Isovalent cation substitution drives structural transformation and infrared nonlinear optical activity in Eu-based chalcogenides

Abstract

The development of Eu-based chalcogenides with exceptional nonlinear optical (NLO) performance in the infrared (IR) region has garnered increasing attention. However, the design and synthesis of such compounds with non-centrosymmetric (NCS) structures remain a significant challenge. In this study, we report the successful synthesis of a novel quaternary Eu-based chalcogenide, β-EuZnGeS₄, achieved through an isovalent cation substitution strategy starting from the ternary parent compound Eu₂GeS₄. This innovative approach induces a structural transformation from centrosymmetric to non-centrosymmetric, thereby enhancing the NLO properties. β-EuZnGeS₄ crystallizes in the orthorhombic Fdd2 space group, with a unique two-dimensional [ZnGeS₄]²⁻ layer structure that accommodates Eu²⁺ cations. Notably, β-EuZnGeS₄ exhibits a well-balanced set of optical properties, including a remarkable phase-matching second-harmonic generation (SHG) effect, with its maximum SHG value being twice that of AgGaS₂ with a 2050 nm laser. Additionally, it exhibits a high laser-induced damage threshold, surpassing AgGaS₂ by a factor of 13.1, along with a broad transparency window extending from 0.39 to 23.7 μm. Theoretical calculations further reveal that these outstanding optical properties stem from the synergistic effects of the highly distorted tetrahedral [ZnS₄] and [GeS₄] motifs within the crystal lattice. This work not only expands the materials database for rare-earth metal chalcogenides but also provides a novel strategy for designing NCS structures with tailored optical properties for a wide range of applications.

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Introduction

Nonlinear optical (NLO) materials have garnered unprecedented attention in laser science and technology because of their ability to facilitate frequency conversion in solid-state laser devices.¹ As is widely recognized, an excellent NLO candidate should meet several crucial prerequisites: a sufficient second-harmonic generation (SHG) intensity (d_eff), a large energy gap (E_g), a wide optically transparent window, a moderate birefringence (Δn), chemical stability, and availability for obtaining large single crystals.² In the infrared (IR) region, numerous vital fields, including optoelectronic instruments, resource exploration, and remote laser communication, have gained widespread attention and interest. Despite the strong d_eff exhibited by commercial IR-NLO crystals such as AgGaQ₂ (Q = S, Se)³ and ZnGeP₂,⁴ which make them suitable for applications in the IR region, they still suffer from limitations in high-power laser systems due to their low laser-induced damage thresholds (LIDT) or detrimental two-photon absorption, primarily attributed to their small E_g. However, integrating these optical performances into a single crystal is extremely challenging because they typically depend on competing structural requirements, such as the trade-off between wide E_g and strong d_eff.⁵ Therefore, it is of scientific and technological significance to explore new IR-NLO crystals with outstanding comprehensive performance to overcome these challenges.

Rare-earth (RE) element based chalcogenides have garnered significant attention in the IR-NLO field due to their unique f-electron configurations, strong positive charges, and the high coordination numbers of RE cations. These characteristics often result in distinctive NLO responses and exceptional thermal stability, positioning RE-based chalcogenides as a promising and active area of research.⁶ A number of RE-based chalcogenides with novel non-centrosymmetric (NCS) structures have been discovered, several of which exhibit strong SHG responses, such as La₂Sr₃Sn₃S₁₂ (1.4 × AgGaS₂@200–250 μm),^7a La₄InSbS₉ (1.5 × AgGaS₂@150–210 μm),^7b Sm₄GaSbS₉ (3.8 × AgGaS₂@46–74 μm),^7c and La₆Ga₂GeS₁₄ (4.8 × AgGaS₂@74–106 μm).^7d While significant progress has been made, challenges remain that hinder the full potential of this material system. These include: (i) optical E_g issues: many of these materials suffer from narrow optical E_g (<2.33 eV), which limits their ability to mitigate harmful two-photon or free-carrier absorption under fundamental 1064 nm laser excitation. (ii) Phase matching challenges: achieving efficient phase matching is difficult due to the small birefringence (Δn), which complicates their use in practical NLO devices. (iii) Synthesis limitations: the difficulty in synthesizing high-quality crystals, particularly those exceeding millimeter-scale dimensions. Therefore, this system still holds significant potential for further development and exploration.

