An overview of Mg-based IR nonlinear optical materials

Abstract

Infrared nonlinear optical (IR-NLO) materials play a vital role in generating IR laser output and have significant applications in the fields of communication, medicine, and security. At present, commercial IR-NLO crystals suffer from various performance drawbacks that constrain their range of applications. Therefore, the pursuit of designing and exploring new IR-NLO materials has emerged as an important avenue for the advancement of the IR laser industry. Benefiting from the various structural compositions, wide energy gaps, sufficient second-harmonic-generation intensities, strong laser-induced damage thresholds and favorable phase matching features, Mg-based IR-NLO materials have attracted wide attention in recent years. However, there has not been a specific review of this attractive family. In this overview, the recent advancements of Mg-based IR-NLO materials are summarized. These non-centrosymmetric compounds (including 36 chalcogenides and 4 pnictides) can be categorized into three types based on their chemical compositions: (i) ternary MgGa₂Se₄, MgSiP₂, MgSiAs₂, and Mg₃Si₆As₈; (ii) quaternary Li₄MgGe₂S₇, Li₂Mg₂M^III₂S₆ (M^III = Si, Ge), AEMg₆Ga₆S₁₆ (AE = Ca, Sr, Ba), RE₆MgSi₂S₁₄ (RE = Y, La–Nd, Sm, and Gd–Er), Li₂MgM^IVSe₄ (M^IV = Ge, Sn), Na₄MgM^III₂Se₆ (M^III = Si, Ge), Cu₂MgM^IVQ₄ (M^IV = Si, Ge; Q = S, Se), M^IMg₃M^III₃Q₈ (M^I = Na, Cu, Ag; M^III = Al, Ga; Q = S, Se), and Mg₂In₃Si₂P₇; and (iii) quinary Ba₆Cu_1.9Mg_1.1Ge₄S₁₆ and Ba₆Cu_1.94Mg_1.06Sn₄S₁₆. Their solid-state synthesis, crystal structures, optical properties and structure–activity relationships are systematically discussed. Finally, some useful conclusions and outlooks on this topic have been put forward.

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1. Introduction

Nonlinear optical (NLO) crystals are crucial components of full-state lasers as they possess the capacity to enhance the frequency range, making them applicable in a variety of aspects such as laser spectroscopy, long distance laser communication, signal processing and so on.^1–18 Due to the limitations of laser wavelength, significant research has been conducted on second order NLO materials, owing to their eminent ability to generate second harmonic generation (SHG). According to the various application bands, NLO materials can be divided into three groups, including ultraviolet (UV), visible-near infrared (Vis-NIR), mid- and far-infrared (MFIR) groups. Among them, NLO materials of UV and Vis-NIR wavelengths have already been deeply researched and commercialized in the past decades, such as KBe₂BO₃F₂ (KBBF),¹⁹ β-BaB₂O₄ (β-BBO),²⁰ LiB₃O₅ (LBO),²¹ KH₂PO₄ (KDP),²² and KTiOPO₄ (KTP).²³ Although traditional commercialized IR-NLO materials, such as AgGaS₂,²⁴ AgGaSe₂,²⁵ and ZnGeP₂,²⁶ have strong SHG coefficients (d_eff), they still possess some inevitable drawbacks such as an imperfect laser-induced damage threshold (LIDT) of AgGaS₂, non-phase-matching property of AgGaSe₂ and negative two-photon absorption of ZnGeP₂.^27,28 Therefore, the development of new outstanding IR-NLO materials is not only urgent but also challenging.

In order to meet the requirements of modern laser technology, high-performance IR-NLO materials need to fulfil the following conditions: (1) suitable birefringence (Δn at the range of 0.03–0.10) for phase-matching; (2) sufficient d_eff (>0.5 × AgGaS₂, 13 pm V⁻¹ for AgGaS₂); (3) high LIDT (>1 × AgGaS₂); (4) wide band gap E_g (>3.0 eV) and transparent range (covering the 3–5 μm and 8–12 μm atmospheric windows); (5) easiness to achieve growth of large size single crystals; and (6) satisfactory chemical and physical stability (mainly low hygroscopicity, resistance to the atmosphere, and possibility of cutting and grinding).^29–40 In addition to the performance requirements mentioned above, it is also imperative that the material be crystallized in a non-centrosymmetric space group. This is because it is a prerequisite for it to function as an IR-NLO candidate.^41–43 In recent decades, several design strategies have been developed. Among these, the most commonly used method for obtaining non-centrosymmetric structures is the introduction of various asymmetric building units (ABUs) into one structure. The common ABUs for IR-NLO materials are as follows: (i) distorted [MQ₄] tetrahedra (M = main-group elements; Q = chalcogen);^44–52 (ii) [MQ_n] polyhedra (M = transition-metal elements; n = 2, 3, and 4);^53–57 (iii) distorted [REQ_n] polyhedra (RE = rare-earth-metal elements);^58–61 (iv) lone-pair-cation-based [MQ_n] polyhedra (M = As(III), Sb(III), Bi(III), Pb(II), and Sn(II));^62–71 and (v) mixed-anion [MO_xQ_y] polyhedra.^72–81

Recently, the introduction of Mg-based ABUs into the non-centrosymmetric structures has attracted considerable interest due to the following reasons: (i) Mg possesses large electropositivity (χ = 1.31), has a high Z/R ratio of 2.8 (Z, cation charge; R, cation radius), has light atomic mass and is non-poisonous. (ii) Mg is more inclined to form stable covalent bonds with chalcogen and pnictide atoms than are Ca, Sr, and Ba, which have strong ionic properties within the same family, for example, tetrahedral [MgQ₄] and [MgP_n4] (P_n = P, As) ABUs and octahedral [MgQ₆] ABUs. (iii) Due to the absence of d–d and f–f electron transitions, Mg is beneficial for obtaining wide E_g values and expanding the IR transparent region.^82–96 Moreover, highly polarizable Mg-based ABUs are helpful in maintaining strong d_eff and suitable Δn. However, a specific summary of non-centrosymmetric Mg-based materials has not been provided, even though they have been discovered to display excellent IR-NLO performances.

