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Qian X, Yu G, Zhou N. Nonsteady dynamics at the dynamic depinning transition in the two-dimensional Gaussian random-field Ising model. Phys Rev E 2023; 107:064108. [PMID: 37464630 DOI: 10.1103/physreve.107.064108] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/16/2023] [Accepted: 05/17/2023] [Indexed: 07/20/2023]
Abstract
With large-scale Monte Carlo simulations, we investigate the nonsteady relaxation at the dynamic depinning transition in the two-dimensional Gaussian random-field Ising model. The dynamic scaling behavior is carefully analyzed, and the transition fields as well as static and dynamic exponents are accurately determined based on the short-time dynamic scaling form. Different from the usual assumption, two distinguished growth processes of spatial correlation lengths for the velocity and height of the domain wall are found. Thus, the universality class of the depinning transition is established, which significantly differs from that of the quenched disorder equation but agrees with that of the recent experiment as well as other simulations works. Under the influence of the mesoscopic time regime, the crossover from the second-order phase transition to the first-order one is confirmed in the weak-disorder regime, yielding an abnormal disorder-dependent nature of the criticality.
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Affiliation(s)
- Xiaohui Qian
- School of Physics, Hangzhou Normal University, Hangzhou 311121, China
| | - Gaotian Yu
- School of Physics, Hangzhou Normal University, Hangzhou 311121, China
| | - Nengji Zhou
- School of Physics, Hangzhou Normal University, Hangzhou 311121, China
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Del Bianco L, Spizzo F, Barucca G, Marangoni G, Sgarbossa P. Glassy Magnetic Behavior and Correlation Length in Nanogranular Fe-Oxide and Au/Fe-Oxide Samples. MATERIALS (BASEL, SWITZERLAND) 2019; 12:E3958. [PMID: 31795308 PMCID: PMC6926589 DOI: 10.3390/ma12233958] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 11/03/2019] [Revised: 11/18/2019] [Accepted: 11/26/2019] [Indexed: 01/13/2023]
Abstract
In nanoscale magnetic systems, the possible coexistence of structural disorder and competing magnetic interactions may determine the appearance of a glassy magnetic behavior, implying the onset of a low-temperature disordered collective state of frozen magnetic moments. This phenomenology is the object of an intense research activity, stimulated by a fundamental scientific interest and by the need to clarify how disordered magnetism effects may affect the performance of magnetic devices (e.g., sensors and data storage media). We report the results of a magnetic study that aims to broaden the basic knowledge of glassy magnetic systems and concerns the comparison between two samples, prepared by a polyol method. The first can be described as a nanogranular spinel Fe-oxide phase composed of ultrafine nanocrystallites (size of the order of 1 nm); in the second, the Fe-oxide phase incorporated non-magnetic Au nanoparticles (10-20 nm in size). In both samples, the Fe-oxide phase exhibits a glassy magnetic behavior and the nanocrystallite moments undergo a very similar freezing process. However, in the frozen regime, the Au/Fe-oxide composite sample is magnetically softer. This effect is explained by considering that the Au nanoparticles constitute physical constraints that limit the length of magnetic correlation between the frozen Fe-oxide moments.
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Affiliation(s)
- L. Del Bianco
- Dipartimento di Fisica e Scienze della Terra, Università di Ferrara, I-44122 Ferrara, Italy;
| | - F. Spizzo
- Dipartimento di Fisica e Scienze della Terra, Università di Ferrara, I-44122 Ferrara, Italy;
| | - G. Barucca
- Dipartimento SIMAU, Università Politecnica delle Marche, I-60131 Ancona, Italy;
| | - G. Marangoni
- Dipartimento di Ingegneria Industriale, Università di Padova, I-35131 Padova, Italy; (G.M.); (P.S.)
| | - P. Sgarbossa
- Dipartimento di Ingegneria Industriale, Università di Padova, I-35131 Padova, Italy; (G.M.); (P.S.)
