LaMg6Ga6S16: a chemical stable divalent lanthanide chalcogenide

Divalent lanthanide inorganic compounds can exhibit unique electronic configurations and physicochemical properties, yet their synthesis remains a great challenge because of the weak chemical stability. To the best of our knowledge, although several lanthanide monoxides epitaxial thin films have been reported, there is no chemically stable crystalline divalent lanthanide chalcogenide synthesized up to now. Herein, by using octahedra coupling tetrahedra single/double chains to construct an octahedral crystal field, we synthesized the stable crystalline La(II)-chalcogenide, LaMg6Ga6S16. The nature of the divalent La2+ cations can be identified by X-ray photoelectron spectroscopy, X-ray absorption near-edge structure and electron paramagnetic resonance, while the stability is confirmed by the differential thermal scanning, in-situ variable-temperature powder X-ray diffraction and a series of solid-state reactions. Owing to the particular electronic characteristics of La2+(5d1), LaMg6Ga6S16 displays an ultrabroad-band green emission at 500 nm, which is the inaugural instance of La(II)-based compounds demonstrating luminescent properties. Furthermore, as LaMg6Ga6S16 crystallizes in the non-centrosymmetric space group, P−6, it is the second-harmonic generation (SHG) active, possessing a comparable SHG response with classical AgGaS2. In consideration of its wider band gap (Eg = 3.0 eV) and higher laser-induced damage threshold (5×AgGaS2), LaMg6Ga6S16 is also a promising nonlinear optical material.

LaMg 6 Ga 6 S 16 : a chemical stable divalent lanthanide chalcogenide Yujie Zhang 1 , Jiale Chen 1 , Kaixuan Li 1 , Hongping Wu 1 , Zhanggui Hu 1 , Jiyang Wang 1 , Yicheng Wu 1 & Hongwei Yu 1 Divalent lanthanide inorganic compounds can exhibit unique electronic configurations and physicochemical properties, yet their synthesis remains a great challenge because of the weak chemical stability.To the best of our knowledge, although several lanthanide monoxides epitaxial thin films have been reported, there is no chemically stable crystalline divalent lanthanide chalcogenide synthesized up to now.Herein, by using octahedra coupling tetrahedra single/double chains to construct an octahedral crystal field, we synthesized the stable crystalline La(II)-chalcogenide, LaMg 6 Ga 6 S 16 .The nature of the divalent La 2+ cations can be identified by X-ray photoelectron spectroscopy, X-ray absorption near-edge structure and electron paramagnetic resonance, while the stability is confirmed by the differential thermal scanning, in-situ variable-temperature powder X-ray diffraction and a series of solid-state reactions.Owing to the particular electronic characteristics of La 2+ (5d 1 ), LaMg 6 Ga 6 S 16 displays an ultrabroad-band green emission at 500 nm, which is the inaugural instance of La(II)-based compounds demonstrating luminescent properties.Furthermore, as LaMg 6 Ga 6 S 16 crystallizes in the noncentrosymmetric space group, P−6, it is the second-harmonic generation (SHG) active, possessing a comparable SHG response with classical AgGaS 2 .In consideration of its wider band gap (E g = 3.0 eV) and higher laser-induced damage threshold (5×AgGaS 2 ), LaMg 6 Ga 6 S 16 is also a promising nonlinear optical material.
Lanthanide inorganic compounds with low oxidation state (+2) that are capable of exhibiting intriguing physicochemical properties due to the presence of outer shell 4f or 5d conduction carriers in divalent lanthanides ions have showcased the immense potential for application in various frontier fields such as superconductivity, magnetics, photoluminescence [1][2][3][4][5][6][7][8] .However, one intractable drawback to divalent lanthanide compounds is the chemical stability, which seriously precludes their development 9,10 .Recently, although several new types of divalent lanthanide monoxides epitaxial thin films, including YO and LaO, have been prepared, the surfaces of these films must be capped in-situ AlO x layer to prevent the oxidation at room temperature 9,11 .Thus, synthesizing the chemically stable divalent lanthanide compounds is still faced by great challenges.To date, as we know, no any successful stable crystalline divalent lanthanide chalcogenide has been synthesized.
Based on the first-principles calculations, Li et al. have uncovered the octahedral crystal field is vitally pivotal for the formation of the divalent lanthanum in LaO 12 .We have also noticed that almost all the divalent lanthanides (Ln 2+ ) in lanthanide monoxides and monochalcogenides are coordinated by six Q (Q = O or S) atoms to form the [LnQ 6 ] octahedra 4,13 .On the contrary, the high-oxidation-state lanthanides (Ln 3+ ) is typically found in the high-coordinated [LnQ x ] (x = 7 or 8) polyhedra, e.g., La 2 S 3 conforms to Pauling's well-known second rule, i.e., high-valence is favored for high coordination 22 .On the other hand, Evans and Meyer et al.'s research show that the construction of the proper anionic frameworks in combination with lanthanide cations can enhance chemical stability by its gain in lattice energy 23 , as corroborated via the synthesis of a series of stable divalent lanthanide organic complexes, including [ (18-crown-6)  10 .
Clearly, the above studies have implied that the strong octahedral crystal fields and proper anionic framework are crucial for the formation of stable divalent lanthanide compounds.In the recent research, by adopting octahedra to couple tetrahedra single/double chains strategy, a stable crystalline [Mg/Ga-S] ∞ anionic framework with octahedral channel (C 3h ) has been constructed by our group and Pan's group 25,26 , where alkali and alkaline-earth or even other monovalent or divalent cations can be filled (Fig. 1), and all of the resulting compounds exhibit the similar crystal structures, e.g., AMg 3 M 3 Q 8 (A=Li, Na, Ag; M=Al, Ga; Q = S, Se) and AeMg 6 Ga 6 S 16 (Ae=Ca, Sr, Ba).Based on these, we speculated that the framework should be also available for the syntheses of the divalent lanthanide chalcogenide because of its particular structural feature and strong accommodating ability for a wide range of elements and oxidation states.Guided by these ideas, we introduced the lanthanum (La) into the stable [Mg/Ga-S] ∞ anionic framework and successfully synthesized the crystalline La(II)-chalcogenide, LaMg 6 Ga 6 S 16 .In its structure, the stable [Mg/Ga-S] ∞ framework channels create the strong [LaS 6 ] octahedra crystal field, which results in the formation of stable divalent La 2+ possessing the presence of outer shell 5d 1 conduction carriers.Interestingly, owing to the unique electronic characteristics of La 2+ (5d 1 ), LaMg 6 Ga 6 S 16 exhibits an ultrabroad-band green emission at 500 nm with an excitation of 360 nm.This is the inaugural instance of La(II)-based compounds to display luminescent properties.Additionally, as LaMg 6 Ga 6 S 16 crystallizes in the noncentrosymmetric space group of P−6, the excellent nonlinear optical (NLO) properties are also observed in LaMg 6 Ga 6 S 16 , including the relatively large second-order harmonic generation (SHG) response (~0.8×AgGaS 2 ), wide band gap (E g = 3.0 eV), high laserinduced damage threshold (LIDT) (5 × AgGaS 2 ), and wide transparent window (0.41-20 μm).These make LaMg 6 Ga 6 S 16 a promising NLO crystal.Herein, we will report its synthesis, structure, and luminescent and NLO properties.

