Achieving a strong second harmonic generation response and a wide band gap in a Hg-based material

Abstract

A new Hg-based infrared nonlinear optical (IR NLO) crystal, [Ba₄Cl₂][HgGa₄S₁₀], was synthesized based on a property-oriented structural design strategy. It crystallizes in the noncentrosymmetric tetragonal space group (I4̄) and consists of a 3D [HgGa₄S₁₀]⁶⁻ anionic moiety formed by corner-sharing tetrahedral HgS₄ and supertetrahedral Ga₄S₁₀ clusters, as well as a 3D [Ba₄Cl₂]⁶⁺ cation network. The physical property measurements show that it can exhibit well-balanced NLO performances, including a large second-harmonic generation (SHG) response (1.5 × AgGaS₂), wide band gap (2.95 eV), and high laser damage threshold (∼15 × AgGaS₂). First-principles calculations indicate that the large SHG response of [Ba₄Cl₂][HgGa₄S₁₀] mainly originates from the strong covalent HgS₄ and GaS₄ tetrahedra and the ionic bonding [Ba₄Cl₂]⁶⁺ guest network contributes to the wide band gap of [Ba₄Cl₂][HgGa₄S₁₀].

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Infrared nonlinear optical (IR NLO) crystals are of immense scientific and technological interest because of their capabilities of generating tunable coherent lasers in the mid-IR region (2.5–25 μm), which are urgently needed by numerous advanced science and technologies, such as medical treatment, atmospheric monitoring, infrared countermeasures, and laser communication.^1–7 Hitherto, practically used IR NLO crystals mainly consist of chalcopyrite-type AgGaS₂, AgGaSe₂, and ZnGeP₂. Although these crystals can exhibit a wide IR transparent window and large NLO responses, the low laser-induced damage threshold of AgGaS₂ and AgGaSe₂, and the unexpected multiple-photon absorptions of ZnGeP₂ tremendously hinder their applications under high-power conditions.^8–10 Hence, it is imperative to explore new IR NLO crystals with balanced properties.

Generally, an excellent IR NLO crystal should satisfy the following crucial NLO criteria: (i) a strong phase-matching SHG response (d_ij > 0.5 AgGaS₂); (ii) a high LDT (>10 AgGaS₂) and a wide band gap (E_g > 3.0 eV); (iii) a broad transmission region (3–12 μm); and (iv) good physicochemical stability. Nevertheless, it is well-known that large SHG responses mainly derive from the covalency of a compound, whereas a high laser-induced damage threshold strongly depends on its ionicity. This implies the undesired contradiction between SHG responses and the laser-induced damage threshold.¹¹ Therefore, achieving large SHG responses and a high laser-induced damage threshold is always a significant challenge among these NLO criteria. To balance this relationship, many attempts have been made and resulted in the discovery of a series of high-performance IR NLO crystals, e.g., LiGaS₂, Li₂In₂SiS₆, Li₂CdSnS₄, Na₂ZnGe₂S₆, and BaGa₂GeQ₆ (Q = S, Se). Most of these strategies are mainly focused on using higher electropositive alkali or alkaline-earth cations to substitute the Ag⁺ cations in chalcopyrite-type AgGaS₂ and AgGaSe₂ to widen band gaps, while introducing as many as possible NLO-active functional motifs, MQ₄, (M = Ga, In, Ge, Sn etc., Q = S, Se) to optimize the SHG response.^12–16 Although these attempts are effective and fruitful, they also suffer from some difficulties arising from the fact that ionic and covalent structural units are usually mixed in various assembly processes, whereas the processes favoring good NLO performances can be hardly determined.^17,18