In this review, the recent advancements of Mg-based IR-NLO materials are summarized. These non-centrosymmetric compounds (including 36 chalcogenides and 4 pnictides) can be categorized into three types based on their chemical composition: (i) ternary MgGa₂Se₄, MgSiP₂, MgSiAs₂, and Mg₃Si₆As₈; (ii) quaternary Li₄MgGe₂S₇, Li₂Mg₂M^III₂S₆ (M^III = Si, Ge), AEMg₆Ga₆S₁₆ (AE = Ca, Sr, Ba), Li₂MgM^IVSe₄ (M^IV = Ge, Sn), RE₆MgSi₂S₁₄ (RE = Y, La–Nd, Sm, and Gd–Er), Na₄MgM^III₂Se₆ (M^III = Si, Ge), Cu₂MgM^IVQ₄ (M^IV = Si, Ge; Q = S, Se), M^IMg₃M^III₃Q₈ (M^I = Na, Cu, Ag; M^III = Al, Ga; Q = S, Se), and Mg₂In₃Si₂P₇; and (iii) quinary Ba₆Cu_1.9Mg_1.1Ge₄S₁₆ and Ba₆Cu_1.94Mg_1.06Sn₄S₁₆. Their solid-state synthesis, crystal structures, optical properties and structure–activity relationships are systematically discussed. Finally, some useful conclusions and outlooks on this topic have been put forward.

2. The survey on Mg-based IR-NLO materials

2.1 Ternary Mg-based chalcogenides and pnictides

2.1.1 MgGa₂Se₄. The first defect-chalcopyrite-like Mg-based chalcogenide MgGa₂Se₄, with a non-centrosymmetric I4̄ space group, was successfully designed and constructed via a structure prediction and experiment combined method by Li and co-workers in 2022. They used high-temperature solid-state reactions to create it, by mixing MgSe, Ga, and Se in a stoichiometric ratio of 1 : 2 : 3 at 1223 K.⁸²

As shown in Fig. 1, Mg and Ga atoms both coordinate with Se atoms, forming a four-coordinated model represented by tetrahedral [MgSe₄] and [GaSe₄] ABUs. In the [Ga₂Se₇] channel, [MgSe₄] ABUs are embedded via corner-sharing with adjacent [Ga1Se₄] and [Ga2Se₄], as depicted in Fig. 1b and c, resulting in a three-dimensional (3D) defect-chalcopyrite-like structure. Furthermore, this structure can also be achieved by utilizing chalcopyrite-like AgGaSe₂, as depicted in Fig. 1d. When one Mg atom and one vacancy replace two Ag atoms in AgGaSe₂, defect-chalcopyrite-like MgGa₂Se₄ is produced.

Fig. 1 (a) Coordination environment of asymmetric building units in MgGa₂Se₄; (b) the arrangement of isolated [MgSe₄], [Ga1Se₄], and [Ga2Se₄] tetrahedra in the bc plane; (c) [Ga₂Se₇]⁸⁻ anionic framework (left) and 3D structure of MgGa₂Se₄ (right); (d) structural evolution from AgGaSe₂ (left) to MgGa₂Se₄ (right). Copyright 2022 Wiley.

The developed MgGa₂Se₄ possesses a wide optical E_g (ca. 2.96 eV), a high LIDT (ca. 3.0 × AgGaS₂), a broad transparency window (covering 3–12 μm), and a suitable phase-matching d_eff (ca. 0.9 × AgGaS₂@150–200 μm). Therefore, MgGa₂Se₄ shows great potential as an IR-NLO candidate. Additionally, theoretical calculations reveal that the strong d_eff of MgGa₂Se₄ mainly originates from the [GaSe₄] ABUs and nonbonding Se 4p states, and indicate that the tetrahedral [MgSe₄] ABUs can effectively broaden the E_g of chalcopyrite-like compounds.

2.1.2 MgSiP₂ and MgSiAs₂. In 2018, He's group conducted a systematic study of the electronic structures, linear and NLO properties, and thermodynamic stability of the MgM^IVP_n2 (M^IV = Si, Ge, Sn; P_n = P, As) system through first-principles research. The aim of the study was to evaluate their potential in IR-NLO applications.⁸³ In the same year, Kovnir and his colleagues successfully synthesized MgSiAs₂ by reacting raw materials in the molar ratio of Mg : Si : As = 1.2 : 1 : 2 at the temperature of 1123 K.⁸⁴ To obtain a single crystal, they performed three cycles of annealing and grinding coupled with acid treatment (HCl : H₂O = 1 : 1). Recently, Ye and co-workers successfully obtained millimeter-level crystals of MgSiP₂ (1.3 × 2.3 × 0.5 mm³) by mixing Mg, Si, P, and BaCl₂ flux in a molar ratio of 1.33 : 1 : 2 : 2.67 and heating it to 1373 K.⁸⁵

MgSiAs₂ and MgSiP₂ possess a classical chalcopyrite structure (space group: I4̄2d), with a 3D covalent framework comprising tetrahedral [SiP_n4] (P_n = P, As) ABUs. The tunnels are filled with Mg²⁺ cations, which are coordinated with four closest P_n atoms (as depicted in Fig. 2). Computational and optical investigations have revealed that MgSiAs₂ and MgSiP₂ display direct E_g semiconductor properties with an optical E_g of 1.83 eV and 2.33 eV, respectively. MgSiAs₂ exhibits a moderate d_eff (ca. 0.6 × AgGaS₂@55–88 μm) and comparable LIDT (ca. 1.1 × AgGaS₂), while MgSiP₂ possesses a strong d_eff (3.5 × AgGaS₂@150–212 μm), and a broad IR transparency window (0.53–10.3 μm). These studies indicate that the desired balance between E_g and d_eff can be achieved by rationally adjusting the ionicity–covalency–metallicity properties.

Fig. 2 Crystal structure of II–IV–V₂. Copyright 2018 IOP Publishing.

