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.
