  We studied the novel multiferroic material Sr$_2$FeSi$_2$O$_7$, and found 3
absorption modes above the magnetic ordering transition temperature using
time-domain terahertz spectroscopy. These absorption modes can be explained as
the optical transitions between the spin-orbit coupling and crystal field split
3d$^6$ Fe$^{2+}$ ground state term in this material. Consideration of the
compressed tetrahedral environment of the Fe$^{2+}$ site is crucial to
understand the excitations. We point out, however, discrepancies between the
single-site atomic picture and the experimental results.