Recently, our research was centered on Eu-based chalcogenides, primarily due to the unique valence state and coordination characteristics of Eu(II) in comparison with other RE(III) elements in IR-NLO materials.⁸ Through the facile boron-chalcogen method,⁹ we have successfully synthesized a series of promising Eu-based materials. In the course of our ongoing experiments, we obtained a previously reported ternary compound, Eu₂GeS₄.¹⁰ Despite the presence of asymmetric [GeS₄] units within the structure, these units are arranged in an antiparallel configuration, which leads to crystallization in the centrosymmetric (CS) space group. As a result, this compound does not exhibit NLO activity. It is well-established that crystallization in the NCS space group is a prerequisite for a material to become a viable NLO candidate.¹¹ Among various strategies for obtaining NCS structures, chemical substitution stands out as one of the simplest and most effective approaches, particularly when cation substitution is applied to CS compounds as the parent structure.¹² There are several successful examples of this method: for instance, in the compound CS Rb₄Hg₂Ge₂S₈, replacing Rb with Na in a 3 : 1 ratio led to the formation of the NCS (Na₃Rb)Hg₂Ge₂S₈.¹³ Similarly, by substituting As with Ga in CS Ba₂AsGaSe₅, the NCS compound Ba₂As₂Se₅ was obtained.¹⁴ Another example includes the substitution of Sb in CS K₂Sb₄S₇ with Ag, resulting in the formation of NCS K₂Ag₃Sb₃S₇.¹⁵ However, to the best of our knowledge, there have been no reports to date regarding the substitution of RE metals with transition metals to induce a CS-to-NCS structural transformation.

Guided by the considerations mentioned above, a novel quaternary NCS Eu-based chalcogenide, β-EuZnGeS₄, was synthesized using an isovalent cation substitution strategy, with the ternary CS compound Eu₂GeS₄ serving as the structural template. As anticipated, β-EuZnGeS₄ exhibits a well-balanced set of optical properties, including a significant phase-matching SHG effect (2.0 × AgGaS₂@46–74 μm), a high LIDT of 13.1 × AgGaS₂, and a broad transparency window ranging from 0.39 to 23.7 μm. These outstanding characteristics position β-EuZnGeS₄ as a promising candidate for IR-NLO applications. In this work, we systematically report its synthesis, crystal structure, optical properties, and theoretical calculations.

Results and discussion

Red-brown single crystals of β-EuZnGeS₄ were successfully synthesized through a straightforward boron-chalcogen reaction, using a molar ratio of Eu₂O₃ : Zn : Ge : S : B = 1 : 2 :2 : 8 : 2, with a total mass of 500 mg, at a reaction temperature of 1173 K (see the “Experimental section” for detailed synthesis procedures). Elemental distribution maps, obtained via scanning electron microscopy (SEM), demonstrate that Eu, Zn, Ge, and S are uniformly distributed throughout the crystal structure (Fig. 1a). Energy-dispersive X-ray (EDX) spectroscopy analysis further confirmed that the elemental composition of the synthesized crystals matches the stoichiometric formula determined from single-crystal X-ray diffraction (XRD) data (Fig. S1†). Powder XRD patterns confirm the high purity of the synthesized β-EuZnGeS₄ crystals (Fig. 1b). Thermal stability was assessed using thermogravimetric-differential thermal analysis (TG-DTA), which showed that β-EuZnGeS₄ remains thermally stable up to 1073 K, as depicted in Fig. 1c. This indicates the compound's excellent stability at elevated temperatures, further enhancing its suitability for high-performance applications in nonlinear optics and other fields. To investigate their optical properties, UV–vis–NIR diffuse reflectance spectra of β-EuZnGeS₄ and Eu₂GeS₄ were recorded and are shown in Fig. 1d and S2.† The diffuse reflectance spectra were converted to absorbance data using the Kubelka–Munk function.¹⁶ The experimental optical E_g for β-EuZnGeS₄ and Eu₂GeS₄ were determined to be 2.42 eV and 2.17 eV, respectively, which are in good agreement with their crystal colors. Notably, these values are higher than those reported for most Eu-based IR-NLO materials, such as EuHgGeSe₄ (E_g = 1.97 eV),¹⁷ EuHgGeS₄ (E_g = 2.04 eV),¹⁸ EuHgSnS₄ (E_g = 2.14 eV),¹⁷ and EuCdGeSe₄ (E_g = 2.25 eV).¹⁹ Moreover, Fig. S3† displays the variation of E_g as a function of unit cell volume (V Å⁻³) for the phases in the X^II–M^II–M^IVQ₄ (X^II = Eu, Sr, Ba; M^II = Zn, Cd, Hg; M^IV = Si, Ge, Sn; Q = S, Se) family with the space group Fdd2. When all compounds are considered, the coefficient of determination (R²) is 0.455. However, excluding the Eu-based materials increases the R² to 0.658. Some similar linear relationships are observed in the A-M^II₄-M^III₅-Q₁₂ and A₂-M^II-M^IV₃-Q₈ systems.^20,21 As shown in the inset map in Fig. 1d, millimeter-sized single crystals of β-EuZnGeS₄ were successfully grown, and the crystals exhibit excellent air stability, maintaining their integrity for over 6 months without noticeable degradation (see Fig. S4† for details). Furthermore, β-EuZnGeS₄ exhibits a broad optical transparency spanning the range of 0.39 to 23.7 μm (Fig. 1e), making it a promising candidate for a variety of optical applications. Additionally, two distinct absorption peaks are observed in the 16–21 μm range. The energy of the absorptions in this region is too high to correspond to any vibrational or phonon modes of β-EuZnGeS₄. These absorptions may instead be related to the low-frequency phonon modes of the lattice.

