Synthesis, Crystal Structure, and Optical and Magnetic Properties of the New Quaternary Erbium Telluride EuErCuTe3: Experiment and Calculation

This paper reports for the first time on a new layered magnetic heterometallic erbium telluride EuErCuTe3. Single crystals of the compound were obtained from the elements at 1120 K using CsI as a flux. The crystal structure of EuErCuTe3 was solved in the space group Cmcm (a = 4.3086(3) Å, b = 14.3093(9) Å, and c = 11.1957(7) Å) with the KZrCuS3 structure type. In the orthorhombic structure of erbium telluride, distorted octahedra ([ErTe6]9−) form two-dimensional layers (Er(Te1)2/2e(Te2)4/2k−)∞2, while distorted tetrahedra ([CuTe4]7−) form one-dimensionally connected substructures (Cu(Te1)2/2e(Te2)2/1t5−∞1) along the [100] direction. The distorted octahedra and tetrahedra form parallel two-dimensional layers (CuErTe32−∞2) between which Eu2+ ions are located in a trigonal-prismatic coordination environment (EuTe610−). The trigonal prisms are connected by faces, forming chains (Eu(Te1)2/2(Te2)4/22−∞1) along the [100] direction. Regularities in the variations in structural parameters were established in the series of erbium chalcogenides (EuErCuCh3 with Ch = S, Se, and Te) and tellurides (EuLnCuTe3 with Ln = Gd, Er, and Lu). Ab-initio calculations of the crystal structure, phonon spectrum, and elastic properties of the compound EuErCuTe3 were performed. The types and wavenumbers of fundamental modes were determined, and the involvement of ions in the IR and Raman modes was assessed. The experimental Raman spectra were interpreted. The telluride EuErCuTe3 at temperatures below 4.2 K was ferrimagnetic, as were the sulfide and selenide derivatives (EuErCuCh3 with Ch = S and Se). Its experimental magnetic characteristics were close to the calculated ones. The decrease in the magnetic phase transition temperature in the series of the erbium chalcogenides was discovered.

The compounds EuErCuCh 3 (Ch = S, Se, and Te) contain two magnetically active cations, Eu 2+ and Er 3+ , which contribute to the magnetic ordering of the chalcogenides.The magnetic moment of the Er 3+ ion (9.59 µ B ) is larger than that of the Eu 2+ ion (7.94 µ B ), suggesting that the EuErCuCh 3 compounds exhibit ferrimagnetic properties [16,18].Indeed, the EuErCuCh 3 compounds (Ch = S and Se) undergo a transition from ferrimagnetic to paramagnetic states at 4.8 K [18] and 4.7 K [16], respectively.The synthesis and properties of EuErCuTe 3 have not been reported yet.However, based on the magnetic ions involved, a ferrimagnetic transition can be expected in this compound.The orthorhombic EuErCuCh 3 compounds (Ch = S and Se) crystallize in the space group Pnma (a structural type Eu 2 CuS 3 ) and the space group Cmcm (a structural type KZrCuS 3 ), respectively.Thus, with an increase in the chalcogen radius from r i (S 2− ) = 1.84 Å to r i (Se 2− ) = 1.98 Å [26], a change in the space group to a higher symmetry can occur.According to L.A. Koscielski's review [17], compounds of this type crystallize only in the Pnma and Cmcm space groups, and so it can be assumed that despite a further increase in the chalcogen radius to r i (Te 2− ) = 2.21 Å [26], the EuErCuTe 3 compound will crystallize in the Cmcm space group.Quantum-mechanical calculations have been previously performed for the EuErCuTe 3 compound, assuming it crystallizes in the KZrCuSe 3 structural type [27,28].
Recently, the chalcogenidation of a multi-component oxide mixture obtained by the thermolysis of co-crystallized nitrates [3,[29][30][31] or commercial oxides [31,32] has been actively used for the synthesis of quaternary chalcogenides, providing a high yield of the target phase.However, the toxicity and instability of tellurium hydride limit the applicability of this method for obtaining EuErCuTe 3 .In our opinion, the most effective and safe method for obtaining this compound would be the halide flux method using elements, which allows for the growth of single crystals in a sealed ampoule, with a relatively low synthesis temperature, and the absence of impurities would enable the study of the physical properties of the samples.
The aim of this study was to synthesize single crystals of the quaternary telluride EuErCuTe 3 , determine its crystal structure, and investigate its magnetic and optical properties.In addition, computational studies were conducted to shed light on the optical properties of EuErCuTe 3 .

