Tailoring the energy landscape of a bloch point domain wall with curvature.

Topological defects, or singularities, play a key role in the statics and dynamics of complex systems. In magnetism, Bloch point singularities represent point defects that mediate the nucleation of textures such as skyrmions and hopfions. While these textures are typically stabilised in chiral magnets, the influence of chirality and symmetry breaking on Bloch point singularities remains relatively unexplored. Here, we harness advanced three-dimensional nanofabrication to explore the influence of symmetry breaking on Bloch point textures by introducing controlled nano-curvature in a ferromagnetic nanowire. Combining X-ray magnetic microscopy with the application of in situ magnetic fields, we demonstrate that Bloch point singularity-containing domain walls are stabilised in straight regions of the sample, and determine that curvature can be used to tune the energy landscape of the Bloch points. Not only are we able to pattern pinning points but, by controlling the gradient of curvature, we define asymmetric potential wells to realise a robust Bloch point texture shift-register with non-reciprocal behaviour. These insights into the influence of symmetry on singularities offer a route to the controlled nucleation and propagation of topological textures, providing opportunities for logic and computing devices.