Fig. 1 Experimental characterization results of β-EuZnGeS₄: (a) SEM image and corresponding elemental distribution maps; (b) experimental (blue) and simulated (red) powder XRD patterns; (c) TG-DTA test curves; (d) UV–vis–NIR spectrum (inset: photograph of the title crystals); and (e) optical transmittance spectrum.

The ternary maternal structure of Eu₂GeS₄ belongs to the monoclinic system and contains two unique Eu atoms (Wyckoff site: 2e), one unique Ge atom (Wyckoff site: 2e), and three unique S atoms (Wyckoff sites: 2e and 4f) in the asymmetric unit. In this structure, the Ge⁴⁺ cation occupies the center of its regular tetrahedron, with Ge–S bond lengths ranging from 2.203 to 2.212 Å and ∠S–Ge–S bond angles spanning from 100.55° to 115.63°. When the Eu–S bonds are excluded, the Eu₂GeS₄ structure exhibits a pseudo-zero-dimensional (0D) arrangement, as all the [GeS₄] tetrahedral units are isolated, with counterbalancing Eu²⁺ cations located between them (Fig. 2a). Unfortunately, the [GeS₄] tetrahedra in the structure are arranged centrosymmetrically in a reverse orientation, leading to the cancellation of microscopic second-order polarizability. Consequently, Eu₂GeS₄ does not exhibit NLO activity.

Fig. 2 Structure evolution from ternary CS Eu₂GeS₄ to quaternary NCS β-EuZnGeS₄ through an isovalent cation substitution strategy: (a) view of the 0D isolated structure of Eu₂GeS₄ along the bc plane (Eu–S bonds are omitted); (b) view of the 2D layered structures of β-EuZnGeS₄ along the ab plane (Eu–S bonds are omitted); (c) view of the 2D [ZnGeS₄]²⁻ layer of β-EuZnGeS₄ along the bc plane with the (d) 12-MR rings [Zn₃Ge₃S₁₆]¹⁴⁻ marked; (e) a 2D Eu–S layer in the Eu₂GeS₄ composed of polyhedral [EuS₆] motifs; and (f) 3D Eu–S framework in β-EuZnGeS₄ composed of polyhedral [EuS₈] motifs.

