Fourth-order spin Hamiltonian terms for Fe2+ in rutile structure antiferromagnet FeF2

The paper deals with the spectroscopic and magnetic properties of Fe²⁺ ions in FeF₂. The microscopic spin Hamiltonian theory for Fe²⁺ in crystalline environments with second-kind orthorhombic symmetry is considered. Explicit formulas for the parameters B₀⁽²⁾(D),B₂⁽²⁾(E), g_x, g_y, g_z and, for the first time in the literature, the fourth-order parameters B₀⁽⁴⁾, B₂⁽⁴⁾ and B₄⁽⁴⁾, are derived. Using semi-empirical data for the ⁵D-term energy levels of Fe²⁺ ion in FeF₂, the pressure dependence of the parameters B_q^(k) in the region from 0 to 133 kbar is discussed. The relative role of the fourth-order parameters with respect to the second-order ones is found to increase strongly with pressure (e.g. in the region studied, D increases only by a factor of 3, whereas B₀⁽⁴⁾ increases by a factor of nearly 20). The magnetocrystalline anisotropy of FeF₂; is considered in the strong anisotropy model taking into account the fourth-order spin Hamiltonian terms. The uniaxial anisotropy constants K₁ and K₂ are derived theoretically and their pressure dependence is discussed quantitatively. The theory and numerical results of this paper are useful with regard to Fe²⁺ in other isomorphic fluorides, namely: MgF₂, ZnF₂, VF₂ and MnF₂. It is found that the fourth-order spin Hamiltonian parameters are accessible to experimental detection from spectroscopic studies on Fe²⁺ in non-magnetic fluorides and magnetic studies on Fe²⁺ : MnF₂ and FeF₂, preferably under high pressure.     

First-principles study of the electronic structure and magnetism of SrFe0.5Ru0.5O2

We study the electronic structures and magnetism of SrFe_0.5Ru_0.5O₂ by first-principles calculations in the framework of density functional theory (DFT) with generalized gradient approximation plus on site repulsion (GGA+U). The DFT calculations were carried out with ten kinds of Fe-site doping form. Calculations show that the d-orbital electronic configurations of Fe²⁺ and Ru²⁺ ions are (d_z²)²(d_yzd_xz)²(d_xy)²(d_x²_−y²)¹ and (d_z²)²(d_yzd_xz)³(d_xy)¹(d_x²_−y²) , respectively, which are independent of the doping form. The degenerated (d_xzd_yz) orbitals of Ru²⁺ ions are occupied by three electrons, so it gives rise to the Jahn–Teller distortion. The calculated magnetic moments of Fe²⁺ and Ru²⁺ ions are 3.7 μ_B and 1.6 μ_B, respectively. The exchange parameters including nearest neighbor (NN) ions and next nearest neighbor (NNN) ions are calculated by using Heisenberg model and the magnetic frustration in the ordered structure is explained by the competition of the exchange parameters. We also study the external pressure effect on the compound. A pressure-induced orthorhombic to tetragonal structure transition accompanied by an insulator to half-metal transition and an antiferromagnetic (or spin glass) to ferromagnetic state transition is observed.     

Protonh 2 11/2 and octupole excitations in148 66Dy82 and149 66Dy83

The yrast states of¹⁴⁸Dy and¹⁴⁹Dy have been studied by γ-ray and conversion electron measurements in (α, xn) and (¹⁶O,xn) reactions on enriched¹⁵²Gd and¹³⁵Ce targets. Level schemes to above 4 MeV for the two nuclei are reported. The πh ² _11/2 spectrum identified in¹⁴⁸Dy and the πh _11/2 effective chargee _eff=1.52±0.05e, derived from the measuredE2 transition rate between the (πh ² _11/2) 10⁺ and 8⁺ states, are discussed and compared with results for other two-particle nuclei. The yrast cascades in¹⁴⁸Dy and¹⁴⁹Dy continue above the (πh ² _11/2) 10⁺ and πh ² _11/2 vf _7/2) 27/2^? states by ～ 1 MeVE1 transitions de-exciting the lowest members of octupole multiplets built on these states. The energy shifts for the observed members of the πh ² _11/2 × 3^? multiplet are analyzed in terms of twoparticle-phonon exchange coupling using an empirical coupling strength extracted from the one valence particle nucleus¹⁴⁷Tb. The dominantvf _7/2×3^? character of low-lying 13/2⁺ isomers in¹⁴⁹Dy and otherN=83 nuclei is emphasized.     

