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Magnetic bubble refraction and quasibreathers in inhomogeneous antiferromagnets
Authors:J. M. Speight
Affiliation:(1) School of Mathematics, University of Leeds, Leeds, LS2 9JT, UK
Abstract:We study the dynamics of magnetic bubble solitons in a two-dimensional isotropic antiferromagnetic spin lattice 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 space-time with a spatially inhomogeneous metric determined by J. We use the geodesic approximation to describe the low-energy soliton dynamics in this system: the n-soliton motion is approximated by geodesic motion in the moduli space M n of static n-solitons equipped with the L 2 metric γ. We obtain explicit formulas for γ for various natural choices of J(x, y). Based on these, we show that single soliton trajectories are refracted with J−1 being analogous to the refractive index and that this refraction effect allows constructing simple bubble lenses and bubble guides. We consider the case where J has a disk inhomogeneity (with the value J + outside a disk and J < J + inside) in detail. We argue that for sufficiently large J +/J , this type of antiferromagnet supports approximate quasibreathers: two or more coincident bubbles confined within the disk spin internally while their shape oscillates with a generically incommensurate period. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 152, No. 1, pp. 191–208, July, 2007.
Keywords:topological soliton  geodesic approximation  Heisenberg antiferromagnet
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