Spin dynamics of the block orbital-selective Mott phase.

Iron-based superconductors display a variety of magnetic phases originating in the competition between electronic, orbital, and spin degrees of freedom. Previous theoretical investigations of the one-dimensional multi-orbital Hubbard model revealed the existence of an orbital-selective Mott phase (OSMP) with block spin order, where the spins of the localized orbital form antiferromagnetically coupled ferromagnetic (FM) islands. Recent inelastic neutron scattering (INS) experiments on the quasi-1D BaFe$_2$Se$_3$ ladder compound confirmed the relevance of the block-OSMP. Moreover, the INS spectrum presents a rich and unexpected structure, containing low-energy acoustic and high-energy optical modes with an intensity strongly dependent on the transfered momenta. In this work we present the first theoretical study of the dynamical spin structure factor $S(q,\omega)$ within a block-OSMP regime using the density-matrix renormalization group method. In excellent agreement with experiments we find two modes: a dispersive (acoustic) mode for momentum $q \pi/2$. We provide evidence that the former represents the spin-wave-like dynamics of the FM islands, while the latter is attributed to a novel type of local on-site spin excitations controlled by the Hund coupling.