Weak exchange interactions in the heteronuclear crystal CuPr2(CCl3COO)8·6H2O

The new heteronuclear crystal CuPr₂(CCl₃COO)₈·6H₂O, constructed of chains containing copper and praseodymium atoms, has been synthesized and investigated by EPR at 9.3 GHz at temperatures ranging from room temperature down to 10 K. At temperatures T∼300–130 K, EPR spectra are observed which are characteristic of isolated polyhedra of copper ions with g _z=2.330±0.005, g _x,y =2.053±0.005, A _z=139×10⁻⁴ cm⁻¹, and A _x,y <26×10⁻⁴ cm⁻¹. At temperatures T<130 K a complex spectrum is observed, associated with the appearance of weak exchange interactions between the copper ions in the chain (J _Cu-CuΣS _i·S _i+1), comparable in magnitude with the hyperfine interactions J _Cu-Cu=0.015 cm⁻¹ at T=10 K. The magnitude of the exchange interaction decreases smoothly as the temperature is raised. It is conjectured that orbitals of the praseodymium ions participate in the process of indirect exchange between the copper ions. Fiz. Tverd. Tela (St. Petersburg) 41, 2154–2157 (December 1999)     

A spin-3/2 Ising model on a square lattice

The spin-3/2 Ising model described by the most general Hamiltonian with up-down symmetry, −βH=Σ_〈ij〉{JS _i S _j +KS ₂ ⁱ S ₂ ^j +LS ₃ ⁱ S ₃ ^j +M/2(S _i S ₃ ^j +S _j S ₃ ⁱ )}−ΔΣ_i S ₂ ⁱ , is investigated on a square lattice. It is shown that this model is reducible to an eight-vertex model on a surface in the parameter space spanned by the coupling constants J, K, L, and M. It is shown that this model is equivalent to an exactly solvable free fermion model along two lines in the parameter space. Consequently, the critical behavior and, in particular, the critical temperature for the second-order phase transitions of the model is found exactly. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 4, 270–275 (25 February 1996) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Spin state and exchange in the quasi-one-dimensional antiferromagnet KFeS2

We report the optical spectra and single crystal magnetic susceptibility of the one-dimensional antiferromagnet KFeS₂. Measurements have been carried out to ascertain the spin state of Fe³⁺ and the nature of the magnetic interactions in this compound. The optical spectra and magnetic susceptibility could be consistently interpreted using aS=1/2 spin ground state for the Fe³⁺ ion. The features in the optical spectra have been assigned to transitions within thed-electron manifold of the Fe³⁺ ion, and analysed in the strong field limit of the ligand field theory. The high temperature isotropic magnetic susceptibility is typical of a low-dimensional system and exhibits a broad maximum at ∼565K. The susceptibility shows a well defined transition to a three dimensionally ordered antiferromagnetic state atT _N=250 K. The intra and interchain exchange constants,J andJ′, have been evaluated from the experimental susceptibilities using the relationship between these quantities, andχ _max,T _max, andT _N for a spin 1/2 one-dimensional chain. The values areJ=−440.71 K, andJ′=53.94 K. Using these values ofJ andJ′, the susceptibility of a spin 1/2 Heisenberg chain was calculated. A non-interacting spin wave model was used belowT _N. The susceptibility in the paramagnetic region was calculated from the theoretical curves for an infiniteS=1/2 chain. The calculated susceptibility compares well with the experimental data of KFeS₂. Further support for a one-dimensional spin 1/2 model comes from the fact that the calculated perpendicular susceptibility at 0K (2.75×10⁻⁴ emu/mol) evaluated considering the zero point reduction in magnetization from spin wave theory is close to the projected value (2.7×10⁻⁴ emu/mol) obtained from the experimental data.     