Single-crystal XRD analysis of β-EuZnGeS₄ reveals that it crystallizes in the orthorhombic system, specifically within the NCS space group Fdd2 (no. 43), with a Pearson symbol of oF240 and an idealized Wyckoff sequence of a²b¹³. The unit cell parameters are a = 20.6941(8) Å, b = 20.4059(6) Å, and c = 12.2283(4) Å (Table S1†). The asymmetric unit contains three crystallographically independent Eu atoms (occupying Wyckoff sites 8a and 16b), two independent Zn atoms (Wyckoff site 16b), two independent Ge atoms (Wyckoff site 16b), and eight independent S atoms (Wyckoff site 16b). The atomic parameters and selective bond lengths, summarized in Tables S2 and S3,† reveal bond distances ranging from 2.292 to 2.407 Å for tetrahedral [ZnS₄] units and from 2.194 to 2.234 Å for tetrahedral [GeS₄] units. These values are in good agreement with those reported for similar Zn- and Ge-based chalcogenides.²² As shown in Fig. 2b, β-EuZnGeS₄ is constructed by filling the voids within 2D [ZnGeS₄]²⁻ layers, which extend along the ab plane, with charge-balanced Eu²⁺ cations. Fig. 2c illustrates that adjacent [ZnS₄] and [GeS₄] tetrahedra (a total of six) are interconnected through vertex and edge-sharing, forming [Zn₃Ge₃S₁₆]¹⁴⁻ 12-membered rings (12-MRs). These 12-MR [Zn₃Ge₃S₁₆]¹⁴⁻ rings further link together by corner-sharing to create a 2D [ZnGeS₄]²⁻ layer that extends along the bc plane, as highlighted in the red-shaded area in Fig. 2d.

The structural evolution from the ternary CS Eu₂GeS₄ to the quaternary NCS β-EuZnGeS₄, achieved through an isovalent cation substitution strategy, is depicted in Fig. 2. The choice of substituting Eu²⁺ with Zn²⁺ is driven by two key considerations: first, from a structural perspective, the ionic radii of Eu²⁺ and Zn²⁺ differ significantly, leading to distinct coordination preferences. Eu²⁺, with its larger ionic radius, tends to form multiple coordination numbers (CNs), while Zn²⁺, with a smaller ionic radius, favors the formation of 4-coordination structures. This difference in coordination preferences is crucial for disrupting the original CS structure and enabling the formation of an NCS structure. Second, from a functional standpoint, the introduction of Zn²⁺, a d¹⁰ cation with a relatively small covalent radius, into the crystal structure has been shown to increase the E_g while maintaining a relatively large SHG effect.²³ This effect has been previously validated in analogous systems, where the incorporation of Zn²⁺ ions enhances the material's NLO properties. These dual structural and functional advantages underscore the rationale for selecting Zn²⁺ as an isovalent substitute for Eu²⁺ in this context. As anticipated, notable structural changes occurred following the substitution: (i) increased distortion of tetrahedra: the degree of distortion in the [GeS₄] tetrahedra increased significantly, from 0.003 in Eu₂GeS₄ to 0.015 in β-EuZnGeS₄. Additionally, the distortion in the newly introduced [ZnS₄] tetrahedra was also more pronounced, with a distortion degree of 0.046. This indicates that the substitution of Zn²⁺ for Eu²⁺ introduces greater geometric flexibility, which is reflected in the increased distortion of the tetrahedral units. (ii) Changes in the Eu–S bonding and coordination: in CS Eu₂GeS₄, Eu and S form a 2D layered structure, while in NCS β-EuZnGeS₄, the Eu–S bonding results in a more complex 3D framework structure. This transition is accompanied by a change in the CN of the Eu atoms, from a coordination number of 6 in Eu₂GeS₄ to 8 in β-EuZnGeS₄, as illustrated in Fig. 2e, 2f and S5, S6.†

