  This work is devoted to the study of how spin texture excitations are
affected by the presence of a static nonmagnetic impurity whenever they lie on
a conical support. We realize a number of novelties as compared to the flat
plane case. Indeed, by virtue of the conical shape, the interaction potential
between a soliton and an impurity appears to become stronger as long as the
cone is tighten. As a consequence, a new kind of solitonic excitation shows up
exhibiting lower energy than in the absence of such impurity. In addition, we
conclude that such an energy is also dependent upon conical aperture, getting
lower values as the latter is decreased. We also discuss how an external
magnetic field (Zeeman coupling) affects static solitonic textures, providing
instability to their structure.
