Critical depinning dynamics of domain walls with internal degrees of freedom

Abstract

The bursty motion of magnetic domain walls (DWs) in disordered ferromagnets, known as Barkhausen noise, exhibits critical behavior in its depinning dynamics, giving rise to universal power laws [1]. For example, the average DW velocity V depends on the external magnetic field B as (B-Bd)θ for a depinning field Bd and a critical exponent θ [2], and the distribution of velocity burst sizes S goes like P(S) ~ S-τ for a critical exponent τ [3]. This is similar to many critical systems in statistical physics, ranging from earthquakes and geophysical flows [4] to dislocation avalanches in plastically deforming crystals [5]. However, current studies exploring the critical depinning dynamics of Barkhausen noise using micromagnetic modeling is severely limited by small system sizes [6]. We develop an effective model for the motion of domain walls in perpendicular magnetic anisotropy (PMA) thin films, by reducing the description of the magnet to a one-dimensional description of the DW, allowing access to large system sizes. For such Bloch-type DWs, the direction of in-plane magnetization is an important dynamical variable that leads to inertial effects in the DW dynamics, such as Walker Breakdown and the formation of Bloch lines (Fig. 1). We consider the critical depinning dynamics of such DWs in quenched disorder. For weak disorder strengths, the internal dynamics are suppressed, so the DW motion reduces to the quenched Edwards-Wilkinson (qEW) equation. With increasing disorder strength, the internal dynamics of the DW become increasingly important, leading to nucleation of Bloch lines. Using our effective model to access large system sizes, we characterize the critical exponents of the depinning problem, and explore the effect of internal dynamics and Bloch lines on the critical behavior.