English

• Due to the unique capability of infrared (IR) nonlinear optical (NLO) materials to convert frequencies and produce different wavelengths based on intrinsic light, they are utilized as an essential component in solid-state laser devices within military and civilian fields [1-5]. So far, commercial IR-NLO crystals have been limited in their applications due to inherent defects that lead to low utilization efficiency. For instance, AgGaS₂ [6] has a low laser-induced damage threshold (LIDT), AgGaSe₂ [7] cannot achieve phase matching (PM) behavior and also has a small LIDT, and ZnGeP₂ [8] exhibits severe two-photon absorption. The aforementioned limitations are primarily caused by the narrow band gaps (E_g) of these materials. In addition, there is an incompatible relationship between a wide E_g and a big second–harmonic-generation (SHG) coefficient (d_eff) [9-14]. Therefore, it is of great significance and importance to explore new materials that exhibit a well-balanced performance in terms of IR-NLO properties.

  In recent decades, extensive research has been conducted on transition metal-based chalcogenides, establishing them as leading candidates for IR-NLO applications [15-19]. Among these chalcogenides, Hg-based ones have gained significant popularity compared to their counterparts, such as Zn and Cd [20]. This popularity is attributed to their unique structural advantages, which include diverse coordination methods like linear [HgQ₂], trigonal-planar [HgQ₃], and tetrahedral [HgQ₄]. The highly polarized Hg-Q bonds present in these materials are beneficial for achieving strong effective d_eff and significant refractive index variations (Δn). Moreover, Hg-based chalcogenides offer a wider range of IR transmission, covering two crucial atmospheric windows at 3–5 µm and 8–12 µm. So far, all reported Hg-based IR-NLO materials have focused on multivariate systems, such as the chalcogenide system of AHgPS₄ [21] and AEHgM^ⅣQ₄ [22-25] (A = alkali-metal elements; AE = alkaline-earth-metal elements; M^Ⅳ = group 14 elements; Q = chalcogen), as well as the salt-inclusion chalcogenide system of [Ba₄Cl₂][HgGa₄S₁₀] [26] and [AX][Hg₃P₂S₈] (X = halogen) [27]. However, research on ternary systems is relatively scarce. Recently, the ternary transition-metal-rich M₄^ⅡM^ⅣQ₆ family system has caught our attention, particularly compound Hg₄GeS₆ [28,29]. Despite being reported as early as 1968, it has not yet undergone thorough investigation regarding its NLO performance [30]. Although theoretical calculations indicate a significant d_eff of approximately 50 pm/V, preliminary experimental characterization suggests that the SHG signal at of this material is relatively weak under 2050 nm frequency doubling light conditions. This weakness can primarily be attributed to the strong absorption of the both fundamental and frequency-doubled light, which is caused by the material's low optical E_g (ca. 1.3 eV). On the other hand, Hg₄GeS₆ possesses a dense 3D tetrahedral-stacking framework. However, due to the slight anisotropy of this structure, its birefringence index is exceedingly small (Δn < 0.01), rendering PM unattainable within the working band. Consequently, this limitation hinders its potential for further applications.

  In this work, we have implemented a bandgap engineering strategy that involves alkali metal introduction and Hg/Ge ratio regulation to address the limitations of Hg₄GeS₆ mentioned above. The rationale behind this approach is based on the following considerations. Firstly, the introduction of alkali metals with high electronegativity is helpful in obtaining higher E_g. Additionally, it helps in disrupting the original compact structure, leading to the formation of a lower-dimensional structure. This alteration in structure enhances its anisotropy, which in turn results in higher Δn values. Furthermore, by reducing the Hg/Ge ratio, i.e., increasing the Ge content in the component, which can also achieve higher E_g. After multiple attempts, we have successfully obtained two new non-centrosymmetric (NCS) quaternary Hg-based chalcogenides, namely Rb₂HgGe₃S₈ and Cs₂HgGe₃S₈, using the high-temperature solid-phase method. As anticipated, both compounds exhibit excellent IR-NLO performances including sufficient d_eff (0.55–0.70 × AgGaS₂), wide E_g (3.27 and 3.41 eV), huge LIDTs (17.4–19.7 × AgGaS₂), broad optical transmission intervals (0.32–17.5 µm), and suitable Δn (0.069–0.086@2050 nm). These findings indicate that these compounds hold great potential as candidates for IR-NLO applications. In this report, we will provide details on their synthesis, crystal structures, optical properties, and theoretical calculation analysis.

