Taking into account the coupling between the position of the wall and an internal degree of freedom, namely its phase $ϕ$, we examine, in the rigid wall approximation, the dynamics of a magnetic domain wall subject to a weak pinning potential. We determine the corresponding force-velocity characteristics, which display several unusual features when compared to standard depinning laws. At zero temperature, there exists a bistable regime for low forces, with a logarithmic behavior close to the transition. For weak pinning, there occurs a succession of bistable transitions corresponding to different topological modes of the phase evolution. At finite temperature, the force-velocity characteristics become non-monotonous. We compare our results to recent experiments on permalloy nanowires.
Magnetic field driven domain wall dynamics in a ferrimagnetic GdFeCo thin film with perpendicular magnetic anisotropy is studied using low temperature magneto-optical Kerr microscopy. Measurements performed in a practically athermal condition allow for the direct experimental determination of the velocity ($ β= 0.30 \pm 0.03 $) and correlation length ($ ν= 1.3 \pm 0.3 $) exponents of the depinning transition. The whole family of exponents characterizing the transition is deduced, providing evidence that the depinning of magnetic domain walls is better described by the quenched Edwards-Wilkinso…
Domain wall dynamics in ferromagnets is complicated by internal degrees of freedom of the domain walls. We develop a model of domain walls in disordered thin films with perpendicular magnetic anisotropy capturing such features, and use it to study the depinning transition. For weak disorder, excitations of the internal magnetization are rare, and the depinning transition takes on exponent values of the quenched Edwards-Wilkinson equation. Stronger disorder results in disorder-dependent exponents concurrently with nucleation of an increasing density of Bloch lines within the domain wall.
We report first principle numerical study of domain wall (DW) depinning in two-dimensional magnetic film, which is modeled by 2D random-field Ising system with the dipole-dipole interaction. We observe nonconventional activation-type motion of DW and reveal its fractal structure of DW near the depinning transition. We determine scaling functions describing critical dynamics near the transition and obtain universal exponents establishing connection between thermal softening of pinning potential and critical dynamics. We observe that tuning the strength of the dipole-dipole interaction switches …
We study adsorption at periodically corrugated substrates formed by scoring rectangular grooves into a planar solid wall which interacts with the fluid via long-range (dispersion) forces. The grooves are assumed to be macroscopically long but their depth, width and separations can all be molecularly small. We show that the entire adsorption process can be divided into three parts consisting of (i) \emph{filling} the grooves by a capillary liquid; (ii) \emph{depinning} of the liquid-gas interface from the wall edges; and (iii) \emph{unbinding} of the interface from the top of the wall, which is…
Dynamics of a ferromagnetic domain wall: avalanches, depinning transition and the Barkhausen effect
研究了在外加磁场作用下，无序介质中铁磁畴壁的动力学行为。钉扎结构之间的畴壁的雪崩式运动产生了称为巴克豪森效应的噪声。我们讨论了软铁磁材料的实验结果，参考畴结构和样品的几何形状，并报告巴克豪森噪声测量Fe $_{21}$ Co $_{64}$ B $_{15}$非晶合金。我们建立了一个柔性畴壁的运动方程，随着电场的增加，畴壁呈现出退钉扎的转变。长程偶极相互作用被示出设置上临界尺寸为$d_c=3$，这意味着平均场指数（可能的对数校正），预计描述巴克豪森效应。我们介绍了一个平均场的无限范围模型，并表明它是等效于以前介绍的单自由度模型，已知重现几个实验结果。我们在$d=3$中数值模拟了方程，证实了理论预测。我们计算的雪崩分布的磁场驱动率和退磁场的强度的函数。标度指数与驱动率成线性关系，而分布的截止点由退磁场决定，与实验结果非常吻合。
Magnetic domain wall motion is at the heart of new magneto-electronic technologies and hence the need for a deeper understanding of domain wall dynamics in magnetic systems. In this context, numerical simulations using simple models can capture the main ingredients responsible for the complex observed domain wall behavior. We present a scalar-field model for the magnetization dynamics of quasi-two-dimensional systems with a perpendicular easy axis of magnetization which allows a direct comparison with typical experimental protocols, used in polar magneto-optical Kerr effect microscopy experime…
We propose a kind of Ginzburg--Landau equation with quenched randomness. There is a pinning--depinning transition in the system when the external magnetic force is changed. The transition is self-organized when the external magnetic field is slowly changed under the demagnetizing effect. The total magnetization increases stepwise and the probability distribution of the increase in the total magnetization approximately obeys a power law. A hysteresis loop is obtained when the external magnetic field is changed reciprocally. In our model, the coercivity in the magnetization curve is expressed as…
