Layered orthorhombic single crystals of EuYCuTe3 are synthesized using the ampoule method from the elemental precursors taken in the ratio of 1 Eu:1 Y:1 Cu:3 Te by heating up to 1120 K with an excess of CsI as flux. The orthorhombic structure of EuYCuTe3 is established, and structural parameters are obtained using X-ray diffraction. At ambient conditions, the sample crystallizes in the space group Pnma with the unit cell parameters a = 11.2730(7) Å, b = 4.3214(3) Å, c = 14.3271(9) Å. The structure is composed of vertex-connected [CuTe4]7- tetrahedra, which form chains along the [010] direction, and of edge-connected [YTe6]9- octahedra, which form layers parallel to the (010) plane. The Eu2+ cations are found in a capped trigonal prismatic coordination of Te2- anions. The structural phase transition from the α to the β phase is discovered upon heating the sample to 323 K, which comes accompanied with a decrease of [CuTe4]7- tetrahedral distortion. The symmetry of the high-temperature phase is established as ordered in the space group Cmcm (a = 4.3231(3) Å, b = 14.3328(9) Å, c = 11.2843(7) Å). The nature and microscopic mechanism of the phase transition is discussed. By cooling it down below 3 K, the soft ferromagnetic properties of EuYCuTe3 are discovered. The correlation of the ferromagnetic transition temperature in the series of chalcogenides EuYCuCh3 (Ch = S, Se, Te) with the ionic radius of the chalcogenide anion is established. The structural dynamical elastic properties of α- and β-EuYCuTe3 were calculated within the ab initio approach. The vibrational mode frequencies and decomposition on irreducible representations, as well as the degree of ion involvement in each mode, were determined. The calculations reveal an imaginary mode in the Y-point of the Brillouin zone in the high symmetry β-EuYCuTe3 phase. This finding explains the nature of structural reconstruction in EuYCuTe3 crystal as a second-order phase transition induced by soft mode condensation at the edge of the Brillouin zone. The exfoliation of a single layer is simulated theoretically. The exfoliation energy is estimated, and the dynamical properties of EuYCuTe3 single layers are studied.

Single crystals of the layered EuRECuTe3 series with RE = Nd, Sm, Tb and Dy are obtained for the first time, completing the series of studies on quaternary tellurides synthesized using the halide flux method. These compounds crystallize in the orthorhombic space group Pnma (no. 62) with unit cell parameters ranging from a = 11.5634(7) Å, b = 4.3792(3) Å and c = 14.3781(9) Å for EuNdCuTe3 to a = 11.2695(7) Å, b = 4.3178(3) Å and c = 14.3304(9) Å for EuDyCuTe3. The influence of prismatic polyhedra [EuTe6+1]7− structural units on the stabilization of 3d framework composed by 2d layered fragments [RECuTe3]2−, which have a key role in the interlayer interaction, is established. A comparative analysis of structural and magnetic properties dependence on the rare-earth element radius ri(RE3+) in the EuRECuTe3 series (RE = Sc, Y, Nd–Lu) is carried out. The structural contraction, including decrease in degree of tetrahedral polyhedra distortion, bond lengths shortening and unit cell volume shrinking with increasing ri(RE3+), is established. It is shown that the structural alternation leads to transition from ferromagnetic to ferrimagnetic ordering. It was established that changes in the cationic sublattice have a more significant impact on structural transitions in the series of quaternary tellurides than changes in the anionic sublattice. The electronic structure and elastic and dynamic properties were estimated using ab initio calculations. The exfoliation energy for each compound is obtained by estimation of monolayer ground state energy as a result of structure relaxation. The symmetry and structural properties of monolayer EuRECuTe3 (RE = Nd, Sm, Tb, Dy) compound are established and the orthorhombic symmetry is obtained with layer group pm2_1b.

