt, C.; Reichhardt, C. J. O. Physical Review B, Vol. 99, Issue 10 https://doi.org/10.1103/PhysRevB.99.104418	journal	March 2019
Kibble-Zurek mechanism for nonequilibrium phase transitions in driven systems with quenched disorder Reichhardt, C. J. O.; del Campo, A.; Reichhardt, C. Communications Physics, Vol. 5, Issue 1 https://doi.org/10.1038/s42005-022-00952-w	journal	July 2022
Kibble-Zurek Mechanism for Dynamical Ordering in a Driven Vortex System Maegochi, S.; Ienaga, K.; Okuma, S. Physical Review Letters, Vol. 129, Issue 22 https://doi.org/10.1103/PhysRevLett.129.227001	journal	November 2022
Direct observation of the skyrmion Hall effect Jiang, Wanjun; Zhang, Xichao; Yu, Guoqiang Nature Physics, Vol. 13, Issue 2 https://doi.org/10.1038/nphys3883	journal	September 2016

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Title: Kibble-Zurek scenario and coarsening across nonequilibrium phase transitions in driven vortices and skyrmions

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