Results and discussion
Experimental synthesis and structure determination of LaMg 6 Ga 6 S 16 Polycrystalline LaMg 6 Ga 6 S 16 was synthesized through a conventional solid-state technique in sealed silica tubes at 1233 K and the purity of phase was verified by the powder X-ray diffraction (XRD) (Supplementary Fig. 1).Furthermore, the energy-dispersive spectroscopy measurement showed the existence of La/Mg/Ga/S, and their average atomic ratios were approximately equal to the theoretical ones, 3.45%, 20.69%, 20.69%, and 55.12% (Supplementary Fig. 2).Then, the millimeter-sized single crystals of LaMg 6 Ga 6 S 16 were grown by melting and re-crystallizing the stoichiometric pure phase.By using these crystals, the crystal structure of LaMg 6 Ga 6 S 16 was determined by single crystal XRD.It indicates that LaMg 6 Ga 6 S 16 crystallizes in the noncentrosymmetric hexagonal space group P-6 (No.174), with cell parameters of a = 16.7154(5)Å, c = 7.4147(3) Å, and V = 1794.15(13)Å 3 (Supplementary Table 1).In the asymmetric unit, there are three unique La, six unique Mg, three unique Ga, and eleven S atoms (Supplementary Table 2).The Mg atoms are six-coordinated forming [MgS 6 ] octahedra with the Mg−S distances ranging from 2.482(11) to 2.834(18) Å.All of the Ga atoms are coordinated by four S atoms to form [GaS 4 ] tetrahedra, and the Ga-S distances range from 2.226(7) to 2.333(6) Å.The La atoms are coordinated by six S atoms to form [LaS 6 ] octahedra with La-S distances ranging from 2.963(7) to 2.994(7) Å.All of these distances (Supplementary Table 3) are consistent with those in other chalcogenides 17,27,28 .
The structure of LaMg 6 Ga 6 S 16 is shown in Fig. 2. Clearly, LaMg 6 Ga 6 S 16 features a three-dimensional (3D) framework with C 3h symmetry along the c axis and constructed by the [MgS 6 ] octahedra coupling [GaS 4 ] tetrahedra single/double chains (Fig. 2a).In detail, the MgS 6 octahedra are connected with each other via corner-sharing and face-sharing (in the a-b plane) and edge-sharing (along the c-axis) to fabricate a [Mg-S] ∞ framework, as shown in Fig. 2b.While the [GaS 4 ] tetrahedra are connected via corner-sharing to form two types of Ga-S chains along the c-axis, i.e., [Ga(1)S 3 ] ∞ single chains (Fig. 2c) and [Ga(2,3) 2 S 4 ] ∞ double chains (Fig. 2d).Furthermore, the resulting [Ga(1) S 3 ] ∞ single chains are connected and fixed in the [Mg-S] ∞ framework by the Ga-S bonds to create the [Mg/Ga-S] ∞ framework (Fig. 2e), which are further linked by the [Ga(2,3) 2 S 4 ] ∞ double chains to construct the 3D framework structure of LaMg 6 Ga 6 S 16 .The La atoms fill the channel-like cavities of the 3D framework to balance the residual charges (Fig. 2f).
To better characterize the chemical valence of La in LaMg 6 Ga 6 S 16 , the synchrotron X-ray absorption spectroscopy (XAS) measurements of LaMg 6 Ga 6 S 16 and La 2 S 3 were performed.As indicated by the La L-edge X-ray absorption near-edge structure (XANES) spectra (Fig. 3b), LaMg 6 Ga 6 S 16 exhibits an absorption edge with energy lower than that of La 2 S 3 , indicating a lower valence state La in LaMg 6 Ga 6 S 16 than that of La 2 S 3 (+3) 31,32 .This is in good agreement with the XPS results.Further, we also used electron paramagnetic resonance (EPR) to characterize the La 2+ (5d Further, the thermal behavior of LaMg 6 Ga 6 S 16 was studied by differential thermal scanning (DSC) measurements.Clearly, only one endothermic peak at 1140 °C was observed on the heating DSC curve (Supplementary Fig. 3), suggesting that LaMg 6 Ga 6 S 16 did not undergo the decomposition and structural phase transitions when the temperature was increased from room temperature