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Echevarria-Bonet C, Rojas DP, Espeso JI, Rodríguez Fernández J, de la Fuente Rodríguez M, Fernández Barquín L, Rodríguez Fernández L, Gorria P, Blanco JA, Fdez-Gubieda ML, Bauer E, Damay F. Magnetic phase diagram of superantiferromagnetic TbCu₂ nanoparticles. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2015; 27:496002. [PMID: 26593408 DOI: 10.1088/0953-8984/27/49/496002] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
The structural state and static and dynamic magnetic properties of TbCu2 nanoparticles are reported to be produced by mechanical milling under inert atmosphere. The randomly dispersed nanoparticles as detected by TEM retain the bulk symmetry with an orthorhombic Imma lattice and Tb and Cu in the 4e and 8h positions, respectively. Rietveld refinements confirm that the milling produces a controlled reduction of particle sizes reaching ≃6 nm and an increase of the microstrain up to ≃0.6%. The electrical resistivity indicates a metallic behavior and the presence of a magnetic contribution to the electronic scattering which decreases with milling times. The dc-susceptibility shows a reduction of the Néel transition (from 49 K to 43 K) and a progressive increase of a peak (from 9 K to 15 K) in the zero-field-cooled magnetization with size reduction. The exchange anisotropy is very weak (a bias field of ≃30 Oe) and is due to the presence of a disordered (thin) shell coupled to the antiferromagnetic core. The dynamic susceptibility evidences a critical slowing down in the spin-disordered state for the lowest temperature peak associated with a spin glass-like freezing with a tendency of zv and β exponents to increase when the size becomes 6 nm (zv ≃ 6.6 and β ≃ 0.85). A Rietveld analysis of the neutron diffraction patterns 1.8 ≤ T ≤ 60 K, including the magnetic structure determination, reveals that there is a reduction of the expected moment (≃80%), which must be connected to the presence of the disordered particle shell. The core magnetic structure retains the bulk antiferromagnetic arrangement. The overall interpretation is based on a superantiferromagnetic behavior which at low temperatures coexists with a canting of surface moments and a mismatch of the antiferromagnetic sublattices of the nanoparticles. We propose a novel magnetic phase diagram where changes are provoked by a combination of the decrease of size and the increase of microstrain.
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Affiliation(s)
- C Echevarria-Bonet
- DbibIMAC, Facultad de Ciencias, Universidad de Cantabria, 39005 Santander, Spain
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Kataja M, van Dijken S. Magneto-optical Kerr effect susceptometer for the analysis of magnetic domain wall dynamics. THE REVIEW OF SCIENTIFIC INSTRUMENTS 2011; 82:103901. [PMID: 22047306 DOI: 10.1063/1.3647313] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
Domain wall dynamics in thin magnetic films with perpendicular and in-plane anisotropy is studied using a novel magneto-optical Kerr effect susceptometery method. The method allows for measurements of domain wall motion under ac field excitation and the analysis of dynamic modes as a function of driving frequency and magnetic field amplitude. Domain wall dynamics in the perpendicular anisotropy system, a Co/Pt multilayer, is characterized by thermally activated creep motion. For this dynamic mode, a polydispersivity exponent of β = 0.50 ± 0.03 is derived at small excitation energy, which is in excellent agreement with theoretical models. The dynamics of the other system, a Co wire with transverse uniaxial anisotropy, is dominated by viscous slide motion in a regular magnetic stripe pattern. Analytical expressions are derived for this magnetic configuration and by using these expressions, accurate values for the depinning field and the domain wall mobility are extracted from the susceptibility measurements.
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Affiliation(s)
- Mikko Kataja
- NanoSpin, Department of Applied Physics, Aalto University School of Science, Aalto, Finland
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Badini Confalonieri GA, Vega V, Ebbing A, Mishra D, Szary P, Prida VM, Petracic O, Zabel H. Template-assisted self-assembly of individual and clusters of magnetic nanoparticles. NANOTECHNOLOGY 2011; 22:285608. [PMID: 21654034 DOI: 10.1088/0957-4484/22/28/285608] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
The deliberate control over the spatial arrangement of nanostructures is the desired goal for many applications such as, for example, in data storage, plasmonics or sensor arrays. Here we present a novel method to assist the self-assembly process of magnetic nanoparticles. The method makes use of nanostructured aluminum templates obtained after anodization of aluminum discs and the subsequent growth and removal of the newly formed alumina layer, resulting in a regular honeycomb-type array of hexagonally shaped valleys. The iron oxide nanoparticles, 20 nm in diameter, are spin-coated onto the surface of honeycomb nanostructured Al templates. Depending on the size, each hexagon site can host up to 30 nanoparticles. These nanoparticles form clusters of different arrangements within the valleys, such as collars, chains and hexagonally closed islands. Ultimately, it is possible to isolate individual nanoparticles. The strengths of the magnetic interaction between particles in a cluster are probed using the memory effect known from the coupled state in superspin glass systems.
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Affiliation(s)
- G A Badini Confalonieri
- Ruhr-Universität Bochum, Institut für Experimentalphysik/Festkörperphysik, Bochum 44780, Germany.
