The dynamics of micrometer-sized magnetic domains in ultra-thin ferromagnetic films is so dramatically slowed down by quenched disorder that the spontaneous elastic tension collapse becomes unobservable at ambient temperature. By magneto-optical imaging we show that a weak zero-bias AC magnetic field can assist such curvature-driven collapse, making the area of a bubble to reduce at a measurable rate, in spite of the negligible effect that the same curvature has on the average creep motion driven by a comparable DC field. An analytical model explains this phenomenon quantitatively.
Ferroelectric switching and nanoscale domain dynamics were investigated using atomic force microscopy on monocrystalline Pb(Zr0.2Ti0.8)O3 thin films. Measurements of domain size versus writing time reveal a two-step domain growth mechanism, in which initial nucleation is followed by radial domain wall motion perpendicular to the polarization direction. The electric field dependence of the domain wall velocity demonstrates that domain wall motion in ferroelectric thin films is a creep process, with the critical exponent mu close to 1. The dimensionality of the films suggests that disorder is at…
We study the ultra slow domain wall motion in ferromagnetic thin films driven by a weak magnetic field. Using time resolved magneto-optical Kerr effect microscopy, we access to the statistics of the intermittent thermally activated domain wall jumps between deep metastable states. Our observations are consistent with the existence of creep avalanches: roughly independent clusters with broad size and ignition waiting-time distributions, each one composed by a large number of spatio-temporally correlated thermally activated elementary events. Moreover, we evidence that the large scale geometry o…
With Monte Carlo simulations, we study the creep motion of a domain wall in the two-dimensional random-field Ising model with a driving field. We observe the nonlinear fieldvelocity relation, and determine the creep exponent μ. To further investigate the universality class of the creep motion, we also measure the roughness exponent ζ and energy barrier exponent ψ from the zero-field relaxation process. We find that all the exponents depend on the strength of disorder.
We report piezo-response force microscopy studies of the static and dynamic properties of domain walls (DWs) in 11 to 36 nm thick films of crystalline ferroelectric poly(vinylidene-fluoride-trifluorethylene). The DW roughness exponent ζ ranges from 0.39 to 0.48 and the DW creep exponent μ varies from 0.20 to 0.28, revealing an unexpected effective dimensionality of ~1.5 that is independent of film thickness. Our results suggest predominantly 2D ferroelectricity in the layered polymer and we attribute the fractal dimensionality to DW deroughening due to the correlations between the in-plane and…
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…
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…
Atomic force microscopy was used to investigate ferroelectric switching and nanoscale domain dynamics in epitaxial PbZr0.2Ti0.8O3 thin films. Measurements of the writing time dependence of domain size reveal a two-step process in which nucleation is followed by radial domain growth. During this growth, the domain wall velocity exhibits a v ~ exp[-(1/E)^mu] dependence on the electric field, characteristic of a creep process. The domain wall motion was analyzed both in the context of stochastic nucleation in a periodic potential as well as the canonical creep motion of an elastic manifold in a d…
Magnetic field driven domain wall velocities in [Co/Ni] based multilayers thin films have been measured using polar magneto-optic Kerr effect microscopy. The low field results are shown to be consistent with the universal creep regime of domain wall motion, characterized by a stretched exponential growth of the velocity with the inverse of the applied field. Approaching the depinning field from below results in an unexpected excess velocity with respect to the creep law. We analyze these results using scaling theory to show that this speeding up of domain wall motion can be interpreted as due …
We present a quantitative and comparative study of magnetic field driven domain wall depinning transition in different ferromagnetic ultrathin films over a wide range of temperature. We reveal a universal scaling function accounting for both drive and thermal effects on the depinning transition, including critical exponents. The consistent description we obtain for both the depinning and subthreshold thermally activated creep motion should shed light on the universal glassy dynamics of thermally fluctuating elastic objects pinned by disordered energy landscapes.
The static configuration of ferroelectric domain walls was investigated using atomic force microscopy on epitaxial PbZr0.2Ti0.8O3 thin films. Measurements of domain wall roughness reveal a power law growth of the correlation function of relative displacements B(L) ~ L^(2zeta) with zeta ~ 0.26 at short length scales L, followed by an apparent saturation at large L. In the same films, the dynamic exponent mu was found to be ~ 0.6 from independent measurements of domain wall creep. These results give an effective domain wall dimensionality of d=2.5, in good agreement with theoretical calculations…
The thermally activated creep motion of an elastic interface weakly driven on a disordered landscape is one of the best examples of glassy universal dynamics. Its understanding has evolved over the last 30 years thanks to a fruitful interplay between elegant scaling arguments, sophisticated analytical calculations, efficient optimization algorithms and creative experiments. In this article, starting from the pioneer arguments, we review the main theoretical and experimental results that lead to the current physical picture of the creep regime. In particular, we discuss recent works unveiling t…
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…
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 $h_0$. The phase diagram in the 3-d space of temperature, driving force amplitude and freque…
We report a comparative study of magnetic field driven domain wall motion in thin films made of different magnetic materials for a wide range of field and temperature. The full thermally activated creep motion, observed below the depinning threshold, is shown to be described by a unique universal energy barrier function. Our findings should be relevant for other systems whose dynamics can be modeled by elastic interfaces moving on disordered energy landscapes.
Magnetic field-driven domain wall motion in an ultrathin Pt/Co(0.45nm)/Pt ferromagnetic film with perpendicular anisotropy is studied over a wide temperature range. Three different pinning dependent dynamical regimes are clearly identified: the creep, the thermally assisted flux flow and the depinning, as well as their corresponding crossovers. The wall elastic energy and microscopic parameters characterizing the pinning are determined. Both the extracted thermal rounding exponent at the depinning transition, $ψ=$0.15, and the Larkin length crossover exponent, $ϕ=$0.24, fit well with the numer…
We explore universal behaviors of magnetic domain wall driven by the spin-transfer of an electrical current, in a ferromagnetic (Ga,Mn)(As,P) thin film with perpendicular magnetic anisotropy. For a current direction transverse to domain wall, the dynamics of the thermally activated creep regime and the depinning transition are found to be compatible with a self-consistent universal description of magnetic field induced domain wall dynamics. This common universal behavior, characteristic of the so-called quenched Edwards-Wilkinson universality class, is confirmed by a complementary and independ…
We discuss the universal dynamics of elastic interfaces in quenched random media. We focus in the relation between the rough geometry and collective transport properties in driven steady-states. Specially devised numerical algorithms allow us to analyze the equilibrium, creep, and depinning regimes of motion in minimal models. The relevance of our results for understanding domain wall experiments is outlined.
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…
