Statistical theory of the pinning of Bloch walls by randomly distributed defects

Hilzinger, H. R.; Kronmüller, H.

doi:10.1016/0304-8853(75)90098-0

Cited by 118 publications

(19 citation statements)

References 20 publications

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“…The defects act as pinning centers which prevent smooth movement of domain walls. It has been shown that the coercive field is proportional to square root of the density of defects and that it also depends on the domain wall area [13]. Since our single crystals are of the nearly the same chemical composition (within the sensitivity of EDX) and T C values, sample invariable values of the exchange and magnetic anisotropic energy in all samples may be expected, which should result in comparable domain-wall areas in all our samples.…”

Section: Resultsmentioning

confidence: 71%

Effect of thermal history on magnetism in UCoGa

Opletal

Proschek

Vondráčková

et al. 2019

Journal of Magnetism and Magnetic Materials

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Single crystals of UCoGa have been grown in different conditions and subsequently annealed in order to provide a collection of samples representing various quality as to concentration of lattice defects. The different sample quality "grades" have been characterized by values of residual electrical resistivity. Correlations of magnetic parameters (coercive field, Curie temperature) with residual resistivity have been determined and domain-wall pinning by crystal defects has been confirmed as the underlying mechanism of coercive field in strongly anisotropic ferromagnets.

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Section: Resultsmentioning

confidence: 71%

Effect of thermal history on magnetism in UCoGa

Opletal

Proschek

Vondráčková

et al. 2019

Journal of Magnetism and Magnetic Materials

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“…Is Rayleigh behavior a property of a single interface moving either rigidly or via bowing (23), an average response of multiple noninteracting interfaces, or collective behavior emerging in a system of multiple interacting interfaces? (7) Can the individual defect centers be ascribed with individual double-well potentials, providing microstructural analogs for Preisach hysterons?…”

mentioning

confidence: 99%

Collective dynamics underpins Rayleigh behavior in disordered polycrystalline ferroelectrics

Bintachitt

Jesse

Damjanović

et al. 2010

Proc. Natl. Acad. Sci. U.S.A.

118

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Nanoscale and mesoscopic disorder and associated local hysteretic responses underpin the unique properties of spin and cluster glasses, phase-separated oxides, polycrystalline ferroelectrics, and ferromagnets alike. Despite the rich history of the field, the relationship between the statistical descriptors of hysteresis behavior such as Preisach density, and micro and nanostructure has remained elusive. By using polycrystalline ferroelectric capacitors as a model system, we now report quantitative nonlinearity measurements in 0.025-1 μm 3 volumes, approximately 10 6 times smaller than previously possible. We discover that the onset of nonlinear behavior with thickness proceeds through formation and increase of areal density of micron-scale regions with large nonlinear response embedded in a more weakly nonlinear matrix. This observation indicates that large-scale collective domain wall dynamics, as opposed to motion of noninteracting walls, underpins Rayleigh behavior in disordered ferroelectrics. The measurements provide evidence for the existence and extent of the domain avalanches in ferroelectric materials, forcing us to rethink 100-year old paradigms.piezoelectric | ferroelectric | piezoelectric force microscopy | lead zirconate titanate | thin films H ysteretic response to external stimuli is a ubiquitous feature of disordered systems ranging from friction, capillary condensation, metal-insulator transitions, to magnetic, ferroelectric, and ferroelastic materials. Hysteresis in ferroic systems is utilized in many applications, including magnetic and ferroelectric memory technologies (1) and shape-memory and high-toughness materials (2). The traditional objects of study in the field of ferroic materials driven by information technology applications are strong-field hysteresis loops corresponding to complete switching of material between the limiting states. However, equally important are hysteretic responses in weak (subcoercive) fields, which directly underpin the enhanced properties often observed in disordered and multidomain materials (3 and 4). For ferroelectrics, enhanced electromechanical coupling and dielectric responses enabled by domain wall motion strongly influence electromechanical energy conversion in medical transducers, actuators for precise positioning, and piezoelectric and composite magnetostrictive sensors (5). At the same time, local hysteresis is the primary mechanism of energy losses and dissipation. Design of materials with high coupling coefficients and acceptable losses necessitates deciphering fundamental mechanisms behind lowfield hysteresis behavior.In disordered magnetic systems, the weak-field hysteresis has been a field of active study since the seminal 1870 work by Rayleigh (6), who described the universal parabolic law for ferromagnetic minor loops,where MðHÞ is the field-dependent magnetization, χ init is the initial susceptibility, H max is the maximum applied magnetic field, and α is the irreversible Rayleigh constant. The same constant defines the field-dependent suscep...

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“…This is considerably closer to the value derived by Wohlfarth (1984), and falls within the range of theoretical predictions. Hilzinger and Kronmüller (1975) predicted H C ∝ v −2/3 act for strongly pinned domain walls, similarly the Kersten inclusion theory of domain-wall motion also predicts the same relationship (Wohlfarth, 1984).…”

Section: Activation Volumesmentioning

confidence: 61%

“…If the variation in M S is ignored, using the data available to Wohlfarth (1984) yields x = 0.74; this small difference in x is likely to be within rounding errors. Theoretical estimates for x depend on reversal mechanisms, and range from 0.5 < x < 1 (e.g., Néel, 1951;Hilzinger and Kronmüller, 1975;Luo, 1990, 1991). It is generally predicted that x = 1 for uniaxial SD particles, but there are several discrepancies between domain wall theories, for example, Liu and Luo (1991) predict x = 1 for all reversal mechanisms, in contrast to a lower value of 0.5 by Hilzinger and Kronmüller (1975).…”

Section: Activation Volumesmentioning

confidence: 99%

Thermal fluctuation fields in basalts

2009

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The thermal fluctuation field (H f ) is central to thermoremanent acquisition models, which are key to our understanding of the reliability of palaeomagnetic data, however, H f is poorly quantified for natural systems. We report H f determinations for a range of basalts, made by measuring rate-dependent hysteresis. The results for the basalts were found to be generally consistent within the space of H f versus the coercive force H C , i.e., the "Barbier plot", which is characterized by the empirically derived relationship; log H f ∝ 1.3 log H C obtained from measurements on a wide range of different magnetic materials. Although the basalts appear to occupy the correct position within the space of the Barbier plot, the relationship within the sample set, log H f ∝ 0.54 log H C , is different to the Barbier relationship. This difference is attributed to the original Barbier relationship being derived from a wide range of different synthetic magnetic materials, and not for variations within one material type, as well as differences in methodology in determining H f . We consider the relationship between H C and the activation volume, v act , which was found to be H C ∝ v −0.68 act for our mineralogically homogeneous samples. This compares favourably with theoretical predictions, and with previous empirical estimates based on the Barbier plot, which defined the relationship as H C ∝ v −0.73 act .

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Statistical theory of the pinning of Bloch walls by randomly distributed defects

Cited by 118 publications

References 20 publications

Effect of thermal history on magnetism in UCoGa

Effect of thermal history on magnetism in UCoGa

Collective dynamics underpins Rayleigh behavior in disordered polycrystalline ferroelectrics

Thermal fluctuation fields in basalts

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