2.1.3 Mg₃Si₆As₈. In 2018, Kovnir and co-workers reported the discovery of Mg₃Si₆As₈, which is the second ternary pnictide in the Mg–Si–As family. Single crystals of Mg₃Si₆As₈ (3 × 1.5 × 1 mm³) were prepared through stoichiometric ratios of Mg, Si, and As and a 50 molar excess of Bi flux at 1150 K.⁸⁴ It represents a new structure type and belongs to the non-centrosymmetric P4₃32 space group. The crystal structure of Mg₃Si₆As₈ is composed of a complex 3D Si–As network with interspersed Mg cations. Two distinct environments can be observed for the Mg cations: i.e., tetrahedral [MgAs₄] and octahedral [MgAs₆] ABUs. Moreover, the Si–As network found in Mg₃Si₆As₈ is similar to that of the binary SiAs, where six As atoms surround Si–Si dumbbells in both cases. The structure of Mg₃Si₆As₈ creates a 3D rhombus grid fashion of Si₂@As₆ octahedra, as depicted in Fig. 3a. In contrast, these octahedra in the SiAs crystal structure form two-dimensional (2D) layers, as shown in Fig. 3b.

Fig. 3 (a) Crystal structure of the 3D Si–As network in Mg₃Si₆As₈ and (b) SiAs with Si₂@As₆ marked as purple octahedra. Green atom: Mg; blue atom: Si; black atom: As. Copyright 2018 Wiley.

Mg₃Si₆As₈ displays more significant thermal stability than MgSiAs₂ with a difference of 100 K (1240 K compared to 1140 K). Additionally, its experimental E_g is recorded as 2.02 eV. Unfortunately, it does not have SHG response due to its 432 Laue class.

2.2 Quaternary Mg-based chalcogenides and pnictides

2.2.1 Li₄MgGe₂S₇. The first alkali and alkaline-earth metal defect-chalcopyrite-like Mg-based chalcogenide Li₄MgGe₂S₇, with a monoclinic Cc space group, was successfully designed based on the chemical substitute-oriented strategy in the M^I₄–M^II–M^IV₂–Q₇ system by Li and co-workers in 2021.⁸⁶ Colorless block-shaped crystals of Li₄MgGe₂S₇ were prepared by a high-temperature solution reaction using the starting materials Li₂S, Mg, Ge, and S in the molar ratio of 2.5 : 1 : 2 : 5 at 1223 K.

Like other diamond-like chalcogenides, Li₄MgGe₂S₇ can be seen as a derivative of wurtzite β-ZnS.⁹⁷ Each metal is coordinated by four S atoms, forming tetrahedral [LiS₄], [MgS₄], and [GeS₄] ABUs. The six [LiS₄] ABUs are interconnected by sharing common sulfur atoms, creating a fascinating 6-membered ring (6-MR), with the [Ge1S₄] tetrahedron located in the middle of this unit. Furthermore, the one-dimensional (1D) [GeMgS₅] zigzag chains connect to the 6-MRs to construct a 2D honeycomb-like layer (Fig. 4a). The assembly of this honeycomb layer along the [101] direction is achieved via shared S atoms, resulting in the final 3D diamond-like framework (Fig. 4b). When viewed along the [203] direction, a clear depiction of the honeycomb-like 3D framework with an internal diameter of about 4.3 Å is observed (Fig. 4c). Additionally, unique [Ge₂S₇]⁶⁻ dimers are discovered in Li₄MgGe₂S₇ (Fig. 4d).

Fig. 4 Crystal structure of Li₄MgGe₂S₇: (a) 3D diamond-like structure; (b) single 2D layered fragment viewed along the [102] direction; (c) honeycomb-like 3D framework with an internal diameter of about 4.3 Å; (d) coordination environment of [Ge₂S₇]⁶⁻ dimers. Copyright 2021 Wiley.

The obtained Li₄MgGe₂S₇ exhibits the widest experimental E_g of 4.12 eV among reported quaternary metal chalcogenides. Additionally, it shows a suitable phase-matching d_eff (ca. 0.7 × AgGaS₂ at 2090 nm, granularity range 15–200 μm) and a high LIDT (7 × AgGaS₂ at 1064 nm), making it an excellent IR-NLO candidate for high-power laser applications. Theoretical calculations indicate that alkali metal Li and alkaline-earth metal Mg effectively enhance E_g, while covalent [Ge₂S₇]⁶⁻ dimers contribute to a strong d_eff. This study enriches the diversity of diamond-like chalcogenides and offers a new route for the design and exploration of new IR-NLO materials with broad E_g and significant d_eff.

2.2.2 Li₂Mg₂M^III₂S₆ (M^III = Si, Ge). The first Li-containing members of the A_12−nxM_xⁿ⁺(T₂Q₆)₂ family, Li₂Mg₂Si₂S₆ and Li₂Mg₂Ge₂S₆, were reported by Aitken and co-workers in 2022.⁸⁷ Transparent and colorless single crystals of Li₂Mg₂Si₂S₆ and Li₂Mg₂Ge₂S₆ were obtained by the traditional high-temperature solid-phase technology using stoichiometric amounts of the reagents at 1173 K.

These two new compounds belong to the non-centrosymmetric polar space group P31m (No. 157) and represent a new structure type. As indicated in Fig. 5, each octahedral [LiS₆] ABU shares its edge with three other [LiS₆] ABUs to build a 2D layer in the ab plane, resulting in holes in the c direction. This layer is designated as “layer 1”. Similarly, along the c axis, there exist nearly identical layers formed by the octahedral [MgS₆] ABUs, which are subsequently referred to as “layer 2”. These two layers, layer 1 and layer 2, are then interconnected along the c axis via face sharing of their respective octahedra to generate a 3D framework. These staggered ethane-like [Si₂S₆]⁶⁻ groups are nestled within the holes present in layer 2 of the Mg–S layer, whereas the holes in layer 1 of the Li–S layer remain unoccupied. Each [MgS₆] corner shares six of its corners with three ethane-like [Si₂S₆]⁶⁻ units, and the orientation of Si–Si bonds is perpendicular to the [MgS₆] layers.

