Phononic, magnetic, and inter-band Raman scattering in K$_{0.75}$Fe$_{1.75}$Se$_{2}$ superconductor*

We have analyzed collective excitations in K$_{0.75}$Fe$_{1.75}$Se$_{2}$ single crystal ($T_{c}\sim $ 32 K) by polarized Raman scattering in the energy shift range of 20-8000 cm$^{-1}$, the temperature range of 10-300 K, and laser excitation energies from 1.8 to 3.0 eV. Seven $B_{g}$ and nine $A_{g}$ phonon modes are observed at 300K. Below $\sim $150 K an extra $A_{g}$ mode appears at 165 cm$^{-1}$. The amplitudes of the $A_{g}$ modes at $\sim $67, 112, and 124 cm$^{-1}$ are reduced, while the amplitude of 183 cm$^{-1} \quad A_{g}$ mode is enhanced by factor of five as temperature decreases from 300 to 40 K. Magnetic scattering bands at 1000-2000 cm$^{-1 }$consist of at least three distinct peaks each, implying different Fe-Fe AFM exchange coupling constants for underlying structure. Inter-band transitions are observed at $\sim $3700 and 4600 cm$^{-1}$ at 300 K in the $A_{g}$ and $B_{g}$ channels, respectively. Below 140 K these excitations are hardened to $\sim $4040 and 4820 cm$^{-1}$.