EuAl$_4$ is a rare earth intermetallic in which competing itinerant and/or indirect exchange mechanisms give rise to a complex magnetic phase diagram, including a centrosymmetric skyrmion lattice. These phenomena arise not in the tetragonal parent structure but in the presence of a charge density wave (CDW), which lowers the crystal symmetry and renormalizes the electronic structure. Microscopic knowledge of the corresponding atomic modulations and their driving mechanism is a prerequisite for a deeper understanding of the resulting equilibrium of electronic correlations and how it might be manipulated. Here, we use synchrotron single-crystal X-ray diffraction, inelastic X-ray scattering, and lattice dynamics calculations to clarify the origin of the CDW in EuAl$_4$. We observe a broad softening of a transverse acoustic phonon mode that sets in well above room temperature and, at $T_\mathrm{CDW}=142$ K, freezes out in an atomic displacement mode described by the superspace group $Immm(00\gamma)s00$. In the context of previous work, our observation is a clear confirmation that the CDW in EuAl$_4$ is driven by electron-phonon coupling. This result is relevant for a wider family of BaAl$_4$ and ThCr$_2$Si$_2$-type rare-earth intermetallics known to combine CDW instabilities and complex magnetism.

The phase formation of terbium chromoborate TbCr3(BO3)4 in the bismuth trimolybdate and lithium tungstate melt-solutions has been studied. The absence of the terbium chromoborate trigonal phase in the bismuth trimolybdate-based system at all component ratios has been shown. The component ratio in the lithium tungstate-based system has been found at which the TbCr3(BO3)4 trigonal crystals are formed at temperatures above 1100 degrees C; below this temperature, the monoclinic phase dominates. The structural and magnetic properties of the grown crystals have been studied. It has been established that the trigonal and monoclinic TbCr3(BO3)4 crystals synthesized from the lithium tungstate-based solvent exhibit identical magnetic properties. At the same time, a significant difference of the magnetic properties of the single crystals synthesized from the bismuth molybdate melt-solution has been observed. This difference has been attributed to the effect of Bi3+ ions that partially replace Tb3+ ions.

The topology of electronic and phonon band structures of graphene is well studied and known to exhibit a Dirac cone at the K point of the Brillouin zone. Here, we applied inelastic x-ray scattering (IXS) along with ab initio calculations to investigate phonon topology in graphite, the 3D analog of graphene. We identified a pair of modes that form a very weakly gapped linear anticrossing at the K point that can be essentially viewed as a Dirac cone approximant. The IXS intensity in the vicinity of the quasi-Dirac point reveals a harmonic modulation of the phonon spectral weight above and below the Dirac energy, which was previously proposed as an experimental fingerprint of the nontrivial topology. We illustrate how the topological winding of IXS intensity can be understood in terms of atomic displacements and highlight that the intensity winding is not in fact sensitive in telling quasi- and true Dirac points apart.

HoFe1-xMnxO3 (0 < x < 1) single crystals have been grown by the optical floating zone technique. A structural transition from the orthorhombic to hexagonal modification has been established in the crystals in the concentration range of 0.7-0.8, which has been confirmed by the X-ray diffraction data. For a series of the rhombic crystals, the room-temperature Mossbauer study and magnetic measurements in the temperature range of 4.2-1000 K have been carried out. It has been observed that, with an increase in the manganese content in the samples, the temperature of the spin-reorientation transition increases significantly: from 60 K in the HoFeO3 compound to room temperature in HoFe0.6Mn0.4O3. The magnetic measurements have shown that, upon substitution of manganese for iron, the magnetic orientational type transition changes from a second-order transition (AxFyGz -> CxGyFz) to first-order one (AxFyGz -> GxCyAz) with a weak ferromagnetic moment only in the b direction (for Pnma notation). The growth of the spin-reorientation transition temperature has been attributed to the change in the value of the indirect exchange in the iron subsystem under the action of manganese, which has been found when studying the Mossbauer effect in the HoFe1-xMnxO3 (x < 0.4) compound.