The discovery of β-EuZnGeS₄ completes a long-missing piece in the X^II–M^II–M^IV–Q₄ (X^II = Eu, Sr, Ba; M^II = Zn, Cd, Hg; M^IV = Si, Ge, Sn; Q = S, Se) family.²⁴ Remarkably, this family includes four distinct NCS structural types, all of which crystallize in orthorhombic space groups (i.e., Fdd2 (no. 43), Ama2 (no. 40), and Pnn2 (no. 34)). These structures share similar unit cell parameters that are capable of doubling, and they possess a polar 2-fold screw axis along the c-axis. As illustrated in Fig. 3a, the structures of these compounds can be broadly classified into two categories: (1) 2D structures, formed by various methods of linking 12MR [M^II₃M^IV₃Q₁₆]¹⁴⁻ rings, and (2) 1D chain structures, consisting of dimers [M^IIM^IVQ₆] connected through shared edges. The relationship between the degree of structural distortion, quantified by Δd and Δθ, and the space groups is shown in Fig. 3b and further detailed in Table S4.† The analysis reveals several key trends: (i) within the brown region, where Δd < 0.07 Å and Δθ < 22°, the compounds crystallize in the Ama2 space group, and the anionic groups predominantly form 1D chains; (ii) within the blue region, where 0.07 < Δd < 0.17 Å and 22° < Δθ < 32°, the compounds adopt the Fdd2 space group, with the anionic groups favoring a 2D layered arrangement; and (iii) within the yellow region, where Δd > 0.17 Å and Δθ > 32°, the compounds belong to either the Ama2 or Pnn2 space group, with anionic groups again forming 2D layers. These findings align with the conclusions drawn by Yu et al. in the AE–M^II–M^IV–Q₄ (AE = alkaline-earth metal) system and underscore the importance of carefully selecting tetrahedral [MQ₄] structural units with varying degrees of distortion. Such an approach enables the design and synthesis of chalcogenides with different space groups within the X^II–M^II–M^IV–Q₄ family. This structural flexibility provides a promising pathway for tailoring optical properties, opening new possibilities for the development of materials with enhanced NLO performance.

Fig. 3 (a) Comparison of four distinct structural types within the X^II–M^II–M^IV–Q₄ (X^II = Eu, Sr and Ba; M^II = Zn, Cd, and Hg; M^IV = Si, Ge and Sn; Q = S, Se) family; (b) the relationship between the degree of structural distortion, quantified by Δd (Δd = (d_longest–d_shortest) and (Δd1 + Δd2)/2), Δθ (Δθ = (θ_largest–θ_smallest) and (Δθ1 + Δθ2)/2), and the space groups. The compounds corresponding to the numbers in this figure are listed in Table S4.†

Compared to CS α-EuZnGeS₄ [space group: Fddd (no. 70)], β-EuZnGeS₄ crystallizes in the NCS space group Fdd2 (no. 43), making it a promising candidate for NLO applications. With the modified Kurtz–Perry method,²⁵ the SHG intensity of β-EuZnGeS₄ was evaluated by irradiating it with a 2050 nm laser, using AgGaS₂ as a benchmark. As shown in Fig. 4a, the SHG intensity exhibited a positive correlation with particle size, eventually leveling off, indicating phase-matching behavior. The strongest SHG intensity of β-EuZnGeS₄, at a particle size of 46–75 μm, was approximately twice that of AgGaS₂, and about 0.8 times that of AgGaS₂ at the largest particle size range of 150–210 μm. From these results, the effective SHG coefficient (d_eff) was indirectly calculated using the formula: d_eff = d_eff,_R (I²ω/I_R²ω)^1/2, where d_eff, AgGaS₂ = 13.4 pm V⁻¹,²⁵ yielding a value of 12.1 pm V⁻¹ for β-EuZnGeS₄. This indicates its strong NLO response and is comparable with those recently reported for RE-based IR-NLO chalcogenides Nd₃[Ga₃O₃S₃][Ge₂S₇] (0.8 × AgGaS₂),²⁶ LaCaGa₃OS₆ (0.9 × AgGaS₂),²⁷ KYGeS₄ (1.0 × AgGaS₂),²⁸ K₃HoP₂S₈ (1.1 × AgGaS₂),²⁹ and LaCa₂(BS₃)(SiS₄) (1.1 × AgGaS₂).³⁰ Another crucial parameter for NLO materials is the LIDT, which is important for high-power laser applications. The powder LIDT was measured by gradually increasing the laser output energy until material damage was observed under an optical microscope.³¹ The LIDT of polycrystalline β-EuZnGeS₄ was found to be 36.94 MW cm⁻², approximately 13.1 times that of commercial AgGaS₂ (2.83 MW cm⁻²) under identical conditions. This LIDT value is competitive with those of other recently reported IR-NLO crystals, such as [Ba₄(Ba₆S)][(VO₃S)₆] (7.65 × AgGaS₂),³² LiCaPS₄ (10 × AgGaS₂),³³ LaBS₃ (14 × AgGaS₂),³⁴ and Sr₂GeGa₂OS₆ (12.4 × AgGaS₂).³⁵ Additionally, Fig. 4b compares the comprehensive NLO performance of β-EuZnGeS₄ with that of the commercial benchmark AgGaS₂. The larger the area of the radar chart, the better the overall optical performance. Notably, β-EuZnGeS₄ outperforms AgGaS₂ in several key aspects: it demonstrates a favorable phase-matching (PM) feature, a strong SHG response (0.8 × AgGaS₂), a giant LIDT (13.1 × AgGaS₂), a sufficient bandgap (E_g > 2.33 eV), and an exceptionally broad IR transmission cut-off range (0.39–23.7 μm). These properties make β-EuZnGeS₄ a promising material for advanced IR-NLO applications.