Fig. 5 Polyhedral stacking structure of Li₂Mg₂M^III₂S₆ viewed along the bc plane. Copyright 2022 Wiley.

The optical E_g values of Li₂Mg₂Si₂S₆ and Li₂Mg₂Ge₂S₆ have been estimated through optical diffuse reflectance spectra, which are 3.24 eV and 3.18 eV, respectively. These compounds exhibit moderate d_eff of approximately 0.24 × KDP and 2.9 × α-SiO₂ for Li₂Mg₂Si₂S₆, and 0.17 × KDP and 2.1 × α-SiO₂ for Li₂Mg₂Ge₂S₆ when exposed to a Nd:YAG laser at 1064 nm.

The theoretical calculation results indicate that the atomic orbitals of Li and Mg atoms do not significantly contribute to the state near the valence band maximum. This finding is significant due to their positive electrical properties and the potential interaction with the primary sulfur ions.

2.2.3 AEMg₆Ga₆S₁₆ (AE = Ca, Sr, Ba). The first examples of a double alkaline-earth metal chalcogenide, AEMg₆Ga₆S₁₆ (AE = Ca, Sr, Ba), were successfully discovered by Yu's group in 2022.⁸⁸ Millimeter-level pale-yellow crystals of AEMg₆Ga₆S₁₆ were prepared by the solid-state method in sealed silica tubes using the starting materials MgS, Ga₂S₃, and AES in the molar ratio 1.22 : 0.6 : 0.21 at 1323 K.

As a representative, SrMg₆Ga₆S₁₆ (space group: P6̄) is adopted to describe the structure. In this structure, octahedral [MgS₆] ABUs share both corners and faces to form [Mg₃S₁₄] trimers, while tetrahedral [GaS₄] ABUs interconnect through vertex-sharing to create two distinct kinds of 1D Ga–S chains along the c direction, namely, [Ga(1)S₃]_∞ single chains (Fig. 6a) and [Ga(2,3)₂S₄]_∞ double chains (Fig. 6b). Then, these [Mg₃S₁₄] trimers connect through vertex-sharing (in the a–b plane) and edge-sharing (along the c-axis) with two types of 1D Ga–S chains to form a 3D open [Mg₆Ga₆S₁₆]²⁻ framework (Fig. 6c). Finally, charge-balancing Sr atoms are introduced to fill the channels of this framework (Fig. 6d).

Fig. 6 (a) Coordination environment of [Mg₃S₁₄] trimers and 1D [Ga(1)S₃] chain; (b) 1D [Ga(2,3)₂S₄] chain; (c) 3D [(Mg/Ga)S]_∞ framework and (d) crystal structure of SrMg₆Ga₆S₁₆ viewed along the ab plane. Copyright 2022 Wiley.

The obtained chalcogenides melt congruently and are stable in both air and water, which facilitates the growth of single crystals. Performance characterization demonstrates that they can achieve a well-balanced combination of large phase-matching d_eff (ca. 0.7–0.8 × AgGaS₂ at 2090 nm, granularity range 180–250 μm), wide E_g (3.50–3.54 eV), high LIDTs (ca. 11 × AgGaS₂ at 1064 nm), and broad IR transparent windows (0.35–20 μm), which suggests that AEMg₆Ga₆S₁₆ are potential IR-NLO candidates. Upon further studying the structure–property relationships, it has been shown that the excellent NLO properties of the material predominantly arise from the combined contribution of the polarizable [GaS₄] and [MgS₆] ABUs in the 3D open [Mg₆Ga₆S₁₆]²⁻ framework. These findings offer a brand-new family for developing IR-NLO candidates with stable framework structures and excellent properties.

2.2.4 RE₆MgSi₂S₁₄ (RE = Y, La–Nd, Sm, and Gd–Er). RE₆MgSi₂S₇ (RE = Y, La–Nd, Sm, and Gd–Er) with a NCS P6₃ space group were systematically researched by zur Loye's group in 2023.⁸⁹ With the exception of La₆MgSi₂S₇,⁹⁸ these compounds were all discovered for the first time. These compounds were synthesized by the flux method and crystallized by combining the boron chalcogen mixture method⁹⁹ and the molten flux method.

The crystal structure of RE₃Mg_0.5SiS₇ contains three types of olyhedral: [MgS₆], [SiS₄], and [RES₈]. The 3D structure (Fig. 7a) is constructed from bi-capped trigonal prisms of [RES₈], which are shared at the edges and corners to produce a ring-shaped arrangement (Fig. 7b). Isolated [SiS₄] tetrahedra (Fig. 7c) are distributed throughout the structure, positioned between the ring-shaped [RES₈] assemblies (Fig. 7d). Furthermore, face-sharing [MgS₆] octahedra are situated centrally within each ring arrangement and interact with their neighbouring assemblies.

Fig. 7 (a) Crystal structure of RE₆MgSi₂S₁₄ from the c-axis; coordination environment of (b) 3D RE-S network, (c) 1D chains of face-sharing [MgS₆] octahedra (left) and isolated [GeS₄] tetrahedra (right), and (d) [RES₈] polyhedron. Copyright 2023 American Chemistry Society.

The experimental values for RE₃Mg_0.5SiS₇ are an E_g of 2.77 eV and an approximate d_eff of 0.16 × KDP at a wavelength of 1064 nm. However, the SHG activity was not tested in any other samples due to difficulties in measuring it arising from crystal colouration in other compositions.

2.2.5 Li₂MgM^IVSe₄ (M^IV = Ge, Sn). Two new diamond-like chalcogenides with the formula of Li₂MgM^IVSe₄ (M^IV = Ge, Sn) have been reported by Pan and co-workers in 2021.⁹⁰ Both of them adopt the NCS space group of Pmn2₁ and were synthesized by direct combination of the stoichiometric elements at 1153 K. As depicted in Fig. 8, all of the ions within the structures occupy general sites and exhibit tetrahedral coordination models. The 3D diamond-like framework of Li₂MgM^IVSe₄ is formed by tetrahedral [(Li/Mg)Se₄] [LiSe₄] and [M^IVSe₄] ABUs through corner-sharing Se atoms (Fig. 8a and c). For both compounds, there are similar channel-like structures with a channel diameter of approximately 6 Å on the ab direction, as given in Fig. 8b and d.