to 1140 °C.Moreover, in-situ variable-temperature powder X-ray diffraction and a series of solid-state reactions in the sealed silica tubes with the different calcinated temperatures show LaMg 6 Ga 6 S 16 has no phase transition when its polycrystalline sample was heated from 10 K to 1273 K (Supplementary Fig. 4), which also manifest that LaMg 6 Ga 6 S 16 is thermally stable.Meanwhile, the crystal of LaMg 6 Ga 6 S 16 was placed in the air and water at room temperature for one week with no decomposition or degradation observed (Supplementary Fig. 5).In addition, Global Instability Index (GII) of LaMg 6 Ga 6 S 16 is calculated 33,34 , and the result (0.088) is lower than 0.2 v.u.That also indicates the structural stability of LaMg 6 Ga 6 S 16 35-37   .The nature of the stable divalent La 2+ cations in LaMg 6 Ga 6 S 16 could be attributed to the unique [Mg/Ga-S] ∞ anionic framework.Comparing LaMg 6 Ga 6 S 16 with LaO and LaS, it can be seen that these La 2+ cations exhibit the similar coordination features, i.e., La 2+ cations are six-coordinated in LaO 6 or LaS 6 octahedral crystal fields (Fig. 3d), while the previous studies in LaO also elucidate that octahedral crystal field is helpful for the formation of divalent lanthanum 12 .In LaO and LaS, LaO 6 and LaS 6 octahedra are connected with each other via edgesharing to build the whole structure, respectively.According to Pauling's third rule 22 , such connections are disadvantageous for structural stability owing to the increased cation-cation electrostatic repulsion.Also, the calculated results of their GII show that LaO (0.215) and LaS (0.349) have greater than 0.2 valence unit (v.u) 34 , which indicates their structures are indeed metastable.Importantly, previous research finds that constructing the proper anionic frameworks to couple lanthanum cations can enhance the chemical stability of compounds by effectively harnessing the gain in lattice energy 23 .The formation of both divalent lanthanum organic complexes is an excellent example to demonstrate this concept (Fig. 3e).Similar to the case with organic complexes, we developed a crystalline [Mg/Ga-S] ∞ structural framework by adopting octahedra coupling tetrahedra single/double chains strategy.Of note, such a framework possesses interconnected structures in which the neatly arranged [Ga-S] chains were connected by the [Mg-S] framework via covalent bonds.Such interconnected structure endowed [Mg/Ga-S] ∞ structural framework with strong chemical stability, which has also been demonstrated in the reported covalent organic frameworks 38 .Additionally, the stable structural framework can be used as a template to accommodate a series of A atoms (A=Li, Na, Ca, Sr, Ba, and even La) while spatially confining these atoms into atomic-scale channels via coordination configurations.In particular, the coordination bond lengths of A-S are in the range of 2.934-3.138Å, which provides a suitable micro-environment for La because the bond lengths of La-S are about 3.000 Å 16,39 .More importantly, the crystalline [Mg/Ga-S] ∞ framework channels possess C 3h symmetry along the caxis, in which the six-coordinated LaS 6 octahedral crystal field can be created (Fig. 3f).That facilitates the formation of divalent lanthanum when introducing La into the crystalline [Mg/Ga-S] ∞ anionic framework.Further, the LaS 6 octahedra in LaMg 6 Ga 6 S 16 are isolated and aligned arrangements along the c-axis with a longer La-La distance of 7.4147 Å than 4.1394 Å in LaS, which greatly reduces electrostatic repulsion between La 2+ .These structural attributes of LaMg 6 Ga 6 S 16 will be able to promote it exhibiting good chemical stability.

