Symmetry Breaking in a Three-Dimensional (3D) Flux-Closure Domain Structure

Abstract

In a submicron-scaled patterned ferromagnetic thin film, a flux-closure magnetization configuration along the pattern boundaries appears on the film plane to reduce the magnetostatic energy while compromising the exchange energy, e.g., a Landau domain structure in a square disk or a vortex structure in a circular disk [1]. As increasing the film thickness, a flux-closure configuration also forms along the thickness direction, resulting in a complex three-dimensional (3D) structure, asymmetric Bloch wall (ABW) with Néel caps [2, 3] as shown in Fig. 1(a). In this system, there are two degenerate states of ABWs whose rotating sense is clockwise (CW) or counter-clockwise (CCW) as shown in the insets of Fig. 1(a). By utilizing magnetic transmission soft X-ray microscopy (MTXM) [4], we observe that a simple Landau domain structure in a square disk transforms to an ABW structure as shown in Fig. 1(b). I.e., symmetric vortex core structure at the center of Landau domain is shifted along +y direction by an external in-plane magnetic field along +x direction and it abruptly transformed to the ABW structure. Surprisingly, we found the symmetry breaking in this transition; top and bottom vortex core structures are always separated to +x and –x directions, respectively. As a result, the rotation sense of the ABW is always CCW. In contrast, the opposite sense of ABW is formed when the magnetic field applied –x direction. From these results accompanying with micromagnetic simulations, we conclude that the energy states of ABW with opposite rotating sense are not the degenerate states anymore and energetically flavored orientation might be determined by the position of transformation.