d$^6$versus d$^{10}$, Which is better for second harmonic generation susceptibility? A Case Study of K$_2$TGe$_3$Ch$_8$ (T = Fe, Cd; Ch = S, Se)

Abstract

Two acentric chalcogenide compounds, K$_2$CdGe$_3$S$_8$ and K$_2$CdGe$_3$Se$_8$, were synthesized via conventional high-temperature solid-state reactions. The crystal structures of K$_2$CdGe$_3$S$_8$ and K$_2$CdGe$_3$S$_8$ were accurately determined by single-crystal X-ray diffraction and crystallize in the K$_2$CdGe$_3$S$_8$ structure type. K$_2$CdGe$_3$S$_8$ is isostructural to K$_2$CdGe$_3$S$_8$ with superior nonlinear optical properties. For the second harmonic generation (SHG) response, K$_2$CdGe$_3$S$_8$ is 18× K$_2$FeGe$_3$S$_8$ for samples of particle size of 38–55 μm. The superior nonlinear optical properties of K$_2$CdGe$_3$S$_8$ over K$_2$FeGe$_3$S$_8$ are mainly contributed by the chemical characteristics of Cd compared with Fe, which are elucidated by nonlinear optical property measurements, electronic structure calculations, and density functional theory calculations. The [CdS$_4$] tetrahedra within K$_2$CdGe$_3$S$_8$ exhibit a higher degree of distortion and larger volume compared to the [FeS4] tetrahedra in K$_2$FeGe$_3$S$_8$. This study possesses a good platform to investigate how d-block elements contribute to the SHG response. The fully occupied d10-elements are better for SHG susceptibility than d6-elements in this study. K$_2$CdGe$_3$S$_8$ is a good candidate as an infrared nonlinear optical material of high SHG response (2.1× AgGaS$_2$, samples of particle size of 200–250 μm), type-I phase-matching capability, high laser damage threshold (6.2× AgGaS$_2$), and good stability.