Domain-wall dynamics and spatial fluctuations are closely related to each other and to universal features of disordered systems. Experimentally measured roughness exponents characterizing spatial fluctuations have been reported for magnetic thin films, with values generally different from those predicted by the equilibrium, depinning and thermal reference states. Here, we study the roughness of domain walls in GdFeCo thin films over a large range of magnetic field and temperature. Our analysis is performed in the framework of a model considering length-scale crossovers between the reference st…
We study the low temperature phase equilibria of a fluid confined in an open capillary slit formed by two parallel walls separated by a distance $L$ which are in contact with a reservoir of gas. The top wall of the capillary is of finite length $H$ while the bottom wall is considered of macroscopic extent. This system shows rich phase equilibria arising from the competition between two different types of capillary condensation, corner filling and meniscus depinning transitions depending on the value of the aspect ratio $a=L/H$ and divides into three regimes: For long capillaries, with $a<2/π$,…
We study complete wetting of solid walls that are patterned by parallel nanogrooves of depth $D$ and width $L$ with a periodicity of $2L$. The wall is formed of a material which interacts with the fluid via a long-range potential and exhibits first-order wetting transition at temperature $T_w$, should the wall is planar. Using a non-local density functional theory we show that at a fixed temperature $T>T_w$ the process of complete wetting depends sensitively on two microscopic length-scales $L_c^+$ and $L_c^-$. If the corrugation parameter $L$ is greater than $L_c^+$, the process is continuous…
In presence of impurities, ferromagnetic and ferroelectric domain walls slide only above a finite external field. Close to this depinning threshold, they proceed by large and abrupt jumps, called avalanches, while, at much smaller field, these interfaces creep by thermal activation. In this work we develop a novel numerical technique that captures the ultra-slow creep regime over huge time scales. We point out the existence of activated events that involve collective reorganizations similar to avalanches, but, at variance with them, display correlated spatio-temporal patterns that resemble the…
Pinning and thermal creep determine the response of numerous systems containing superstructures, e.g., vortices in type II superconductors, domain walls in ferroics, or dislocations in metals. The combination of drive and thermal fluctuations lead to the superstructure's depinning and its velocity $v$ determines the electric, magnetic, or mechanical response. It is commonly believed that pinning and creep collapse above the critical drive $F_c$, entailing a sharp rise in the velocity $v$. We challenge this perception by studying the effects of thermal fluctuations within the framework of stron…
The creep motion of domain walls driven by external fields in magnetic thin films is described by universal features related to the underlying depinning transition. One key parameter in this description is the roughness exponent characterizing the growth of fluctuations of the domain wall position with its longitudinal length scale. The roughness amplitude, which gives information about the scale of fluctuations, however, has received less attention. Albeit their relevance, experimental reports of the roughness parameters, both exponent and amplitude, are scarce. We report here experimental va…
We study the phase equilibria of a fluid confined in an open capillary slit formed when a wall of finite length $H$ is brought a distance $L$ away from a second macroscopic surface. This system shows rich phase equilibria arising from the competition between two different types of capillary condensation, corner filling and meniscus depinning transitions depending on the value of the aspect ratio $a=L/H$. For long capillaries, with $a<2/π$, the condensation is of type I involving menisci which are pinned at the top edges at the ends of the capillary characterized by an edge contact angle. For i…
Along with experiments, numerical simulations are key to gaining insight into the underlying mechanisms governing domain wall motion in thin ferromagnetic systems. However, a direct comparison between numerical simulation of model systems and experimental results still represents a great challenge. Here, we present a tuned Ginzburg-Landau model to quantitatively study the dynamics of domain walls in quasi two-dimensional ferromagnetic systems with perpendicular magnetic anisotropy. This model incorporates material and experimental parameters and the micromagnetic prescription for thermal fluct…
We present a theoretical study aimed to elucidate the origin of the inverse symmetry breaking transition observed in ultrathin magnetic films with perpendicular anisotropy. We study the behavior of the dipolar frustrated Ising model in a mean field approximation as well as two other models with simple domain walls. By a numerical analysis we show that the internal degrees of freedom of the domain walls are decisive for the presence of the inverse symmetry breaking transition. In particular, we show that in a sharp domain wall model the inverse transition is absent. At high temperatures the add…
