Magnetic bubble refraction and quasibreathers in inhomogeneous antiferromagnets
J. M. Speight University of Leeds
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
$\mathsf M_n$ of static
$n$-solitons equipped with the
$L^2$
metric
$\gamma$. We obtain explicit formulas for
$\gamma$ 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.
Keywords:
topological soliton, geodesic approximation, Heisenberg antiferromagnet.
DOI:
10.4213/tmf6080
Fulltext:
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