  The crystal structure of Hg₄GeS₆ is significantly complicated, consisting of 4 independent [HgS₄] tetrahedra and 1 [GeS₄] tetrahedra. The three-dimensional (3D) framework can be described as a combination of 3D Hg–Ge–S stacks and 2D Hg–S parts (Fig. 1a, and a more detailed structure is shown in Fig. S1 in Supporting information). In the 3D Hg–Ge–S parts, the [Hg₂GeS₇] layers are connected to each other by sharing S atoms, stacking in an ABABAB manner. Within each [Hg₂GeS₇] layer, interesting 12-membered rings (12-MRs) [Hg₂GeS₉] and 6-membered rings (6-MRs) [Hg₂GeS₇] are formed through vertex-sharing [Hg2S₄], [Hg4S₄], and [GeS₄]. Each 12-MR is linked to four neighboring 12-MRs and four 6-MRs through Hg/Ge–S bonds. The 2D Hg–S parts are formed by stacking [Hg₂S₅] layers along the a-axis. Within these layers, zigzag 12-MRs [HgS₃] are formed through vertex-sharing [Hg1S₄] and [Hg3S₄]. Unfortunately, due to the slight anisotropy of this dense 3D tetrahedral-stacking framework, the Δn index of Hg₄GeS₆ is exceedingly small (< 0.01). Therefore, achieving perfect PM feature within the working band is not possible. On the other hand, the high Hg/Ge ratio in the Hg₄GeS₆ results in a low optical E_g (ca. 1.3 eV). This low E_g presents a challenge in obtaining a high LIDT, thereby restricting its application in the high-energy laser band. In order to address the limitations of the ternary compound Hg₄GeS₆, we have successfully synthesized two quaternary NCS Hg-based chalcogenides, namely Rb₂HgGe₃S₈ and Cs₂HgGe₃S₈. This achievement was accomplished by employing a bandgap engineering approach, which included the introduction of alkali metals and regulation of the Hg/Ge ratio.

  Figure 1

  

  Figure 1.  Structure transformation from (a) 3D Hg₄GeS₆ to (b) 2D A₂HgGe₃S₈; (c) A 2D [HgGe₃S₈]^2– layer viewed along the bc plane with the coordination environment of (d) [HgGeS₇] polyhedron and (e) [Ge₂S₆] dimer marked.

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  The single X-ray diffraction data accurately correlates to the orthorhombic system [space group: P2₁2₁2₁ (No. 19)]; Pearson symbol: oP60; idealized Wyckoff sequence: a¹⁴] for A₂HgGe₃S₈ (A = Rb, Cs) is accurately correlated. Detailed crystallographic parameters for both compounds are listed in Table S1 (Supporting information). In each unit, there are two crystallographically independent A atoms, one Hg, three Ge, and eight S atoms, all occupying the 4a Wyckoff site (Table S2 in Supporting information). As shown in Fig. 1b, A₂HgGe₃S₈ (A = Rb, Cs) compounds exhibit a 2D [HgGe₃S₈]^2– layer, which is aligned along the c axis in the form of ABABAB fashion, with A⁺ cations inserted to maintain charge balance. Fig. 1c illustrates that each 2D [HgGe₃S₈]^2– layer consists of 1D chains composed of [HgGeS₆]^6–. These 1D chains are linked by [HgGeS₇] tetrahedra (Fig. 1d), alternating via corner-sharing along the a direction. Moreover, the neighboring chains are linked together into a layer through [Ge₂S₆]^4– dimers (Fig. 1e), which share corners along the c direction (Fig. 1c). As listed in Tables S3 and S4 (Supporting information), the Hg and Ge atoms are in distorted tetrahedral coordination with 4 S atoms, and the bond lengths of Hg–S and Ge–S are in the ranges of 2.499(3)–2.554(3) Å and 2.156(3)–2.281(3) Å, respectively, which are comparable to those of reported Hg-based and Ge-based chalcogenides [31-38]. In addition, the A⁺ cations are coordinated by 8 and 11 S atoms to form [AS₈] and [AS₁₁] polyhedra respectively. The Rb–S bond distances range from 3.373 Å to 4.281 Å, while the Cs–S bond lengths range from 3.467 Å to 4.501 Å (Fig. S2 in Supporting information). These measurements are consistent with the bond distances observed in other alkali-metal sulfides [39-43].

