Heisenberg-like spins lying on the pseudosphere (a 2-dimensional infinite space with constant negative curvature) cannot give rise to stable soliton solutions. Only fractional solutions can be stabilized on this surface provided that at least a hole is incorporated. We also address the issue of 'in-plane' vortices, in the XY regime. Interestingly, the energy of a single vortex no longer blows up as the excitation spreads to infinity. This yields a non-confining potential between a vortex and a antivortex at large distances so that the pair may dissociate at arbitrarily low temperature. *

We investigate the influence of artificial defects ͑small holes͒ inserted into magnetic nanodisks on the vortex core dynamics. One and two holes ͑antidots͒ are considered. In general, the core falls into the hole; but, in particular, we would like to note an interesting phenomenon not yet observed, which is the vortex core switching induced by the vortex hole interactions. It occurs for the case with only one hole and for very special conditions involving the hole size and position as well as the disk size. Any small deformation in the disk geometry such as the presence of a second antidot completely changes the vortex dynamics, and the vortex core eventually falls into one of the defects. After trapped, the vortex center still oscillates with a very high frequency and small amplitude around the defect center.

Defects introduced in ferromagnetic nanodisks may deeply affect the structure and dynamics of stable vortex-like magnetization. Here, analytical techniques are used for studying, among other dynamical aspects, how a small cylindrical cavity modify the oscillatory modes of the vortex. For instance, we have realized that if the vortex is nucleated out from the hole its gyrotropic frequencies are shifted below. Modifications become even more pronounced when the vortex core is partially or completely captured by the hole. In these cases, the gyrovector can be partially or completely suppressed, so that the associated frequencies increase considerably, say, from some times to several powers. Possible relevance of our results for understanding other aspects of vortex dynamics in the presence of cavities and/or structural defects are also discussed. Pacs: 75.75.+a; 75.70.Rf

We study the Heisenberg Model on cylindrically symmetric curved surfaces. Two kinds of excitations are considered. The first is given by the isotropic regime, yielding the sine-Gordon equation and π-solitons are predicted. The second one is given by the XY model, leading to a vortex turning around the surface. Helical states are also considered, however, topological arguments can not be used to ensure its stability. The energy and the anisotropy parameter which stabilizes the vortex state are explicitly calculated for two surfaces: catenoid and hyperboloid. The results show that the anisotropy and the vortex energy depends on the underlying geometry.