The layered orthorhombic quaternary tellurides EuRECuTe3 (RE = Ho, Tm, Sc) with Cmcm symmetry were first synthesized. Single crystals of the compounds up to 500 μm in size were obtained by the halide-flux method at 1120 K from elements taken in a ratio of Eu/RE/Cu/Te = 1:1:1:3. In the series of compounds, the changes in lattice parameters were in the ranges a = 4.3129(3)–4.2341(3) Å, b = 14.3150(9)–14.1562(9) Å, c = 11.2312(7)–10.8698(7) Å, V = 693.40(8)–651.52(7) Å3. In the structures, the cations Eu2+, RE3+ (RE = Ho, Tm, Sc), and Cu+ occupied independent crystallographic positions. The structures were built with distorted copper tetrahedra forming infinite chains [CuTe4]7− and octahedra [RETe6]9− forming two-dimensional layers along the a-axis. These coordination polyhedra formed parallel two-dimensional layers CuRETe32−∞2. Between the layers, along the a-axis, chains of europium trigonal prisms [EuTe6]10− were located. Regularities in the variation of structural parameters and the degree of distortion of coordination polyhedra depending on the ionic radius of the rare-earth metal in the compounds EuRECuCh3 (RE = Ho, Er, Tm, Lu, Sc; Ch = S, Se, Te) were established. It is shown that with a decrease in the ionic radius ri(RE3+) in the compounds EuRECuTe3, the unit-cell volume, bond length d(RE–Te), distortion degree [CuTe4]7−, and crystallographic compression of layers [RECuTe3]2− decreased. The distortion degree of tetrahedral polyhedra [CuCh4]7−, as well as the structural parameters in europium rare-earth copper tellurides EuRECuTe3, were higher than in isostructural quaternary chalcogenides. Ab initio calculations of the crystalline structure, phonon spectrum, and elastic properties of compounds EuRECuTe3 (RE = Ho, Tm, and Sc) ere conducted. The types and wave numbers of fundamental modes were determined, and the involvement of ions in IR and Raman modes was assessed. The calculated data of the crystal structure correlated well with the experimental results.

The structure and properties of three layered heterometallic quaternary sulfides SrLaCuS3, SrNdCuS3 and SrTmCuS3 were studied for the first time using first-principles calculations in the stoichiometric and nonstoichiometric approximations. The applied DFT-based computations were performed using a hybrid functional with the contribution of nonlocal exchange in the Hartree-Fock formalism. It was revealed that the nonstoichiometry of SrLaCuS3 and SrNdCuS3 must be considered for modeling phonon spectra, elastic properties and band gaps. The wavenumbers and types of the Raman and “silent” modes at the Г-point were determined. From the analysis of displacement vectors, the degree of participation of ions in each mode was determined. The elastic constants and elastic moduli of the reported sulfides were calculated.

Crystals of bismuth fluoride BiF3 grown from a melt were studied for the first time by optical spectroscopy methods and calculated from first principles in the phonon excitations region. A study of IR reflectance spectra in polarized light was carried out. The parameters of optical phonons were obtained. In the IR reflectance spectra, a low-frequency rise in the range <500 cm–1, characteristic of conductive materials, is observed. The reflection spectra were analyzed within the framework of the Drude–Lorentz model, taking into account the contribution of ionic conductivity. An ab initio calculation of the phonon spectrum of a BiF3 crystal was carried out and the relationship between theoretical and experimental data was analyzed.

Within the framework of the DFT approach, with a hybrid functional PBE0 that takes into account the contribution of nonlocal exchange in the Hartree-Fock formalism, the structure of impurity centers Gd2Ti2O7:Eu3+, Gd2Ti2O7:Dy3+ and Tb2Ti2O7:Eu3+ was calculated. It has been shown that there is practically no lattice distortion in these impurity centers.

