Magnetic properties of rare earth iron borates: Spectroscopic investigation by the method of rare earth probe

The magnetic phase transitions and magnetic structures in RFe₃(BO₃)₄ (R = Y, Gd-Er) iron borates have been investigated by the method of erbium spectroscopic probe. The magnetic ordering temperatures have been determined. On the basis of the comparison of the character of splitting of the spectral lines of the probe Er³⁺ ion in RFe₃(BO₃)₄(R = Y, Dy-Er) iron borates and in GdFe₃(BO₃)₄, a complicated whose magnetic structure is known, a conclusion is drawn about the orientation of the magnetic moments of iron: in dysprosium and terbium iron borates, an easy-axis magnetic structure is implemented, whereas an easy-plane structure occurs in holmium, erbium, and yttrium iron borates.     

Comparative study of the spectral and structural properties of EuAl<Subscript>3</Subscript>(BO<Subscript>3</Subscript>)<Subscript>4</Subscript> single crystals with different morphologies

Europium alumoborate EuAl₃(BO₃)₄ microcrystals have been synthesized by the flux method at a temperature of 1050°C. The obtained crystals have different morphologies: both plane-faced and skeletal microcrystals have been observed. Infrared spectroscopy, cathodeluminescence, and transmission electron microscopy investigations of individual microcrystals showed that the spectral and structural characteristics of these morphological forms coincide. The obtained crystals are characterized by the rhombohedral symmetry (sp. gr. R32) with the inclusions of C2/c monoclinic phase domains.     

Comparative Study of the Magnetoelectric Effect in HoAl<Subscript>3</Subscript>(BO<Subscript>3</Subscript>)<Subscript>4</Subscript> and HoGa<Subscript>3</Subscript>(BO<Subscript>3</Subscript>)<Subscript>4</Subscript> Single Crystals

The comparative study of the magnetoelectric properties and magnetostriction of HoGa₃(BO₃)₄ and HoAl₃(BO₃)₄ single crystals has been carried out. The investigated compounds exhibit qualitatively similar magnetodielectric and inverse magnetoelectric ME _E effects with the close absolute values, which is indicative of the weak effect of a nonmagnetic metal ion. On the contrary, the magnetostriction of the galloborate has been found to be threefold higher than that of the alumoborate. In addition, the difference between the qualitative behaviors of magnetostriction has been established: the magnetic-field dependence of magnetostriction for the alumoborate has the maximum near 70 kOe at T = 4.2 K, while the galloborate magnetostriction has no maximum and does not saturate in a field of 140 kOe.     

Infrared spectroscopy of europium borates Eu<Emphasis Type="Italic">M</Emphasis><Subscript>3</Subscript>(BO<Subscript>3</Subscript>)<Subscript>4</Subscript> (<Emphasis Type="Italic">M</Emphasis> = Al,Cr, Fe,Ga) with a huntite mineral type of structure

Huntite-like EuM ₃(BO₃)₄ crystals (M = Al, Cr, Fe, or Ga) are synthesized by means of spontaneous crystallization from a solution in a melt. The infrared spectra of the compounds are measured. The experimental data and the results from ab initio DFT calculations are compared. The comparison shows that the compounds have a primarily noncentrosymmetric rhomboherdal structure with the R32 space group. This indicates these compounds could exhibit magnetoelectric and nonlinear optical properties.     

On correlators for high multiplicity events

We present the results of the study of the energy correlators K₂(n) and K₃(n) and their ratio R₃(n) as a function of the hadron multiplicity at the LHC. The PYTHIA generator has been used. PYTHIA predicts that R₃(n) is not dependent on multiplicity. K₂(n), K₃(n), and the R₃(n) ratio can be studied at ATLAS.     

Electrical properties of zinc oxide under uniform pressure up to 25 GPa

The dependences of the Hall coefficient R _H (P) and resistivity ρ(P) of bulk n-ZnO crystals on hydrostatic pressure up to 8 GPa and quasi-hydrostatic pressure up to 25 GPa at T = 300 K have been measured. With an increase in pressure up to the polymorphic transition P _pt ? 9 GPa, an exponential increase in R(P) and ρ(P) is observed, which is caused by the increase in the ionization energy of the shallow-energy donor center. At P > P _pt, the resistivity decreases by several orders of magnitude.     

