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Balk AL, Li F, Gilbert I, Unguris J, Sinitsyn NA, Crooker SA. Broadband spectroscopy of thermodynamic magnetization fluctuations through a ferromagnetic spin-reorientation transition. PHYSICAL REVIEW. X 2018; 8:10.1103/PhysRevX.8.031078. [PMID: 30984473 PMCID: PMC6459195 DOI: 10.1103/physrevx.8.031078] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
We use scanning optical magnetometry to study the broadband frequency spectra of spontaneous magnetization fluctuations, or "magnetization noise", in an archetypal ferromagnetic film that can be smoothly tuned through a spin reorientation transition (SRT). The SRT is achieved by laterally varying the magnetic anisotropy across an ultrathin Pt/Co/Pt trilayer, from the perpendicular to in-plane direction, via graded Ar+ irradiation. In regions exhibiting perpendicular anisotropy, the power spectrum of the magnetization noise, S(ν), exhibits a remarkably robust ν -3/2 power law over frequencies ν from 1 kHz to 1 MHz. As the SRT region is traversed, however, S(ν) spectra develop a steadily-increasing critical frequency, ν 0, below which the noise power is spectrally flat, indicating an evolving low-frequency cutoff for magnetization fluctuations. The magnetization noise depends strongly on applied in- and out-of-plane magnetic fields, revealing local anisotropies and also a field-induced emergence of fluctuations in otherwise stable ferromagnetic films. Finally, we demonstrate that higher-order correlators can be computed from the noise. These results highlight broadband spectroscopy of thermodynamic fluctuations as a powerful tool to characterize the interplay between thermal and magnetic energy scales, and as a means of characterizing phase transitions in ferromagnets.
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Affiliation(s)
- A L Balk
- National High, Magnetic Field Laboratory, Los Alamos National Laboratory, Los Alamos, NM 87545, USA
| | - F Li
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USA
- Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, NM 87545, USA
| | - I Gilbert
- Center for Nanoscale Science and Technology, National Institute of Standards and Technology, Gaithersburg, MD 20899, USA
| | - J Unguris
- Center for Nanoscale Science and Technology, National Institute of Standards and Technology, Gaithersburg, MD 20899, USA
| | - N A Sinitsyn
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USA
| | - S A Crooker
- National High, Magnetic Field Laboratory, Los Alamos National Laboratory, Los Alamos, NM 87545, USA
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Chen YJ, Zapperi S, Sethna JP. Crossover behavior in interface depinning. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:022146. [PMID: 26382382 DOI: 10.1103/physreve.92.022146] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/09/2014] [Indexed: 06/05/2023]
Abstract
We study the crossover scaling behavior of the height-height correlation function in interface depinning in random media. We analyze experimental data from a fracture experiment and simulate an elastic line model with nonlinear couplings and disorder. Both exhibit a crossover between two different universality classes. For the experiment, we fit a functional form to the universal crossover scaling function. For the model, we vary the system size and the strength of the nonlinear term and describe the crossover between the two universality classes with a multiparameter scaling function. Our method provides a general strategy to extract scaling properties in depinning systems exhibiting crossover phenomena.
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Affiliation(s)
- Y J Chen
- LASSP, Physics Department, Cornell University, Ithaca, New York 14853-2501, USA
| | - Stefano Zapperi
- Center for Complexity and Biosystems, Department of Physics, University of Milano, via Celoria 26, 20133 Milano, Italy; CNR-Consiglio Nazionale delle Ricerche, IENI, Via R. Cozzi 53, 20125, Milano, Italy; ISI Foundation, Via Alassio 11/c 10126 Torino, Italy; and Department of Applied Physics, Aalto University, P.O. Box 14100, FIN-00076, Aalto, Finland
| | - James P Sethna
- LASSP, Physics Department, Cornell University, Ithaca, New York 14853-2501, USA
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Aragón LE, Jagla EA, Rosso A. Seismic cycles, size of the largest events, and the avalanche size distribution in a model of seismicity. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 85:046112. [PMID: 22680543 DOI: 10.1103/physreve.85.046112] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/26/2012] [Indexed: 06/01/2023]
Abstract
We address several questions on the behavior of a numerical model recently introduced to study seismic phenomena, which includes relaxation in the plates as a key ingredient. First, we make an analysis of the scaling of the largest events with system size and show that, when parameters are appropriately interpreted, the typical size of the largest events scale as the system size, without the necessity to tune any parameter. Second, we show that the temporal activity in the model is inherently nonstationary and obtain from here justification and support for the concept of a "seismic cycle" in the temporal evolution of seismic activity. Finally, we ask for the reasons that make the model display a realistic value of the decaying exponent b in the Gutenberg-Richter law for the avalanche size distribution. We explain why relaxation induces a systematic increase in b from its value b≃0.4 observed in the absence of relaxation. However, we have not been able to justify the actual robustness of the model in displaying a consistent b value around the experimentally observed value b≃1.