  The high-yield bulk crystal A₂HgGe₃S₈ (A = Rb, Cs) is synthesized by fully mixing of HgS, Ge, S and RbBr/CsBr at high temperature of 1073 K (experimental details can be found in Supporting information). The experimental powder XRD pattern of A₂HgGe₃S₈ (A = Rb, Cs) matches the simulated pattern, indicating that the synthesis process described above can achieve a high phase purity of the crystals (Fig. S3 in Supporting information). SEM and EDX spectrum analysis were conducted, and the results showed that the compounds had a uniform distribution of A/Hg/Ge/S ratio, with an approximate ratio of 2:1:3:8, which is consistent with the theoretical element content ratio of the title compounds (Fig. S4 in Supporting information). As indicated by UV–vis-NIR absorption spectroscopy, the experimental E_g values are 3.41 and 3.27 eV for Rb₂HgGe₃S₈ and Cs₂HgGe₃S₈, respectively, which correspond to their crystal colours (the inset in Figs. 2a and b). Comparing the E_g values greater than 2.33 eV (Table S3 in Supporting information) of typical Hg-based IR-NLO chalcogenides in Fig. 2c, only Zn₂HgP₃S₈ [44], AEHgGeS₄ (AE = Sr, Ba) [25] and SrHgSiS₄ [24] have been able to break through the E_g of 3.0 eV. The A₂HgGe₃S₈ (A = Rb, Cs) not only surpassed the 3.0 eV E_g, but Rb₂HgGe₃S₈ also possesses the largest E_g (3.41 eV) among all reported Hg-based IR-NLO materials. It is worth noting that in the A₂M^ⅡM₃^ⅣQ₈ system (A = alkali-metal elements; M^Ⅱ = divalent transition-metal elements, M^Ⅳ = group 14 elements, Q = chalcogen) with space groups of P2₁, P2₁/c and P2₁2₁2₁, there is a strong correlation between the experimental E_g (measured in eV) and the cell volume (measured in ų) of the reported compounds (Fig. S5 in Supporting information). This correlation can be calculated using the formula E_g = –0.0041 × V + 9.5448 (with an R² value of 0.878). In addition, the IR spectra (Fig. S6 in Supporting information) indicate that there are no noticeable absorption peaks in the range of 4000–600 cm^–1, suggesting that A₂HgGe₃S₈ (A = Rb, Cs) possess a wide IR transmission region. Specifically, Rb₂HgGe₃S₈ has a transmission region of 17.2 µm, while Cs₂HgGe₃S₈ has a transmission region of 17.5 µm. This enables coverage of two important atmospheric windows, which are the 3–5 µm and 8–12 µm ranges. As shown in Fig. S7 (Supporting information), the TG-DSC curves of A₂HgGe₃S₈ (A = Rb, Cs) indicate no significant weight loss until reaching 800 K. However, as the temperature increases further, the title compounds undergo decomposition, which can be confirmed by powder XRD results (Fig. S8 in Supporting information).

  Figure 2

  

  Figure 2.  (a, b) UV–visible–NIR diffuse reflectance spectra of A₂HgGe₃S₈ (A = Rb, Cs) based on the powder samples (inset: photographs of the crystals). (c) Comparison of reported IR-NLO Hg-based materials with E_g > 2.33 eV. (d) SHG intensity vs. particle size of compounds under 2050 nm laser irradiation.

