Optically induced transient absorption related to formation of small polarons in Sn$_2$P$_2$S$_6$ in the sub-100-fs time domain

The interaction of sub-100-fs light pulses with single crystals of nominally undoped Sn$_2$P$_2$S$_6$ is studied in the NIR spectral range ($590-1630$ nm). A predominant contribution of two-photon absorption (TPA) is verified. Scans over the photon energy show that the TPA coefficient increases in a superlinear way for photon energies exceeding $E_{\mathrm g}/2$; for any photon energy it is nearly independent of propagation direction and polarization of the incident beam. The coefficient saturates at a maximum value of $\beta\approx 8$ cm\,GW$^{-1}$ at $E_{\mathrm p}\approx 1.8$ eV. It drops when reaching the bandgap $E_{\mathrm g}$. The TPA coefficients are higher by a factor of two than the values reported for other wide bandgap ferroelectrics, such as LiNbO$_3$, while being lower in comparison to semiconductor crystals. Using fs-pump-probe measurements at 626 nm, a transient absorption is observed that persists for probe pulse delays much longer than the pump pulse duration, up to 2.5 ns. Such transients are typical for a variety of wide bandgap ferroelectrics, where they are described by optically generated polaronic states. We discuss our results in the frame of the microscopic structure of Sn$_2$P$_2$S$_6$ with emphasis on the optical generation of S$^-$ small hole polarons.