Thermal depolarization in crystals of calcium fluoride doped with oxygen

The study of thermally induced depolarization (TD) in crystals of calcium fluoride doped with oxygen reveals the existence of nearest-neighbour (nn) dipolar complexes comprising substitutional oxide ions (O_s^2?) and fluoride ion vacancies (F_v^?) on nn sites. Evidence for this relaxation is seen in TD experiments both on pure calcium fluoride doped with oxygen and on Na⁺ doped CaF₂ crystals that had been heated in air. Similar measurements on CaF₂: Y³⁺, O^2? reveal six separate relaxations, two of which are due to Y_s^3??F_i^? complexes that do not involve oxygen, one is due to O_s^2??F_v^? dipoles, and one is t the T₁ complex, Y_s³⁺ (O^2?)₄(F_v^?)₃. The remaining two relaxations were not identified but are probably d larger defect clusters.     

Rotational analysis of visible bands of nitrogen dioxide using polarization spectroscopy

Polarization labeling spectroscopy is used to simplify the visible absorption spectrum of NO₂. State-selected spectra of the ²B₂-²A₁ transition in the range 16 600–17 000 and 17 350–17 850 cm^?1 are developed using a narrow-band pump operated (1) near 545 nm, where the pumped transitions also belong to the ²B₂ system, and (2) near 436 nm on a selected transition of the ²B₁-²A₁ (Douglas-Huber) band system. Rotational analyses are given for the K_a = 0 and K_a = 1 subbands of 11 vibronic bands and limited observations reported for the K_a = 0 or 1 manifold of a further 8 bands. Polarization-labeling experiments within the ²B₁-²A₁ band system are also described.     

Analysis of nuclear spin-lattice relaxation rates in transition metal dihydrides,TMH2 (TM = Sc,Ti, V and Nb) based on LAPW electronic band calculations

The spin-lattice relaxation rates (T _1e T)^?1 of transition metal nuclei ⁴⁵Sc, ⁴⁹Ti, ⁵¹V and ⁹³Nb in cubic dihydrides ScH₂, TiH₂, VH₂ and NbH₂ are calculated on the basis of scalar-relativistic self-consistent LAPW band structure calculations. It is found that the s and p electron contributions to the relaxation rates are negligibly small for all the hydrides studied here due to their very low partial densities of electron states at the Fermi level. The d- orbital contributions are dominant and the core polarization and d-dipolar contributions play a minor role. The theoretical relaxation rates reproduce the experiments very well for ScH₂ and TiH₂ but less satisfactory for VH₂ and NbH₂. The experimental data were taken from our earlier studies and the results of additional measurements on ⁹³Nb in NbH₂ are reported. These have been made in the 30–292K temperature range and at a magnetic field of 7 T.     

Resolution of a Coulomb reorientation ambiguity in 18O

Elastic scattering data and inelastic excitation of the lowest 2⁺ state in ¹⁸O from 120 MeV ¹⁸O incident on ²⁰⁸Pb are analyzed in coupled channels including couplings to the second 2⁺ state of ¹⁸O. This analysis favors the positive sign for the product of the four E2 matrix elements, p₄ = M₀₁₂₁,M₀₁₂₂M₂₁₂₂M₂₁₂₁ where M_ij = ?〈i∥M(E2)∥j〉. This is in agreement with shell-model calculations.     

