  We theoretically investigate a scheme to enhance spin squeezing in a
two-component Bose-Einstein condensate (BEC) by utilizing the inherent
mean-field dynamics of the condensate. Due to the asymmetry in the scattering
lengths, the two components exhibit density oscillations where they spatially
separate and recombine. The effective non-linearity responsible for spin
squeezing is increased by up to three orders of magnitude when the two
components spatially separate \cite{treutlein2010}. We perform a multi-mode
simulation of the system using the truncated Wigner method, and show that this
method can be used to create significant spin squeezing in systems where the
effective nonlinearity would ordinarily be too small, and that strong spatial
dynamics resulting from large particle numbers aren't necessarily detrimental
to generating spin-squeezing. We develop a simplified semi-analytic model that
gives good agreement with our multi-mode simulation, and will be useful for
predicting spin-squeezing in a range of different systems.