The low-temperature spin dynamics of the orthorhombic TbFeO_3 perovskite has been studied. It has been found that the inelastic neutron scattering (INS) spectrum contains two modes corresponding to different sublattices in the compound. The iron subsystem orders antiferromagnetically at T_N = 632 K and exhibits the high-energy magnon dispersion. Magnetic dynamics of this subsystem has been described using the linear spin wave theory and our solution yields sizable anisotropy between in-plane and out-of-plane exchange interactions. This approach was previously used to describe the magnon dispersion in the TmFeO_3 compound. Three non-dispersive crystal electric field levels corresponding to Tb^3+ ions have been established in the region below 40 meV at about 17, 26, and 35 meV. Study of diffuse scattering at different temperatures has elucidated the behavior of the magnetic correlation length. The behavior of the Tb^3+ ion subsystem has been numerically described in the framework of the point charge model. The numerical data agree satisfactorily with the experiment and with the general concept of the single-ion approximation applied to the rare-earth subsystem of orthorhombic perovskites.

Single crystals of trigonal neodymium scandoborate NdSc 3 (BO_3) 4 were grown by the group method from a solution-melt based on bismuth trimolybdate. The molar heat capacity C(T) was studied in the temperature range 2-300 K and magnetic fields up to 9 T. The experimental curve was approximated by the combined Debye-Einstein model. The lattice contribution was determined from ab-initio calculations. Schottky anomaly was observed in the low-temperature region C(T) with the applied magnetic field. Keywords: crystal growth, magnetoelectrics, heat capacity, Schottky anomaly.

Single crystals of the Pb2Fe2_xMnxGe2O9 (x = 0.16) antiferromagnet have been grown. Using the specific heat measurements, a Ne acute accent el temperature of T-N = (42.0 +/- 0.5) K for the synthesized crystals has been found. It has been shown using the magnetic measurements that, due to the competition between the magnetoanisotropic contributions of the iron and manganese subsystems in the crystals, near a temperature of T-c = 22 K, a spontaneous spin-reorientation transition occurs, the tem-perature of which in an applied magnetic field changes with the field value and orientation relative to the rhombic axes of the crystal. Based on the analysis of the temperature and field dependences of the magnetization obtained at different orientations of the magnetic field, it has been established that, below T-c, an inclined magnetic structure is formed in the crystal. The antiferromagnetic vector of the inclined structure rotates smoothly in the rhombic bc plane with increasing tem-perature from a direction close to the b axis at T = 4.2 K and tends to the rhombic c axis at T = T-c. The rotation of the antiferromagnetic vector occurs also at fixed temperatures T < T-c with increasing magnetic field. In the temperature range of T-c < T < T-N, the antiferromagnetic vector is oriented along the rhombic c axis. Magnetic phase diagrams of states have been built for different magnetic field orientations relative to the rhombic axes of the crystal. The richest phase diagram is shown to correspond to the orientation H||c and contains, along with the above-listed states, one more inclined phase, in which the antiferromagnetic vector rotates toward the rhombic a axis direction with a change in temperature or magnetic field.

The physical properties of the NiB4O7 and CoB4O7 tetraborate compounds in three structural modifications with the sp. gr. Pbca, Cmcm, and P6522 have been calculated using the density functional theory in the VASP software package. The pressure dependences of the enthalpy of the compounds in the investigated structural modifications have been calculated. The calculated electron densities of states and band structures showed that the compounds under study in all the considered modifications are dielectrics with a band gap of 3–4 eV. The calculation of the magnetic exchange constants in the Heisenberg model have shown qualitative agreement with the experiment.