Fig. 8 Crystal structure of Li₂MgM^IVSe₄ (M^IV = Ge, Sn): (a and c) 3D diamond-like structures viewed along the c direction; (b and d) 3D channel-like structures viewed along the ab plane.

The calculated results suggest that the d₃₃ of Li₂MgSnSe₄ and Li₂MgGeSe₄ are 12.19 and 14.77 pm V⁻¹, respectively, which primarily stem from the tetrahedral [M^IVSe₄] ABUs and are comparable to that of the widely accepted reference material AgGaS₂ (d₁₄ = 13.7 pm V⁻¹). The calculated E_g for Li₂MgSnSe₄ and Li₂MgGeSe₄ was 2.42 and 2.44 eV, correspondingly. Notably, these two selenides represent the first series in the M^I₂–M^II–M^IV–Q₄ system to feature alkali and alkaline-earth metals, thereby expanding the variety of structures found among diamond-like chalcogenides.

2.2.6 Na₄MgM^III₂Se₆ (M^III = Si, Ge). Na₄MgM^III₂Se₆ (M^III = Si, Ge), with a C2 non-centrosymmetric space group, were first reported by Pan's group in 2015.⁹¹ They were discovered using traditional solid-state reactions with reaction materials Na, Mg, M^III, Ge in a molar ratio of 4 : 1 : 2 : 6 at 973 K (for Na₄MgSi₂Se₆) and 873 K (for Na₄MgGe₂Se₆).

Due to their similar structures, Na₄MgSi₂Se₆ has been chosen as the representative. The Mg atoms are coordinated with six Se atoms to generate octahedral [MgSe₆] ABUs, which are then connected with [Si₂Se₆] ABUs to build a 2D layered structure. Finally, charge-balancing Na⁺ cations fill the channels and interlayer spaces to further form a 3D framework (Fig. 9a). When compared to the formerly reported Na₈Pb₂(Si₂Se₆)₂ (Fig. 9b),¹⁰⁰ which also owns the same ethane-like [Si₂Se₆] dimers, a significant difference occurs in their different space groups (C2/m vs. C2).

Fig. 9 Crystal structures of (a) Na₄MgSi₂Se₆ and (b) Na₈Pb₂(Si₂Se₆)₂ viewed along the ab plane. Copyright 2015 American Chemistry Society.

Significantly, they display high power LIDTs of 9 and 7 times that of AgGaS₂, moderate phase-matching d_eff of 0.5 and 1.3 times that of AgGaS₂ within the particle size range of 150–200 μm, and wide IR transmission windows of 0.45–20 μm. These properties could potentially remove the key drawbacks, such as small LIDTs and harmful TPA, observed in commercially available IR-NLO crystals. Based on the calculation results, that calculated Δn values are close to 0.10 for Na₄MgM^III₂Se₆ at the wavelength of 1064 nm and the charge transitions from Se 4p, M^III 3p/4p and Mg 2p play the important role for d_eff.

2.2.7 Cu₂MgM^IVQ₄ (M^IV = Si, Ge; Q = S, Se). Three new diamond-like chalcogenides with the formula Cu₂MgM^IVQ₄ (M^IV = Si, Ge; Q = S, Se) have been obtained by the traditional high-temperature solid-state method by Guo and co-workers in 2013.⁹² All of them belong to the non-centrosymmetric space group of Pmn2₁ in the wurtzite-type superstructure and synthesized by direct combination of the stoichiometric elements at 1223 K. As depicted in Fig. 10, all of the ions within the structures occupy general sites and exhibit tetrahedral coordination models. Each Q²⁻ anion is tetrahedrally coordinated with one Mg²⁺ cation, one M⁴⁺ cation, and two Cu⁺ cations, resulting in a 3D honeycomb structure. The remarkable structural characteristic of Cu₂MgM^IVQ₄ is the introduction of a tetrahedrally coordinated Mg²⁺ cation to the M^II sites of diamond-like chalcogenides with the formula M^I₂–M^II–M^IV–Q₄ (where M^I = group 11 metals and Li; M^II = group 12 metals; M^IV = group 14 metals; Q = S, Se).

Fig. 10 3D diamond-like structure of Cu₂MgM^IVQ₄ viewed slightly along the c direction. Copyright 2013 Elsevier.

The experimental E_g were determined to be 3.20 and 2.36 eV for Cu₂MgSiS₄ and Cu₂MgGeS₄, respectively. Although both of them belong to the non-centrosymmetric space group, no noticeable SHG response was observed when testing a modified /Kurtz-NLO system with 1064 and 2100 nm laser radiation.

2.2.8 M^IMg₃M^III₃Q₈ (M^I = Na, Cu, Ag; M^III = Al, Ga; Q = S, Se). M^IMg₃M^III₃Q₈ (M^I = Na, Cu, Ag; M^III = Al, Ga; Q = S, Se) represents a newly discovered quaternary chalcogenide family within the M^I₂Q–M^IIQ–M^III₂Q₃ system. These 9 materials constitute the first series discovered in this family by Li and co-workers in 2022.⁹³ The NaMg₃Ga₃Q₈, NaMg₃Al₃Q₈ and CuMg₃Ga₃S₈ compounds were synthesized utilizing a flux method. The necessary initial reactant, Na/Cu, Mg, and Ga/Al, along with S/Se, were used in a molar ratio of 2 : 3 : 3 : 8. The synthesis process was carried out at a temperature of 1273 K. For the AgMg₃Ga₃Q₈ and LiMg₃Ga₃Q₈ compounds, the same method was applied; however, Ga₂O₃ replaced Ga as the raw material.

