Dynamics and morphology of chiral magnetic bubbles in perpendicularly magnetized ultra-thin films

Abstract

We study bubble domain wall dynamics using micromagnetic simulations in perpendicularly magnetized ultra-thin films with disorder and Dzyaloshinskii-Moriya interaction. Disorder is incorporated into the material as grains with randomly distributed sizes and varying exchange constant at the edges. As expected, magnetic bubbles expand asymmetrically along the axis of the in-plane field under the simultaneous application of out-of-plane and in-plane fields. Remarkably, the shape of the bubble has a ripple-like part which causes a kink-like (steep decrease) feature in the velocity versus in-plane field curve. We show that these ripples originate due to the nucleation and interaction of vertical Bloch lines. Furthermore, we show that the Dzyaloshinskii-Moriya interaction field is not constant but rather depends on the in-plane field. We also extend the collective coordinate model for domain wall motion to a magnetic bubble and compare it with the results of micromagnetic simulations.

Bloch-to-Néel domain wall transition evinced through morphology of magnetic bubble expansion in Ta/CoFeB/MgO layers

“…4 for films with ID ≤ 12 × 10 18 He + /m 2 , suggesting that the dependence of σ on H x may not be the only modification to the creep law that needs to be considered to explain the influence of H x on bubble expansion in these samples. Some studies have proposed that other effects may be at play, such as a domain width dependence on H x [37,46], DW stiffness [47], or a dependence of the DW depinning field on H x [48]. Interestingly, the data presented in all these works share some features with our left and right velocity curves, such as asymmetry about the minimum velocity and matching velocities in the high field region.…”

“…Matching velocities for up and down portions of the bubble indicate identical internal DW structures, which can only arise if the clockwise/anticlockwise ordering of the DW magnetisation around the bubble is broken. This occurs when vertical Bloch lines nucleate (overcoming the local dipolar energy barrier) and give rise to head-to-head or tail-totail configurations within the DW [22,37].…”

Measuring interfacial Dzyaloshinskii-Moriya interaction in ultra-thin magnetic films

“…They also speculated that nucleation and annihilation of Bloch points may be responsible for a peculiar flattening of magnetic bubbles, which could in turn cause the observed velocity asymmetry. This again was confirmed through micromagnetic simulations by Sarma et al (2018). Pellegren et al (2017) argued that under an applied H x , where the DW energy density σ becomes anisotropic with respect to the DW orientation in the film plane, the correct elastic energy that should be considered to describe the creep regime does not simply identify with σ, as typically assumed in the phenomenological model of creep (Lemerle et al, 1998).…”

“…Several analytical and numerical study were devoted to understand these features. Kim et al (2016a) attributed the asymmetry in the DW energy density σ, to the asymmetric variation of DW width with H x , later confirmed by micromagnetic simulations (Sarma et al, 2018). Lau et al (2016) the described the velocity asymmetry in terms of the Wulff construction, which yields a methodology to determine the shape of a magnetic bubble, although it does not explicitly provide a model for the velocity as a function of in-plane field.…”

Measuring interfacial Dzyaloshinskii-Moriya interaction in ultrathin magnetic films

“…Several analytical and numerical studies were devoted to understanding these features. Kim, Kim, and Choe (2016) attributed the asymmetry in the DW energy density σ to the asymmetric variation of the DW width with H x , which was later confirmed by micromagnetic simulations (Sarma et al, 2018). Lau et al (2016) described the velocity asymmetry in terms of the Wulff construction, which yields a methodology determining the shape of a magnetic bubble, although it does not explicitly provide a model for the velocity as a function of the in-plane field.…”