Within a framework of the density functional theory using the VASP software package, physical properties of tetraborate compounds NiB4O7 and CoB4O7 in three structural modifications with space symmetry groups of Pbca, Cmcm and P6522 were calculated. The dependences of the enthalpy of compounds on pressure in studied structural modifications are calculated. The calculated electron densities of states and band structures showed that studied compounds in all considered modifications are dielectrics with a band gap of 3-4 eV. The calculation of the magnetic exchange constants was carried out in the Heisenberg model, which showed qualitative agreement with experiment.

Single crystals of trigonal neodymium scandoborate NdSc3(BO3)4 were grown by the group method from a solution-melt based on bismuth trimolybdate. The molar heat capacity C(T) was studied in the temperature range 2-300 K and magnetic fields up to 9 T. The experimental curve was approximated by the combined Debye-Einstein model. The lattice contribution was determined from ab-initio calculations. Schottky anomaly was observed in the low-temperature region C(T) with the applied magnetic field.

We present a comprehensive investigation of lattice dynamics in the double-helix antiferromagnet FeP by means of high-resolution time-of-flight neutron spectroscopy and ab initio calculations. Phonons can hybridize with the magnetic excitations in noncollinear magnets to significantly influence their properties. We observed a rich spectrum of phonon excitations, which extends up to similar to 50 meV. We performed detailed analysis of the observed and calculated spectra for all high-symmetry points and high-symmetry directions of the Brillouin zone. We show that the DFT calculations quantitatively capture the essential features of the observed phonons, including both dispersions and scattering intensities. By making use of the detailed intensity comparison between the theory and the data, we were able to identify displacement vectors for the majority of the observed modes. The overall excellent agreement between the DFT predictions and the experimental results breaks down for the lowest mode at the Y point, whose energy is lower than calculated by similar to 13%. The present study provides vital information on the lattice dynamics in FeP and demonstrates applicability of the DFT to novel pressure-induced phenomena in related materials, such as MnP and CrAs.

Single crystals of solid solutions of HoFe3-xGax(BO3)(4) with x = 0, 0.5, 1, 1.5, and 3 were obtained using flux synthesis. The conditions of the synthesis are described in detail. The structural properties of each of the synthesized samples were studied using X-ray powder diffraction analysis at several temperature points (303, 403, and 503 K). The structural parameters of the obtained samples and the "pure" compounds HoFe3(BO3)(4) and HoGa3(BO3)(4) were compared. The Raman spectra of the obtained solid solutions HoFe3-xGax(BO3)(4) were studied in a wide temperature range (T = 10-400 K). The vibrational spectra and eigenvectors of the HoFe3Ga(BO3)(4) and HoGa3(BO3)(4) in R32 phase and HoFe3Ga(BO3)(4) in P3(1)21 phase were calculated within density functional theory. The features of the Raman spectra of HoFe2Ga(BO3)(4), HoFe2.5Ga0.5(BO3)(4), HoFe3(BO3)(4) crystals associated with the R32 -> P3(1)21 structural phase transition, which have a strong dependence on the degree of substitution x, were investigated. Peculiarities of the Raman spectra, which are associated with magnetic ordering in HoFe1.5Ga1.5(BO3)(4), HoFe2Ga(BO3)(4), and HoFe2.5Ga0.5(BO3)(4) crystals, were detected.

We present the detailed inelastic neutron scattering measurements of the noncollinear antiferromagnet Mn$_3$Ge. Time-of-flight and triple-axis spectroscopy experiments were conducted at the temperature of 6~K, well below the high magnetic ordering temperature of 370~K. The magnetic excitations have a 5-meV gap and display an anisotropic dispersive mode reaching $\simeq 90$~meV at the boundaries of the magnetic Brillouin zone. The spectrum at the zone center shows two additional excitations that demonstrate characteristics of both magnons and phonons. The \textit{ab initio} lattice-dynamics calculations show that these can be associated with the magnon-polaron modes resulting from the hybridization of the spin fluctuations and the low-energy optical phonons. The observed magnetoelastic coupling agrees with the previously found negative thermal expansion in this compound and resembles the features reported in the spectroscopic studies of other antiferromagnets with the similar noncollinear spin structures.

