Dynamics of interfaces and dislocations in disordered media

Ioffe, L. B.; Винокур, В. М.

doi:10.1088/0022-3719/20/36/016

Cited by 181 publications

(262 citation statements)

References 8 publications

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“…We have omitted a prefactor, which is beyond our accuracy. This formula is valid for T ≪Ẽ B (h) and was found first by Ioffe and Vinokur [15] (see also [16]). In the opposite case T ≫Ẽ B (h) we expect a linear relation between the driving force and the velocity: v ≃ γh.…”

Section: Thermally Activated Creep Of Domain Wallssupporting

confidence: 56%

Hysteresis mediated by a domain wall motion

Nattermann

Pokrovsky

2004

Physica A: Statistical Mechanics and its Applications

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The position of an interface (domain wall) in a medium with random pinning defects is not determined unambiguously by a current value of the driving force even in average. Based on general theory of the interface motion in a random medium we study this hysteresis, different possible shapes of domain walls and dynamical phase transitions between them. Several principal characteristics of the hysteresis, including the coercive force and the curves of dynamical phase transitions obey scaling laws and display a critical behavior in a vicinity of the mobility threshold. At finite temperature the threshold is smeared and a new range of thermally activated hysteresis appears. At a finite frequency of the driving force there exists a range of the non-adiabatic regime, in which not only the position, but also the average velocity of the domain wall displays hysteresis.

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Section: Thermally Activated Creep Of Domain Wallssupporting

confidence: 56%

Hysteresis mediated by a domain wall motion

Nattermann

Pokrovsky

2004

Physica A: Statistical Mechanics and its Applications

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“…In the most naive description, the system can now overcome barriers via thermal activation, leading to a thermally assisted flow 19 and a linear response at small force of the form v ∼ e −∆/T f , where ∆ is some typical barrier. It was realized [20][21][22][23] that because of the glassy nature of the static system, the motion is actually dominated by barriers which diverge as the drive f goes to zero, and thus the flow formula with finite barriers is incorrect. Well below the threshold critical force, the barriers are very high and thus the motion, usually called "creep" is extremely slow.…”

Section: Introductionmentioning

confidence: 99%

Creep and depinning in disordered media

2000

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Elastic systems driven in a disordered medium exhibit a depinning transition at zero temperature and a creep regime at finite temperature and slow drive f . We derive functional renormalization group equations which allow to describe in details the properties of the slowly moving states in both cases. Since they hold at finite velocity v, they allow to remedy some shortcomings of the previous approaches to zero temperature depinning. In particular, they enable us to derive the depinning law directly from the equation of motion, with no artificial prescription or additional physical assumptions, such as a scaling relation among the exponents. Our approach provides a controlled framework to establish under which conditions the depinning regime is universal. It explicitly demonstrates that the random potential seen by a moving extended system evolves at large scale to a random field and yields a self-contained picture for the size of the avalanches associated with the deterministic motion. At finite temperature T > 0 we find that the effective barriers grow with lenghtscale as the energy differences between neighboring metastable states, and demonstrate the resulting activated creep law v ∼ exp −C f −µ /T where the exponent µ is obtained in a ǫ = 4 − D expansion (D is the internal dimension of the interface). Our approach also provides quantitatively a new scenario for creep motion as it allows to identify several intermediate lengthscales. In particular, we unveil a novel "depinning-like" regime at scales larger than the activation scale, with avalanches spreading from the thermal nucleus scale up to the much larger correlation length RV . We predict that RV ∼ T −σ f −λ diverges at small drive and temperature with exponents σ, λ that we determine.

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“…Examples include vortices in type II superconductors, charge density waves (CDW) in solids, stripe phases, Wigner crystals, dislocations in crystals, domain walls in magnets and many others [1]. Having appeared first in the context of dislocation dynamics [2], the scaling theory of glassy dynamic state of random elastic media came to fruition in the context of CDW [3] and vortex lattices in high temperature superconductors [4,3], and enjoyed an impressive success in explaining a wealth of phenomenology of the low temperature vortex state [5]. A closely related subject is the zero temperature depinning transition first studied for CDWs [6,7] and domain walls [8,9].…”

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confidence: 99%

Hysteretic Dynamics of Domain Walls at Finite Temperatures

2001

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Theory of domain wall motion in a random medium is extended to the case when the driving field is below the zero-temperature depinning threshold and the creep of the domain wall is induced by thermal fluctuations. Subject to an ac drive, the domain wall starts to move when the driving force exceeds an effective threshold which is temperature and frequency-dependent. Similarly to the case of zero-temperature, the hysteresis loop displays three dynamical phase transitions at increasing ac field amplitude h0. The phase diagram in the 3-d space of temperature, driving force amplitude and frequency is investigated.Pinning dominated driven dynamics of elastic media in random environment is a paradigm for a vast diversity of physical systems. Examples include vortices in type II superconductors, charge density waves (CDW) in solids, stripe phases, Wigner crystals, dislocations in crystals, domain walls in magnets and many others [1]. Having appeared first in the context of dislocation dynamics [2], the scaling theory of glassy dynamic state of random elastic media came to fruition in the context of CDW [3] and vortex lattices in high temperature superconductors [4,3], and enjoyed an impressive success in explaining a wealth of phenomenology of the low temperature vortex state [5]. A closely related subject is the zero temperature depinning transition first studied for CDWs [6,7] and domain walls [8,9]. Despite the significant recent progress, several key questions specific to glassy dynamics are yet poorly understood. One of such fundamental key issues, although known and extensively studied for more than hundred years in magnets, is hysteresis of interfaces subject to the applied ac drive and related aging and memory effects. A quest for urgent progress in understanding hysteretic behavior of magnetic domain walls is motivated also by emerging technological nano-scale magnetic systems whose ac properties are controlled by the hysteretic dynamics of interfaces.A step towards theoretical description of hysteretic behavior of disordered interfaces has been undertaken in [10], where the cyclic motion of the domain wall at zero temperature under the ac field was investigated and the resulting magnetization hysteretic loop was described. A finite temperature may change drastically the interface dynamics: thermally activated creep motion becomes possible at any small drive.In this Letter we develop a unified description of thermally activated and over-threshold domain wall dynamics in impure magnets. We demonstrate that at finite temperature new scales of length, activation energy and force appear leading to emergence of a new, temperature and frequency-dependent threshold field in the case of ac drive. The latter is the first in a series of dynamical phase transitions. To be specific, we will speak on magnetic domain walls. Accordingly we will be using either of terms "force" or "field" equivalently.

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Dynamics of interfaces and dislocations in disordered media

Cited by 181 publications

References 8 publications

Hysteresis mediated by a domain wall motion

Hysteresis mediated by a domain wall motion

Creep and depinning in disordered media

Hysteretic Dynamics of Domain Walls at Finite Temperatures

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