Given that M^IMg₃M^III₃Q₈ adopt the same non-centrosymmetric P6̄ space group and exhibit similar structural features, AgMg₃Ga₃S₈ has been chosen as the representative. The S atoms are coordinated with Mg, Ga and Ag atoms to form octahedral [MgS₆], tetrahedral [GaS₄] and triangle-planar [AgS₃] ABUs (Fig. 11a). Interestingly, diverse connection modes such as vertex-, edge-, and face-sharing between these ABUs can be found in this structure. For example, [GaS₄] ABUs interconnect to form 1D [GaS₄]_∞ and [Ga₂S₇]_∞via corner-sharing. Meanwhile, [MgS₆] ABUs connect together to construct 1D [MgS₆]_∞ and [Mg₂S₉]_∞ chains via edge- or/and face-sharing (Fig. 11b). Moreover, the resulting 1D [GaS₄]_∞ and [MgS₆]_∞ chains arrange alternately by vertex-sharing, creating a distinctive windmill-like [Mg₃Ga₃S₂₄] unit (Fig. 11c). Finally, the [Mg₃Ga₃S₂₄] units are linked by the 1D [Ga₂S₇]_∞ and [Mg₂S₉]_∞ chains, and the Ag atoms are positioned in the interior of the [Mg₃Ga₃S₂₄] channels, forming the 3D framework of AgMg₃Ga₃S₈ (Fig. 11d). Compared to the [Ga₆S₁₈] unit in AgGaS₂, the [Mg₃Ga₃S₂₄] unit is formed by replacing three meta-position [GaS₄] ABUs with three [MgS₆] ABUs (Fig. 11d).

Fig. 11 (a) Coordinated environment of [AgS₃], [MgS₆], and [GaS₄] atoms; (b) 1D [GaS₄], [Ga₂S₇], [MgS₆], and [Mg₂S₉] chains; (c) 1D Ga–S chains and [Mg₃Ga₃S₂₄] groups viewed along the ab plane; (d) 3D structure of AgMg₃Ga₃S₈ (left) and AgGaS₂ (right) with the [Ga₆S₁₈] units marked (yellow dashed circle). Copyright 2022 American Chemistry Society.

The experimental results suggest that NaMg₃Ga₃Se₈ has potential as an IR-NLO candidate due to its sufficient d_eff (∼1 × AgGaS₂@180–212 μm), wide selenide E_g (2.77 eV), suitable Δn (0.079@546 nm), and large LIDT (∼2.3 × AgGaS₂). Moreover, the SHG-density maps indicate that the large d_eff in NaMg₃Ga₃Se₈ is mainly provided by the NLO-active [GaSe₄] ABUs. Besides, the optical and NLO parameters of other compounds are presented in Table 1.

Table 1 A summary of reported Mg-based IR-NLO materials

Compound	Mg polyhedron	Unit cell	Space group	E g ^a (eV)	Window of transparence (μm)	d eff	LIDT^b	Δn^c	PM/NPM^d	Ref.
a Experimental value. b Powder sample. c Theoretical value. d PM = phase-matchability, NPM = nonphase-matchability. e N/A = not available.
MgGa2Se4	MgSe4	Tetragonal	I4̄	2.96	1.35–12.43	0.9 × AgGaS2 (@2.09 μm)	3.0 × AgGaS2	0.048 (@0.55 μm)	PM	82
MgSiP2	MgP4	Tetragonal	I4̄2d	2.34	0.53–10.3	3.5 × AgGaS2 (@2.05 μm)	N/A^e	N/A	PM	84
MgSiAs2	MgAs4	Tetragonal	I4̄2d	1.83	N/A	0.6 × AgGaS2 (@2.09 μm)	1.12 × AgGaS2	N/A	PM	85
Li4MgGe2S7	MgS4	Monoclinic	Cc	4.12	N/A	0.7 × AgGaS2 (@2.09 μm)	7.0 × AgGaS2	0.035 (@1.06 μm) (exp.)	PM	86
Li2Mg2Si2S6	MgS6	Trigonal	P31m	3.24	N/A	0.3 × KDP (@1.06 μm)	N/A	N/A	N/A	87
Li2Mg2Ge2S6	MgS6	Trigonal	P31m	3.18	N/A	0.2 × KDP (@1.06 μm)	N/A	N/A	N/A	87
CaMg6Ga6S16	MgS6	Hexagonal	P6̄	3.54	0.35–20	0.7 × AgGaS2 (@2.09 μm)	11.7 × AgGaS2	0.046 (@1.06 μm) (exp.)	PM	88
SrMg6Ga6S16	MgS6	Hexagonal	P6̄	3.51	0.35–20	0.7 × AgGaS2 (@2.09 μm)	11.5 × AgGaS2	0.042 (@1.06 μm) (exp.)	PM	88
BaMg6Ga6S16	MgS6	Hexagonal	P6̄	3.50	0.35–20	0.7 × AgGaS2 (@2.09 μm)	11.5 × AgGaS2	0.041 (@1.06 μm) (exp.)	PM	88
Gd6MgGe2S14	MgS6	Hexagonal	P63	2.77	N/A	0.2 × KDP (@1.06 μm)	N/A	N/A	N/A	89
Li2MgGeSe4	(Li/Mg)Se4	Orthorhombic	Pmn21	2.44 (cal.)	N/A	d 33 = 12.19 pm V^−1 (cal.)	N/A	0.012 (@1.06 μm)	N/A	90
Li2MgSnSe4	(Li/Mg)Se4	Orthorhombic	Pmn21	2.62	N/A	d 33 = 14.77 pm V^−1 (cal.)	N/A	0.011 (@1.06 μm)	N/A	90
Na4MgSi2Se6	MgSe6	Monoclinic	C2	2.53	0.45–20	0.5 × AgGaS2 (@2.09 μm)	9.0 × AgGaS2	0.100 (@1 μm)	PM	91
Na4MgGe2Se6	MgSe6	Monoclinic	C2	2.85	0.45–20	1.3 × AgGaS2 (@2.09 μm)	7.0 × AgGaS2	0.092 (@1 μm)	PM	91
AgMg3Ga3S8	MgS6	Hexagonal	P6̄	3.59	N/A	d 11 = 3.74 pm V^−1 (cal.)	N/A	0.091 (@1.06 μm)	N/A	93
AgMg3Ga3Se8	MgS6	Hexagonal	P6̄	2.43 (cal.)	N/A	d 11 = 10.2 pm V^−1 (cal.)	N/A	0.17 (@1.06 μm)	N/A	93
NaMg3Ga3S8	MgS6	Hexagonal	P6̄	3.70	N/A	d 11 = 3.24 pm V^−1 (cal.)	N/A	0.030 (@1.06 μm)	N/A	93
NaMg3Ga3Se8	MgSe6	Hexagonal	P6̄	2.77	N/A	1.0 × AGS (@2.09 μm)	2.3 × AgGaS2	0.079 (@0.55 μm) (exp.)	PM	93
NaMg3Al3S8	MgS6	Hexagonal	P6̄	4.20	N/A	d 11 = 2.45 pm V^−1	N/A	0.010 (@1.06 μm)	N/A	93
NaMg3Al3Se8	MgS6	Hexagonal	P6̄	3.72 (cal.)	N/A	d 11 = 3.93 pm V^−1	N/A	0.038 (@1.06 μm)	N/A	93
Mg2In3Si2P7	(In/Mg)P4	Monoclinic	P21	2.21	0.56–16.4	7.1 × AgGaS2 (@2.05 μm)	N/A	0.107 (@2.05 μm)	PM	94
Ba6Cu1.9Mg1.1Ge4S16	(Cu/Mg)S4	Cubic	I4̄3d	2.92	N/A	2.3 × AgGaS2 (@2.09 μm)	6.2 × AgGaS2	N/A	NPM	95
Ba6Cu1.9Mg1.1Sn4S16	(Cu/Mg)S4	Cubic	I4̄3d	2.4	N/A	2.5 × AgGaS2 (@2.09 μm)	2.5 × AgGaS2	N/A	NPM	96

