Magnetic domain wall creep and depinning: A scalar field model approach

Abstract

Magnetic domain wall motion is at the heart of new magnetoelectronic 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 experiments. We show that the thermally activated creep and depinning regimes of domain wall motion can be reached and the effect of different quenched disorder implementations can be assessed with the model. In particular, we show that the depinning field increases with the mean grain size of a Voronoi tessellation model for the disorder.

Degradation of domains with sequential field application

“…Motivated by recent experimental observations of pronounced domain area reduction under the application of alternating magnetic fields in ferromagnetic thin films [8], hitherto not predicted theoretically, we propose a numerical protocol to study the same effect in a very simple two-dimensional scalar-field model. The model only considers the main and basic ingredients of ferromagnetic systems [31], and has the advantage of being material-independent (no physical units need to be specified a priori). Its simplicity allows us to do extremely long simulations to study domain area loss under several combinations of magnetic pulses.…”

“…In the case we are interested in, i.e. ferromagnetic thin films with perpendicular magnetic anisotropy, as discussed in detail in [31], ϕ represents the normalized projection of the magnetization along the easy axis. η is a damping parameter, T the temperature of the system, H is a force acting at each position ⃗ r in the system, that represents an external magnetic field favoring the +1 state, and α and γ are constants proportional to the out-of-plane magnetic anisotropy and the exchange stiffness, respectively.…”

“…For ε = 1, the velocity-field response of a domain with these characteristics was shown to display a depinning field H d ≃ 0.0598 [31]. For the nucleation-equivalent step, we define an initial circular domain of radius R i = 100, and we let it grow until it reaches a radius R 0 = 500 under the application of a field H i = 0.06 at T = 0.01.…”

“…The great advantage of Ginzburg-Landau type models is that domain properties may be studied in combination with interface characteristics in a very simple way. Typical protocols used in experiments to observe ferromagnetic domains in ultrathin films may be emulated, and effects in the different dynamical regimes may be studied [31]. Moreover, this simplistic description allows us the exploration of system sizes which are comparable to experimental ones [33].…”

Microscopic interplay of temperature and disorder of a one-dimensional elastic interface

“…A possible cause can be that the AC field effectively increases the disorder correlation length in the sample, thus unveiling the B(r) ∼ r 2ζ dis regime. It is worth investigating the existence of such scaling regime in interfaces, and to test its robustness to features such as overhangs (for instance in disordered Ginzburg-Landau models [67], known to reduce to qEW in some limit [57]). Adding a driving force generates a small velocity in a non-linear so-called 'creep regime', whose scaling is controlled by the static geometrical exponents.…”