Conservation laws for classical and relativistic collisions. I

On the basis of simple kinematic arguments it is shown that any quantity, depending only on the nature and velocity of a particle, that is conserved in a collision must, in classical mechanics, be of the form λ+Σ_iμ_iυ_i+1/2vυ ² or in relativistic mechanics of the form λ+Σ_iμ_iυ_i[1−(υ ²/c ²)]^−1/2+νc [1−(υ ²/c ²)]^−1/2 where λ,μ _i, andν are particle parameters.     

Conservation laws for classical and relativistic collisions. II

On the basis of elementary symmetry arguments it is shown that (1) if in classical mechanics there exists a quantity λ+Σ_iμ_iυ_i+1/2νυ ² that is conserved, where λ,μ _i, andν are particle parameters, then theμ _i andν are all proportional to a single parameterμ and the quantityAμ+Σ_iB_iμυ_i+C(λ+ 1/2Dμυ ²), whereD ≡ν/μ, is conserved for all values ofA, B _i, andC; (2) if in relativistic mechanics there exists a quantity λ+Σ_iμ_iυ_i[1−(υ ²/c ²)]^−1/2+νc[1−(υ ²/c ²)]^−1/2 that is conserved, then theμ _i andν are all proportional to a single parameterμ and the quantityAλ+Σ_iB_iμν_i[1−(υ ²/c ²)]^−1/2+Cμc [1−(υ ²/c ²)]^−1/2 is conserved for all values ofA, B _i, andC.     

Quasi-one-dimensional spin chains in CuSiO3: an EPR study

Temperature-dependent electron paramagnetic resonance (EPR) studies were performed on CuSiO₃. This recently discovered compound is isostructural with the spin-Peierls compound CuGeO₃. The EPR signals show characteristics different from those of CuGeO₃ and are due to Cu²⁺ spins located along quasi one-dimensional chains. ForT>8.2 K the spin susceptibility closely follows the predictions of anS=1/2 one-dimensional Heisenberg antiferromagnet withJ/k _B=21 K. BelowT=8.2 K the spin susceptibility immediately drops to zero indicating long-range magnetic order.     

Multi-Hamiltonian structure of kdv hierarchy by Drienfeld-Sokolov formalism

Conserved quantities and the multi-Hamiltonian structure for the integrable coupled kdv system which is associated with the isospectral flow [(∑ _i=0 ^N−1 ε _i λ ⁱ )∂² + ∑ _i=0 ^N−l V ₁λ ⁱ ]φ=λ ^N φ are deduced by the Drienfeld-Sokolov formalism.     

Modeling a dimer state in CuGeO3 in the two-dimensional anisotropic Heisenberg model with alternated exchange interaction

The two-dimensional Heisenberg spin-1/2 model with alternated exchange interaction along the c axis and an anisotropic distribution of the exchange interaction in the lattice, J _b/J _c=0.1, is examined. A quantum Monte Carlo method is used to calculate the phase diagrams of the antiferromagnet, the dimer state in a plane, the value of the alternation δ of the exchange interaction, and the anisotropy Δ=1−J ^xy/J ^z of the exchange interaction, Δ∼δ ^0.58(6). The following characteristics are calculated for Δ=0.25: the dependence of the temperature of the dimer-state-paramagnet transition on the alternation of the exchange interaction, T _c(δ)=0.55(4)(δ−0.082(6))^0.50(3), the singlet-triplet energy gap, and the dependence of the magnetization on the external field for some values of δ. The value of the exchange interaction, J _c=127 K, the alternation of the exchange interaction, δ=0.11J _c, and the correlation radius along the c axis, ξ _c≈28c, are determined. Finally, it is found that the temperature dependence of the susceptibility and the specific heat are in good agreement with the experimental data. Zh. éksp. Teor. Fiz. 112, 2184–2197 (December 1997)     

Temperature dependence of self-broadening in molecular-oxygen spectrum

Summary The ^p P(k=9) magnetic-dipole transition of the oxygen 0-0 vibrational band of the red systemb ¹Σ _g ⁺ ←X ³Σ _g ⁻ was observed with absorption spectroscopy using a tunable CW diode laser. A systematic investigation of the self-collisional broadening was performed for different gas pressures and temperatures. The temperature dependence of the self-broadening coefficient was determined to beT ^{−(1.02±0.05)}. Our results are of interest for collisional theory and as reference data in atmospheric monitoring applications. The authors of this paper have agreed to not receive the proofs for correction.     