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Affiliation(s)
- L E Aragón
- Centro Atómico Bariloche and Instituto Balseiro, Comisión Nacional de Energía Atómica, 8400 Bariloche, Argentina.
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Chan PY, Tsekenis G, Dantzig J, Dahmen KA, Goldenfeld N. Plasticity and dislocation dynamics in a phase field crystal model. PHYSICAL REVIEW LETTERS 2010; 105:015502. [PMID: 20867460 DOI: 10.1103/physrevlett.105.015502] [Citation(s) in RCA: 25] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/26/2010] [Indexed: 05/29/2023]
Abstract
The critical dynamics of dislocation avalanches in plastic flow is examined using a phase field crystal model. In the model, dislocations are naturally created, without any ad hoc creation rules, by applying a shearing force to the perfectly periodic ground state. These dislocations diffuse, interact and annihilate with one another, forming avalanche events. By data collapsing the event energy probability density function for different shearing rates, a connection to interface depinning dynamics is confirmed. The relevant critical exponents agree with mean field theory predictions.
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Affiliation(s)
- Pak Yuen Chan
- Department of Physics, University of Illinois at Urbana-Champaign, Loomis Laboratory of Physics, 1110 West Green Street, Urbana, Illinois, 61801-3080, USA
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Chandni U, Ghosh A, Vijaya HS, Mohan S. Criticality of tuning in athermal phase transitions. PHYSICAL REVIEW LETTERS 2009; 102:025701. [PMID: 19257290 DOI: 10.1103/physrevlett.102.025701] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/24/2008] [Indexed: 05/27/2023]
Abstract
We experimentally address the importance of tuning in athermal phase transitions, which are triggered only by a slowly varying external field acting as tuning parameter. Using higher order statistics of fluctuations, evidence consistent with the existence a singular critical instability is detected, in spite of an apparent universal self-similar kinetics over a broad range of driving force. The results as well as the experimental technique are likely to be of significance to many slowly driven nonequilibrium systems from geophysics to material science which display avalanche dynamics.
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Affiliation(s)
- U Chandni
- Department of Physics, Indian Institute of Science, Bangalore 560 012, India.
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Deutsch JM, Mai T. Mechanism for nonequilibrium symmetry breaking and pattern formation in magnetic films. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2005; 72:016115. [PMID: 16090044 DOI: 10.1103/physreve.72.016115] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/11/2005] [Indexed: 05/03/2023]
Abstract
Magnetic thin films exhibit a strong variation in properties depending on their degree of disorder. Recent coherent x-ray speckle experiments on magnetic films have measured the loss of correlation between configurations at opposite fields and at the same field, upon repeated field cycling. We perform finite temperature numerical simulations on these systems that provide a comprehensive explanation for the experimental results. The simulations demonstrate, in accordance with experiments, that the memory of configurations increases with film disorder. We find that nontrivial microscopic differences exist between the zero field spin configuration obtained by starting from a large positive field and the zero field configuration starting at a large negative field. This seemingly paradoxical behavior is due to the nature of the vector spin dynamics and is also seen in the experiments. For low disorder, there is an instability which causes the spontaneous growth of linelike domains at a critical field, also in accord with experiments. It is this unstable growth, which is highly sensitive to thermal noise, that is responsible for the small correlation between patterns under repeated cycling. The domain patterns, hysteresis loops, and memory properties of our simulated systems match remarkably well with the real experimental systems.
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Affiliation(s)
- J M Deutsch
- Department of Physics, University of California, Santa Cruz, California 95064, USA
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Deutsch JM, Dhar A, Narayan O. Return to return point memory. PHYSICAL REVIEW LETTERS 2004; 92:227203. [PMID: 15245257 DOI: 10.1103/physrevlett.92.227203] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/12/2003] [Indexed: 05/24/2023]
Abstract
We describe a new class of systems exhibiting return point memory (RPM), different from those discussed before in the context of ferromagnets. We show numerically that one-dimensional random Ising antiferromagnets have exact RPM when evolving from a large field, but not when started at finite field, unlike the ferromagnetic case. This implies that the standard approach to understanding ferromagnetic RPM will fail for this case. We also demonstrate RPM with a set of variables that keeps track of spin flips at each site. Conventional RPM for the spins is a projection of this result, suggesting that spin flip variables might be a more fundamental representation of the dynamics. We also present a mapping that embeds the antiferromagnetic chain in a two-dimensional ferromagnet, and prove RPM for spin-exchange dynamics in the interior of the chain with this mapping.