Synthesis
Single crystals of EuErCuTe 3 were synthesized by mixing stoichiometric amounts of copper, tellurium, and lanthanide elements (1 Cu: 1 Eu: 1 Er: 3 Te) in the presence of an excess of CsI halide flux in a glovebox under an argon atmosphere.The weighing of the samples into quartz ampoules was carried out in an inert atmosphere inside the glovebox.The glovebox was used to prevent the interaction of the elemental substances with the oxygen and carbon dioxide in the air and water vapors, which would lead to the formation of thermodynamically stable oxides, carbonates, and hydroxycarbonates at room temperature [33,34].To prevent the formation of silicate oxides during the synthesis process due to the interactions of the starting components with quartz, a pyrolytic thin layer of amorphous carbon was applied to the inner wall of the quartz ampoules prior to beginning.The quartz ampoules were evacuated to a pressure of 2 × 10 −3 mbar, sealed, and heated in a muffle furnace from room temperature to 1120 K.The heating was carried out from room temperature to 1120 K for 30 h and kept at this temperature for 96 h, then it was cooled to 570 K for 140 h, and finally, it was cooled to room temperature for 3 h.The reaction product was purified from the residual flux using demineralized water.The product consisted of black needle-like crystals of EuErCuTe 3 with sizes of up to 500 µm (Figure 1).The obtained crystals were suitable for single crystal X-ray diffraction analysis and taking measurements of their magnetic and optical properties.Unfortunately, highquality powder diffraction patterns could not be obtained, as copper compounds are strong absorbers of molybdenum radiation.copper, tellurium, and lanthanide elements (1 Cu: 1 Eu: 1 Er: 3 Te) in the excess of CsI halide flux in a glovebox under an argon atmosphere.The w samples into quartz ampoules was carried out in an inert atmosphere inside The glovebox was used to prevent the interaction of the elemental substa oxygen and carbon dioxide in the air and water vapors, which would lead to of thermodynamically stable oxides, carbonates, and hydroxycarbonates at ature [33,34].To prevent the formation of silicate oxides during the synthes to the interactions of the starting components with quartz, a pyrolytic thin phous carbon was applied to the inner wall of the quartz ampoules prior The quartz ampoules were evacuated to a pressure of 2 × 10 −3 mbar, sealed, a muffle furnace from room temperature to 1120 K.The heating was carried temperature to 1120 K for 30 h and kept at this temperature for 96 h, then it 570 K for 140 h, and finally, it was cooled to room temperature for 3 h.The uct was purified from the residual flux using demineralized water.The pro of black needle-like crystals of EuErCuTe3 with sizes of up to 500 µm (Figu tained crystals were suitable for single crystal X-ray diffraction analysis and urements of their magnetic and optical properties.Unfortunately, high-q diffraction patterns could not be obtained, as copper compounds are stron molybdenum radiation.

X-ray Diffraction Analysis
The intensities from a single crystal of the EuErCuTe3 of 0.05 × 0.05 × mensions were collected at 293(2) K using a SMART APEX II single-crystal (Bruker AXS, Billerica, MA, USA) equipped with a CCD-detector, graphite tor, and Mo-Kα radiation source.The parameters of the elementary cell we and refined for a set of 11880 reflections.The parameters of the element sponded to the orthorhombic crystal system.The space group Cmcm was de the statistical analysis of all the intensities.Absorption corrections were app SADABS (2008) program.The crystal structure was solved by direct meth SHELXS (2013) program and refined in an anisotropic approximation usin (2013) program [35].Structural investigations for the presence of missing ments were conducted using the PLATON (2009) program [36].The crystal were deposited in the Cambridge Crystallographic Data Centre.The data loaded from www.ccdc.cam.ac.uk/data_request/cif (accessed on 25 Februa

Electron-Beam Microprobe Analysis
The SEM (scanning electron microscopy) image of the EuErCuTe3 was a Photograph of an EuErCuTe 3 (in yellow circle) crystal placed in a capillary for the X-ray diffraction analysis (the single crystal image was made using a Horiba XploRA Raman spectrometer (HORIBA Scientific, Kyoto, Japan)).

