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The dynamics of N point vortices in a fluid is described by the Helmholtz-Kirchhoff (HK) equations which lead to a completely integrable Hamiltonian system for N=2 or 3 but chaotic dynamics for N>3. Here we consider a generalization of the HK equations to describe the dynamics of magnetic vortices within a collective-coordinate approximation. In particular, we analyze in detail the dynamics of a system of three magnetic vortices by a suitable generalization of the solution for three point vortices in an ordinary fluid obtained by Groebli more than a century ago. The significance of our results for the dynamics of ferromagnetic elements is briefly discussed.
Recent acoustic and electrical-circuit experiments have reported the third-order (or octupole) topological insulating phase, while its counterpart in classical magnetic systems is yet to be realized. Here we explore the collective dynamics of magneti
We propose an alternative route to engineer Majorana zero modes (MZMs), which relies on inducing shift or spin vortex defects in magnetic textures which microscopically coexist or are in proximity to a superconductor. The present idea applies to a va
Model of quantum depinning of magnetic vortex cores from line defects in a disk geometry and under the application of an in-plane magnetic field has been developed within the framework of the Caldeira-Leggett theory. The corresponding instanton solut
The continuous need for miniaturization and increase in device speed exerts pressureon the electronics industry to explore new avenues of information processing. One possibility is to use the spin to store, manipulate and carry information. Indeed,sp
The increasing need to store large amounts of information with an ultra-dense, reliable, low power and low cost memory device is driving aggressive efforts to improve upon current perpendicular magnetic recording technology. However, the difficulties