Block magnetic excitations in the orbitally-selective Mott insulator BaFe$_2$Se$_3$*

We investigate the spectrum of magnetic excitations in the Fe-based two-leg ladder material BaFe$_2$Se$_3$ by means of broad-band inelastic neutron scattering. BaFe$_2$Se$_3$ garnered recent attention due to its quasi-1D structure and as hosting an exotic block magnetic ground-state where 4 Fe spins co-align to form Fe$_4$ plaquettes. Our neutron results provide a detailed understanding of magnetic excitations originating from the Fe$_4$ block ground-state. Consisting of a 50 meV wide band of quasi-1D acoustic spin-waves and three high-energy modes around 100 meV and 200 meV, the spin fluctuations and the static moment carry a total squared magnetic moment of 16 $\mu_{\rm B}^2$ per Fe, indicative of orbital selectiveness for localized spins. We develop an effective Heisenberg model that accounts for the observed spectrum and provides a set of exchange interactions to understand how exotic magnetism stems from strong lattice, orbital and electronic correlations in iron chalcogenides.