Rare-earth orthoferrites are a promising platform for antiferromagnetic spintronics with a rich variety of terahertz spin and lattice dynamics phenomena. For instance, it has been experimentally demonstrated that the light-driven optical phonons can coherently manipulate macroscopic magnetic states via nonlinear magnetophononic effects. Here using TbFeO3 as an example, we reveal the origin of the mode mixing between the LO and TO phonons, which is important for understanding of nonlinear phononics. We performed a comprehensive study of the lattice dynamics of the TbFeO3 single crystal by polarized infrared and Raman scattering spectroscopic techniques, and experimentally obtained and carefully analyzed the spectra of anisotropic complex dielectric functions in the far-infrared spectral range. This allowed us to reliably identify the symmetries and parameters of most infrared- and Raman-active phonons. Next, the experimental studies were supplemented by the lattice dynamics calculations which allowed us to propose the normal mode assignments. We reveal that the relation between LO and TO polar phonons is complex and does not strictly follow the "LO-TO rule" due to the strong mode mixing. We further analyze how displacements of different ions contribute to phonon modes and reveal that magnetic Fe ions are not involved in Raman-active phonons, thus shedding light on a lack of spin phonon coupling for such phonons. The obtained results establish a solid basis for further in-depth experimental research in the field of nonlinear phononics and magnetophononics in rare-earth orthoferrites.

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.

R2Zr2O7 (R = La–Lu) crystals were studied by DFT/GCA calculations. The phonon frequencies at the Γ point were found. The components of the elastic tensor for the entire R2Zr2O7 (R = La–Lu) crystal series and their hardness were calculated. The change in the phonon frequencies upon hydrostatic compression was described.

We report on the novel heterometallic quaternary selenide EuCeCuSe3, the fabrication of which has been a challenge until this work. The structure of the reported selenide was elucidated from the powder X-ray diffraction data, which revealed the formation of EuCeCuSe3 with excellent yield (96.7%) accompanied with a minor fraction of CeSe2 (3.3%), and was best solved in orthorhombic space group Pnma with the BaLaCuS3 structural type. Thus, the crystal structure of the title compound completes the row of the heterometallic quaternary selenides EuRECuSe3 (RE 1/4 La, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, Lu, Y), of which the cerium-based derivative exclusively belongs to the BaLaCuS3 structural type. The distortion of the CuSe4 polyhedron was compared for the whole series of EuRECuSe3 compounds using the i4-descriptor for four coordinated ions, which revealed the highest degree of distortion for the Ce3 thorn -containing selenide, fol-lowed by the La3 thorn -based derivative. Furthermore, the crystallographic and geometrical parameters of the reported selenide were discussed in comparison to the Ce3 thorn -based sulfides SrCeCuS3 and EuCeCuS3. Ab initio calculations of the crystal structure, a phonon spectrum and elastic constants for the crystal of EuCeCuSe3 were also performed. The types and wavenumbers of fundamental modes were determined and the involvement of ions participating in the phonon modes was assessed. The experimental IR spectrum of the reported selenide was interpreted and found to be in agreement with the calculated spectrum. The experimental direct band gap of EuCeCuSe3 was measured to be 1.36 eV that is consistent with the concept of its origin due to interband transitions between orbitals emerging mainly from 4f (valence band) and 5d (conduction band) levels of the Eu2 thorn cation. The dependence of the Young's modulus on the direction demonstrates the anisotropy of the elastic properties, while the Vickers hardness for EuCeCuSe3 was calculated to be 5.2 GPa. Finally, the title compound is paramagnetic above 4 K.(c) 2022 Chinese Society of Rare Earths. Published by Elsevier B.V. All rights reserved.

EuScCuSe3 was synthesized from the elements for the first time by the method of cesium-iodide flux. The crystal belongs to the orthorhombic system (Cmcm) with the unit cell parameters a = 3.9883(3) Å, b = 13.2776(9) Å, c = 10.1728(7) Å, V = 538.70(7) Å3. Density functional (DFT) methods were used to study the crystal structure stability of EuScCuSe3 in the experimentally obtained Cmcm and the previously proposed Pnma space groups. It was shown that analysis of elastic properties as Raman and infrared spectroscopy are powerless for this particular task. The instability of EuScCuSe3 in space group Pnma space group is shown on the basis of phonon dispersion curve simulation. The EuScCuSe3 can be assigned to indirect wide-band gap semiconductors. It exhibits the properties of a soft ferromagnet at temperatures below 2 K.

