Flat-band spin dynamics and phonon anomalies of the saw-tooth spin-chain system Fe$_2$O(SeO$_3$)$_2$

Fe$^{3+}$ $S = 5/2$ ions form saw-tooth like chains along the $a$ axis of the oxo-selenite Fe$_2$O(SeO$_3$)$_2$ and an onset of long-range magnetic order is observed for temperatures below $T_C = 105$ K. This order leads to distinct fingerprints in phonon mode linewidths and energies as resolved by Raman scattering. In addition, new excitations with small linewidths emerge below $T = 150$ K, and are assigned to two-magnon scattering processes with the participation of flat-band and high energy magnon branches. From this a set of exchange coupling constants is estimated. The specific ratio of the saw-tooth spine-spine and spine-vertex interactions may explain the instability of the dimer quantum ground state against an incommensurate 3D magnetic order.