Effect of the Lattice and Spin-Phonon Contributions on the Temperature Behavior of the Ground State Splitting of Gd<Superscript>3+</Superscript> in SrMoO<Subscript>4</Subscript>

The temperature behavior of the EPR spectra of the Gd³⁺ impurity center in single crystals of SrMoO₄ in the temperature range T = 99–375 K is studied. The analysis of the temperature dependences of the spin Hamiltonian b ₂ ⁰ (T) = b₂(F) + b₂(L) and P ₂ ⁰ (T) = P₂(F) + P₂(L) (for Gd¹⁵⁷) describing the EPR spectrum and contributing to the Gd³⁺ ground state splitting ΔE is carried out. In terms of the Newman model, the values of b₂(L) and P₂(L) depending on the thermal expansion of the static lattice are estimated; the b₂(F) and P₂(F) spin-phonon contributions determined by the lattice ion oscillations are separated. The analysis of b ₂ ⁰ (T) and P ₂ ⁰ (T) is evidence of the positive contribution of the spin-phonon interaction; the model of the local oscillations of the impurity cluster with close frequencies ω describes well the temperature behavior of b₂(F) and P₂(F).     

Electron paramagnetic resonance of Mn<Superscript>2+</Superscript> ions in single crystals of yttrium aluminum borate YAl<Subscript>3</Subscript>(BO<Subscript>3</Subscript>)<Subscript>4</Subscript>

Single crystals of yttrium aluminum borate YAl₃(BO₃)₄ doped with manganese ions are studied using electron paramagnetic resonance spectroscopy. It is shown that manganese ions introduced at low concentrations into the sample predominantly occupy yttrium ion sites in the crystal structure. The shape of the electron paramagnetic resonance spectrum unambiguously indicates that the valence of manganese ions in this case is equal to 2+. The parameters of the spin Hamiltonian of Mn²⁺ ions in the YAl₃(BO₃)₄ matrix are determined at room temperature. The magnitude and sign of the fine structure parameter D allow the conclusion that the YAl₃(BO₃)₄ single crystals doped with manganese ions have a strong crystal field at the yttrium ion sites and easy-axis anisotropy.     

Optical properties and electronic structure of rare-earth ferroborates

The optical absorption spectra of single-crystal ferroborate GdFe₃(BO₃)₄ and GdFe_2.1Ga_0.9(BO₃)₄ are measured and interpreted. It is found that the absorption edge and the absorption bands A, B, and C observed below the edge are close to those for FeBO₃. A many-electron model of the band structure of GdFe₃(BO₃)₄ is suggested including strong electron correlations between the iron d states. It is shown that GdFe₃(BO₃)₄ has a charge-transfer dielectric gap. A rise in pressure is predicted to result in a crossover between the high-spin and low-spin states of the Fe³⁺ ion, collapse of the magnetic moment, a weakening of Coulomb correlations, an abrupt reduction in the energy gap, and an insulator-semiconductor transition.     

Magnetoresistance hysteresis in granular HTSCs as a manifestation of the magnetic flux trapped by superconducting grains in YBCO + CuO composites

Hysterestic behavior of the magnetoresistance of granular HTSCs and its interaction with the magnetic hysteresis are studied by measuring magnetoresistance R(H) and critical current I _c(H) of composites formed by HTSC Y_0.75Lu_0.25Ba₂Cu₃O₇ and CuO. A network of Josephson junctions is formed in such composites, in which the nonsuperconducting component plays the role of barriers between HTSC grains. Hysteretic dependences R(H) of magnetoresistance are studied in a wide range of transport current density j and are analyzed in the framework of the two-level model of a granular superconductor, in which dissipation takes place in the Josephson medium and the magnetic flux can be pinned both in grains and in the Josephson medium. The interrelation between the hysteresis of critical current I _c(H) and the evolution of the hysterestic dependence R(H) of the magnetoresistance upon transport current variation is demonstrated experimentally. The effect of the magnetic past history on the hysteretic behavior of R(H) and the emergence of a segment with a negative magnetoresistance are analyzed. It is shown for the first time that the R(H) dependences are characterized by a parameter that is independent of the transport current, viz., the width of the R(H) hysteresis loop.     

Magnetic and thermal properties of single-crystal NdFe<Subscript>3</Subscript>(BO<Subscript>3</Subscript>)<Subscript>4</Subscript>

The neodymium ferroborate NdFe₃(BO₃)₄ undergoes an antiferromagnetic transition at T _N = 30 K, which manifests itself as a λ-type anomaly in the temperature dependence of the specific heat C and as inflection points in the temperature dependences of the magnetic susceptibility χ measured at various directions of an applied magnetic field with respect to the crystallographic axes of the sample. Magnetic ordering occurs only in the subsystem of Fe³⁺ ions, whereas the subsystem of Nd³⁺ ions remains polarized by the magnetic field of the iron subsystem. A change in the population of the levels of the ground Kramers doublet of neodymium ions manifests itself as Schottky-type anomalies in the C(T) and χ(T) dependences at low temperatures. At low temperatures, the magnetic properties of single-crystal NdFe₃(BO₃)₄ are substantially anisotropic, which is determined by the anisotropic contribution of the rare-earth subsystem to the magnetization. The experimental data obtained are used to propose a model for the magnetic structure of NdFe₃(BO₃)₄.     

