S. Komineas
Physikalisches Institut, Universitat Bayreuth
D-95440 Bayreuth, Germany
Abstract
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 ferromagnetic solitons and observe
a right angle scattering pattern which is familiar
from relativistic models. We offer a resolution of this
highly nontrivial dynamical behavior by examining the Hamiltonian
structure of the model, specifically the linear momentum
of the two solitons.
We also investigate the dynamics of vortices in a modified
nonlinear $\sigma$ 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 nontrivial generalization of our theory is given for
this relativistic model which leads to an understanding of the
observed dynamical behavior of vortices.