Scattering of magnetic solitons in two dimensions

Solitons which have the form of a vortex–antivortex pair have recently been found in the Landau–Lifshitz equation which is the standard model for the ferromagnet. We simulate numerically head-on collisions of two vortex–antivortex pairs and observe a right-angle scattering pattern. We offer a resolution of this nontrivial dynamical behavior by examining the Hamiltonian structure of the model, specifically the linear momentum of the two solitons. We further investigate the dynamics of vortices in a modified nonlinear σ-model which arises in the description of antiferromagnets. We confirm numerically that a robust feature of the dynamics is the right-angle scattering of two vortices which collide head-on. A generalization of our theory is given for this model which offers arguments towards an understanding of the observed dynamical behavior.