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  The powder SHG measurements of Rb₂HgGe₃S₈ and Cs₂HgGe₃S₈ were carried out under laser irradiation at 2050 nm using the modified Kurtz–Perry method [45]. It was observed that there is a positive correlation between the particle size and SHG intensity, indicating that both compounds exhibit type-Ⅰ PM behavior (Fig. 2d). In the particle size range of 150–210 µm, the SHG intensities of Rb₂HgGe₃S₈ and Cs₂HgGe₃S₈ are approximately 0.55 and 0.70 times that of the benchmark AgGaS₂, respectively. To the best of our knowledge, both compounds are the first examples of NLO activity among all reported A₂M^ⅡM₃^ⅣQ₈ systems with a space group of P2₁2₁2₁, breaking the trade-off relationship between large E_g (> 3.0 eV) and sufficient d_eff (> 0.5 × AgGaS₂) in Hg-based IR-NLO chalcogenides (Table S4 in Supporting information). The E_g is a major factor that affects the LIDT, and a wide E_g is beneficial for achieving high LIDT [46-49]. The measured power LIDTs [50] of Rb₂HgGe₃S₈ and Cs₂HgGe₃S₈ are 49.1 and 55.4 MW/cm², respectively, which is approximately 17.4 times and 19.7 times that of AgGaS₂ (2.82 MW/cm²) [51-55].

  To investigate the relationship between NCS structure and optical performance, we conducted a study on the electronic structure of the title compounds using first-principles computational methods [56,57]. The electron band structures reveal that the minimum value of the conduction band (CB) and the maximum value of the valence band (VB) occur at different points, indicating an indirect E_g for the product. The calculated E_g values are 2.16 eV and 2.19 eV, respectively (Fig. S9 in Supporting information) and the first Brillouin zone with high symmetry points was provided in Fig. S10 (Supporting information). However, it is important to note that due to the discontinuity of the exchange-related energy of the GGA functionals, the theoretical calculated E_g value will be lower than the experimentally measured one [58,59]. We also utilized the PBE approach to calculate the partial densities of states (PDOS) of A₂HgGe₃S₈ (A = Rb, Cs) in the energy range from –10 eV to 10 eV. These results are displayed in Figs. 3a and b. According to the PDOS, it can be observed that the contribution of VB maximum is minimum S-3p and Hg-5d orbitals, with a small contribution from Hg-6p orbitals. Conversely, the contribution of CB minimum is mainly arises from Ge-4s and S-3p orbitals, with a small contribution from Ge-4p and Hg-6s orbitals. Based on these findings, we can deduce that the optical band gap primarily consists of Ge-4s, S-3p, Hg-5d orbitals. Therefore, the optical band gap of A₂HgGe₃S₈ (A = Rb, Cs) is primarily determined by the functional units [GeS₄] and [HgS₄].

  Figure 3

  

  Figure 3.  Theoretical calculation results of A₂HgGe₃S₈ (A = Rb, Cs): (a, b) PDOS; (c) frequency-dependent SHG coefficient d₁₄; (d) theoretical birefringence (Δn); (e, f) the calculated shortest type-Ⅰ PM cut-off wavelength.

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  Due to the restriction of Kleinman symmetry [60], A₂HgGe₃S₈ (A = Rb, Cs) belongs to the orthogonal space group, with only one independent nonzero second-order nonlinear coefficient, i.e., d₁₄ = d₂₅ = d₃₆. The calculated results for Rb₂HgGe₃S₈ and Cs₂HgGe₃S₈ are 0.721 pm/V and 0.684 pm/V at the wavelength of 2050 nm, respectively (Fig. 3c), which is consistent with the trend obtained from the experiment. Additionally, the theoretically calculated Δn values for Rb₂HgGe₃S₈ and Cs₂HgGe₃S₈ at 2050 nm are 0.086 and 0.069 (Fig. 3d), respectively. The moderate Δn index is conducive to PM, and the experimental results also confirmed that the title compounds exhibit PM behaviour. According to the condition of type-Ⅰ phase matching [n_e(2ω) = n_o(ω)], where n_e and n_o represent the refractive index of extraordinary light and ordinary light, respectively, it can be concluded that the shortest PM cut-off edges for Rb₂HgGe₃S₈ and Cs₂HgGe₃S₈ are 650 nm and 570 nm, respectively (Figs. 3e and f) [61-64].

