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

Abstract

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 (${}_{\infty }{}^2\left\{{\left[\mathrm{E}\mathrm{r}{\left(\mathrm{T}\mathrm{e}1\right)}_{2/2}^e{\left(\mathrm{T}\mathrm{e}2\right)}_{4/2}^k\right]}^{-}\right\})$, while distorted tetrahedra ([CuTe₄]⁷⁻) form one-dimensionally connected substructures (${}_{\infty }{}^1\left\{{\left[\mathrm{C}\mathrm{u}{\left(\mathrm{T}\mathrm{e}1\right)}_{2/2}^e{\left(\mathrm{T}\mathrm{e}2\right)}_{2/1}^t\right]}^{5-}\right\}$) along the [100] direction. The distorted octahedra and tetrahedra form parallel two-dimensional layers (${}_{\infty }{}^2\left\{{\left[\mathrm{C}\mathrm{u}\mathrm{E}\mathrm{r}{\mathrm{T}\mathrm{e}}_3\right]}^{2-}\right\})$ between which Eu²⁺ ions are located in a trigonal-prismatic coordination environment (${\left[{\mathrm{E}\mathrm{u}\mathrm{T}\mathrm{e}}_6\right]}^{10-})$. The trigonal prisms are connected by faces, forming chains (${}_{\infty }{}^1\left\{{\left[{\mathrm{E}\mathrm{u}\left(\mathrm{T}\mathrm{e}1\right)}_{2/2}{\left(\mathrm{T}\mathrm{e}2\right)}_{4/2}\right]}^{2-}\right\}$) 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.

1. Introduction

Heterometallic chalcogenides based on erbium have been of constant interest to researchers due to their structural possibilities, including their channel, tunnel, and layered structures, as well as their potential valuable optoelectronic, magnetic, semiconductor, and thermoelectric properties [1,2,3,4,5,6,7,8,9,10,11,12,13]. Doping erbium chalcogenides improves the optical characteristics of the material in terms of conductivity, reduces the bandgap energy, and enhances electrical conductivity and light absorption. Erbium-doped tellurides have found potential applications in solar cell and optical devices [14]. New heterometallic erbium chalcogenides are formed in ternary systems, such as M₂Ch–EuCh–Er₂Ch₃ (M = d-element and Ch = chalcogen) [15,16,17,18], and they can combine the properties of corresponding binary phases. Magnetic semiconductors based on europium chalcogenides are attractive due to their wide range of magnetic properties, as they can be ferro-, meta-, or antiferromagnetic [19]. They exhibit high saturation magnetization, a strong magneto-optical effect, magnetoresistance, and spin filtration effects, all arising from the unusual combination of electronic, magnetic, and optical properties in the europium chalcogenides [19,20,21]. Europium chalcogenides have the potential to create new magnetoelectronic devices, including magnetic random-access memory and magnetic tunneling transistors [19,20]. Bulk EuTe is an antiferromagnetic Heisenberg II type with a Néel temperature of T_N = 9.6 K [21,22,23,24] and a wide bandgap semiconductor with a bandgap width of 2.5 eV [24]. The optical and magnetic properties of europium tellurides can be controlled by changing their sizes [21,24,25]. In isolated monolayers, both ferrimagnetic and antiferromagnetic phase transitions can occur [23], and nanoparticles exhibit pronounced superantiferromagnetic transitions between 2 K and 20 K [21].

The compounds EuErCuCh₃ (Ch = S, Se, and Te) contain two magnetically active cations, Eu²⁺ and Er³⁺, which contribute to the magnetic ordering of the chalcogenides. The magnetic moment of the Er³⁺ ion (9.59 μ_B) is larger than that of the Eu²⁺ ion (7.94 μ_B), suggesting that the EuErCuCh₃ compounds exhibit ferrimagnetic properties [16,18]. Indeed, the EuErCuCh₃ 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 EuErCuTe₃ have not been reported yet. However, based on the magnetic ions involved, a ferrimagnetic transition can be expected in this compound. The orthorhombic EuErCuCh₃ compounds (Ch = S and Se) crystallize in the space group Pnma (a structural type Eu₂CuS₃) and the space group Cmcm (a structural type KZrCuS₃), respectively. Thus, with an increase in the chalcogen radius from r_i(S²⁻) = 1.84 Å to r_i(Se²⁻) = 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(Te²⁻) = 2.21 Å [26], the EuErCuTe₃ compound will crystallize in the Cmcm space group. Quantum-mechanical calculations have been previously performed for the EuErCuTe₃ compound, assuming it crystallizes in the KZrCuSe₃ 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 EuErCuTe₃. 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 EuErCuTe₃, 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 EuErCuTe₃.