Based on the study of the structure–property relationship, it is clear that the SHG response mainly depends on NLO-active functional motifs, MQ₄, possessing strong covalency. Meanwhile, the 12 group transition metal tetrahedra and 13 and 14 group element tetrahedra are usually employed as the NLO-active units to generate large SHG responses in compounds.^19–21 Especially for transition metal Hg²⁺ cations, they have a heavy atomic mass and highly polarizable characteristics. When they are introduced into chalcogenides, the materials can produce much larger SHG coefficients and a wider IR transparency region than other 12 group transition metals, making the materials highly competitive IR NLO materials, e.g., KHg₄Ga₅Se₁₂ exhibits a large phase-matching SHG response (20 AgGaS₂).²² Remarkably, the narrow band gaps of Hg-based compounds, e.g., KHg₄Ga₅Se₁₂ (1.61), BaHgSnSe₄ (1.98 eV), SrHgSnSe₄ (2.07 eV), Li₄HgSn₂Se₇ (2.10 eV), and SrHgSnS₄ (2.72 eV), are unfavorable for them to display a high laser-induced damage threshold.^23,24 In addition, according to Guo's investigation on the electron localization function map,¹⁷ the introduction of strong ionic components has a positive effect on the band gap of the material. Subsequently, it is expected that introducing strongly ionic metal–halogen bonds into Hg-based chalcogenides would be able to increase the band gaps of materials and achieve a good balance between SHG responses and band gaps.²⁵

Guided by these ideas, a new Hg-based chalcogenide, [Ba₄Cl₂][HgGa₄S₁₀], has been successfully designed and synthesized by finely mixing three types of chemical bonds with different covalency and ionicity, including covalent Ga–S and Hg–S, and strong ionic Ba–Cl/S bonds. As expected, this compound can exhibit well-balanced IR NLO properties, including a large SHG response (1.5 × AgGaS₂), wide band gap (2.95 eV), high laser-induced damage threshold (15 × AgGaS₂), and wide transparent window (0.42–25 μm). The results demonstrate that fine mixing of covalent and ionic bonds in the structure is an effective approach for achieving the balance between the SHG response and the band gap.

Polycrystalline [Ba₄Cl₂][HgGa₄S₁₀] was synthesized through a solid-state reaction in a sealed silicon-tube at 750 °C, and its purity was confirmed by powder X-ray diffraction (Fig. S1†). Then, a millimeter-sized single crystal of [Ba₄Cl₂][HgGa₄S₁₀] was grown with BaCl₂ as the flux. By using these crystals, the structure of [Ba₄Cl₂][HgGa₄S₁₀] was determined by single-crystal XRD analysis, which reveals that [Ba₄Cl₂][HgGa₄S₁₀] crystallizes in the noncentrosymmetric tetragonal space group, I4̄ (no. 82).²⁶ The energy-dispersive spectroscopy measurement corroborates the existence of Ba/Cl/Hg/Ga/S with an average atomic ratio of 18.49% : 9.48% : 4.75% : 20.57 : 46.71, which is approximately equal to the theoretical one, 19.05% : 9.52% : 4.76% : 19.05 : 47.62 (Fig. S2†).

The crystal structure of [Ba₄Cl₂][HgGa₄S₁₀] is shown in Fig. 1. Its asymmetric unit contains one Ga, one Hg, one Ba, three S, and two Cl atom(s). All the Ga atoms are coordinated by four S atoms to form GaS₄ tetrahedra with Ga–S distances of 2.244(5)–2.290(5) Å, and every four GaS₄ tetrahedra connect with each other through corner-sharing to form T2-type Ga₄S₁₀ supertetrahedra (Fig. 1a). For Hg atoms, they are also coordinated by four S atoms to form HgS₄ tetrahedra with a Hg–S distance of 2.548(5) Å, and each HgS₄ tetrahedron is bonded by four Ga₄S₁₀ T2-supertetrahedra through corner-sharing forming a three-dimensional (3D) ³_∞[HgGa₄S₁₀]⁶⁻ covalent framework (Fig. 1b). The residual charges of the ³_∞[HgGa₄S₁₀]⁶⁻ covalent framework are balanced by a 3D [Ba₄Cl₂]⁶⁺ guest network, which is composed of the highly distorted [Cl(1)Ba₄] and [Cl(2)Ba₄] tetrahedra via corner- and edge-sharing (Fig. 1c). For Ba–Cl and Ba–S bonds, their bond lengths range from 3.048(1) to 3.107(1) Å and 3.243(5) to 3.644(5) Å, respectively. The bond valence sum calculations resulted in values of 2.01 for Ba²⁺, 2.16 for Hg²⁺, 3.04 for Ga³⁺, 1.95–1.99 for S²⁻ and 1.30–1.52 for Cl⁻.²⁷ The slightly high oxidation states for Cl⁻ result from the slightly short Ba–Cl bond lengths owing to the extreme difference of electronegativity between Ba and Cl atoms, which is comparable with those of reported chalcogenides, e.g., [CsBa₂Cl][Ga₄S₈] and [Ba₄Cl₂][ZnGa₄S₁₀].^28,29 Importantly, [Ba₄Cl₂][HgGa₄S₁₀] contains three types of chemical bonds with different covalency and ionicity, including covalent Ga–S and Hg–S, and strong ionic Ba–Cl/S bonds, which is conducive to obtaining well-balanced NLO properties.^30,31