Photoluminescence (PL) properties
Given the electronic characteristics of divalent lanthanum, we investigated the luminescence features of LaMg 6 Ga 6 S 16 .The PL excitations at room temperature (298 K) were measured under the excitation of 340-380 nm.As shown in Fig. 4a, the optimal excitation wavelength is about 360 nm.Under the excitation of 360 nm at room temperature, LaMg 6 Ga 6 S 16 shows an ultrabroad-band green emission at 500 nm with a full width at half maximum (FWHM) of 127 nm (Fig. 4b).The ultrabroad emission band cover almost the whole visible light region and could find applications in the field of human-centric full-visiblespectrum lighting 40 .Meanwhile, this characteristic green emission under 360 nm excitation endows LaMg 6 Ga 6 S 16 with the potential lightemitting diode application under the excitation of commercial near ultraviolet chips 41 .Further, to investigate the origin of luminescence properties, the thermoluminescence (TL) measurement of LaMg 6 Ga 6 S 16 is performed.As shown in Fig. 4c, the sample shows a very weak TL glow curve in the range of 290 K to 450 K, indicating a low content of defects in LaMg 6 Ga 6 S 16 .By fitting the TL curve with two Gaussian bands peaking at 346 K and 384 K, the characteristic trap depths (E T ) were estimated to be 0.69 and 0.77 eV by using the crude relationship E T = T m /500 eV, where T m represents the temperature (K) of the TL fitting peak 42,43 .In view of the EPR results (g = 2.008) (Fig. 3c), it is evident that the two trap depths originate from the intrinsic defects, corresponding to the slight S vacancies defect 44,45 .Based on these studies, the strong green emission observed in LaMg 6 Ga 6 S 16 does not stem from intrinsic defects of exceedingly low content.In order to find out the origin of PL property of LaMg 6 Ga 6 S 16 , we also measured the luminescence features of CaMg 6 Ga 6 S 16 and SrMg 6 Ga 6 S 16 , which are isomorphous to LaMg 6 Ga 6 S 16 with chemical substitutions from La to Ca or Sr. Experimental results indicate CaMg 6 Ga 6 S 16 (Fig. 4d) and SrMg 6 Ga 6 S 16 (Supplementary Fig. 6) have no PL emission.Also, when the polycrystalline samples of CaMg 6 Ga 6 S 16 , SrMg 6 Ga 6 S 16 and LaMg 6 Ga 6 S 16 were radiated by the UV irradiation, only LaMg 6 Ga 6 S 16 exhibited the green light emission (Supplementary Fig. 7).These results suggest that the PL property of LaMg 6 Ga 6 S 16 should come from the La cations, rather than the [Mg/Ga-S] ∞ anionic frameworks.But, the previous research 46 has confirmed that the trivalent La 3+ cations cannot exhibit luminescent properties (we also measured the PL spectrum of La 2 S 3 (Supplementary Fig. 8), which show that La 2 S 3 with the trivalent La 3+ cations have no PL property).So, these results also further indicate the nature of the divalent La 2+ (5d 1 ) cations in LaMg 6 Ga 6 S 16 .Referencing Li's, et al. firstprinciples calculations on the octahedral crystal-field splitting gap between the upper-lying e g and lower-lying t 2g for the La 2+ 5d orbitals in monoxide LaO, we can conclude that the green emission position at 500 nm in LaMg 6 Ga 6 S 16 should originate from the d-d transition of the La 2+ within the low-coordinated octahedral crystal field, because the octahedral crystal-field splitting gap for the La 2+ 5d orbitals is approximately 2.50 eV (Fig. 4e) 1,10,12,47 , which is precisely consistent with the green emission position at 500 nm in LaMg 6 Ga 6 S 16 .
Meanwhile, the decay curve of LaMg 6 Ga 6 S 16 under excitation at 360 nm, monitored at the peak of 500 nm at room temperature is presented in Fig. 4f.The decay curve can be fitted using a double exponential decay formula (1) 48

