Magnetic bubble refraction and quasibreathers in inhomogeneous antiferromagnets

Abstract

The dynamics of magnetic bubble solitons in a two-dimensional isotropic antiferromagnetic spin lattice is studied, in the case where the exchange integral J(x,y) is position dependent. In the near continuum regime, this system is described by the relativistic O(3) sigma model on a spacetime with a spatially inhomogeneous metric, determined by J. The geodesic approximation is used to describe low energy soliton dynamics in this system: n-soliton motion is approximated by geodesic motion in the moduli space of static n-solitons, equipped with the L^2 metric. Explicit formulae for this metric for various natural choices of J(x,y) are obtained. From these it is shown that single soliton trajectories experience refraction, with 1/J analogous to the refractive index, and that this refraction effect allows the construction of simple bubble lenses and bubble guides. The case where J has a disk inhomogeneity (taking the value J_1 outside a disk, and J_2<J_1 inside) is considered in detail. It is argued that, for sufficiently large J_1/J_2 this type of antiferromagnet supports approximate quasibreathers: two or more coincident bubbles confined within the disk which spin internally while their shape undergoes periodic oscillations with a generically incommensurate period.