Fig. 1 HgS₄ tetrahedron and Ga₄S₁₀ T2-supertetrahedron (a). A 3D anionic covalent framework of ³_∞[HgGa₄S₁₀]⁶⁻ (b). A 3D [Ba₄Cl₂]⁶⁺ guest network made of 1D [Ba₄Cl₂]⁶⁺ chains that are connected alternately by highly distorted [Cl(1)Ba₄] and [Cl(2)Ba₄] building units along the b direction (c). A 3D host structure of [Ba₄Cl₂][HgGa₄S₁₀] with Ba²⁺ cations and Cl⁻ anions residing in the cavities as viewed along the b-axis (d).

The UV-vis-NIR diffuse reflectance and absorption spectra of [Ba₄Cl₂][HgGa₄S₁₀] are shown in Fig. 2a. It displays a wider band gap (2.95 eV) than those of commercially used AgGaS₂ (2.70 eV), AgGaSe₂ (1.83 eV), and ZnGeP₂ (1.75 eV). Meanwhile, [Ba₄Cl₂][HgGa₄S₁₀] contains alkaline-earth Ba²⁺ cations without unwanted d–d or f–f electron transitions, the strongly electronegative Cl atom with a blue-shift effect,⁶ and an ionic-bonded 3D [Ba₄Cl₂]⁶⁺ guest network, which contributes to the wide band gap of [Ba₄Cl₂][HgGa₄S₁₀].¹⁷ The wide band gap is positively related to the large laser-induced damage threshold. Furthermore, the laser-induced damage threshold of [Ba₄Cl₂][HgGa₄S₁₀] has also been measured based on the single-pulse powder laser-induced damage threshold method with AgGaS₂ as the reference using a 1064 nm pulse laser (110 A, 1 Hz, 20 ns). The result reveals that [Ba₄Cl₂][HgGa₄S₁₀] has a high powder laser-induced damage threshold of 310 MW cm⁻², which is ∼15 × AgGaS₂. Furthermore, a wide IR transmission region is also essential for the application of NLO crystals. The IR and Raman spectra of [Ba₄Cl₂][HgGa₄S₁₀] are shown in Fig. 2b. The IR spectrum shows that [Ba₄Cl₂][HgGa₄S₁₀] has no obvious absorption in the region of 4000–400 cm⁻¹ (i.e., 2.5–25 μm), indicating its potential as an IR NLO crystal.³² The Raman peaks at 353 and 379 cm⁻¹ belong to the characteristic vibrations of the Ga–S bonds. The absorption peak at 256 cm⁻¹ can be assigned to Hg–S bond interactions.

Fig. 2 The UV-Vis-NIR diffuse reflectance spectrum, inset: band gap (a) and the FTIR spectrum, inset: Raman spectrum (b) of [Ba₄Cl₂][HgGa₄S₁₀]. Particle size dependence of the SHG intensities of [Ba₄Cl₂][HgGa₄S₁₀] and AgGaS₂ (c). SHG intensities of [Ba₄Cl₂][HgGa₄S₁₀] and AGS at a particle size of 180–250 μm (d).