The frequencies of lattice vibrations in the RFe 3 (BO 3 ) 4 (R = Pr, Nd, Tb, Dy, or Ho) crystals in the high-temperature R 32 phase and their temperature dependence have been calculated using the quasi-harmonic approximation. It has been found that, at the boundary point Λ of the Brillouin zone, the frequency of the unstable vibration mode the structural phase transition R 32 → P 3 1 21 is related to strong changes with temperature in the TbFe 3 (BO 3 ) 4 , DyFe 3 (BO 3 ) 4 , and HoFe 3 (BO 3 ) 4 crystals. With increasing temperature, the frequency of the soft mode stabilizes and takes a real value. No significant changes in the phonon spectra, including the boundary point Λ, with increasing temperature for the PrFe 3 (BO 3 ) 4 and NdFe 3 (BO 3 ) 4 crystals have been observed.

Vibrational, polarization, magnetic, and electronic properties of double perovskites CaMnTi2O6 and CaFeTi2O6 with a rare type of “column” ordering of divalent metal cations have been calculated based on the density functional theory. Analysis of the crystal lattice dynamics for paraelectric phase P42/nmc of both compounds has revealed that ferroelectric instability exists only in CaMnTi2O6. It is found that the structure distortion of the paraphrase of CaMnTi2O6 in the eigenvector of the unstable polar mode leads to a structure with the P42/nmc space group. The calculated spontaneous polarization for the ferroelectric phase of CaMnTi2O6 is Ps = 25 μC/cm2. The spin-polarization calculations have shown that the ground state is ferromagnetic in the CaFeTi2O6 crystal and antiferromagnetic in the CaMnTi2O6 crystal. The exchange interaction constants have been calculated using the Heisenberg model and the mean field approximation; the phase transition temperature for each compound has been estimated.

The lattice dynamic calculations and calculation of temperature dependence of the vibrational frequencies in the quasi-harmonic approximation were carried out for RFe3(BO3)4 crystals (R = Pr, Nd, Tb, Dy, Ho) in high temperature phase R32. It was obtained that in the boundary point Λ of Brillouin zone the frequency of instable vibrational mode, which associated with structural phase transition R32 -> P3121, change intensely with temperature in TbFe3(BO3)4, DyFe3(BO3)4 and HoFe3(BO3)4 crystals. The frequency of “soft” mode stabilizes with temperature increasing and takes a real value. Significant changes in phonon spectra, including in the boundary point Λ, in PrFe3(BO3)4 and NdFe3(BO3)4 crystals with temperature increasing were not observed.

Ab initio calculations of the structural, electronic, and optical properties of the CdB 4 O 7 and HgB 4 O 7 tetraborate compounds in three structural modifications with the Pbca , Cmcm , and Pmn 2 1 symmetry have been performed in the framework of the density functional theory using the VASP package. The calculations of the electronic band structure showed that these compounds in all the investigated modifications are dielectrics with a band gap of 2–4 eV. The calculation of the structural properties of the tetraborates under pressure showed that the phase transition between the Pbca and Pmn 2 1 structures in cadmium and mercury tetraborates occurs under pressures of 4.8 and 4.7 GPa, respectively.

AbstractAb initio calculations of the structural, electronic, and optical properties of the CdB_4O_7 and HgB_4O_7 tetraborate compounds in three structural modifications with the Pbca , Cmcm , and Pmn 2_1 symmetry have been performed in the framework of the density functional theory using the VASP package. The calculations of the electronic band structure showed that these compounds in all the investigated modifications are dielectrics with a band gap of 2–4 eV. The calculation of the structural properties of the tetraborates under pressure showed that the phase transition between the Pbca and Pmn 2_1 structures in cadmium and mercury tetraborates occurs under pressures of 4.8 and 4.7 GPa, respectively.