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2.2.9 Mg₂In₃Si₂P₇. By implementing a “rigidity-flexibility coupling” approach, a quaternary Mg-based phosphide Mg₂In₃Si₂P₇ was successfully discovered by Ye's group in 2021.⁹⁴ Millimeter-level red crystals of Mg₂In₃Si₂P₇ (2.5 × 1.5 × 0.5 mm³) were obtained by the solid-state method in sealed silica tubes using the starting materials of Mg, In, Si, P and flux BaBr₂ in the molar ratio of 1.33 : 1.5 : 1 : 3.5 : 2.67 at 1073 K.

The Mg₂In₃Si₂P₇ crystal structure displays a diamond-like pattern, which is created by the vertex-sharing [(Mg/In)P₄], [(In/Si)P₄] and [SiP₄] ABUs (Fig. 12a). The tetrahedral [SiP₄] ABUs are integrated into the 12-MR rings of [(Mg/In)₆P₆], thereby generating 1D [(Mg/In)₆SiP₁₆]_∞ chains (Fig. 12a), and the tetrahedral [(In/Si)P₄] ABUs interlink through corner-sharing and form zigzag 1D [(In/Si)P₃]_∞ chains. These two kinds of 1D chains are interconnected to build 2D layers (Fig. 12b), which are arranged in an ABAB fashion, giving rise to a 3D polar structure (Fig. 12a). Additionally, Mg₂In₃Si₂P₇ exhibits a hexagonal close-packed structure that closely resembles wurtzite (Fig. 12c), which was confirmed by the experimental results of the selected area electron diffraction patterns (Fig. 12d).

Fig. 12 (a) Structural evolution from ZnGeP₂ (right) to Mg₂In₃Si₂P₇ (left); (b) single 2D tetrahedral-stacking layer composed of 1D [(Mg/In)₆SiP₁₆] and [In/SiP₃] chains in Mg₂In₃Si₂P₇. (c) Structural evolution from wurtzite ZnS (left) to Mg₂In₃Si₂P₇ (right); (d) electron diffraction patterns of Mg₂In₃Si₂P₇ along the [010] and [100] zone axes. Copyright 2021 American Chemistry Society.

Noticeably, Mg₂In₃Si₂P₇ has achieved rare coexistence of huge d_eff (2 × ZnGeP₂ and 7.1 × AgGaS₂, granularity range 150–212 μm), a sufficient E_g of 2.21 eV, a large Δn of 0.107, and a wide IR transparent window of 0.56–16.4 μm. Theoretical calculations have revealed that the colossal d_eff and large Δn can be attributed to the favorable arrangement of tetrahedral [InP₄] and [SiP₄] ABUs. These findings not only open up a new route for sophisticated IR-NLO crystal design but also have the potential to inspire more discoveries in the quaternary diamond-like families.

2.3 Quinary Mg-based chalcogenides

2.3.1 Ba₆Cu_1.9Mg_1.1Ge₄S₁₆ and Ba₆Cu_1.94Mg_1.06Sn₄S₁₆. Ba₆Cu_1.9Mg_1.1Ge₄S₁₆ and Ba₆Cu_1.94Mg_1.06Sn₄S₁₆ were reported by Wang's group in 2021 and 2022, respectively.^95,96 Both of them can be obtained through the traditional high-temperature solid-state method using the stoichiometric amounts of the reagents at 1073 K, with the difference being that the former requires the use of KI salt as the flux, while the latter does not.

Ba₆Cu_1.9Mg_1.1Ge₄S₁₆ and Ba₆Cu_1.94Mg_1.06Sn₄S₁₆ are both members of the M^II₆M^I₄M^IV₄Q₁₆ (M^II = Sr, Ba; M^I = Li, Cu, Ag; M^IV = Ge, Sn; Ch = S, Se) family.^101,102 These two compounds feature mixed locations at the Li/Cu/Ag atomic sites, where M^I metals are replaced by M^II metals. Since both compounds belong to the same non-centrosymmetric I4̄3d space group and exhibit similar structural features, Ba₆Cu_1.9Mg_1.1Ge₄S₁₆ has been chosen as the representative. The 3D framework is formed by tetrahedral [(Cu/Mg)S₄] and [GeS₄] ABUs through corner-sharing S atoms, where the charge-balanced Ba²⁺ packing in the empty spaces. The polyhedral and ball–stick modes of Ba₆Cu_1.9Mg_1.1Ge₄S₁₆ are displayed in Fig. 13a and b, respectively. Besides, the coordination environment between the tetrahedral [(Cu/Mg)S₄] and [GeS₄] ABUs is highlighted in Fig. 13c.

