The effective theory for the microstructure in antiferromagnets in the continuum limit is given by a nonlinear sigma model. We consider an antiferromagnet with the chiral Dzyaloshinskii-Moriya (DM) interaction. This is instrumental for the stabilisation of a spiral solution in one dimension and of skyrmions, that are topological magnetic solitons, in two dimensions.

In addition, the chiral interaction has a profound effect on the magnetization dynamics. In the first example, we show that skyrmions exhibit solitary wave behavior in antiferromagnets, in stark contrast to ferromagnets. The relativistic limit is linked to the spiral phase transition. In the second example, we describe nonlinear oscillations of the skyrmion radius (breathing). We show that a skyrmion can eventually collapse by a singularity formation in finite time due to internal (breathing) dynamics.

Furthermore, we will discuss the relation of our results to (a) fractons in higher-rank gauge theories, (b) merons that where proposed as a mechanism for quark confinement. Also, (c) we will discuss problems related to the numerical simulation of the sigma model.

Stavros Komineas obtained his Diploma in Physics from the University of Patras (Greece) in 1990 and his MSc and PhD in Theoretical Physics from the Department of Physics at the University of Crete in 1997 (Greece). From 1998 until 2002, he was a postdoctoral researcher at the University of Bayreuth, Germany. From 2002 until 2006 he was an EPSRC postdoctoral fellow at the Cavendish Laboratory, University of Cambridge, U.K., and from 2006 until 2008, a postdoctoral researcher at the Max-Planck-Institute for the Physics of Complex Systems in Dresden, Germany. He joined the Department of Applied Mathematics of the University of Crete as an Assistant Professor in 2008.

He is currently an Associate Professor at the Department of Mathematics and Applied Mathematics of the University of Crete and associate faculty member of the Institute of Applied and Computational Mathematics (IACM) of the Foundation for Research and Technology - Hellas (FORTH).

His research interests lie on field theories and mathematical modeling in condensed matter. He focuses on topological solitons (such as vortices and skyrmions) and their dynamics in magnetic materials. He has further extensively worked on solitons, quantized vortices, and vortex rings in Bose-Einstein condensates. A large part of his work lies at the interface of Physics and Applied Mathematics.