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Singamaneni S, Bliznyuk VN, Binek C, Tsymbal EY. Magnetic nanoparticles: recent advances in synthesis, self-assembly and applications. ACTA ACUST UNITED AC 2011. [DOI: 10.1039/c1jm11845e] [Citation(s) in RCA: 383] [Impact Index Per Article: 29.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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Carpenter MA, Buckley A, Taylor PA, Darling TW. Elastic relaxations associated with the Pm3m-R3c transition in LaAlO(3): III. Superattenuation of acoustic resonances. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2010; 22:035405. [PMID: 21386288 DOI: 10.1088/0953-8984/22/3/035405] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
Resonant ultrasound spectroscopy has been used to characterize elastic softening and anelastic dissipation processes associated with the Pm3m <--> R3c transition in single crystal and ceramic samples of LaAlO(3). Softening of the cubic structure ahead of the transition point is not accompanied by an increase in dissipation but follows different temperature dependences for the bulk modulus, (1/3)(C(11) + C(12)), and the shear components, (1/2)(C(11) + C(12)) and C(44), as if the tilting instability contains two slightly different critical temperatures. The transition itself is marked by the complete disappearance of resonance peaks (superattenuation), which then reappear below ∼700 K in spectra from single crystals. Comparisons with low frequency, high stress data from the literature indicate that the dissipation is not due to macroscopic displacement of needle twins. An alternative mechanism, local bowing of twin walls under low dynamic stress, is postulated. Pinning of the walls with respect to this displacement process occurs below ∼350 K. Anelasticity maps, analogous to plastic deformation mechanism maps, are proposed to display dispersion relations and temperature/frequency/stress fields for different twin wall related dissipation mechanisms. These allow comparisons to be made of anelastic loss mechanisms under mechanical stress with elastic behaviour observed by means of Brillouin scattering at high frequencies which might also be related to microstructure.
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Affiliation(s)
- M A Carpenter
- Department of Earth Sciences, University of Cambridge, Downing Street, Cambridge CB2 3EQ, UK.
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Bliznyuk V, Singamaneni S, Sahoo S, Polisetty S, He X, Binek C. Self-assembly of magnetic Ni nanoparticles into 1D arrays with antiferromagnetic order. NANOTECHNOLOGY 2009; 20:105606. [PMID: 19417526 DOI: 10.1088/0957-4484/20/10/105606] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/20/2023]
Abstract
In this paper, we report on the magnetic properties of isolated nanoparticles and interacting nanochains formed by the self-assembly of Ni nanoparticles. The magnetic properties were studied using superconducting quantum interference device (SQUID) magnetometry and magnetic force microscopy (MFM). We demonstrate that single-domain Ni nanoparticles spontaneously form one-dimensional (1D) chains under the influence of an external magnetic field. Furthermore, such magnetic field-driven self-assembly in conjunction with surface templating produces regular arrays of 1D nanochains with antiferromagnetic intra-chain order. The antiferromagnetic order, which is in striking contrast to what is found for non-interacting nanoparticle assemblies within the chains, can be evidenced from MFM and SQUID measurements.
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Affiliation(s)
- V Bliznyuk
- College of Engineering and Applied Sciences, Western Michigan University, Kalamazoo, MI 49008, USA.
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He YY, Zheng B, Zhou NJ. Logarithmic correction to scaling in domain-wall dynamics at Kosterlitz-Thouless phase transitions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009; 79:021107. [PMID: 19391706 DOI: 10.1103/physreve.79.021107] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/25/2008] [Indexed: 05/27/2023]
Abstract
With Monte Carlo simulations, we investigate the relaxation dynamics of domain walls at the Kosterlitz-Thouless phase transition, taking the two-dimensional XY model as an example. The dynamic scaling behavior is carefully analyzed, and a domain-wall roughening process is observed. Two-time correlation functions are calculated and aging phenomena are investigated. Inside the domain interface, a strong logarithmic correction to scaling is detected.
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Affiliation(s)
- Y Y He
- Zhejiang University, Zhejiang Institute of Modern Physics, Hangzhou 310027, People's Republic of China
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Metaxas PJ, Jamet JP, Mougin A, Cormier M, Ferré J, Baltz V, Rodmacq B, Dieny B, Stamps RL. Creep and flow regimes of magnetic domain-wall motion in ultrathin Pt/Co/Pt films with perpendicular anisotropy. PHYSICAL REVIEW LETTERS 2007; 99:217208. [PMID: 18233251 DOI: 10.1103/physrevlett.99.217208] [Citation(s) in RCA: 125] [Impact Index Per Article: 7.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/26/2007] [Indexed: 05/25/2023]
Abstract
We report on magnetic domain-wall velocity measurements in ultrathin Pt/Co(0.5-0.8 nm)/Pt films with perpendicular anisotropy over a large range of applied magnetic fields. The complete velocity-field characteristics are obtained, enabling an examination of the transition between thermally activated creep and viscous flow: motion regimes predicted from general theories for driven elastic interfaces in weakly disordered media. The dissipation limited flow regime is found to be consistent with precessional domain-wall motion, analysis of which yields values for the damping parameter, alpha.
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Affiliation(s)
- P J Metaxas
- Laboratoire de Physique des Solides, Université Paris-Sud, CNRS, UMR 8502, F-91405 Orsay Cedex, France.
