Vacancy-driven tetrahedral distortion leading to exceptional second harmonic generation

In this work, cation vacancies induced the tetrahedral distortion, enhancing the second harmonic generation (SHG) response in the diamond-like (DL) structure compounds. Concretely, the high valence and electronegativity of P⁵⁺ were introduced to substitute the Ge⁴⁺ in Cd₄GeS₆, which shows a general SHG response of 1.1 × AgGaS₂ (AGS) at 2050 nm. Thus, the isomorphic defective DL Cd_3.5PS₆ was obtained with inherent Cd²⁺ vacancies, leading to an 8.5-fold increase in [CdS₄] tetrahedral distortion degree than Cd₄GeS₆. As a result, Cd_3.5PS₆ has a high SHG response of 2 × AGS at 2050 nm and a laser-induced damage threshold (LIDT) of 9.4 × AGS. Furthermore, equivalent Hg²⁺ substitution concentrates Cd²⁺ vacancies at the Cd(2) site, leading to a 2.66-fold [CdS₄] tetrahedral distortion degree than Cd_3.5PS₆. Consequently, Hg_0.5Cd₃PS₆ possesses a high SHG response of 2.73 × AGS at 2050 nm and LIDT of 5 × AGS with a birefringence of 0.076@2050 nm. The results indicate that the cation vacancies and radius scale of mixed atoms provide effective ways to design high-performance nonlinear optical crystals.