IðtÞ = I
where I(t) and I 0 denote the luminescence intensity, A 1 and A 2 are the corresponding fitting constants, and τ 1 and τ 2 are the decay time for an exponential component.As shown in Fig. 4f, by using the above fitting equation, the decay time for LaMg 6 Ga 6 S 16 can be fitted to τ 1 = 1.32 μs and τ 2 = 15.01 μs.According to the formula (2) 43 , the value of average lifetimes (τ ave ) was calculated to be 6.63 μs, which is similar to divalent lanthanide compounds with lifetimes in the microsecond time-range (0.5-10 μs) 1,3,48,49 .

NLO properties
Since LaMg 6 Ga 6 S 16 belongs to the non-centrosymmetric class and features the stable [Mg/Ga-S] ∞ frameworks constructed by the NLOactive [GaS 4 ] tetrahedra and [MgS 6 ] octahedra, the NLO properties are also investigated.As a result, LaMg 6 Ga 6 S 16 shows a phase-matchable (PM) SHG response of 0.8×AgGaS 2 @2090 nm (Fig. 5a and Supplementary Table 4) [58][59][60] .The birefringence of LaMg 6 Ga 6 S 16 was also measured on a plate-shaped crystal.It indicates that the birefringence of LaMg 6 Ga 6 S 16 at visible light is 0.041 (Fig. 5b and Supplementary Fig. 9) 61,62 .Meanwhile, the ultraviolet-vis-NIR diffusion spectrum shows that the band gap of LaMg 6 Ga 6 S 16 is 3.0 eV (Fig. 5c).The relatively large band gap causes LaMg 6 Ga 6 S 16 to generate a high powder LIDT (~105 MW•cm −2 ) [63][64][65] , which is more than five times that of AgGaS 2 (~20 MW•cm −2 ) 66 .Furthermore, Fourier transformation infrared (IR) (Fig. 5d) and Raman spectra (Fig. 5e) indicates that LaMg 6 Ga 6 S 16 has no obvious absorption in a wide IR range from 4000 to 500 cm −1 (i.e., 2.5 ~20 μm).Especially, compared with commercial AgGaS 2 and other important IR NLO crystals, LaMg 6 Ga 6 S 16 exhibits well-balanced NLO properties, including wide transmission region and band gaps, high LIDT, moderate birefringence as well as PM SHG responses (Fig. 5f and Supplementary Table 5).These suggest that LaMg 6 Ga 6 S 16 is also a promising IR NLO crystal.It is worth noting that the excellent NLO properties of LaMg 6 Ga 6 S 16 can, to some extent, be attributed to the particular contribution of La 2+ cations.Since rare-earth La 2+ cation can exhibit similar polarizability with the transition Ag + and Zn 2+ cations and comparable electropositivity with the alkali and alkaline-earth cations, LaMg 6 Ga 6 S 16 can combine the advantages of large SHG responses of transition-cations chalcogenides and large band gaps of alkali and alkaline-earth chalcogenides and achieve a better balance between large SHG response and wide band gap.