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Kleemann W, Rhensius J, Petracic O, Ferré J, Jamet JP, Bernas H. Modes of periodic domain wall motion in ultrathin ferromagnetic layers. PHYSICAL REVIEW LETTERS 2007; 99:097203. [PMID: 17931031 DOI: 10.1103/physrevlett.99.097203] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/21/2007] [Indexed: 05/25/2023]
Abstract
Magnetization reversal in a periodic magnetic field is studied on an ultrathin, ultrasoft ferromagnetic Pt/Co(0.5 nm)/Pt trilayer exhibiting weak random domain wall (DW) pinning. The DW motion is imaged by polar magneto-optic Kerr effect microscopy and monitored by superconducting quantum interference device susceptometry. In close agreement with model predictions, the complex linear ac susceptibility corroborates the dynamic DW modes segmental relaxation, creep, slide, and switching.
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Affiliation(s)
- W Kleemann
- Angewandte Physik, Universität Duisburg-Essen, D-47048 Duisburg, Germany.
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Colaiori F, Durin G, Zapperi S. Loss separation for dynamic hysteresis in ferromagnetic thin films. PHYSICAL REVIEW LETTERS 2006; 97:257203. [PMID: 17280387 DOI: 10.1103/physrevlett.97.257203] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/07/2006] [Indexed: 05/13/2023]
Abstract
We develop a theory for dynamic hysteresis in ferromagnetic thin films, on the basis of the phenomenological principle of loss separation. We observe that, remarkably, the theory of loss separation, originally derived for bulk metallic materials, is applicable to disordered magnetic systems under fairly general conditions regardless of the particular damping mechanism. We confirm our theory both by numerical simulations of a driven random-field Ising model, and by reexamining several experimental data reported in the literature on dynamic hysteresis in thin films. All the experiments examined and the simulations find a natural interpretation in terms of loss separation. The power losses' dependence on the driving field rate predicted by our theory fits satisfactorily all the data in the entire frequency range, thus reconciling the apparent lack of universality observed in different materials.
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Affiliation(s)
- Francesca Colaiori
- CNR-INFM, SMC, Dipartimento di Fisica, Università La Sapienza, P.le A. Moro 2, 00185 Roma, Italy
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Jezewski W, Kuczyński W, Hoffmann J. Dielectric relaxation in chevron surface stabilized ferroelectric liquid crystals. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 73:061702. [PMID: 16906844 DOI: 10.1103/physreve.73.061702] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/09/2005] [Indexed: 05/11/2023]
Abstract
The dielectric response of surface stabilized ferroelectric liquid crystals with chevron layer structure is studied within low and intermediate frequency ranges, characteristic for collective molecular excitations. By analytically solving the dynamic equation for collective molecular fluctuations under a weak alternating electric field, it is demonstrated that chevron cells stabilized by both nonpolar and polar surface interactions undergo at medium frequencies two Debye relaxation processes, connected with two chevron slabs, on opposite sides of the interface plane. This result is confirmed, experimentally, making use of the electro-optic technique. Based on qualitative arguments supported by microscopic observations of zigzag defects at different frequencies and amplitudes of the external electric field, it is shown that, at low frequencies, the electro-optic response of chevron samples is determined by three kinds of motions of zigzag walls. The first two dynamic categories are related to collective relaxation processes at weak fields, within smectic A layers forming zigzag walls, and drift or creep motions of thick walls occurring at stronger field amplitudes. Dynamic processes of the third kind correspond to sliding of zigzag walls, which appear at yet stronger field amplitudes, but below the switching threshold.
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Affiliation(s)
- W Jezewski
- Institute of Molecular Physics, Polish Academy of Sciences, Smoluchowskiego 17, 60-179 Poznań, Poland
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Braun T, Kleemann W, Dec J, Thomas PA. Creep and relaxation dynamics of domain walls in periodically poled KTiOPO4. PHYSICAL REVIEW LETTERS 2005; 94:117601. [PMID: 15903888 DOI: 10.1103/physrevlett.94.117601] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/26/2004] [Indexed: 05/02/2023]
Abstract
Creep and relaxation of domain walls under ac electric fields are observed in an ideal model system, periodically poled KTiOPO4, to occur in different regimes, which are separated by dynamic phase transitions at frequencies f(m)(T)=f(m0)exp((-DeltaE/k(B)T), with f(m0)=3 x 10(9) Hz and DeltaE=0.6 eV. Power law dispersion of the creep susceptibility, chi proportional to 1+(iomegatau)(-beta), with beta approximately equal to 0.4, and large nonlinearity encountered at f < f(m), is contrasted with Cole-Cole-type relaxational dispersion, chi proportional to (1+[iomegatau](1-alpha))(-1), with alpha approximately 0.3, at f > f(m).
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Affiliation(s)
- Th Braun
- Angewandte Physik, Universitát Duisburg-Essen, D-47048 Duisburg, Germany
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