  In order to further investigate the source of the SHG effect, we conducted a detailed analysis of the cut-off energy dependent static d₁₄ based on the length specification [65,66], as shown in Fig. 4. The results indicate that d₁₄ exhibits an upward trend in the VB-1 (−3.8~0.0 eV), CB-1 (2.1–3.0 eV), CB-3 (5.5–7.7 eV), and CB-5 (8.4–9.3 eV) regions. This implies that these four regions play a crucial role in the SHG response. By considering the charge density of PDOS and related components, we can conclude that the SHG response is a result of the synergistic effect between the NLO-activity [HgS₄] and [GeS₄] BBUs, specifically within the 2D [HgGe₃S₈]^2– layer.

  Figure 4

  

  Figure 4.  Theoretical analysis of the SHG source: (a) Cut-off-energy-dependent variation of static coefficient d₁₄; (b) charge density maps in the VB-1, CB-1, CB-3, and CB-5 regions along the bc plane.

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  In conclusion, the introduction of alkali metals and regulation of the Hg/Ge ratio in the ternary narrow-band-gap parent Hg₄GeS₆ has led to the successful discovery and systematic characterization of two new Hg-based IR-NLO chalcogenides, namely Rb₂HgGe₃S₈ and Cs₂HgGe₃S₈. These compounds belong to the NCS P2₁2₁2₁ space group and exhibit interesting 2D layered structures composed of [HgS₄] and [GeS₄] tetrahedra. They demonstrate excellent performance balance in terms of PM d_eff (0.55–0.70 × AaGgS₂), E_g (3.27–3.41 eV), optical transparency window (0.32–17.5 µm), and LIDTs (17.4–19.7 × AaGgS₂). Furthermore, detailed theoretical studies support the notion that tetrahedral [HgS₄] and [GeS₄] motifs play a pivotal role in the enhancing d_eff and E_g of these materials. This research expands our understanding of the structure-activity relationship of Hg-based chalcogenides and contributes to the design of high-performance IR-NLO candidates.

  Declaration of competing interest

  The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

  Acknowledgments

  This work was supported by the National Natural Science Foundation of China (Nos. 22175175 and 22193043), Natural Science Foundation of Fujian Province (Nos. 2022L3092 and 2023H0041), Fujian Science & Technology Innovation Laboratory for Optoelectronic Information of China (No. 2021ZR118), and the Youth Innovation Promotion Association CAS (No. 2022303). The authors thank Prof. Bing-Xuan Li at FJIRSM for helping with the NLO measurements and Prof. Yong-Fan Zhang at Fuzhou University for helping with the DFT calculations.

  Supplementary materials

  Supplementary material associated with this article can be found, in the online version, at doi:10.1016/j.cclet.2023.109377.

  
  
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  Figure 1  Structure transformation from (a) 3D Hg₄GeS₆ to (b) 2D A₂HgGe₃S₈; (c) A 2D [HgGe₃S₈]^2– layer viewed along the bc plane with the coordination environment of (d) [HgGeS₇] polyhedron and (e) [Ge₂S₆] dimer marked.

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  Figure 2  (a, b) UV–visible–NIR diffuse reflectance spectra of A₂HgGe₃S₈ (A = Rb, Cs) based on the powder samples (inset: photographs of the crystals). (c) Comparison of reported IR-NLO Hg-based materials with E_g > 2.33 eV. (d) SHG intensity vs. particle size of compounds under 2050 nm laser irradiation.

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  Figure 3  Theoretical calculation results of A₂HgGe₃S₈ (A = Rb, Cs): (a, b) PDOS; (c) frequency-dependent SHG coefficient d₁₄; (d) theoretical birefringence (Δn); (e, f) the calculated shortest type-Ⅰ PM cut-off wavelength.

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  Figure 4  Theoretical analysis of the SHG source: (a) Cut-off-energy-dependent variation of static coefficient d₁₄; (b) charge density maps in the VB-1, CB-1, CB-3, and CB-5 regions along the bc plane.

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