Fig. 4 (a) SHG intensities vs. particle size at λ = 2050 nm for β-EuZnGeS₄ and AgGaS₂; (b) radar chart (five directions representing the PM feature, IR transmission, SHG, LIDT, and E_g, respectively; the colored shadows represent the areas surrounded by these optical parameters of β-EuZnGeS₄ and AgGaS₂, respectively).

To gain a deeper understanding of the relationship between the crystal structure and the properties of β-EuZnGeS₄, we performed first-principles density functional theory (DFT) calculations to investigate its microscopic mechanisms, including the E_g, partial density of states (PDOS), frequency-dependent SHG coefficients (d_ij), and refractive index dispersion curves, with a focus on the shortest PM cutoff wavelength.³⁶ The linear optical properties, in terms of the complex dielectric function ε(ω) = ε₁(ω) + iε₂(ω), were calculated, and optical constants were derived from the imaginary part of the dielectric function ε₂(ω) using the Kramers–Kronig transformation (see the “Computational details” for detailed calculation procedures and parameter settings in the ESI† section). As shown in Fig. 5a, the theoretical calculations reveal that the valence band maximum (VBM) and conduction band minimum (CBM) are both located at the same G point, confirming that β-EuZnGeS₄ is a direct E_g semiconductor. The theoretical E_g was calculated to be 2.40 eV, which closely matches the experimentally measured value of 2.42 eV. The PDOS analysis further elaborates on the energy contributions from various atomic orbitals (Fig. 5b). The valence band (VB-1), near the Fermi level, is primarily composed of Zn-3d, S-3p, and Ge-4p orbitals, while the conduction band (CB-1), also near the Fermi level, is largely influenced by Eu-4f, Zn-4s, Ge-4s, and S-3p orbitals. This analysis highlights the significant role of the [ZnS₄] and [GeS₄] tetrahedral units, particularly the impact of the 2D [ZnGeS₄]²⁻ layers, in determining the electronic structure and, by extension, the optical properties of β-EuZnGeS₄.

Fig. 5 Theoretical results of electronic structures and optical parameters of β-EuZnGeS₄: (a) band structure; (b) partial density of states; (c) calculated nonzero independent SHG coefficient d_ij (pm V⁻¹); and (d) calculated refractive index dispersion curves with the shortest type-I PM cut-off wavelength.

β-EuZnGeS₄ crystallizes in the NCS Fdd2 space group and belongs to the mm2 point group, which, according to Kleinman's symmetry rule,³⁷ supports three independent non-zero tensors (d₁₅, d₂₄, and d₃₃) for SHG. As illustrated in Fig. 5c, the theoretical SHG coefficients under a phonon energy of 0.61 eV (corresponding to a 2050 nm wavelength) are d₁₅ = 56.37 pm V⁻¹, d₂₄ = 45.34 pm V⁻¹, and d₃₃ = 28.95 pm V⁻¹. Additionally, the refractive indices along the principal optical axes (n_x, n_γ, and n_z) of β-EuZnGeS₄ were calculated, revealing significant optical anisotropy, as demonstrated by a Δn value of approximately 0.19 at 2050 nm (Fig. S7†), which is notably larger than that of AgGaS₂ (Δn = 0.04 at 2050 nm).³⁸ This pronounced Δn value suggests that β-EuZnGeS₄ can theoretically meet the PM conditions for efficient SHG over a broad wavelength range. The substantial refractive index difference is attributed to the material's unique 2D layered structure, which plays a crucial role in enhancing its optical anisotropy and overall NLO performance. From the PM condition for type-I NLO processes, where n_e(2ω) = n_o(ω), the theoretical PM cutoff wavelength for β-EuZnGeS₄ was determined to be around 526 nm (Fig. 5d),³⁹ indicating that this material can efficiently support SHG over a broad spectral range. Together, these insights suggest that β-EuZnGeS₄ is a highly promising material for advanced IR-NLO applications, with a strong SHG response, significant optical anisotropy, and favorable PM characteristics.