2. Experimental

2.1. Materials

Eu (99.99%), Er (99.9%), CsI (99.9%), and Te (99.9%) were purchased from ChemPur (Karlsruhe, Germany). Cu (99.999%) was obtained from Aldrich (Milwaukee, WI, USA).

2.2. Synthesis

Single crystals of EuErCuTe₃ 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 EuErCuTe₃ 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, high-quality powder diffraction patterns could not be obtained, as copper compounds are strong absorbers of molybdenum radiation.

2.3. X-ray Diffraction Analysis

The intensities from a single crystal of the EuErCuTe₃ of 0.05 × 0.05 × 0.45 mm³ 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).

2.4. Electron-Beam Microprobe Analysis

The SEM (scanning electron microscopy) image of the EuErCuTe₃ was acquired using an electron-beam X-ray microprobe (SX-100, Cameca, Gennevilliers, France). The EDX (energy dispersive X-ray spectroscopy) spectra for several examples roughly confirmed the 1:1:1:3 stoichiometry of all the investigated EuErCuTe₃ compounds.

2.5. 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 EuErCuTe₃ 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.

2.6. Spectroscopy of the Raman Scattering

Raman spectra of the single crystal sample of EuErCuTe₃ 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.

2.7. 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 (5s²5p⁶) [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.

3. Results

3.1. Crystal Structures of the EuErCuTe₃

According to the X-ray crystallographic analysis of the single crystals, the compound EuErCuTe₃ crystallized in the orthorhombic space group Cmcm with a KZrCuS₃ structural type. The crystallographic data, data collection details, atomic coordinates, thermal displacement parameters, bond lengths, and valence angles are presented in

Table 1. Main parameters of the processing and refinement of the EuErCuTe₃ sample.

	EuErCuTe3
Molecular weight	765.56
Space group	Cmcm
Structure type	KZrCuS3
Z	4
a (Å)	4.3086(3)
b (Å)	14.3093(9)
c (Å)	11.1957(7)
V (Å3)	690.25(8)
ρcal (g/cm3)	7.367
μ (mm−1)	36.369
Reflections measured	6748
Reflections independent	477
Reflections with Fo > 4σ(Fo)	411
2θmax (°)	27.48
h, k, l limits	−5 ≤ h ≤ 5, −18 ≤ k ≤ 18, −14 ≤ l ≤ 14
Rint	0.070
Refinement results
Number of refinement parameters	24
R1 with Fo > 4σ(Fo)	0.026
wR2	0.056
Goof	1.084
Δρmax(e/Å3)	1.438
Δρmin(e/Å3)	−1.386
Extinction coefficient, ε	0.0026(2)
CSD-number	2261647

,

Table 2. Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters of the EuErCuTe₃ sample.

Atom	x/a	y/b	z/c	Ueq (Å2)
Eu	0	0.75485(6)	1/4	0.0288(3)
Er	0	0	0	0.0229(2)
Cu	0	0.47077(14)	1/4	0.0287(4)
Te1	0	0.08068(6)	1/4	0.0204(3)
Te2	0	0.35822(5)	0.06307(6)	0.0218(2)

,

Table 3. Atomic displacement parameters (Ų) of the EuErCuTe₃ sample.