Theoretical analysis
To better understand the structure-performance relationship, the electronic structures of LaMg 6 Ga 6 S 16 were calculated by the firstprinciples calculations.The calculated electronic band structure shows that LaMg 6 Ga 6 S 16 is an indirect bandgap compound with a band gap of 2.2 eV (Fig. 6a), which is smaller than the experimental value (3.0 eV) due to the limitation of using a generalized gradient approximation as the exchange-correlation functional 67 .Further, the partial densities of states of LaMg 6 Ga 6 S 16 were analyzed (Fig. 6b).It can be found that the tops of valence bands (VBs) are composed of S 3p, Mg 2p, and La 5d orbitals, and the La 5d orbitals possess the vital contribution to the top of VBs.The bottom of the conduction bonds (CBs) region is mainly Ga 4s, Ga 4p, Mg 3s, Mg 3p, La 6s, La 5d, and S 3p orbitals.These results indicate that the 5d electronic states of the La atom have a crucial effect on the band gap of the optical properties of LaMg 6 Ga 6 S 16 .In addition, we also calculated SHG coefficients based on the electronic structure by the first-principles calculations.Clearly, the calculated SHG coefficients of LaMg 6 Ga 6 S 16 (d 11 = 12.27 pm/V and d 22 = 4.00 pm/V) are greater than that of the AeMg 6 Ga 6 S 16 (Ae = Ca, Sr, Ba) (Supplementary Table 6), suggesting divalent La make the partial contribution to SHG response of LaMg 6 Ga 6 S 16 .
In summary, the chemically stable crystalline La(II)-chalcogenide, LaMg 6 Ga 6 S 16 has been synthesized by constructing the strong [LaS 6 ] octahedra crystal field in the [Mg/Ga-S] ∞ framework structure.XPS, XANES and EPR unequivocally identified the nature of the La 2+ in LaMg 6 Ga 6 S 16 .Meanwhile, DSC, in-situ variable-temperature powder XRD and a series of solid-state reactions further illustrate its stability.
Benefiting from the unique electronic configurations of La 2+ , an ultrabroad-band green emission at 500 nm with FWHM of 127 nm was discovered in LaMg 6 Ga 6 S 16 .In particular, compared with a few synthesized divalent lanthanides organic complexes, the thermal stable divalent lanthanides inorganic compounds are still rarely researched.LaMg 6 Ga 6 S 16 may be able to provide some insights for the efficient syntheses of other low oxidation state lanthanide compounds.

Syntheses
For the preparation of LaMg 6 Ga 6 S 16 , reactants of La (0.2 mmol), Ga 2 S 3 (0.6 mmol), MgS (1.2 mmol), S (0.3 mmol) were mixed and respectively loaded into graphite crucible and then they are sealed into the silica tube and flame-sealed under 10 -3 Toor.The tubes were placed in a temperature-controlled furnace with the following heating process: firstly, heated to 773 K at a rate of 5 K/h and held this temperature for 10 h, then heated to 1273 K at a rate of 5 K/h and kept at that temperature for 100 h.Subsequently, the furnace was slowly cooled down to 573 K at a rate of 5 K/h.N, N−dimethylformamide (DMF) solvent was chosen to wash the products.Finally, many millimeter-level pale-yellow crystals of LaMg 6 Ga 6 S 16 was obtained with yields of ∼80 %, and all of them are stable under air and moisture conditions for at least 3 months.In addition, their thermal behaviors were studied by a series of solid-state reactions with the following process: their pure polycrystalline samples were firstly loaded into graphite crucibles.Then the graphite crucibles were put into silica tubes and flame-sealed under 10 -3 Toor.These tubes were heated to 373 K in 10 h and kept at this temperature for about 24 h.Subsequently, they were cooled to room temperature and the mixture in the tube were thoroughly grinded and sealed into silica tubes again.The silica tubes were further heated to a higher temperature, 473 K in 10 h and kept the temperatures for 24 h.Repeating the above process with a 100 K higher calcined temperature than the last reaction.

Structural refinement and crystal data
PXRD patterns were collected setting from the 2θ range 10-70°with a step width size of 0.01°and a step time of 2 s on an automated SmartLab 3KW powder X-ray diffractometer using Cu-K α radiation (λ = 1.54057Å) radiation.The purity of compound LaMg 6 Ga 6 S 16 was verified by PXRD with the results as shown in Supplementary Fig. 1.To study their thermal behaviors, in-situ variable-temperature powder XRD data of LaMg 6 Ga 6 S 16 was collected using an SmartLab 9KW X-ray diffractometer (Supplementary Fig. 4a), meanwhile, a series of solid-state reactions with different reaction temperatures (room temperature-1323 K) were also conducted and shown in Supplementary Fig. 4b.The crystal structure of LaMg 6 Ga 6 S 16 was determined by single-crystal XRD on a Bruker SMART APEX III CCD diffractometer using Mo K α radiation (λ = 0.71073 Å) at 297(2) K and the data was integrated with the SAINT program.All calculations were implemented with programs from the SHELXTL crystallographic software package 68 .Their crystal structures were solved by direct methods using SHELXS and refined with full-matrix least-squares methods on F 2 with anisotropic thermal parameters for all atoms 69 .Crystallographic data for the structure reported in this paper has been deposited with the Cambridge Crystallographic Data Centre (CCDC), under deposition number 2280420.These data can be obtained free of charge via www.ccdc.cam.ac.uk/data_request/cif, or by emailing data_request@ccdc.cam.ac.uk, or by contacting The Cambridge Crystallographic Data Centre, 12 Union Road, Cambridge CB2 1EZ, UK.Crystal data and structure refinement parameters were given in Supplementary Table 1.Some structural parameters including interatomic distances and angles, final refined atomic positions and isotropic thermal parameters are listed in Supplementary Table 2 and Supplementary Table 3, respectively.