Spin-orbit coupling and dissociation of CO2 molecules

Potential surfaces of the CO₂ molecule for the ground and excited ³ B ₂, ¹ B ₂ electronic states are calculated by quantum chemistry methods. The calculation of the spin-orbit coupling in the molecule shows a large the matrix element, which removes the prohibition for the dissociation-recombination process CO₂(X ¹Σ) + M ? CO(X ¹Σ) + O(³ P) + M. The barrier on the potential curve for ³ B ₂, the energy of which exceeds the limit of dissociation into components in the ground states, explains the data on the dissociation and recombination energies measured in experiments with shock tubes. The absorption cross section of CO₂ molecules in the UV spectral region measured at high temperatures allowed us to plot branches of potential curves near their minima for two upper singlet states assigned to the ¹ B ₂ and ¹ A ₂ symmetry.     

Study of the I=2 ππ scattering from the reaction π−d → π−π−psp at 9.0 GeV/c

We have studied the I=2, ππ scattering using the classical Chew-Low extrapolation method. Results are given on the cross sections and the phase shifts δ₀², δ₂² and δ₄² up to 2.2. GeV. δ₀² values are -7.8 ? 3.0° at the K^o mass, -15. ? 1.5° at the ? mass and -29. ? 2.2° of the f^o mass. Above the f^o mass |δ₀²| decreases.     

Effect of anions on the phase stability of γ-FeOOH nanoparticles and the magnetic properties of gamma-ferric oxide derived from lepidocrocite

The effect of anions such as Cl⁻, SO₄²⁻, and HPO₄²⁻ on the phase stability of FeOOH (α or γ) during precipitation is investigated. Oxidation of Fe(OH)₂·xH₂O from FeCl₂ solution with high Cl⁻ concentration ([Cl⁻]/[Fe]=R_Cl≥8) or (NH₄)₂Fe(SO₄)₂ (FAS) with [HPO₄²⁻]/[Fe]=R_P≥0.02 yields phase-pure γ-FeOOH. In the medium ranges of R_Cl and R_P, mixed phases of α-FeOOH and γ-FeOOH are obtained. Replacement of OH⁻ by Cl⁻ with the bridging cations or strongly bonded HPO₄²⁻ ions in the matrix of the intermediate phase (Fe_x²⁺Fe_y³⁺(OH)_2x+2y−nz·xH₂O(A)_zⁿ⁻, where A is anions such as Cl⁻, SO₄²⁻, HPO₄²⁻, etc.), promoted the lower density γ-FeOOH. However, the particles are less developed and have poor crystallinity as evidenced from transmission electron microscope and thermogravimetry-differential thermal analysis of the precipitates. Whereas, monophasic, uniformly sized, nano-lath shaped particles with high aspect ratio >10 are obtained when morphology-controlling cation additives such as Pt⁴⁺, Pd²⁺ or Rh³⁺ are present in FeCl₂ (R_Cl≥8) solution. Preferential adsorption of additives on (0k0) and (h00) planes limits the growth in the perpendicular directions leading to high aspect ratios. The effect of these additives are suppressed by the phosphate ion, a strong complexing ligand, giving rise to fibrous aggregate with the length of individual particles as small as 10-30 nm. While most of the Cl⁻ ion is removed from the final precipitates on washing, phosphate remained as HPO₄²⁻ as evidenced from IR absorption spectra. Maghemite obtained by dehydroxylating γ-FeOOH contains randomly distributed micropores bringing in the relaxation effects of spins on the surface atoms as deciphered from Mössbauer spectroscopy. This leads to the low σ_s (44-48 emu/g) and H_c (120-130 Oe) for γ-Fe₂O_3−δ particles. Whereas nearly pore-free single crystalline particles obtained by reduction followed by reoxidation has high value of σ_s (73 emu/g) and H_c (320 Oe), which decreases to 30 emu/g and 75 Oe, respectively, for nanoparticles obtained from phosphate stabilized lepidocrocite. The mobility of iron ions and counter mobility of vacancies during the topotactic transformation of γ-FeOOH to magnetite to γ-Fe₂O_3−δ renders the particles pore-free.     