To investigate the NLO origins of β-EuZnGeS₄, we performed detailed calculations on the energy-dependent maximum d₁₅ values using the length-gauge formalism,⁴⁰ as shown in Fig. 6a. The results reveal that the d₁₅ coefficient is primarily governed by electronic transitions involving the VB-1, CB-2, and CB-4 regions. These findings are further supported by PDOS analyses (Fig. 5b) and virtual charge density maps (Fig. 6b), which provide additional insight into the electronic structure. The PDOS analysis reveals that VB-1 is mainly composed of S-3p and Zn-3d orbitals, while in the conduction bands CB-2 and CB-4 are dominated by Zn-4s, Ge-4p, and S-3p states. Given the distinctive layered structure of the [ZnGeS₄]²⁻ units, the SHG in β-EuZnGeS₄ primarily arises from electronic transitions between the fundamental building blocks of the crystal: the [ZnS₄] and [GeS₄] tetrahedral units. The layered arrangement of these building blocks enhances the material's NLO properties by facilitating efficient electronic transitions across different bands, thereby contributing significantly to the observed SHG response.

Fig. 6 Theoretical analysis of the intrinsic mechanism of the SHG source for β-EuZnGeS₄: (a) cut-off energy (eV) dependence of the static d₁₅ (pm V⁻¹) and (b) distribution of the partial charge density maps with major contributions in the VB-1, CB-2 and CB-4 regions. Black atoms: Eu; blue atoms: Zn; green atoms: Ge; and yellow atoms: S.

Conclusions

In summary, we successfully designed a new Eu-based chalcogenide, β-EuZnGeS₄, using an isovalent cation substitution strategy and synthesized it via the facile boron-chalcogen method. This innovative approach not only facilitates a structural transformation from CS to NCS configurations but also yields impressive NLO properties. Notably, β-EuZnGeS₄ exhibits a substantial phase-matching SHG response 0.8 times that of AgGaS₂ at 2050 nm, an enhanced LIDT 13.1 times that of AgGaS₂ at 1064 nm, and a wide transparency range spanning from 0.39 to 23.7 μm. Additionally, the material demonstrates a significant birefringence of 0.19 at 2050 nm and remarkable thermal stability, withstanding temperatures up to approximately 1073 K. This work highlights β-EuZnGeS₄ as a promising candidate for IR-NLO applications within the rarely explored Eu-based chalcogenide system. Furthermore, it is poised to stimulate further research into potential rare-earth metal NLO materials.

Author contributions

Ping Feng: investigation, formal analysis, and writing – original draft. Sheng-Hua Zhou: investigation, methodology, and validation. Mao-Yin Ran: investigation, formal analysis, and validation. Bingxuan Li: formal analysis and validation. Xin-Tao Wu: conceptualization and writing – review & editing. Hua Lin: supervision, conceptualization, and writing – review & editing. Qi-Long Zhu: supervision and writing – review & editing.

Data availability

The data supporting this article have been included as part of the ESI.†

Crystallographic data for β-EuZnGeS₄ have been deposited at the CCDC [2385100]† and can be obtained from https://www.ccdc.cam.ac.uk/.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

This work was supported by the National Natural Science Foundation of China (22175175), Natural Science Foundation of Fujian Province (2022L3092 and 2023H0041), Fujian Science & Technology Innovation Laboratory for Optoelectronic Information of China (2021ZR118), and the Youth Innovation Promotion Association CAS (2022303). The authors thank Professor Yong-Fan Zhang at Fuzhou University for helping with the DFT calculations.

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Footnotes

† Electronic supplementary information (ESI) available: Additional experimental and theory results, together with additional tables and figures. CCDC 2385100. For ESI and crystallographic data in CIF or other electronic format see DOI: https://doi.org/10.1039/d4qi03346a

‡ These authors contributed equally to this work.

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