X-Ray photoelectron spectroscopy
The XPS (ESCALLAB250Xi, Thermo Scientific) using a monochromatized Al K α source equipped with Ar ion sputtering was used for depth profiling measurements of ionic valence and composition, where the peak positions were calibrated using the C 1s peak position (284.8eV).

Energy-dispersive spectroscopy
Microprobe elemental analyses and the elemental distribution maps were measured on a field-emission scanning electron microscope (Quanta FEG 250) made by FEI.

Synchrotron X-ray absorption spectroscopy
The XAS measurements were carried out at the XAS Beamline at the Australian Synchrotron in Melbourne, Australia using a set of liquid nitrogen cooled Si (111) monochromator crystals.The electron beam energy is 3.0 GeV.With the associated beamline optics (Si-coated collimating mirror and Rh-coated focusing mirror), the harmonic content of the incident X-ray beam was negligible.Data was collected by using transmission mode, and the energy was calibrated using a Co foil.The beam size was about 1 × 1 mm.Note that a single XAS scan took about 1 h.

Electron paramagnetic resonance spectroscopy
The EPR measurement was conducted on Bruker EMXplus-6/1 EPR spectrometer with a 9.2 GHz magnetic field.

Thermal Analysis
The thermal behavior of LaMg 6 Ga 6 S 16 was performed using an HCT-4 analyzer (Beijing Henven Experimental).The sample of ∼10 mg was sealed in the customized vacuum-sealed tiny silica tubes and heated from 50 to 1300 °C at a rate of 10 °C/min.The measurements were carried out in an atmosphere of flowing N 2 .

Photoluminescence spectroscopy
The PL spectra were measured in room temperature using a fluorescence spectrometer (FLS-980, Edinburgh, UK).A 450 W xenon arc lamp was employed as a continuous excitation light source.The FLS980 spectrometer was configured with Red PMT photomultiplier with spectral coverage from 370 nm to 650 nm.

Thermoluminescence spectroscopy
The TL curve was collected by the TOSL-3DS measuring instrument (PMT detector) with a heating rate of 5 °C/s after pre-irradiation for 5 min.

Birefringence
The birefringence of LaMg 6 Ga 6 S 16 was measured based on a crosspolarizing microscope method with plate-shaped crystals 61 .The thickness of the used crystal is 22.4 μm for LaMg 6 Ga 6 S 16 (Fig. 5b), and the observed interference color is second-order yellow along [0_10] plane of the crystal in the cross-polarizing microscope (Supplementary Fig. 8).Based on the Michal-Levy chart, its retardation (R value) is about 920 nm.According to the equation R = Δn×d (where R, Δn, and d represent retardation, birefringence, and thickness, respectively) 60,62 , the birefringence of LaMg 6 Ga 6 S 16 can be calculated.

UV−vis−NIR diffuse reflectance
The UV−vis−NIR optical diffuse reflectance spectrum of LaMg 6 Ga 6 S 16 in the range of 300-2100 nm was measured on Shimadzu SolidSpec-3700DUV with BaSO 4 as a reference.The band gap was estimated on basis of the absorption spectra that was derived from the reflection spectrum using the Kubelka-Munk formula 70 .

IR and Raman spectroscopy
The IR spectrum in the range of 4000-500 cm  27,71 .

Second harmonic generation measurement
The SHG signals of LaMg 6 Ga 6 S 16 and benchmark AgGaS 2 were investigated under incident laser radiation of 2090 nm by modified Kurtz-Perry method, respectively 72 .Samples LaMg 6 Ga 6 S 16 and AgGaS 2 were sieved into several distinct particle size ranges (54-75, 75-100, 100-125, 125-150, 150-180 and 180-250 μm) for the PM measurements.The SHG signals were detected by a chargecoupled device.The second harmonic efficiency of the LaMg 6 Ga 6 S 16 powder was compared to that of AgGaS 2 powder with the same particle size.