EPR study of clusters of rare-earth ions in mixed fluoride crystals

The EPR spectra of the (BaF₂)_{1 ? x} (CeF₃) _x system are studied for the concentrations x = 0, 0.001, 0.002, 0.005, 0.01, and 0.02. The appearance of new tetragonal centers is detected beginning from x = 0.002, the intensity of these centers being maximal at x = 0.01. The (CaF₂)_{1 ? x ? y} (CeF₃) _x (YF₃) _y double solutions with x = 0.001 and y from 0 to 0.02 are also studied. In addition to the ordinary tetragonal center, beginning from y = 0.001, a new tetragonal center appears with the same structure as in the previously studied mixed crystals based on BaF₂—namely, the Ce³⁺-□-R³⁺ chain elongated along the fourfold axis substitutes the Ca²⁺-Ca²⁺-Ca²⁺ and Ba²⁺-Ba²⁺-Ba²⁺ chains in regular CaF₂ and BaF₂ crystals (□ is the cation vacancy, and R³⁺ is the Ce³⁺, La³⁺, or Y³⁺ trivalent ion).     

Collisional relaxation of ionic2 P 3/2 excited states in rare gases

Optical pumping with theD ₂ line is used to study the depolarization of the first excited² P _3/2 states of alkaline earth ions and Yb⁺ ions in collisions with rare gas atoms. The deorientation cross sections for the even isotopes of Ba⁺ and Yb⁺ ions are obtained (in units of 10^?16 cm²): rare gas He Ne Ar Kr Xeσ ₁ (Ba⁺ 6p ² P _3/2) 79(11) 89(13) 123(18) 152(22) 204(30)σ ₁ (Yb⁺ 6p ² P _3/2) 60(10) 62(9) 107(18) 133(17) 167(37) The cross sections are discussed in comparison with theoretical calculations and those of isoelectronic atoms. The comparison of the² P _3/2 relaxation of even and odd (I=3/2) isotopes of Ba⁺ allows to draw conclusions on the nature of the depolarization interaction.     

Investigation of the EPR g factors and defect structure for the Cu-VNa center in the X-irradiated NaCl: Cu crystal

The g factors of a tetragonally-compressed Cu²⁺ center in NaCl: Cu⁺ crystal X-irradiated at room temperature are calculated from the high-order perturbation formulas based on the two-mechanism model. In the model, the contribution to g factors from both crystal-field (CF) and charge-transfer (CT) mechanisms are included. The calculations are based on the defect model that the tetragonally-compressed Cu²⁺center is assigned to the Cu²⁺ ion (which is caused by Cu⁺ ion (at the Na⁺ site) irradiated by X-ray) associated with a nearest Na⁺ ion vacancy V_Na along C₄ axis due to charge compensation. From the calculations, the g factors g_|| and g_⊥ are explained and the defect structure (charactering by the displacement ΔZ of the Cl⁻ ion intervening in Cu²⁺ and V_Na) of the Cu²⁺ (or Cu²⁺-V_Na) center is obtained. The results are discussed.     

Optical absorption spectra and energy levels of Er3+ ions in glassy lithium tetraborate matrix

The optical absorption spectra of Er:Li₂B₄O₇ glasses are studied in the range 200–800 nm. The lines corresponding to the direct f-f parity-forbidden intraconfigurational transitions from the ground ⁴ I _15/2 state to the levels of the excited ⁴ F _9/2, ⁴ S _3/2, ² H _9/2, ² H _11/2, ⁴ F _7/2, ⁴ F _5/2, ⁴ F _3/2, ² H _9/2, ⁴ G _11/2, ⁴ D _3/2, ⁴ D _1/2, and ² D _3/2 states are found.     

Production of pion and muon pairs in e±e− colliding beams. Extension of the equivalent photon approximation

The reactions e^?e^?→e^?e^?π⁺π^?(μ⁺μ^?) are considered here in the situation where only pions (muons) are recorded and k_⊥ (total transverse momentum of the pair) is not too small (roughly speaking m_e²?k_⊥²?m_π²); this domain gives the main contribution to the cross section. In this paper the differential cross sections have been obtained to an accuracy of (Ink_⊥²/me²)^?1k_⊥/m_π. The amplitudes with one scalar photon have to be taken into account in this approximation. Also the charge asymmetry appears due to the interference of the two-photon and bremsstrahlung diagrams. It is shown what information on amplitudes of the reaction γγ→π⁺π^? and on the pion electromagnetic form factor can be obtained from an experiment in the given set-up.     