X-ray Diffraction Analysis
The intensities from a single crystal of the EuErCuTe 3 of 0.05 × 0.05 × 0.45 mm 3 dimensions were collected at 293(2) K using a SMART APEX II single-crystal diffractometer (Bruker AXS, Billerica, MA, USA) equipped with a CCD-detector, graphite monochromator, and Mo-K α radiation source.The parameters of the elementary cell were determined and refined for a set of 11880 reflections.The parameters of the elementary cell corresponded to the orthorhombic crystal system.The space group Cmcm was determined from the statistical analysis of all the intensities.Absorption corrections were applied using the SADABS (2008) program.The crystal structure was solved by direct methods using the SHELXS (2013) program and refined in an anisotropic approximation using the SHELXL (2013) program [35].Structural investigations for the presence of missing symmetry elements were conducted using the PLATON (2009) program [36].The crystallographic data were deposited in the Cambridge Crystallographic Data Centre.The data can be downloaded from www.ccdc.cam.ac.uk/data_request/cif (accessed on 25 February 2024).

Magnetic Measurements
Magnetic measurements were performed with a Quantum Design Magnetic Property Measurement System (MPMS3), San Diego, CA, USA.The SOUID-magnetometer was used to measure the temperature dependence of the EuErCuTe 3 sample's magnetic moment under a magnetic field of 40 kA•m −1 .These measurements took place in the temperature range 2 to 300 K using the zero-field cooling (ZFC) and field cooling (FC) modes.The isothermal magnetization of up to 4 MA•m −1 was measured at 2 K and 300 K.

Spectroscopy of the Raman Scattering
Raman spectra of the single crystal sample of EuErCuTe 3 were acquired using a Horiba XploRa spectrometer (HORIBA Scientific, Kyoto, Japan).The excitation light at a wavelength of 532 nm was used.The acquisition conditions were as follows: filter-10, hole-300, slit-100, and resolution-2400.

DFT Calculations
Calculations were performed at the theoretical level DFT (density functional theory)/B3LYP.In this approach, we took into account the nonlocality of the exchange interaction, which was necessary for describing the compounds with ionic and covalent bonds.The calculations were carried out in the program CRYSTAL17 [37].For the rare-earth ions, quasi-relativistic pseudopotentials with attached basis sets were used.We used the pseudopotentials ECP53MWB and ECP57MWB with attached basis sets of the TZVP type for the outer shells (5s 2 5p 6 ) [38].The all-electron basis set "Cu_86-4111(41D)G_doll_2000" was used for the copper [37].For the tellurium, an all-electron basis was also used [39].Any diffuse functions with exponents smaller than 0.1 were deleted from the basis sets.A self-consistent field was calculated with an accuracy of 10 −9 a.u.The Monkhorst-Pack mesh used was 8 × 8 × 8.
The use of the pseudopotential for the inner shells of a rare-earth ion reduced the cost of the computer resources and allowed us to calculate the structure and the dynamics of the crystal lattice adequately [15].
The elastic constants and phonon spectrum were calculated for the previously optimized crystal structure.

Crystal Structures of the EuErCuTe 3
According to the X-ray crystallographic analysis of the single crystals, the compound EuErCuTe 3 crystallized in the orthorhombic space group Cmcm with a KZrCuS 3 structural type.The crystallographic data, data collection details, atomic coordinates, thermal displacement parameters, bond lengths, and valence angles are presented in Tables 1-4.A similar structural type was observed in the erbium quarter selenide compound EuErCuSe 3 [16,40].The lattice constants obtained from the DFT calculations a = 4.3401 Å, b = 14.2459Å, and c = 11.2309Å were in good agreement with those determined experimentally (Table 1).Symmetry codes:

Bond angles
The crystal structure of EuErCuTe 3 has a layered-block structure (Figure 2).
The crystal structure of EuErCuTe3 has a layered-block structure (Figure 2).
The values of the valence angles ∠(Te-Cu-Te) deviated from the value of the ideal tetrahedral angle (Table 4).The distortions of the tetrahedra in the EuErCuTe3 structure were evaluated using the τ4 descriptor [41].The value of τ4 was 0.978, indicating a distortion in the coordination geometry around the Cu + by 15% from an ideal tetrahedral structure to a trigonal-pyramidal structure.The degree of distortion in the tetrahedral polyhedra in the telluride EuErCuTe3 was higher than that in the selenide EuErCuSe3 [16] and sulfide EuErCuS3 [15], for which the values of τ4 were 0.984 and 0.986, and the distortion indexes were 11 % and 9 %, respectively.
Between the chains of tetrahedra, there were distorted octahedra ([ErTe 6 ] 9− ) with bond lengths of 3.0277(4) Å and 3.0423(5) Å (Table 4) compared to the theoretical value of d(Er-Te) = 3.1 Å (r i (Er 3+ ) = 0.89 Å, C.N. = 4) [26].The values of the valence angles ∠(Te-Er-Te) deviated from the value of the ideal octahedral angle (Table 4).The distorted octahedra formed two-dimensional layers  [26].In the EuErCuTe 3 structure, six Eu-Te distances were shorter than 3.35 Å, while the seventh and eighth distances were larger than the theoretical value and measured 3.86 Å, which was not accounted for in the coordination polyhedron due to weak interactions.Thus, the three-dimensional crystal structure of EuErCuTe 3 was formed by twodimensional layers consisting of octahedra and tetrahedra in the bc plane separated by one-dimensional chains of trigonal prisms.
A regular increase in the average metal-chalcogen bond lengths was also observed in the chalcogenide series.For example, we observed the following: Thus, the increase in the chalcogen radius led to the transformation of the local geometry around the Eu 2+ , resulting in a change in the type of its coordination polyhedron from a one-capped trigonal prism in EuErCuS 3 [15] to a trigonal prism in EuErCuSe 3 and EuErCuTe 3 , a change in the structural type and space group in the series of EuErCuCh 3 compounds, and an increase in structural parameters.
The volume of the unit cell decreased from 708.42 (8) to 682.02(8) Å 3 in the EuLnCuTe 3 (Ln = Gd, Er, and Lu).Additionally, a consistent decrease in the average metal-tellurium bond length was observed in this series.Thus, we observed the following: Thus, the decrease in the lanthanide radius in the series of EuLnCuTe 3 compounds (Ln = Gd, Er and Lu) was accompanied by a change in the structural type and space group, as well as decreases in the structural parameters.