Laser-induced damage threshold measurement
The LIDTs of the LaMg 6 Ga 6 S 16 and AgGaS 2 powder at the particle size range of 100 − 125 μm were evaluated under using a high-power laser irradiation of 1064 nm (pulse width τ p = 10 ns) by the single-pulse method 73,74 .The measurement processes were performed by gradually increasing the laser power until the damaged spot was observed under a microscope.The damage thresholds were derived from the equation I (threshold) = E/(πr 2 τ p ), where E is the laser energy of a single pulse, r is the spot radius, and τ p is the pulse width.

Computational methods
The electronic band structures, the partial density of states and optical properties for LaMg 6 Ga 6 S 16 were carried out using the CASTEP package based on density functional theory (DFT) 75 .Generalized gradient approximation (GGA) parametrized by Perdew-Burke-Ernzerhof (PBE) functional was chosen for the exchange-correlation energy, and the pseudopotential was set as norm-conserving pseudopotential (NCP) 76 .The valence electrons were set as: La 6s 2 5d 1 , Mg 2s 2 2p 6 3s 2 , Ga 3d 10 4s 2 4p 1 , S 3s 2 3p 4 for LaMg 6 Ga 6 S 16 .The plane-wave energy cutoff value was set at 800.0 eV.The numerical integration of the Brillouin zone was performed using 2 × 2 × 4 Monkhorst-Pack κ-point meshes 77 .The localdensity approximation (LDA) + U approach (where U is the Hubbard energy) was adopted to deal with the strong on-site Coulomb repulsion amongst the localized La 5d electrons [78][79][80] .The SHG coefficients were calculated from the band wave functions using the so-called length-gauge formalism derived by Aversa and Sipe at a zero-frequency limit.The static second-order nonlinear susceptibilities χ αβγ (2) can be reduced as [81][82][83] : Virtual-Hole (VH), Virtual-Electron (VE) and Two-Band (TB) processes play an important role in the total SHG coefficient χ (2) .The TB process can be neglected owing to little contribution for SHG.The formulas for calculating χ αβγ (2) (VE) and χ αβγ (2) (VH) are as follows: Here, α, β, γ are Cartesian components, v and v 0 denote valence bands, c and c 0 refer to conduction bands, and P(αβγ) denotes the full permutation.The band energy difference and momentum matrix elements are denoted as ℏω ij and P ij α , respectively.As we know, the virtual electron (VE) progresses of occupied and unoccupied states are the main contribution to the overall SHG effect 84 .

3 /CuS 3 9 C 3h Fig. 1 |Fig. 2 |Fig. 3 |
Fig. 1 | The accommodating ability of [Mg/Ga-S] ∞ framework.The accommodating ability of [Mg/Ga-S] ∞ framework.Statistics on radius and the coordination of a range of atoms filled in [Mg/Ga-S] ∞ framework.This framework can be filled with alkali and alkaline-earth or even other monovalent divalent cations.

Fig. 4 |
Fig. 4 | Luminescence properties of LaMg 6 Ga 6 S 16 and CaMg 6 Ga 6 S 16 .Excitationdependent PL spectra of LaMg 6 Ga 6 S 16 at room temperature a, the black dashed square indicates the ultrabroad emission range; PL emission spectra of LaMg 6 Ga 6 S 16 under 360 nm excitation at the room temperature b; Fitted TL spectrum of LaMg 6 Ga 6 S 16 , two Gaussian bands peaking at 346 K (yellow dashed line) and 384 K (violet dashed line) c; Excitation-dependent PL spectra of CaMg 6 Ga 6 S 16 at room temperature d; Schematic diagram of the 5d orbitals split of La 2+ driven by the octahedral crystal field in LaMg 6 Ga 6 S 16 e; Room-temperature PL decay curves monitored at 500 nm and excited at 360 nm f.

Fig. 6 |
Fig. 6 | Theoretical calculation results of LaMg 6 Ga 6 S 16 .Calculated band structure a and the projected density of states with the energy region from −5.0 eV to 7.5 eV b of LaMg 6 Ga 6 S 16 .
−1was recorded on a Fourier transform IR spectrometer using Nicolet iS50 FT with ATR.The Raman spectrum of LaMg 6 Ga 6 S 16 in the range of 1000-50 cm −1 was recorded on WITec alpha300R.The characteristic vibrations in the Raman spectrum at 424, 354, and 310 cm −1 correspond to asymmetric and symmetric stretching vibrations of S-Ga-S and S-Mg-S modes, and peaks below 200 cm −1 are due to the La-S and Mg-S vibrations.These coincide with those of other related chalcogenides, such as LaCaGa 3 S 6 O and AeMg 6 Ga 6 S 16 (Ae = Ca, Sr, Ba)