Nuclear vertex constants and asymptotic normalization coefficients for 8Be resonance states from effective-range expansions for αα scattering

The properties of the first excited state of the ⁸Be* nucleus (2⁺) are studied. This state corresponds to the resonance in αα scattering at the energy of E _α = E ₂ ≈ 3 MeV. Use is made of an expansion of the effective-range function K(k ²). The function K(k ²) is sensitive to the value of E ₂. A fit to experimental data on the dependence of the Coulomb-nuclear phase shift δ ₂ ^C on the energy E _α leads to an E ₂ value that is smaller than the average value obtained from an analysis of various reactions. The experimental behavior of δ ₂ ^C (E _α) cannot be described satisfactorily by fixing the average value of E ₂. The renormalized nuclear vertex function for the process α + α → ⁸Be*(2+) and the asymptotic normalization coefficient for the respectiveGamow wave function are calculated by using the set of parameter values found in the present study.     

Electronic structure of dichalcogenide and dipnictide anions

The Self-Consistent-Field Xα Scattered Wave Cluster MO method is used to calculate molecular orbital energy level diagrams for O₂, O₂^?, O₂^2?, S₂, S₂^2?, Se₂^2?, P₂^4?, As₂^4? and AsS^3?. Calculated energies are in good agreement with those measured by photoemission spectroscopy for O₂, S₂, S₂^2? in ZrS₃, Se₂^2? in ZrSe₃ and P₂^4? in TiP₂. For O₂^? the calculated energy of the π_u → π_g transition agrees fairly well with that of the UV absorption observed in LiO₂. The predicted photoemission spectrum of O₂^2? is consistent with a preliminary study on BaO₂. Calculated valence region widths in peroxides are found to be significantly greater than the calculated oxygen atomic valence _s-p separation while valence widths for the other anions closely match atomic valence s-p splittings. This effect arises from the instability of the peroxide antibonding orbitals which correlates with the absence of dsun peroxides and Superoxides. Calculations on a Cin2v geometry FeO₆su9? cluster show that the difference in energy of O2p nonbonding and Fe3d crystal field type orbitals drops sharply as an O-O edge is contracted, providing a mechanism for Fe³⁺ → Fe²⁺ reduction at high pressure.     

Pressure shift and/or broadening of lines in the electronic spectra of Cl2, Br2, I2, O2, HD,AlH and H2CO

Line positions and widths of the B³Π_o⁺u?X¹Σ⁺_g electronic transitions of chlorine and bromine gases are measured in absorption as functions of pressure by means of a scanning Fabry-Perot interferometer spectrometer (resolving power > 10⁶). No dependences on quantum numbers are detected. Deconvolutions of measured full-widths-at-half-maxima (FWHM) reveal collision broadening for pressures between 1 and 225 torr. The ratio of self-broadening to shift is always less than that expected for a van der Waals interaction in the impact approximation, namely -2.77. Accordingly, the Lennard-Jones potential is used to determine the effect of the electronic transitions on C₆ and C₁₂, and there are found 14 and 6% changes in C₆ for Cl₂ and Br₂, respectively. If, instead, one uses the self-broadening only, and a pure van der Waals interaction, the changes are 6 and 5%. Because the effects are in either model unexpectedly small, comparisons are made with less complete measurements (from the literature) for self-broadening in I₂, the B¹Σ⁺_g?X³Σ^-_g system of O₂ and the B^′Σ⁺_g?X¹Σ⁺_g system of HD, and for foreign-gas broadening in the A¹Π?X¹Σ system of A1H and the A̋¹A₂(π¹, n)?X̋¹A₁ system of H₂CO as well as the HD system.