  The spin dynamics in the block magnetic phase of the iron-based ladder
compound \bfs\ has been studied by means of single crystal inelastic neutron
scattering. Using linear spin wave theory and Monte-Carlo simulations, our
analysis points to a magnetic Heisenberg model with effective frustrated
antiferromagnetic couplings only, able to describe both the exotic block order
and its dynamics. This new and purely antiferromagnetic picture offers a
fruitful perspective to describe multiferroic properties but also understand
the origin of the stripe-like magnetic instability observed under pressure as
well as in other parent compounds with similar crystalline structure.
