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An array of spin torque nano-oscillators (STNOs), coupled by dipolar interaction and arranged on a ring, has been studied numerically and analytically. The phase patterns and locking ranges are extracted as a function of the number $N$, their separation, and the current density mismatch between selected subgroups of STNOs. If $N\geq 6$ for identical current densities through all STNOs, two degenerated modes are identified an in-phase mode (all STNOs have the same phase) and an out-of-phase mode (the phase makes a 2$\pi$ turn along the ring). When inducing a current density mismatch between two subgroups, additional phase shifts occur. The locking range (maximum current density mismatch) of the in-phase mode is larger than the one for the out-of-phase mode and depends on the number $N$ of STNOs on the ring as well as on the separation. These results can be used for the development of magnetic devices that are based on STNO arrays.

A detailed analytic and numerical analysis of the interaction between two bubble skyrmions has been carried out. Results from micromagnetic calculations show a strong dependence of the parameters of the skyrmion magnetic profile as a function of the magnetostatic interaction. The magnetic core and edge-width sizes of the skyrmion increase or decrease depending on the relative position between the skyrmions and the uniaxial perpendicular anisotropy. In particular, when a magnetic disk is over another, there is a transition from a Bloch-like skyrmion configuration to a N\'{e}el-like skyrmion configuration as the distance between the disks decreases. This transition is due to the magnetostatic interaction between them. Therefore, it is possible to stabilize a bubble skyrmion with a N\'{e}el configuration without the Dzyaloshinskii-Moriya interaction. Thus, these results can be used for the parameters control of the skyrmions in magnetic spintronic devices that need to use these configurations.

Magnetic nanotubes have been widely studied because they are promising candidates to be part in devices based on spintronic and magnonic technologies. However, the experimental techniques used to prepare these elements could not guarantee to have perfect nanostructures. Therefore, some geometric imperfections can appear. In this direction, the bent of a nanotube could play an essential role in the magnetic properties of a device. In this work, we analyze the influence of curvature on the magnetic properties of a bent nanotube, a topic scarcely studied, and that can have a strong impact on applications., Comment: 17 pages