Barium containing quaternary chalcogenides have recently attracted significant interest due to their promising thermoelectric applications. The novel semiconductor quaternary selenide BaSmCuSe3 of the orthorhombic space group Cmcm with the KZrCuS3 structure type was obtained for the first time using a reductive selenidation method. Structural parameters and optical properties of BaSmCuSe3 were discussed in comparison with the isostructural sulfide BaSmCuS3. Replacing sulfur with selenium in a quaternary chalcogenide leads to a narrowing of the band gap from 2.30 eV to 1.93 eV. The crystal structure and optical properties of the synthesized herein compound were discussed within the ab initio approach. The reults of calculations are in good agreement with the experimental characteristics.

The crystal structure and the phonon spectrum of a La2Zr2O7 crystal have been investigated in terms of the MO LCAO approach using DFT hybrid functionals that take into account the contribution of the nonlocal exchange within the Hartree–Fock formalism. The frequencies, symmetry species, and intensities of IR and Raman active fundamental vibrations are determined. Elastic constants are calculated. The calculations have been carried out using the new version of the CRYSTAL program—CRYSTAL17—designed to model periodic structures within the MO LCAO approach.

Crystal structure and phonon spectrum of rare-earth stannates R $$_2$$ Sn $$_2$$ O $$_7$$ and zirconates R $$_2$$ Zr $$_2$$ O $$_7$$ (R = La–Lu) with the pyrochlore structure were studied within the framework of DFT and MO LCAO approach. The calculations were performed by using hybrid functional PBE0 that take into account nonlocal exchange at the Hartree-Fock formalism. The calculation of the phonon spectrum at the $$\Gamma$$ -point made it possible to supplement the available experimental data on the IR and Raman spectra of stannates and zirconates. In the framework of the ab initio approach, the change of the elastic properties of zirconium oxide t-ZrO $$_2$$ by doping the yttrium was studied. Calculations were performed in the CRYSTAL17 program designed to simulate periodic structures.

In this work, we report on the synthesis, in-depth crystal structure studies as well as optical and magnetic properties of newly synthesized heterometallic quaternary selenides of the Eu+2Ln+3Cu+1Se3 composition. Crystal structures of the obtained compounds were refined by the derivative difference minimization (DDM) method from the powder X-ray diffraction data. The structures are found to belong to orthorhombic space groups Pnma (structure type Ba2MnS3 for EuLaCuSe3 and structure type Eu2CuS3 for EuLnCuSe3, where Ln = Sm, Gd, Tb, Dy, Ho and Y) and Cmcm (structure type KZrCuS3 for EuLnCuSe3, where Ln = Tm, Yb and Lu). Space groups Pnma and Cmcm were delimited based on the tolerance factor t’, and vibrational spectroscopy additionally confirmed the formation of three structural types. With a decrease in the ionic radius of Ln3+ in the reported structures, the distortion of the (LnCuSe3) layers decreases, and a gradual formation of the more symmetric structure occurs in the sequence Ba2MnS3 → Eu2CuS3 → KZrCuS3. According to magnetic studies, compounds EuLnCuSe3 (Ln = Tb, Dy, Ho and Tm) each exhibit ferrimagnetic properties with transition temperatures ranging from 4.7 to 6.3 K. A negative magnetization effect is observed for compound EuHoCuSe3 at temperatures below 4.8 K. The magnetic properties of the discussed selenides and isostructural sulfides were compared. The direct optical band gaps for EuLnCuSe3, subtracted from the corresponding diffuse reflectance spectra, were found to be 1.87–2.09 eV. Deviation between experimental and calculated band gaps is ascribed to lower d states of Eu2+ in the crystal field of EuLnCuSe3, while anomalous narrowing of the band gap of EuYbCuSe3 is explained by the low-lying charge-transfer state. Ab initio calculations of the crystal structures, elastic properties and phonon spectra of the reported compounds were performed.