	U11	U22	U33	U12	U13	U23
Eu	0.0153(4)	0.0231(5)	0.0480(5)	0	0	0
Er	0.0155(3)	0.0205 (4)	0.0328(4)	0	0	−0.0041(3)
Cu	0.0261(10)	0.0263(10)	0.0337(10)	0	0	0
Te1	0.0166(5)	0.0177(5)	0.0269(5)	0	0	0
Te2	0.0149(3)	0.0185(4)	0.0320(4)	0	0	−0.0028(3)

and

Table 4. Bond lengths (d/Å) and bond angles (∠/°) in the crystal structures of the EuErCuTe₃.

Bond lengths
Eu–Te1 i	3.294(1)	Er–Te1	3.0277(4)	Cu–Te2	2.641(1)
Eu–Te1 ii	3.294(1)	Er–Te1 v	3.0277(4)	Cu–Te2 x	2.641(1)
Eu–Te2 iii	3.3479(6)	Er–Te2 vi	3.0423(5)	Cu–Te1 ii	2.667(1)
Eu–Te2 i	3.3479(6)	Er–Te2 vii	3.0423(5)	Cu–Te1 i	2.667(1)
Eu–Te2 ii	3.3479(6)	Er–Te2 viii	3.0423(5)
Bond angles
Te1 i–Eu–Te1 ii	81.68(3)	Te1–Er–Te1 v	180.0	Te2–Cu–Te2 x	104.84(7)
Te1 i–Eu–Te2 iii	139.03(2)	Te1–Er–Te2 vi	87.72(2)	Te2–Cu–Te1 ii	111.08(1)
Te1 ii–Eu–Te2 iii	85.03(1)	Te1 v–Er–Te2 vi	92.28(2)	Te2 x–Cu–Te1 ii	111.08(1)
Te1 i–Eu–Te2 i	85.03(1)	Te1–Er–Te2 vii	92.28(2)	Te2–Cu–Te1 i	111.08(1)
Te1 ii–Eu–Te2 i	139.03(2)	Te1 v–Er–Te2 vii	87.72(2)	Te2 x–Cu–Te1 i	111.08(1)
Te2 iii–Eu–Te2 i	127.56(3)	Te2 vi–Er–Te2 vii	180.00(2)	Te1 ii–Cu–Te1 i	107.74(8)
Te1 i–Eu–Te2 ii	139.03(2)	Te1–Er–Te2 viii	92.28(2)
Te1 ii–Eu–Te2 ii	85.03(1)	Te1 v–Er–Te2 viii	87.72(2)
Te2 iii–Eu–Te2 ii	77.38(2)	Te2 vi–Er–Te2 viii	89.84(2)
Te2 i–Eu–Te2 ii	80.10(2)	Te2 vii–Er–Te2 viii	90.16(2)
Te1 i–Eu–Te2 iv	85.03(1)	Te1–Er–Te2 ix	87.72(2)
Te1 ii–Eu–Te2 iv	139.03(2)	Te1 v–Er–Te2 ix	92.28(2)
Te2 iii–Eu–Te2 iv	80.10(2)	Te2 vi–Er–Te2 ix	90.16(2)
Te2 i–Eu–Te2 iv	77.38(2)	Te2 vii–Er–Te2 ix	89.84(2)
Te2 ii–Eu–Te2 iv	127.56(3)	Te2 viii–Er–Te2 ix	180.00(2)

Symmetry codes: (i) x − ¹/₂, y+¹/₂, z; (ii) x+¹/₂, y+¹/₂, z; (iii) x+¹/₂, y+¹/₂, −z+¹/₂; (iv) x − ¹/₂, y+¹/₂, −z+¹/₂; (v) −x, −y, −z; (vi) −x+¹/₂, −y+¹/₂, −z; (vii) x − ¹/₂, y − ¹/₂, z; and (viii) x+¹/₂, y − ¹/₂, z; (ix) −x − ¹/₂, −y+¹/₂, −z; (x) x, y, −z+¹/₂.

. A similar structural type was observed in the erbium quarter selenide compound EuErCuSe₃ [16,40]. The lattice constants obtained from the DFT calculations a = 4.3401 Å, b = 14.2459 Å, and c = 11.2309 Å were in good agreement with those determined experimentally (Table 1).

The crystal structure of EuErCuTe₃ has a layered-block structure (Figure 2).