In addition, the low-frequency peaks below 200 cm⁻¹ mainly originate from the Ba–S vibrations. The assignments for the Raman peaks are consistent with those of other chalcogenides, such as LiBa₄Ga₅S₁₂, (Na₃Rb)Hg₂Ge₂S₈ and BaHgS₂.^33–35

As [Ba₄Cl₂][HgGa₄S₁₀] crystallizes in the noncentrosymmetric space group of I4̄, and contains the NLO-active [GaS₄] and [HgS₄] tetrahedra, a relatively large SHG response could be expected. The powder SHG measurement for [Ba₄Cl₂][HgGa₄S₁₀] has been carried out using the modified Kurtz-Perry method under irradiation with a 2090 nm laser with AgGaS₂ as a reference. As shown in Fig. 2c, the SHG intensity of [Ba₄Cl₂][HgGa₄S₁₀] is around 1.5 × AgGaS₂ at a particle size of 180–250 μm (Fig. 2d). The effective NLO coefficient d_eff was calculated using the formula (where I^2ω and are SHG intensities for the sample and AgGaS₂, respectively) with polycrystalline d_{eff, AgGaS2} = 11.8 pm V⁻¹ (polycrystalline d_{eff, AgGaS2} is the angular average of single-crystal d_{36, AgGaS2} = 13.7 pm V⁻¹).³⁶ Therefore, the experimental polycrystalline d_eff value is estimated to be 14.7 pm V⁻¹ for [Ba₄Cl₂][HgGa₄S₁₀]. The large SHG response of [Ba₄Cl₂][HgGa₄S₁₀] will be conducive to generating a high conversion efficiency in the application.

To understand the origin of the large SHG response in [Ba₄Cl₂][HgGa₄S₁₀], the electron structure of [Ba₄Cl₂][HgGa₄S₁₀] has been calculated by first-principles calculations. It shows that [Ba₄Cl₂][HgGa₄S₁₀] has a direct band gap of 2.53 eV (Fig. S3†), which is smaller than the experimental value attributable to the discontinuity of exchange–correlation energy.³⁷ The electronic densities of states (DOS) of [Ba₄Cl₂][HgGa₄S₁₀] are shown in Fig. S4.† It is clear that the tops of the valence bands of [Ba₄Cl₂][HgGa₄S₁₀] are mainly composed of S 3p states with a small part of the Ga 4p and Cl 3p states, while the bottoms of the conduction bands are primarily S 3p, Ga 4s, Ga 4p, Hg 6s and Ba 5d states. These results indicate that the [HgGa₄S₁₀]⁶⁻ anionic moiety has the main contribution to the band gap and SHG response of [Ba₄Cl₂][HgGa₄S₁₀]. In order to further understand the contribution, an intrinsic dipole moment calculation was implemented by a simple bond valence model.³⁸ The calculated results are listed in Table S1.† The dipole moments from GaS₄ and HgS₄ tetrahedra are 2.99 and zero Debye (D), respectively. Although the static dipole moment of HgS₄ units in the unit cell is zero, introducing Hg²⁺ in [Ba₄Cl₂][HgGa₄S₁₀] increases the dipole moment in Ga₄S₁₀ supertetrahedra, which is systematically larger than those in [RbBa₂Cl][Ga₄S₈],²⁸ [Ba₄Cl₂][ZnGa₄S₁₀],²⁹ [KBa₃Cl₂][Ga₅Se₁₀],³⁹ and [Ba₄Cl₂][MGa₄Se₁₀] (M = Zn, Cd).⁴⁰ Additionally, the induced dipole moments from the MQ₄ (M = Zn, Ga, Hg and Q = S, Se) units in AgGaS₂, AgGaSe₂, Ba₃KGa₅Se₁₀Cl₂, Ba₂RbGa₄S₈Cl, Ba₄ZnGa₄S₁₀Cl₂, Ba₄ZnGa₄Se₁₀Cl₂, and [Ba₄Cl₂][HgGa₄S₁₀] were also quantified based on the calculation of the empirical “flexibility index” F.^{28,29,39–43} As listed in Table 1, the F value of the [HgS₄] unit in [Ba₄Cl₂][HgGa₄S₁₀] is slightly larger than those of the MQ₄ (M = Zn, Ga and Q = S, Se) units in other chalcogenides, e.g., AgGaS₂, Ba₂RbGa₄S₈Cl and Ba₄ZnGa₄S₁₀Cl₂. The relatively large induced dipole moment is helpful for [Ba₄Cl₂][HgGa₄S₁₀] to generate an enhanced SHG response. In addition, the NLO coefficients of [Ba₄Cl₂][HgGa₄S₁₀] can also be calculated based on the calculated electron structure. According to Kleinman symmetry, [Ba₄Cl₂][HgGa₄S₁₀] has two nonzero independent SHG coefficients, d₁₅ = d₃₁ = 9.40 pm V⁻¹ and d₁₄ = d₃₆ = 22.04 pm V⁻¹. Obviously, the calculated d₃₆ value is about 1.6 times that of AgGaS₂ (d_{36, AgGaS2} = 13.70 pm V⁻¹),¹⁸ which is also matched with the experimental result.

