Discrete Symmetries and Electrodynamic Description of Topological Magnetic Defects - Invited talk by R. Zivieri

The study of topological magnetic defects has received in the last years a great impulse thanks to their technological applications. First, a great deal of work has been devoted to the study of vortex- and anti-vortex configurations in classical ferromagnets. These investigations were stimulated by experimental evidence for the flux-closure configuration developed in circular nanomagnets in the absence of an external magnetic field. Secondly, a few recent works on magnetic skyrmions nucleation in ferromagnetic stripes in the presence of Dzyaloshinskii–Moriya interaction and spin currents (either spin-transfer torque or spin Hall) and an external bias field have inspired a strong interest towards the study of this class of topological magnetic defects and their applications. As for other classes of topological defects investigated in condensed matter physics (e.g. superfluid or superconductor vortices), magnetic defects have a quantized vorticity or topological charge (otherwise called skyrmion number in 3D magnetization textures) and this quantization is typical of these defects treated semi-classically. Here, an electrodynamic description of vortices, anti-vortices and skyrmions as the most representative topological defects in magnetic systems is given. This is accomplished by calculating the circulation, the Amperian current density and the vector potential for every defect studied and for different magnetization textures. It is also shown, by means of simple mathematical and graphical arguments, that the spatial reflection symmetry of a magnetic vortex and of a magnetic skyrmion in the vortex-like configuration, the so-called Bloch skyrmion, is broken by the vortex core magnetization. The analogies and differences with the classical hydrodynamic vortices are highlighted. A topological charge conjugation operator is defined and the physical implications of the corresponding symmetry operation are discussed.