Magnetic Properties of the EuErCuTe 3
The experimental field dependence of the magnetic moment of the sample at a temperature of 300 K had a linear form, characteristic of paramagnetic materials (Figure 3a).From this dependence, assuming the validity of the Curie law m = HCT −1 , the Curie constant C 300K = 0.232 m 3 K•kmol −1 and the corresponding effective magnetic moment µ 300K = 12.14 µ B were calculated.Given the experimental data on the temperature-dependent magnetic moment of the EuErCuTe3 sample, the temperature-dependent inverse molar magnetic susceptibility (Figure 3b,c) was calculated.Taking as a first approximation the Curie-Weiss law (χ −1 = C −1 (T − θp)) at temperatures from 50 to 300 K, the Curie constant C50-300K = 0.241 m 3 •K•kmol −1 and the Weiss constant (Curie paramagnetic temperature) θp = −4.0K, as well as the effective magnetic moment µ50-300K = 12.39 µB, were obtained.
The paramagnetic parameters of the EuErCuTe3 compound corresponded well to the calculated parameters of the free ions (  = √7.94+ 9.58 = 12.44 µB, C = 0.243 m 3 •K•kmol −1 ).However, the Curie paramagnetic temperature of this sample was negative, and the temperature dependence of the inverse susceptibility at low temperatures (Figure 3b,c) had a form characteristic of ferrimagnetic compounds.Therefore, to approximate this dependence in the temperature range 5 to 300 K, the Néel formula for a two-sublattice ferrimagnet model was used (χ −1 = T/C + χ0 −1 − σ/(T − θ)).The calculations showed very good agreement between the experimental points and the theoretical model (Figure 3).Given the experimental data on the temperature-dependent magnetic moment of the EuErCuTe 3 sample, the temperature-dependent inverse molar magnetic susceptibility (Figure 3b,c) was calculated.Taking as a first approximation the Curie-Weiss law (χ −1 = C −1 (T − θ p )) at temperatures from 50 to 300 K, the Curie constant C 50-300K = 0.241 m 3 •K•kmol −1 and the Weiss constant (Curie paramagnetic temperature) θ p = −4.0K, as well as the effective magnetic moment µ 50-300K = 12.39 µ B , were obtained.
The paramagnetic parameters of the EuErCuTe 3 compound corresponded well to the calculated parameters of the free ions (µ = √ 7.94 2 + 9.58 2 = 12.44 µ B , C = 0.243 m 3 •K•kmol −1 ).However, the Curie paramagnetic temperature of this sample was negative, and the temperature dependence of the inverse susceptibility at low temperatures (Figure 3b,c) had a form characteristic of ferrimagnetic compounds.Therefore, to approximate this dependence in the temperature range 5 to 300 K, the Néel formula for a two-sublattice ferrimagnet model was used (χ The calculations showed very good agreement between the experimental points and the theoretical model (Figure 3).The best fit was obtained with the following parameter values: , and θ = 3.1 K. Based on these data, the Néel temperature was determined at χ −1 = 0 using the following formula: T c = (θ − C/χ 0 + ((θ − C/χ 0 ) 2 + 4C(θ/χ 0 + σ)) 0.5 )/2 = 4.2 K.This value was close to the observed temperature at the divergence point of the magnetization curves for the FC and ZFC modes.Similar values for the phase transition points were obtained for EuErCuSe 3 (4.7 K [16]) and EuErCuS 3 (5.0K [18]).
The magnetization in Bohr magnetons per formula unit plotted at 2 K (Figure 4) confirmed the conclusion regarding the ferrimagnetic structure of the moments in this compound.The shape of this curve exhibits the metamagnetic behavior of the moments.In the external fields of 0.03 and approximately 1 MA m −1 , jumps in susceptibility were observed, indicating a change in the magnetic structure.The saturation, which theoretically should approach the value of gS(Eu 2+ ) + g J J(Er 3+ ) = 7 µ B + 9 µ B = 16 µ B , was not achieved until reaching 4 MA•m −1 .
The magnetization in Bohr magnetons per formula unit plotted at 2 K (F firmed the conclusion regarding the ferrimagnetic structure of the moments pound.The shape of this curve exhibits the metamagnetic behavior of the the external fields of 0.03 and approximately 1 MA m −1 , jumps in susceptibi served, indicating a change in the magnetic structure.The saturation, which should approach the value of gS(Eu 2+ ) + gJJ(Er 3+ ) = 7 µB + 9 µB = 16 µB, was until reaching 4 MA•m −1 .
The magnetic properties of the EuErCuTe3 compound were similar EuGdCuTe3.Both are ferrimagnets at low temperatures (lower than 4.2 K for 7.9 K for the second), unlike EuLuCuTe3, which is ferromagnetic under a te 3.0 K.

Band Structure of EuErCuTe 3
We used the points Γ(0,0,0), Y( 1 / 2 , 1 / 2 ,0), T( 1 / 2 , 1 / 2 , 1 / 2 ), Z(0,0, 1 / 2 ), S (0, 1 / 2 ,0), and R(0, 1 / 2 , 1 / 2 ) at the Brillouin zone of the space group Cmcm.The band structure (Figure 5) did not include the 4f states of erbium and europium since they were replaced by a pseudopotential.As can be seen from the figure, copper and tellurium orbitals are the main contributions to the states near the top of the VB.Orbitals of erbium and europium are the main contributions to the bottom of the CB.The calculations predicted for EuErCuTe3 an indirect band gap value of 1.75 eV (it was a HOMO-LUMO estimation).This value was close to the experimental data values for isostructural quaternary chalcogenides [16,18,43].In the series EuErCuCh3 (Ch = S, Se, and Te), decreases in the band gap widths of the compounds were observed (1.93 eV (EuErCuS3) [18] → 1.79 eV (EuErCuSe3) [16] → 1.75 eV (EuErCuTe3)), which was consistent with the data on the narrowing of the band gap in the chalcogenide series [44].Isostructural europium chalcogenides have lower band gap values compared to strontium chalcogenides in the space group Cmcm, for example, in SrRE-CuSe3 (RE = Ho − Lu), the values range from 2.03-2.21eV [43].The narrower band gap of EuRECuCh3 was explained by the presence of a 4f-5d transition in the Eu 2+ ion [45].