Fig. 13 Crystal structural of Ba₆Cu_1.9Mg_1.1Sn₄S₁₆: (a) polyhedral packing model; (b) ball-and-stick model; (c) coordination environment of [(Cu/Mg)S₄] (pink) and [SnS₄] (blue) tetrahedra. Black: Ba; red: Mg; blue: Cu; pink: Sn; yellow: S. Copyright 2021 American Chemistry Society.

The experimental E_g was determined to be 2.92 and 2.24 eV for Ba₆Cu_1.9Mg_1.1Ge₄S₁₆ and Ba₆Cu_1.94Mg_1.06Sn₄S₁₆, respectively. Through the placement of monovalent Cu⁺ with divalent Mg²⁺, the optical properties can be shifted to promote a good balance between d_eff and LIDT. For instance, Ba₆Cu_1.9Mg_1.1Ge₄S₁₆ possesses a strong non-phase-matching d_eff and a high LIDT of 2.3 × AgGaS₂ and 6.2 × AgGaS₂ within the particle size range of 28–55 μm, respectively. Theoretical calculations confirmed that the [(Cu/Mg)S₄] and [GeS₄] ABUs are the major role of the SHG responses.

3. Conclusions and perspectives

Research interest in new IR-NLO candidates has stimulated the rapid development of new NCS Mg-based chalcogenides and pnictides. In this review, we presented a brief introduction to the solid-state synthesis, structural design, and NLO properties together with the structure–property relationship of the recently reported Mg-based IR-NLO materials. The distribution of E_g (eV) in relation to d_eff (× AgGaS₂) and detailed performance comparison for previously reported Mg-based IR-NLO materials are illustrated in Fig. 14, 15 and Table 1, respectively. From this, certain characteristics can be inferred:

(i) The currently reported Mg-based IR-NLO materials (including 36 chalcogenides and 4 pnictides) are mainly quaternary compounds (87.5%), with a small amount of ternary (7.5%) and pentagonal (5%) compounds (Fig. 14a and b). Moreover, they mainly belong to the highly symmetrical crystal systems, such as the hexagonal space group of P6₃ (27.5%) and P6̄ (30%) (Fig. 14c).

Fig. 14 Distributions of the Mg-based IR-NLO materials according to (a) material type, (b) chemical component and (c) the space groups in different crystal systems.

(ii) The Mg-based compounds mentioned above are synthesized using traditional high-temperature solid-state methods. Some of them require the use of fluxes to assist in the reaction, including Bi, NaCl, NaI, KI, CsCl, CaCl₂, BaCl₂, and BaBr₂. Furthermore, it is worth noting the synthesis of RE₆MgSi₂S₁₄, which utilizes a boron chalcogen mixture method. It is anticipated that this method can be expanded to other chalcogenide systems, allowing for the exploration of further captivating physical properties.

(iii) As displayed in Fig. 15, most of them are stronger than commercial AgGaS₂ (E_g = 2.56 eV and d_eff = 1 × AgGaS₂). Remarkably, quaternary pnictide Mg₂In₃Si₂P₇ exhibits the largest d_eff (7.1 × AgGaS₂) due to the most favorable combination and arrangement of ABUs, while NaMg₃Al₃S₈ possesses the widest E_g of 4.20 eV in this system.

Fig. 15 Comparison of the d_eff (× AGS) and E_g (eV) for selected Mg-based materials with IR NLO properties.

(iv) Due to the incompatibility of optical parameters, there are currently no reports of IR-NLO Mg-based materials that can achieve a balance between large E_g (>3.0 eV) and strong phase-matching d_eff (>1.0 × AgGaS₂).

Many distinguished researchers have made significant contributions in exploring and verifying the potential of Mg-based IR NLO materials. However, more research is required to fully uncover the potential of these materials. Some possible avenues for further progress are outlined below:

(1) The pnictide system shows promise for further exploration. However, only a few Mg-based pnictides have been reported, and their usability has been limited by their narrow E_g. To increase the E_g, an effective solution could be to introduce high electronegativity “structure scissors” ions, such as alkali metals, alkaline earth metals, and halogens.

(2) Efforts are underway to synthesize high-performance Mg-based IR-NLO compounds by combining other ABUs. Currently, distorted [MQ₄] tetrahedra (M = group 13 and 14 metal elements) are the most commonly used second ABUs, but it would be worthwhile to experiment with introducing other ABUs, such as, lone-pair-cation-based [MQ_n] ABUs, distorted [REQ_n] ABUs, or mixed-anion [MO_xQ_y] ABUs.

(3) The theoretical calculation system for IR-NLO materials requires further study. Researchers can gain crucial properties through first-principles calculations, reducing the experimental blind spots and deepening the understanding of structure–activity relationships. Due to the development of anionic group theory in the research of oxide systems, there is still a significant difference between the calculation results and single crystal tests when applied to chalcogenides and pnictides. Therefore, there is an urgent need to establish a theoretical system that is suitable for IR-NLO materials.

(4) The study of large-sized crystal growth still requires further enhancement. After identifying crystals with exceptional properties, it is crucial for their scientific and technological development to investigate the possibility of growing them into large-sized crystals for commercial purposes.

Author contributions

Jia-Xiang Zhang: investigation and writing – original draft. Mao-Yin Ran: investigation and formal analysis. Xin-Tao Wu: conceptualization and formal analysis. Hua Lin: supervision, conceptualization and writing – review and editing. Qi-Long Zhu: supervision and writing – review and editing.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

This work was sponsored by the National Natural Science Foundation of China (21771179), Fujian Science & Technology Innovation Laboratory for Optoelectronic Information of China (2021ZR118), and the Natural Science Foundation of Fujian Province (2022L3092 and 2023H0041).

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