Control of magnetic response in curved stripes by tailoring the cross section

Curved magnetic architectures are key enablers of prospective magnetic devices with respect to size, func-tionality, and speed. By exploring geometry-governed magnetic interactions, curvilinear magnetism offers a number of intriguing effects in curved magnetic wires and curved magnetic films. The applicability of the current micromagnetic theory requires that the sample has a constant width and thickness, which does not correspond in many cases to the specificity of experimental sample preparation. Here, we put forth a self-consistent micromagnetic framework of the curvilinear magnetism of nanowires and narrow stripes with a spatially inhomogeneous cross section. The influence of the varying cross section is exploited and illustrated by an example of the simplest topological texture, which is a transversal head-to-head (tail-to-tail) domain wall. The cross-section gradient becomes a source of domain wall pinning which competes with the curvature gradient. Eigenfrequencies of the domain wall free oscillations at the pinning potential are determined by both curvature and cross-section gradients. Prospects for curvilinear magnonics and spintronics are discussed.