Crystal structure and phonon spectrum of La2Zr2O7 were studied within the framework of density functional theory and MO LKAO approach. The calculations were performed by using hybrid functionals that takes into account both local and nonlocal (in the Hartree–Fock formalism) exchange. The frequencies, types, and intensities of Raman and IR modes are determined. The elastic constants have been calculated too. The calculations were performed in the CRYSTAL17 program intended for simulating periodic structures in the MO LCAO approximation.

The phonon spectrum of yttrium stannate Y 2 Sn 2 O 7 is calculated within a general ab initio approach and the frequencies and types of IR and Raman modes are determined. The degree of involvement of ions in phonon modes is determined from the analysis of displacement vectors calculated ab initio. The elastic constants and hardness of Y 2 Sn 2 O 7 are calculated. The impurity ion–ligand distance in Y 2 Sn 2 O 7 :Yb 3+ , Y 2 Sn 2 O 7 :Eu 3+ , Lu 2 Sn 2 O 7 :Yb 3+ , Nd 2 Sn 2 O 7 :Gd 3+ , and Nd 2 Sn 2 O 7 :Tb 3+ impurity centers is calculated.

We report on the novel heterometallic quaternary sulfides SrLnCuS3 (Ln = La, Nd, Tm), obtained as both single crystals and powdered samples. The structures of both the single crystal and powdered samples of SrLaCuS3 and SrNdCuS3 belong to the orthorhombic space group Pnma but are of different structural types, while both samples of SrTmCuS3 crystallize in the orthorhombic space group Cmcm with the structural type KZrCuS3. Three-dimensional crystal structures of SrLaCuS3 and SrNdCuS3 are formed from the (Sr/Ln)S7 capped trigonal prisms and CuS4 tetrahedra. In SrLaCuS3, alternating 2D layers are stacked, while the main backbone of the structure of SrNdCuS3 is a polymeric 3D framework [(Sr/Ln)S7]n, strengthened by 1D polymeric chains (CuS4)n with 1D channels, filled by the other Sr2+/Ln3+ cations, which, in turn, form 1D dimeric ribbons. A 3D crystal structure of SrTmCuS3 is constructed from the SrS6 trigonal prisms, TmS6 octahedra and CuS4 tetrahedra. The latter two polyhedra are packed together into 2D layers, which are separated by 1D chains (SrS6)n and 1D free channels. In both crystal structures of SrLaCuS3 obtained in this work, the crystallographic positions of strontium and lanthanum were partially mixed, while only in the structure of SrNdCuS3, solved from the powder X-ray diffraction data, were the crystallographic positions of strontium and neodymium partially mixed. Band gaps of SrLnCuS3 (Ln = La, Nd, Tm) were found to be 1.86, 1.94 and 2.57 eV, respectively. Both SrNdCuS3 and SrTmCuS3 were found to be paramagnetic at 20–300 K, with the experimental magnetic characteristics being in good agreement with the corresponding calculated parameters.

Ilmenite-type crystals find a variety of technological applications due to their intriguing physical properties. We present the results of the lattice dynamics studies of honeycomb antiferromagnetic ilmenite CoTiO3 single crystal by the complementary polarized infrared, Raman, and dielectric spectroscopic techniques that are supplemented by the DFT calculations. The symmetries and frequencies of all predicted infrared- and Raman-active phonons were uniquely identified. Furthermore, it was found that the dielectric permittivity demonstrates distinct changes below antiferromagnetic ordering temperature in zero magnetic field due to the spontaneous magnetodielectric effect. Our results establish the solid basis for further investigations and more deep understanding of the coupling of phonons with spins and magnetic excitations, as well as their involvement in other physical phenomena in this promising material.