Terahertz excitations of spin-orbital ground state in multiferroic Sr$_2$FeSi$_2$O$_7$

We studied the elementary excitations in Sr$_2$FeSi$_2$O$_7$, a novel multiferroic material, using time domain terahertz spectroscopy. We found 3 absorption modes above the N\'{e}el temperature. These modes can be described as optical transitions between the Fe$^{2+}$ 3d$^6$ energy levels, that are split by the compressive tetrahedral crystal field and spin orbit coupling. The excitations from the singlet spin-orbital ground state to the upper doublets are both magnetic and electric dipole active. We explored the behavior of these transitions at temperatures below T$_{N\'{e}el}$, and as a function of external magnetic field, applied along different crystalline axes.