Table 1 The space groups, SHG responses, and flexibility indices (F) of MQ₄ (M = Ga, Zn, Hg and Q = S, Se) units in AgGaS₂, AgGaSe₂, Ba₃KGa₅Se₁₀Cl₂, Ba₂RbGa₄S₈Cl, Ba₄ZnGa₄S₁₀Cl₂, Ba₄ZnGa₄Se₁₀Cl₂, Ba₄HgGa₄S₁₀Cl₂, and [Ba₄Cl₂][HgGa₄S₁₀]

Compounds	Space groups	MQ4 units	d ij (× AGS, pm V^−1)	F	Ref.
AgGaS2	I4̄2d	GaS4	d 36 = 13.4	0.212	41
AgGaSe2	I4̄2d	GaSe4	d 36 = 33.0	0.211	42
Ba3KGa5Se10Cl2	I4̄	GaSe4	3.6 × AGS	0.258	39
Ba2RbGa4S8Cl	Pmn21	GaS4	0.9 × AGS	0.220–0.236	28
Ba4ZnGa4S10Cl2	I4̄	GaS4	1.1 × AGS	0.183–0.223	29
		ZnS4
Ba4ZnGa4Se10Cl2	I4̄	GaSe4	1.6 × AGS	0.212–0.255	40
		ZnSe4
[Ba4Cl2][HgGa4S10]	I4̄	GaS4	1.5 × AGS	0.226–0.235
		HgS4

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Clearly, [Ba₄Cl₂][HgGa₄S₁₀] can exhibit a relatively large SHG response and a wide band gap, which would be related to the covalent [HgGa₄S₁₀]⁶⁻ anionic moiety and the ionic [Ba₄Cl₂]⁶⁺ cation network, respectively.^{18,29,43–45} To better show the different covalence and ionicity, we also calculated the overlap populations and electron localization function (ELF) of [Ba₄Cl₂][HgGa₄S₁₀] based on first-principles calculations. Given that the overlap populations can represent different electron density localization statuses, i.e., the larger values (>0.5) reflect the localized electron states and the stronger covalent characteristics; inversely, the smaller values (<0.5) represent delocalized electron states and the stronger ionic characteristics.¹⁸ As shown in Fig. 3a, it can be seen that the Ga/Hg–S bonds (0.45–0.66 e) show strong covalency and Ba–S/Cl bonds (0.1–0.13 e) exhibit strong ionicity in [Ba₄Cl₂][HgGa₄S₁₀]. Furthermore, the ELF map of [Ba₄Cl₂][HgGa₄S₁₀] reveals that the covalent Ga/Hg–S and strong ionic Ba–S/Cl bonds present fine mixing in the structure (Fig. 3b), which achieves the expected balance between the SHG response and the band gap in [Ba₄Cl₂][HgGa₄S₁₀].

Fig. 3 Overlap populations (a) and electron localization function (b) of [Ba₄Cl₂][HgGa₄S₁₀].