Elastic Constants and Elastic Modulus
The elastic constants and the elastic modulus of the compound EuErCuTe3 are presented in Table 5.This table presents the bulk module (B), shear module (G), Young's modulus (G), and Poisson's ratio.These are values for a polycrystal, and they are calculated by averaging the schemes of Voigt, Reuss, and Hill.The Voigt scheme assumes the uniformity of local strains.The Reuss scheme assumes the uniformity of local stresses.The Voigt scheme provides the upper bound, while the Reuss scheme provides the lower bound of the value.The Hill approximation provides the arithmetical average of the Voigt and Reuss values [46,47].As can be seen from the figure, copper and tellurium orbitals are the main contributions to the states near the top of the VB.Orbitals of erbium and europium are the main contributions to the bottom of the CB.The calculations predicted for EuErCuTe 3 an indirect band gap value of 1.75 eV (it was a HOMO-LUMO estimation).This value was close to the experimental data values for isostructural quaternary chalcogenides [16,18,43].In the series EuErCuCh 3 (Ch = S, Se, and Te), decreases in the band gap widths of the compounds were observed (1.93 eV (EuErCuS 3 ) [18] → 1.79 eV (EuErCuSe 3 ) [16] → 1.75 eV (EuErCuTe 3 )), which was consistent with the data on the narrowing of the band gap in the chalcogenide series [44].Isostructural europium chalcogenides have lower band gap values compared to strontium chalcogenides in the space group Cmcm, for example, in SrRECuSe 3 (RE = Ho − Lu), the values range from 2.03-2.21eV [43].The narrower band gap of EuRECuCh 3 was explained by the presence of a 4f -5d transition in the Eu 2+ ion [45].

Elastic Constants and Elastic Modulus
The elastic constants and the elastic modulus of the compound EuErCuTe 3 are presented in Table 5.This table presents the bulk module (B), shear module (G), Young's modulus (G), and Poisson's ratio.These are values for a polycrystal, and they are calculated by averaging the schemes of Voigt, Reuss, and Hill.The Voigt scheme assumes the uniformity of local strains.The Reuss scheme assumes the uniformity of local stresses.The Voigt scheme provides the upper bound, while the Reuss scheme provides the lower bound of the value.The Hill approximation provides the arithmetical average of the Voigt and Reuss values [46,47].The Voigt and Reuss estimates were very different (Table 5), which indicated the anisotropy of the elastic properties.The dependence of the Young's modulus on direction also illustrated the strong anisotropy of the elastic properties (Figure 6).The Voigt and Reuss estimates were very different (Table 5), which indicated the anisotropy of the elastic properties.The dependence of the Youngʹs modulus on direction also illustrated the strong anisotropy of the elastic properties (Figure 6).
Figure 6.The Young's modulus (GPa) and its dependence on direction in the crystal EuErCuTe3.
The empirical Formula (1) was used to calculate the hardness.According to [48] the formula was based on correlations between the Vickers hardness (HV) and the ratio of the shear and bulk moduli.The parameters of the formula were determined from reproducing the hardness of more than forty compounds with ionic and covalent bonds [48].In (1), the shear (G) and bulk (B) moduli were determined by the estimate.

Raman, IR, and Phonon Spectra
From the DFT calculations, the wavenumbers and types of modes were determined (Table 6).From the calculations, displacement vectors were obtained.This made it possible to evaluate the participation of each ion in a particular mode.The values of the ion displacements characterized their participation in the modes (Figure 7).The empirical Formula (1) was used to calculate the hardness.According to [48] the formula was based on correlations between the Vickers hardness (H V ) and the ratio of the shear and bulk moduli.The parameters of the formula were determined from reproducing the hardness of more than forty compounds with ionic and covalent bonds [48].In (1), the shear (G) and bulk (B) moduli were determined by the Hill estimate.