Electron paramagnetic resonance in mixed crystals (BaF<Subscript>2</Subscript>)<Subscript>1−<Emphasis Type="Italic">x</Emphasis></Subscript>(LaF<Subscript>3</Subscript>)<Subscript>x</Subscript> activated by Ce<Superscript>3+</Superscript> ions

The electron paramagnetic resonance (EPR) spectra of mixed crystals (BaF₂)_{1?x? y}(LaF₃)_x(CeF₃)_y (y = 0.001 = 0.1%, x = 0–0.02) are investigated in a magnetic field H‖C₄ at a frequency of 9.5 GHz. The angular dependence of the EPR spectrum is measured for the sample with x = 0.02. The lines attributed to Ce³⁺ impurity centers with tetragonal symmetry and g factors (g_‖ = 0.75, g_⊥ = 2.4) close to those measured for the KY₃F₁₀: Ce³⁺ compound are separated in the complex EPR spectrum. The assumption is made that the aforementioned impurity centers are cubooctahedral clusters of the La₆F₃₇ type in which one of the La³⁺ ions is replaced by the Ce³⁺ ion.     

Graviton and scalar propagations on AdS<Subscript>4</Subscript> space in <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>) gravities

We investigate propagations of graviton and additional scalar on four-dimensional anti-de Sitter (AdS₄) space using f(R) gravity models with external sources. It is shown that there is the van Dam–Veltman–Zakharov (vDVZ) discontinuity in f(R) gravity models because f(R) gravity implies GR with additional scalar. This clearly indicates a difference between general relativity and f(R) gravity.     

The robustness of contextuality and the contextuality cost of empirical models

In this paper, we introduce and discuss the robustness of contextuality (RoC) R_C(e) and the contextuality cost C(e) of an empirical model e. The following properties of them are proved. (i) An empirical model e is contextual if and only if R_C(e) > 0; (ii) the RoC function R_C is convex, lower semi-continuous and un-increasing under an affine mapping on the set EM of all empirical models; (iii) e is non-contextual if and only if C(e) = 0; (iv) e is contextual if and only if C(e) > 0; (v) e is strongly contextual if and only if C(e) = 1. Also, a relationship between R_C(e) and C(e) is obtained. Lastly, the RoC of three empirical models is computed and compared. Especially, the RoC of the PR boxes is obtained and the supremum 0.5 is found for the RoC of all no-signaling type (2, 2, 2) empirical models.     

Charge transfer over localized states in a TlS single crystal

It is revealed that TlS single crystals exhibit a variable range hopping conduction along a normal to their natural layers at temperatures T ≤ 230 K in a dc electric field and a nonactivated hopping conduction at low temperatures in strong electric fields. Estimates are made for the density of states near the Fermi level (N _F = 2.8 × 10²⁰ eV^?1 cm^?3 and their energy spread (ΔW = 0.02 eV), the localization radius (a = 33 Å), the average jump distance in the region of activated (R _av(T) = 40 Å) and nonactivated (R _av(F) = 78 Å) hopping conduction, and also the drop in the charge carrier potential energy along the jump distance in an electric field F: eFR = 0.006 and 0.009 eV at F = 7.50 × 10³ and 1.25 × 10⁴ V/cm, respectively.     

Optical properties of lithium niobate and lithium tantalate crystals with impurities and defects

The photoinduced and Raman scattering in lithium niobate and lithium tantalate crystals with impurities and defects have been studied. An exciting laser beam propagated either along the ferroelectric Z axis or perpendicular to it. The conditions for exciting transverse and longitudinal polar optical modes in Raman spectra are established. The regularities of the excitation of Raman spectra in several polarization geometries (X(ZZ)Y, Z(XX, Y Y)Z, Z(XX, Y Y)Z, X(ZX)Y, X(ZX)X and X(ZX)X) have been investigated. Additional (extra) spectral lines are interpreted as a manifestation of a biphonon enhanced by the Fermi resonance and the result of violation of selection rules for pseudoscalar modes of the A ₂ type due to the reduction of the point symmetry group caused by the presence of impurities and defects in real crystals. The conditions for exciting coherent longitudinal and transverse modes in lithium niobate and lithium tantalate single crystals upon stimulated Raman scattering are analyzed. The temperature evolution of the spectra recorded in the X(ZZ)Y geometry near the ferroelectric phase transition point is explained based on the concept of effective soft mode and analysis of the isofrequency opalescence effect. Strong photoluminescence is found in copper-doped lithium niobate crystals.     

