Dzyaloshinskii Domain Wall Creep INVITED

Abstract

The discovery of a significant interfacial Dzyaloshinskii-Moriya Interaction (iDMI) in multi-layer thin films launched a fervent research effort into its impact on the behavior of chiral magnetic objects including domain walls (DWs).[1] The field driven creep of these Dzyaloshinskii domain walls as observed by Kerr microscopy remains a popular tool for evaluating the strength of the iDMI, but results are notoriously challenging to interpret.In this talk, we focus on experimental and theoretical investigations into the asymmetric field-driven expansion of magnetic domains in thin films with iDMI, which provide a fascinating landscape to understand creep of 1D elastic manifolds with an internal order parameter.[2] We will review early models of creep based on the DW energy, which matched well with certain experimental observations – namely, that an in-plane field (Hx) coupled with a perpendicular driving field (Hz) leads to asymmetric expansion of the domain as well as minima in the plot of x-velocity vs Hx. However, other common observations were not explained by this model including that, at large values of Hx, the high energy wall orientations reached or exceeded the velocity of low energy orientations. To explain this, Pellegren at el considered the more general elastic energy of the DW, given by the stiffness [σ(θ) + σ''(θ)].[3] By introducing a dispersive stiffness, which accounts for the finite lengthscale over which the wall deforms, it was indeed shown that the elastic energy of opposite extrema on the domain converge as Hx → ∞. This more general model explains some of the features that have also been explained by an attempt frequency that depends on wall chirality (via a chiral damping parameter).[4] The possible role of chiral damping will be discussed briefly.In more recent experiments, Brock et al showed that, in some cases – especially for weak DMI, the domain adopts a highly preferred growth direction with a dendritic structure that is neither parallel or anti-parallel to Hx.[5] The results cannot be explained by a chiral Bloch component to the DW, which would violate the symmetry of the system. Instead, we identify a steady-state DW substructure that results from the z-field torque on the internal DW magnetization (see figure 1c). This breaks the energetic mirror symmetry along the x-axis and leads to orientations of the DW with vanishing elastic energy (i.e. rapidly increased creep velocity). Remarkable agreement between an augmented form of the dispersive stiffness model (now accounting for steady-state configurations) and the experimental measurements is found. The material parameters that give rise to this seemingly anomalous behavior will be discussed. Other important factors such as internal DW excitations, field-dependent pinning, and a field-dependent DW width will be considered in this presentation as well. **