The cations Eu²⁺, Er³⁺, and Cu⁺ occupy independent crystallographic positions. In the EuErCuTe₃ compound, the structure was formed by distorted tetrahedra (${\left[{\mathrm{C}\mathrm{u}\mathrm{T}\mathrm{e}}_4\right]}^{7–}$), octahedra (${\left[{\mathrm{E}\mathrm{r}\mathrm{T}\mathrm{e}}_6\right]}^{9–})$, and trigonal prisms (${\left[{\mathrm{E}\mathrm{u}\mathrm{T}\mathrm{e}}_6\right]}^{10–})$. The sums of the valence forces for the EuErCuTe₃ compound, taking into account coordination, were Eu (1.64), Er (2.99), and Cu (1.42).

Distorted tetrahedra form chains (${}_{\infty }{}^1\left\{{\left[\mathrm{C}\mathrm{u}{\left(\mathrm{T}\mathrm{e}1\right)}_{2/2}^e{\left(\mathrm{T}\mathrm{e}2\right)}_{2/1}^t\right]}^{5–}\right\})$ along the [100] direction through shared vertex atoms (Te1) (Figure 2). In the tetrahedra, the distances d(Cu–Te) are equal to 2.641(1) Å and 2.667(1) Å (Table 4), indicating a deviation from the theoretical value of d(Cu–Te) = 2.81 Å (calculated based on r_i(Cu⁺) = 0.6 Å, coordination number (C.N.) = 4; r_i(Te²⁻) = 2.21 Å) [26]), which is associated with an increase in the covalent component of the chemical bond.

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 ([ErTe₆]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(Er³⁺) = 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 (${}_{\infty }{}^2\left\{{\left[\mathrm{E}\mathrm{r}{\left(\mathrm{T}\mathrm{e}1\right)}_{2/2}^e{\left(\mathrm{T}\mathrm{e}2\right)}_{4/2}^k\right]}^{-}\right\}$) through the shared vertex atoms (Te1) along the [001] direction and the shared edges (Te2Te2). The distorted octahedra and tetrahedra formed parallel two-dimensional layers $({}_{\infty }{}^2\left\{{\left[\mathrm{C}\mathrm{u}\mathrm{E}\mathrm{r}{\mathrm{T}\mathrm{e}}_3\right]}^{2-}\right\})$ in the [101] plane. Between these layers, there were trigonal prisms that were connected by the faces Te2Te2Te1, forming chains (${}_{\infty }{}^1\left\{{\left[{\mathrm{E}\mathrm{u}\left(\mathrm{T}\mathrm{e}1\right)}_{2/2}{\left(\mathrm{T}\mathrm{e}2\right)}_{4/2}\right]}^{2-}\right\})$ along the [100] direction. The theoretical value of d(Eu–Te) is 3.38 Å (r_i(Eu²⁺) = 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.

Thus, the three-dimensional crystal structure of EuErCuTe₃ was formed by two-dimensional layers consisting of octahedra and tetrahedra in the bc plane separated by one-dimensional chains of trigonal prisms.

In the series of erbium chalcogenides (EuErCuCh₃ (Ch = S, Se, and Te)), a change in the space group from Pnma (EuErCuS₃) to Cmcm (EuErCuSe₃ and EuErCuTe₃) and a change in structural type from Eu₂CuS₃ to KZrCuS₃, respectively, were observed. As the chalcogen radius increased in the compounds (EuErCuCh₃ (Ch = S [15], Se [16], and Te (Table 1))), an increase in the unit cell parameters was observed, as follows:

• a_Pnma(c_Cmcm) = 10.1005(2) Å ($a_{{\mathrm{E}\mathrm{u}\mathrm{E}\mathrm{r}\mathrm{C}\mathrm{u}\mathrm{S}}_3}$) → 10.4602(7) Å ($c_{{\mathrm{E}\mathrm{u}\mathrm{E}\mathrm{r}\mathrm{C}\mathrm{u}\mathrm{S}\mathrm{e}}_3}$)→ 11.1957(7) Å ($c_{{\mathrm{E}\mathrm{u}\mathrm{E}\mathrm{r}\mathrm{C}\mathrm{u}\mathrm{T}\mathrm{e}}_3}$);
• b_Pnma(a_Cmcm) = 3.91255(4) Å ($a_{{\mathrm{E}\mathrm{u}\mathrm{E}\mathrm{r}\mathrm{C}\mathrm{u}\mathrm{S}}_3}$) → 4.0555(3) Å ($c_{{\mathrm{E}\mathrm{u}\mathrm{E}\mathrm{r}\mathrm{C}\mathrm{u}\mathrm{S}\mathrm{e}}_3}$)→ 4.3086(3) Å ($c_{{\mathrm{E}\mathrm{u}\mathrm{E}\mathrm{r}\mathrm{C}\mathrm{u}\mathrm{T}\mathrm{e}}_3}$);
• c_Pnma(b_Cmcm) = 12.8480(2) Å ($a_{{\mathrm{E}\mathrm{u}\mathrm{E}\mathrm{r}\mathrm{C}\mathrm{u}\mathrm{S}}_3}$) → 13.3570(9) Å ($c_{{\mathrm{E}\mathrm{u}\mathrm{E}\mathrm{r}\mathrm{C}\mathrm{u}\mathrm{S}\mathrm{e}}_3}$)→ 14.3093(9) Å ($c_{{\mathrm{E}\mathrm{u}\mathrm{E}\mathrm{r}\mathrm{C}\mathrm{u}\mathrm{T}\mathrm{e}}_3}$).

Correspondingly, the volume of the unit cell increased as follows: 507.737(14) ų (EuErCuS₃) [15] → 566.62(6) ų (EuErCuSe₃) [16] → 690.25(8) ų (EuErCuTe₃) (Table 1).

A regular increase in the average metal-chalcogen bond lengths was also observed in the chalcogenide series. For example, we observed the following:

• d(Eu–Ch): 3.060 Å (Ch = S) → 3.130 Å (Ch = Se) → 3.330 Å (Ch = Te);
• d(Er–Ch): 2.723 Å (Ch = S) → 2. 730 Å (Ch = Se) → 3.037 Å (Ch = Te);
• d(Cu–Ch): 2.350 Å (Ch = S) → 2.468 Å (Ch = Se) → 2.654 Å (Ch = Te).

Thus, the increase in the chalcogen radius led to the transformation of the local geometry around the Eu²⁺, resulting in a change in the type of its coordination polyhedron from a one-capped trigonal prism in EuErCuS₃ [15] to a trigonal prism in EuErCuSe₃ and EuErCuTe₃, a change in the structural type and space group in the series of EuErCuCh₃ compounds, and an increase in structural parameters.

When comparing the structural parameters of the EuErCuTe₃ compound with the already known europium tellurides EuGdCuTe₃ and EuLuCuTe₃ [42], their decrease was observed with a decrease in the ionic radius of Ln³⁺ (r_i(Gd³⁺) = 0.938 Å > r_i(Er³⁺) = 0.89 Å > r_i(Lu³⁺) = 0.861 Å) [26]. The unit cell parameters of EuLnCuTe₃ (Ln = Gd [42], Er (Table 1), Lu) [42] changed as follows:

• a_Pnma(c_Cmcm) = 11.3761(7) Å ($a_{{\mathrm{E}\mathrm{u}\mathrm{G}\mathrm{d}\mathrm{C}\mathrm{u}\mathrm{T}\mathrm{e}}_3}$) → 11.1957(7) Å ($c_{{\mathrm{E}\mathrm{u}\mathrm{E}\mathrm{r}\mathrm{C}\mathrm{u}\mathrm{T}\mathrm{e}}_3}$) → 11.1174(7) Å ($c_{{\mathrm{E}\mathrm{u}\mathrm{L}\mathrm{u}\mathrm{C}\mathrm{u}\mathrm{T}\mathrm{e}}_3}$);
• b_Pnma(a_Cmcm) = 4.3405(3) Å ($a_{{\mathrm{E}\mathrm{u}\mathrm{G}\mathrm{d}\mathrm{C}\mathrm{u}\mathrm{T}\mathrm{e}}_3}$) → 4.3086(3) Å ($c_{{\mathrm{E}\mathrm{u}\mathrm{E}\mathrm{r}\mathrm{C}\mathrm{u}\mathrm{T}\mathrm{e}}_3}$)→ 4.2937(3) Å ($c_{{\mathrm{E}\mathrm{u}\mathrm{L}\mathrm{u}\mathrm{C}\mathrm{u}\mathrm{T}\mathrm{e}}_3}$);
• c_Pnma(b_Cmcm) = 14.3469(9) Å ($a_{{\mathrm{E}\mathrm{u}\mathrm{G}\mathrm{d}\mathrm{C}\mathrm{u}\mathrm{T}\mathrm{e}}_3}$) → 14.3093(9) Å ($c_{{\mathrm{E}\mathrm{u}\mathrm{E}\mathrm{r}\mathrm{C}\mathrm{u}\mathrm{T}\mathrm{e}}_3}$)→ 14.2876(9) Å ($c_{{\mathrm{E}\mathrm{u}\mathrm{L}\mathrm{u}\mathrm{C}\mathrm{u}\mathrm{T}\mathrm{e}}_3}$).

The volume of the unit cell decreased from 708.42(8) to 682.02(8) ų in the EuLnCuTe₃ (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:

• d(Eu–Te): 3.377Å → 3.330 Å → 3.332 Å;
• d(Ln–Te): 3.081 Å → 3.037 Å → 3.017 Å;
• d(Cu–Te): 2.666 Å → 2.654 Å → 2.648 Å.

Thus, the decrease in the lanthanide radius in the series of EuLnCuTe₃ 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.

3.2. Magnetic Properties of the EuErCuTe₃

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 m³ 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 − θ_p)) at temperatures from 50 to 300 K, the Curie constant C_50–300K = 0.241 m³·K·kmol⁻¹ and the Weiss constant (Curie paramagnetic temperature) θ_p = −4.0 K, as well as the effective magnetic moment μ_50–300K = 12.39 μ_B, were obtained.

The paramagnetic parameters of the EuErCuTe₃ compound corresponded well to the calculated parameters of the free ions ($\mu =\sqrt{{7.94}^2+{9.58}^2}=12.44$μ_B, C = 0.243 m³·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). The best fit was obtained with the following parameter values: C = 0.241 m³·K·kmol⁻¹, χ₀⁻¹ = 14.5 kmol·m⁻³, σ = 37 kmol·K·m⁻¹, 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/χ₀ + ((θ − C/χ₀)² + 4C(θ/χ₀ + 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 EuErCuSe₃ (4.7 K [16]) and EuErCuS₃ (5.0 K [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(Eu²⁺) + g_JJ(Er³⁺) = 7 μ_B + 9 μ_B = 16 μ_B, was not achieved until reaching 4 MA·m⁻¹.

The magnetic properties of the EuErCuTe₃ compound were similar to those of EuGdCuTe₃. Both are ferrimagnets at low temperatures (lower than 4.2 K for the first and 7.9 K for the second), unlike EuLuCuTe₃, which is ferromagnetic under a temperature of 3.0 K.

3.3. Band Structure of EuErCuTe₃

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 SrRECuSe₃ (RE = Ho − Lu), the values range from 2.03–2.21 eV [43]. The narrower band gap of EuRECuCh₃ was explained by the presence of a 4f–5d transition in the Eu²⁺ ion [45].

3.4. Elastic Constants and Elastic Modulus

The elastic constants and the elastic modulus of the compound EuErCuTe₃ are presented in

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

C11	C12	C13	C22	C23	C33	C44	C55	C66	Averaging Scheme	B	G	Y	Poisson’s Ratio	HV
122	52	40	95	47	113	10	31	45	Voigt	68	30	78	0.307	3.2
									Reuss	67	23	61	0.349
									Hill	67	26	70	0.328

. 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).

$$H_V=0.92{\left(\frac{G}{B}\right)}^{1.137}{G}^{0.708}$$

(1)

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.