Raman, IR, and Phonon Spectra
From the DFT calculations, the wavenumbers and types of modes were determined (Table 6).From the calculations, displacement vectors were obtained.This made it possible to evaluate the participation of each ion in a particular mode.The values of the ion displacements characterized their participation in the modes (Figure 7).According to the calculations, the phonon spectrum of the crystal at the gamma point lied in the frequency range of up to 170 cm −1 .In this frequency range, not only light copper ions are involved but also tellurium and erbium ions.According to the calculations, the phonon spectrum of the crystal at the gamma point lied in the frequency range of up to 170 cm −1 .In this frequency range, not only light copper ions are involved but also tellurium and erbium ions.
A strong mixing of vibrations in the structural units in the crystal EuErCuSe 3 could be noted.In crystal EuErCuTe 3, europium ions participate in the frequency range of up to ~95 cm −1 .The calculations predicted a gap in the phonon spectrum in the region ~95-110 cm −1 (Figure 7).The calculations predicted that in the crystal EuErCuSe 3, the most intense Raman mode had a frequency of approximately 146 cm −1 (A 1g ) and the most intense infrared mode had a frequency of approximately 123 cm −1 (B 2u ).These modes are illustrated in Figure 8.A strong mixing of vibrations in the structural units in the crystal EuErCuSe3 could be noted.In crystal EuErCuTe3, europium ions participate in the frequency range of up to ~95 cm −1 .The calculations predicted a gap in the phonon spectrum in the region ~95-110 cm −1 (Figure 7).The calculations predicted that in the crystal EuErCuSe3, the most intense Raman mode had a frequency of approximately 146 cm −1 (A1g) and the most intense infrared mode had a frequency of approximately 123 cm −1 (B2u).These modes are illustrated in Figure 8.The largest ion displacement was 0.038 Å.In the case when the displacement was greater than or equal to 0.02 Å, the displacement was indicated by "S".If the displacement did not exceed 0.01 Å, then the displacement was indicated by "W".If the value of the The calculated Raman spectrum in comparison with the experimental one is shown in Figure 9.The results of calculating the phonon spectrum can be useful for interpreting IR and Raman spectra of the rare earth tellurides in EuLnCuTe 3 .
Materials 2024, 17, x FOR PEER REVIEW 14 of 17 A strong mixing of vibrations in the structural units in the crystal EuErCuSe3 could be noted.In crystal EuErCuTe3, europium ions participate in the frequency range of up to ~95 cm −1 .The calculations predicted a gap in the phonon spectrum in the region ~95-110 cm −1 (Figure 7).The calculations predicted that in the crystal EuErCuSe3, the most intense Raman mode had a frequency of approximately 146 cm −1 (A1g) and the most intense infrared mode had a frequency of approximately 123 cm −1 (B2u).These modes are illustrated in Figure 8.The calculated Raman spectrum in comparison with the experimental one is shown in Figure 9.The results of calculating the phonon spectrum can be useful for interpreting IR and Raman spectra of the rare earth tellurides in EuLnCuTe3.The largest ion displacement was 0.038 Å.In the case when the displacement was greater than or equal to 0.02 Å, the displacement was indicated by "S".If the displacement did not exceed 0.01 Å, then the displacement was indicated by "W".If the value of the The largest ion displacement was 0.038 Å.In the case when the displacement was greater than or equal to 0.02 Å, the displacement was indicated by "S".If the displacement did not exceed 0.01 Å, then the displacement was indicated by "W".If the value of the displacement was less than 0.005 Å, then the ion was not mentioned in the column "Participants".

Conclusions
This article discusses the synthesis, structure, and optical and magnetic properties of the new complex telluride EuErCuTe 3 .The compound crystallizes in the KZrCuS 3 structure type.Its crystal structure is built from distorted [ErTe 6 ] 9− octahedra and [CuTe 4 ] 7− tetrahedra, forming two-dimensional layers.Trigonal prisms of [EuTe 6 ] 10− are located between the layers.In the series of EuErCuCh 3 chalcogenides (Ch = S, Se, and Te), a change in the coordination polyhedron of Eu 2+ was observed, along with a change in the structural type and space group and increases in the structural parameters.EuErCuTe 3 contains two magnetic ions, Eu 2+ and Er 3+ , and it undergoes a ferrimagnetic transition at 4.2 K.The obtained results correlate with the observed ferrimagnetic ordering in erbium sulfide and selenide EuErCuCh 3 (Ch = S and Se).EuErCuTe 3 is paramagnetic in the temperature range 300 K to 4.2 K. Within the framework of the DFT approach, the crystal structure and the IR, Raman, and "silent" modes were studied.The elastic constants and elastic moduli were calculated.The experimental Raman spectrum of the synthesized sample was interpreted using the calculated Raman spectra of the EuErCuTe 3 .The theoretical calculations also allowed us to assign vibrational modes as well as to reveal the involved ions responsible for these modes.

