We study Heisenberg model of classical spins lying on the toroidal support, whose internal and external radii are r and R, respectively. The isotropic regime is characterized by a fractional soliton solution. Whenever the torus size is very large, R → ∞, its charge equals unity and the soliton effectively lies on an infinite cylinder. However, for R = 0 the spherical geometry is recovered and we obtain that configuration and energy of a soliton lying on a sphere. Vortex-like configurations are also supported: in a ring torus (R > r) such excitations present no core where energy could blow up. At the limit R → ∞ we are effectively describing it on an infinite cylinder, where the spins appear to be practically parallel to each other, yielding no net energy. On the other hand, in a horn torus (R = r) a singular core takes place, while for R < r (spindle torus) two such singularities appear. If R is further diminished until vanish we recover vortex configuration on a sphere.

The energetics associated to the ferromagnetic, vortex, and onionlike magnetization configurations are explicitly computed in the toroidal geometry. The analysis reveals that the vortex appears to be the most prominent of such states, minimizing total energy in every torus with internal radius r≳10 nm, or even in smaller ones provided that R/ℓex≳1.5 (R is the torus external radius and ℓex is the exchange length). This possibility of having very small nanomagnets comprising a vortex-type state, might have importance in higher density binary logic and/or storage and in novel mechanisms for cancer therapy applications.

Understanding the domain wall dynamics is an important issue in modern magnetism. Here we present results of domain wall displacement in curved cylindrical nanowires at a constant magnetic field. We show that the average velocity of a transverse domain wall increases with curvature. Contrary to what it is observed in stripes, in a curved wire the transverse domain wall oscillates along and rotates around the nanowire with the same frequency. These results open the possibility of new oscillation-based applications.