3.5. Raman, IR, and Phonon Spectra

From the DFT calculations, the wavenumbers and types of modes were determined (

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

Frequency, cm−1	Type	IR		Raman		Involved Ions 1
		Active/ Inactive	Intensity IR (km·mol−1)	Active/ Inactive	Intensity Raman (Arbitrary Units)
33	B1u	A	10	I		Eu S, Er S, Cu W, Te1 S, Te2 S
48	Au	I	0	I		Er S, Te2 S
54	B1g	I	0	A	358	Eu S, Cu S, Te1 S, Te2 W
59	Ag	I	0	A	582	Eu S, Cu S, Te1 S, Te2
61	B2g	I	0	A	287	Eu S, Cu W, Te2
67	B2u	A	18	I		Eu, Er S, Cu S, Te1 S, Te2 W
71	B1u	A	14	I		Eu W, Er S, Cu S, Te1, Te2
81	B3u	A	49	I		Eu, Er, Cu S, Te1 W, Te2
82	B2g	I	0	A	415	Eu, Cu S, Te2
86	Ag	I	0	A	136	Eu S, Cu S, Te2
87	B1g	I	0	A	202	Eu S, Cu S, Te1, Te2
88	B1u	A	90	I		Eu S, Er, Cu, Te2
90	B2u	A	2	I		Eu S, Er, Cu S, Te1 W
92	B3u	A	115	I		Eu S, Er, Cu W, Te1 W, Te2
112	B3u	A	16	I		Eu W, Er S, Cu S, Te1
113	B3g	I	0	A	132	Te2 S
117	Au	I	0	I		Er, Te2
119	B1g	I	0	A	25	Eu W, Cu, Te1 W, Te2
120	B1u	A	374	I		Er, Cu S, Te1 W, Te2
122.66	B2u	A	495	I		Eu, Er, Te2
123.50	B2g	I	0	A	1.5	Eu, Cu, Te1, Te2
131.92	B3u	A	79	I		Eu, Er W, Cu, Te1 S, Te2
131.95	B1g	I	0	A	47	Eu, Cu S, Te1 S, Te2 W
131.97	Ag	I	0	A	119	Eu, Te1, Te2
132.07	B2u	A	135	I		Eu W, Cu S, Te1 S
138	Ag	I	0	A	51	Cu S, Te1, Te2 W
145	B2g	I	0	A	116	Eu W, Cu S, Te1 S, Te2 W
146	Ag	I	0	A	1000	Cu, Te1, Te2
148	B1u	A	5	I		Er, Cu, Te2
151	B2g	I	0	A	59	Cu, Te1, Te2
154	B1u	A	137	I		Er, Cu W, Te1 S, Te2 W
155	B3u	A	185	I		Er, Cu, Te2
159	B3u	A	2	I		Er, Cu, Te1, Te2

¹ The superscripts “S” and “W” denote strong and weak ion displacements in the modes, respectively.

). 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.

A strong mixing of vibrations in the structural units in the crystal EuErCuSe₃ 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.

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 displacement was less than 0.005 Å, then the ion was not mentioned in the column “Participants”.

4. Conclusions

This article discusses the synthesis, structure, and optical and magnetic properties of the new complex telluride EuErCuTe₃. The compound crystallizes in the KZrCuS₃ structure type. Its crystal structure is built from distorted [ErTe₆]⁹⁻ octahedra and [CuTe₄]⁷⁻ tetrahedra, forming two-dimensional layers. Trigonal prisms of [EuTe₆]¹⁰⁻ are located between the layers. In the series of EuErCuCh₃ chalcogenides (Ch = S, Se, and Te), a change in the coordination polyhedron of Eu²⁺ was observed, along with a change in the structural type and space group and increases in the structural parameters. EuErCuTe₃ contains two magnetic ions, Eu²⁺ and Er³⁺, and it undergoes a ferrimagnetic transition at 4.2 K. The obtained results correlate with the observed ferrimagnetic ordering in erbium sulfide and selenide EuErCuCh₃ (Ch = S and Se). EuErCuTe₃ 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 EuErCuTe₃. The theoretical calculations also allowed us to assign vibrational modes as well as to reveal the involved ions responsible for these modes.