Figure 1 .
Figure 1.Photograph of an EuErCuTe3 (in yellow circle) crystal placed in a capilla diffraction analysis (the single crystal image was made using a Horiba XploRA Ram (HORIBA Scientific, Kyoto, Japan)).

Figure 1 .
Figure 1.Photograph of an EuErCuTe 3 (in yellow circle) crystal placed in a capillary for the X-ray diffraction analysis (the single crystal image was made using a Horiba XploRA Raman spectrometer (HORIBA Scientific, Kyoto, Japan)).
oms (Te1) along the [001] direction and the shared edges (Te2Te2).The distorted octahedra and tetrahedra formed parallel two-dimensional layers ( CuErTe ) in the [101] plane.Between these layers, there were trigonal prisms that were connected by the faces Te2Te2Te1, forming chains ( Eu(Te1) / (Te2) / ) along the [100] direction.The theoretical value of d(Eu-Te) is 3.38 Å (ri(Eu 2+ ) = 0.89 Å, C.N. = 4)[26].In the EuErCuTe3 structure, six Eu-Te distances were shorter than 3.35 Å, while the seventh and eighth distances were larger than the theoretical value and measured 3.86 Å, which was not accounted for in the coordination polyhedron due to weak interactions.

Figure 3 .
Figure 3. Field-dependent magnetization at 300 K (a) and temperature-dependent specific magnetization and reciprocal molar magnetic susceptibility at 40 MA m −1 (b,c) of EuErCuTe3 sample.The measurements' temperature-dependent magnetizations were performed in the zero-field cooled (ZFC) and nonzero-field cooled (FC) modes.

Figure 3 .
Figure 3. Field-dependent magnetization at 300 K (a) and temperature-dependent specific magnetization and reciprocal molar magnetic susceptibility at 40 MA m −1 (b,c) of EuErCuTe 3 sample.The measurements' temperature-dependent magnetizations were performed in the zero-field cooled (ZFC) and nonzero-field cooled (FC) modes.

Figure 4 .
Figure 4. Magnetization curves of the EuErCuTe3 sample at 2 K.

Figure 6 .
Figure 6.The Young's modulus (GPa) and its dependence on direction in the crystal EuErCuTe 3 .

Figure 7 .
Figure 7.The values of the ion displacements at the phonon modes in the EuErCuTe3 (space group: Cmcm).

Figure 7 .
Figure 7.The values of the ion displacements at the phonon modes in the EuErCuTe 3 (space group: Cmcm).

Figure 8 .
Figure 8. Ion displacements in the IR and Raman modes with maximum intensity.The calculated Raman spectrum in comparison with the experimental one is shown in Figure9.The results of calculating the phonon spectrum can be useful for interpreting IR and Raman spectra of the rare earth tellurides in EuLnCuTe3.

Figure 9 .
Figure 9. Raman spectrum modeling results.The calculations were carried out for the exciting laser wavelengths λ = 532 nm and T = 300 K.

Figure 8 .
Figure 8. Ion displacements in the IR and Raman modes with maximum intensity.

Figure 8 .
Figure 8. Ion displacements in the IR and Raman modes with maximum intensity.

Figure 9 .
Figure 9. Raman spectrum modeling results.The calculations were carried out for the exciting laser wavelengths λ = 532 nm and T = 300 K.

Figure 9 .
Figure 9. Raman spectrum modeling results.The calculations were carried out for the exciting laser wavelengths λ = 532 nm and T = 300 K.

Table 1 .
Main parameters of the processing and refinement of the EuErCuTe 3 sample.

Table 2 .
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters of the EuErCuTe 3 sample.

Table 5 .
The elastic constants and modulus, and also the Vickers hardness (GPa), of EuErCuTe3.

Table 5 .
The elastic constants and modulus, and also the Vickers hardness (GPa), of EuErCuTe 3 .

Table 6 .
Phonons at the gamma point of the EuErCuTe3.

Table 6 .
Phonons at the gamma point of the EuErCuTe 3 .
1The superscripts "S" and "W" denote strong and weak ion displacements in the modes, respectively.