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Affiliation(s)
- J M Deutsch
- Department of Physics, University of California, Santa Cruz, California 95064, USA
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Kim DH, Choe SB, Shin SC. Direct observation of Barkhausen avalanche in Co thin films. PHYSICAL REVIEW LETTERS 2003; 90:087203. [PMID: 12633456 DOI: 10.1103/physrevlett.90.087203] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/10/2002] [Indexed: 05/24/2023]
Abstract
We report direct full-field magneto-optical observations of Barkhausen avalanches in Co polycrystalline thin films at criticality. We provide experimental evidence for the validity of a phenomenological model of the Barkhausen avalanche originally proposed by Cizeau, Zapperi, Durin, and Stanley [Phys. Rev. Lett. 79, 4669 (1997)]], where the model describes a 180 degrees -type flexible domain wall deformed by a localized defect with consideration of long-range dipolar interaction. The Barkhausen jump areas show a power-law scaling distribution with critical exponent tau approximately 1.33 for all the samples having different thickness from 5 to 50 nm, which is in accord with the two-dimensional prediction of the model.
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Affiliation(s)
- Dong-Hyun Kim
- Department of Physics and Center for Nanospinics of Spintronic Materials, Korea Advanced Institute of Science and Technology, Taejon 305-701, Korea
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Mehta AP, Mills AC, Dahmen KA, Sethna JP. Universal pulse shape scaling function and exponents: critical test for avalanche models applied to Barkhausen noise. PHYSICAL REVIEW E 2002; 65:046139. [PMID: 12005958 DOI: 10.1103/physreve.65.046139] [Citation(s) in RCA: 70] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/07/2001] [Indexed: 11/07/2022]
Abstract
In order to test if the universal aspects of Barkhausen noise in magnetic materials can be predicted from recent variants of the nonequilibrium zero-temperature Random Field Ising Model, we perform a quantitative study of the universal scaling function derived from the Barkhausen pulse shape in simulations and experiment. Through data collapses and scaling relations we determine the critical exponents tau and 1/sigma nu z in both simulation and experiment. Although we find agreement in the critical exponents, we find differences between theoretical and experimental pulse shape scaling functions as well as between different experiments.
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Affiliation(s)
- Amit P Mehta
- Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
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Abstract
Crackling noise arises when a system responds to changing external conditions through discrete, impulsive events spanning a broad range of sizes. A wide variety of physical systems exhibiting crackling noise have been studied, from earthquakes on faults to paper crumpling. Because these systems exhibit regular behaviour over a huge range of sizes, their behaviour is likely to be independent of microscopic and macroscopic details, and progress can be made by the use of simple models. The fact that these models and real systems can share the same behaviour on many scales is called universality. We illustrate these ideas by using results for our model of crackling noise in magnets, explaining the use of the renormalization group and scaling collapses, and we highlight some continuing challenges in this still-evolving field.
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Affiliation(s)
- J P Sethna
- Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca, New York 14853-2501, USA
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Durin G, Zapperi S. Scaling exponents for barkhausen avalanches in polycrystalline and amorphous ferromagnets. PHYSICAL REVIEW LETTERS 2000; 84:4705-4708. [PMID: 10990776 DOI: 10.1103/physrevlett.84.4705] [Citation(s) in RCA: 21] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/07/1999] [Indexed: 05/23/2023]
Abstract
We investigate the scaling properties of the Barkhausen effect by recording the noise in several soft ferromagnetic materials: polycrystals with different grain sizes and amorphous alloys. We measure the Barkhausen avalanche distributions and determine the scaling exponents. In the limit of vanishing external field rate, we can group the samples in two distinct classes, characterized by exponents tau = 1.50+/-0.05 or tau = 1.27+/-0.03, for the avalanche size distributions. We interpret these results in terms of the depinning transition of domain walls and obtain an expression relating the cutoff of the distributions to the demagnetizing factor which is in quantitative agreement with experiments.
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Affiliation(s)
- G Durin
- Istituto Elettrotecnico Nazionale Galileo Ferraris and INFM, Corso M. d'Azeglio 42, I-10125 Torino, Italy
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