  Curved magnetic architectures are key enablers of the prospective magnetic
devices with respect to size, functionality 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
constant width and thickness, which does not correspond in many cases to
specificity of experimental sample preparation. Here, we put forth a
self-consistent micromagnetic framework of curvilinear magnetism of nanowires
and narrow stripes with 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 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.
