Thermal rounding of the depinning transition

Abstract

PACS 64.60.Ht -Dynamic critical phenomena PACS 75.60.Ch -Domain walls and domain structure PACS 05.70.Ln -Nonequilibrium and irreversible thermodynamicsAbstract. -We study thermal effects at the depinning transition by numerical simulations of driven one-dimensional elastic interfaces in a disordered medium. We find that the velocity of the interface, evaluated at the critical depinning force, can be correctly described with the power law v ∼ T ψ , where ψ is the thermal exponent. Using the sample-dependent value of the critical force, we precisely evaluate the value of ψ directly from the temperature dependence of the velocity, obtaining the value ψ = 0.15 ± 0.01. By measuring the structure factor of the interface we show that both the thermally-rounded and the T = 0 depinning, display the same large-scale geometry, described by an identical divergence of a characteristic length with the velocity ξ ∝ v −ν/β , where ν and β are respectively the T = 0 correlation and depinning exponents. We discuss the comparison of our results with previous estimates of the thermal exponent and the direct consequences for recent experiments on magnetic domain wall motion in ferromagnetic thin films.

Thermal rounding exponent of the depinning transition of an elastic string in a random medium

“…For the experimentally relevant case of (1 + 1)-dimensional elastic interfaces moving in a random-bond disorder environment with short-range correlations and short-range elasticity, we have recently reported the value ψ = 0.15 ± 0.01 using Langevin dynamics numerical simulations [30]. This value compares well with the value ψ = 0.16 reported in Ref.…”

“…On the other hand, at forces around the critical value, F ≈ F c , a finite temperature value smears out the transition, which is no longer abrupt. This thermal rounding of the depinning transition can be characterized, exactly at the critical force F = F c , by a power-law vanishing of the velocity with the temperature as V ∼ T ψ , with ψ the thermal rounding exponent [24][25][26][27][28][29][30].…”

Nanoscale studies of ferroelectric domain walls as pinned elastic interfaces

“…At high driving forces, when the interface energy is well above the microscopic details of the disorder landscape, standard linear flow is recovered with v ∼ F , with the pinning contributing essentially a viscous drag. In real systems at finite temperature T > 0, the sharp depinning transition becomes thermally rounded [40]. Thermal activation also allows a quasistatic response to subcritical forces F << F C , where the energy optimisation as a segment of the interface is displaced in the corresponding conjugate field must be balanced against the energy cost of increased interface surface, as well as depolarising and dipolar energies, as appropriate.…”

“…Although no complete solution exists to date to the equations describing the full dynamics of the interface at finite temperature [168], advanced numerical simulations exploring thermal rounding of the dynamic response [40] have allowed accurate predictions of the depinning exponent θ for one-and two-dimensional interfaces in random bond and random field disorder. In addition, these studies suggest superroughening of the interface, with ζ > 1 at depinning [169], although with nonetheless apparently mono-affine scaling.…”

Intrinsic anomalous scaling in a ferromagnetic thin film model

“…states of quiescence alternated with avalanches, before reaching the phase state of moving or pinning. Until today, theoretical approaches to explain the depinning transition of the MDW into disordered medium pushed by an external magnetic field, are based on: (a) the continuous equation of Edwards-Wilkinson with quenched noise (QEW) [29][30][31][32] and (b) discrete models based on microscopic structures and interactions, such as random-field Ising field model with driving (DRFIM) [33][34][35][36][37].…”