To further understand the importance of [Ba₄Cl₂][HgGa₄S₁₀] with fine mixing of covalency and ionicity for exploring IR NLO crystals, a property comparison between [Ba₄Cl₂][HgGa₄S₁₀] and some high-performance IR NLO crystals with Hg-based and Ga–S bonds has been performed. Compared to the recently reported Hg-based compounds (e.g., (Hg₆P₃)(In₂Cl₉) (d_ij = 0.5 × AgGaS₂, E_g = 3.13 eV),⁴⁶ (Hg₂Cd₂S₂Br)Br (E_g = 2.41 eV),⁴⁷ (Hg₃Se₂)(Se₂O₅) (E_g = 2.63 eV),⁴⁸ KHg₄Ga₅Se₁₂ (d_ij = 20 × AgGaS₂, E_g = 1.61 eV),²² SrHgSnS₄ (d_ij = 1.9 × AgGaS₂, E_g = 2.72 eV)²³), and chalcogenides with Ga–S bonds (e.g., Ba₂Ga₈GeS₁₆ (d_ij = 1 × AgGaS₂, E_g = 3.0 eV)⁴⁹ and Ga₂S₃ (d_ij = 0.2 × AgGaS₂, E_g = 2.8 eV)⁵⁰), [Ba₄Cl₂][HgGa₄S₁₀] constructed from the structural units with mixing of covalency (Hg–S and Ga–S bonds) and ionicity (Ba–Cl/S bond) can exhibit a good comprehensive IR NLO performance (d_ij = 1.5 × AgGaS₂ and E_g = 2.95 eV). Additionally, compared to AgGaS₂ and other chalcohalides, [Ba₄Cl₂][HgGa₄S₁₀] exhibits a relatively large SHG response, wide band gap, and high laser-induced damage threshold (Fig. S5 and Table S2†), which achieves the expected balance between the SHG response and the band gap. These results indicate that [Ba₄Cl₂][HgGa₄S₁₀] will be a promising IR NLO crystal, and the Hg-based chalcohalides with mixed covalent and ionic bonds may be a worthwhile materials class for the exploration of IR NLO crystals.

In conclusion, a new noncentrosymmetric chalcohalide, [Ba₄Cl₂][HgGa₄S₁₀], has been successfully synthesized by introducing electronegative halogens in a Hg-based chalcogenide. Its structure consists of a 3D [HgGa₄S₁₀]⁶⁻ anionic moiety formed by corner-sharing tetrahedral HgS₄ (T1) and supertetrahedral Ga₄S₁₀ clusters (T2), as well as a 3D [Ba₄Cl₂]⁶⁺ cation network. The property measurements show that it can exhibit balanced NLO properties, including a large SHG response (1.5 × AgGaS₂ at 2090 nm), wide band gap (2.95 eV), high laser-induced damage threshold (15 × AgGaS₂), and wide transparent window (0.42–25 μm). These results show that [Ba₄Cl₂][HgGa₄S₁₀] would be a promising IR NLO crystal. Furthermore, the overlap populations and ELF map analysis results confirm that the balanced NLO properties of [Ba₄Cl₂][HgGa₄S₁₀] mainly originate from the fine mixing of covalency and ionicity in the structure. This work will provide a feasible way for exploring excellent IR NLO crystals through finely mixing covalency and iconicity.

Author contributions

Y. Z. performed the experiments, data analysis, theoretical calculations, and paper writing. H. W. designed and supervised the experiments. H. Y. provided major revisions of the manuscript. Z. H. supervised the optical experiments. J. W. and Y. W. helped with the analyses of the crystallization process and the data. All the authors discussed the results and commented on the manuscript.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant No. 22071179, 52172006, 51972230, 51890864, 61835014, and 51890865) and the Natural Science Foundation of Tianjin (Grant No. 20JCJQJC00060, and 21JCJQJC00090).

Notes and references

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Footnote

† Electronic supplementary information (ESI) available. CCDC 2168297. For ESI and crystallographic data in CIF or other electronic format see DOI: https://doi.org/10.1039/d2qi00937d

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