Zur Klassifikation der Zustände des 5-dimensionalen harmonischen Oszillators

A classification of the eigenstates of the harmonic quadrupole oscillator is given within the framework of the Lie-AlgebraB ₂ ofR(5). There still exists the problem of complete classification, since the multiplicityd _v (l ₂) for seniority numbersv≧6 may be greater than one. For these multiplicitiesd _v (l ₂) easily managable recursion formulae are derived and therefore their explicit calculation for arbitraryv andl ₂ is easily possible.     

The possibility of the “giant” isotope effect for ultrasound absorption in crystals

The Zeeman effect, magnetization M(H), and differential magnetic susceptibility dM/dH of ErVO₄ crystals in a pulsed magnetic field have been experimentally and theoretically studied. In magnetic fields H ∥ [001] and H ∥ [100], the energy levels of Er³⁺ ions exhibit mutual approach and crossing (the crossover effect), which results in the peaks in dM/dH and the jumps in M(H) curves at low temperatures. The anomalies in the magnetic properties related to the crossover in ErVO₄ for H ∥ [001] are highly sensitive to the electronic structure of Er³⁺ ion, which allows this effect to be used for refining the crystal field parameters. The influence of the temperature, field misorientation from the symmetry axis, parameters of pair interactions, and other factors on the magnitude and character of magnetic anomalies in ErVO₄ crystals is considered.     

Spectra and mean energies of prompt neutrons from <Superscript>238</Superscript>U fission induced by primary neutrons of energy in the region <Emphasis Type="Italic">E</Emphasis><Subscript><Emphasis Type="Italic">n</Emphasis></Subscript><20 MeV

The time-of-flight technique is used to measure the ratios R(E, E _n )=N(E, E _n )/N_Cf(E) of the normalized (to unity) spectra N(E, E _n ) of neutrons accompanying the neutron-induced fission of ²³⁸U at primary-neutron energies of E _n =6.0 and 7.0 MeV to the spectrum N_Cf(E) neutrons from the spontaneous fission of ²⁵²Cf. These experimental data and the results of their analysis are discussed together with data that were previously obtained for the neutron-induced fission of ²³⁸U at the primary energies of E _n =2.9, 5.0, 13.2, 14.7, 16.0, and 17.7 MeV.     

Electron paramagnetic resonance of Cr<Superscript>3+</Superscript>-Li<Superscript>+</Superscript> centers in (Cr,Li): Mg<Subscript>2</Subscript>SiO<Subscript>4</Subscript> synthetic forsterite

Synthetic single crystals of chromium-and lithium-doped forsterite, namely, (Cr,Li): Mg₂SiO₄, are studied using electron paramagnetic resonance spectroscopy. It is revealed that, apart from the known centers Cr³⁺(M1) and Cr³⁺(M2) (with local symmetries C_i and C_s, respectively), these crystals involve two new types of centers with C₁ symmetry, namely, Cr³⁺(M1)′ and Cr³⁺(M2)′ centers. The standard parameters D and E in a zero magnetic field [zero-field splitting (ZFS) parameters expressed in GHz] and principal components of the g tensor are determined as follows: D=31.35, E=8.28, and g=(1.9797, 1.9801, 1.9759) for Cr³⁺(M1)′ centers and D=15.171, E=2.283, and g=(1.9747, 1.9769, 1.9710) for Cr³⁺(M2)′ centers. It is found that the lowsymmetric effect of misalignment of the principal axes of the ZFS and g tensors most clearly manifests itself (i.e., its magnitude reaches 19°) in the case of Cr³⁺(M2)′ centers. The structural models Cr³⁺(M1)-Li⁺(M2) and Cr³⁺(M2)-Li⁺(M1) are proposed for the Cr³⁺(M1)′ and Cr³⁺(M2)′ centers, respectively. The concentrations of both centers are determined. It is demonstrated that, upon the formation of Cr³⁺-Li⁺ ion pairs, the M1 position for chromium appears to be two times more preferable than the M2 position. Reasoning from the results obtained, the R₁ line (the ²E → ⁴A₂ transition) observed in the luminescence spectra of (Cr,Li): Mg₂SiO₄ crystals in the vicinity of 699.6 nm is assigned to the Cr³⁺(M1)′ center.