Quantum Monte Carlo investigation of the 2D Heisenberg model with S=1/2

The two-dimensional (2D) Heisenberg model with anisotropic exchange (Δ = 1−J _x /J _z ) and S=1/2 is investigated by the quantum Monte Carlo method. The energy, susceptibility, specific heat, spin-spin correlation functions, and correlation radius are calculated. The sublattice magnetization (σ) and the Néel temperature of the anisotropic antiferromagnet are logarithmic functions of the exchange anisotropy: 1/σ+1+0.13(1)ln(1/Δ). Crossover of the static magnetic structural factor as a function of temperature from power-law to exponential occurs for T _c /J≈0.4. The correlation radius can be approximated by 1/ξ=2.05T ^1.0(6)/exp(1.0(4)/T). For La₂CuO₄ the sublattice magnetization is calculated as σ=0.45, the exchange is J=(1125–1305) K; for Er₂CuO₄ J∼625 K and the exchange anisotropy Δ∼0.003. The temperature dependence of the static structural magnetic factor and the correlation radius above the Néel temperature in these compounds can be explained by the formation of topological excitations (spinons). Fiz. Tverd. Tela (St. Petersburg) 41, 116–121 (January 1999)     

Non-steady-state photo-EMF in nanostructured GaN and polypyrrole within porous matrices

We report an experimental investigation of the non-steady-state photoelectromotive force in nanostructured GaN within porous glass and polypyrrole within chrysotile asbestos. The samples are illuminated by an oscillating interference pattern created by two coherent light beams and the alternating current is detected as a response of the material. Dependences of the signal amplitude versus temporal and spatial frequencies, light intensity, and temperature are studied for two wavelengths λ=442 and 532 nm. The conductivity of the GaN composite is measured: σ=(1.1–1.6)×10⁻¹⁰ Ω⁻¹ cm⁻¹ (λ=442 nm, I ₀=0.045–0.19 W/cm², T=293 K) and σ=(3.5–4.6)×10⁻¹⁰ Ω⁻¹ cm⁻¹ (λ=532 nm, I ₀=2.3 W/cm², T=249–388 K). The diffusion length of photocarriers in polypyrrole nanowires is also estimated: L _D=0.18 μm.     

Investigation of the effect of uniaxial pressure on antiferromagnetic resonance in KFe11O17 Crystals

The deformation dependence of the resonance field in KFe₁₁O₁₇ single crystals was investigated by the AFMR method. The measurements were performed at T=77 K and ν=47.52 GHz for two orientations of the external pressure. The experimental data are discussed in terms of a model of a very simple easy-plane antiferromagnet taking account of the elastic and magnetoelastic contributions to the thermodynamic potential. The magnetostriction, magnetoelastic, and elastic contants are calculated and the results are λ=1.94×10⁻⁵, B ₁=2.75×10⁸ erg/cm³, and C ₁₁−C ₁₂=1.42×10¹³ erg/cm³, respectively. The alues of these constants imply that the origin of the initial gap in the AFMR spectrum is not of magnetoelastic origin. Fiz. Tverd. Tela (St. Petersburg) 40, 513–515 (March 1998)     

Optical absorption spectrum of Ni2+ doped in ammonium zinc sulphate

The optical absorption spectrum of Ni²⁺ ion doped in ammonium zinc sulphate has been studied at room and liquid air temperatures. From the nature and the positions of the bands a successful interpretation of all the bands could be made assumingO _h symmetry for the Ni²⁺ ion in the crystal. The fine splitting of the³ T ₁ ¹ band at liquid air temperature has been successfully interpreted to be due to spin-orbit interaction. The crystal field and spin-orbit parameters derived areDq=1000 cm⁻¹;B=750 cm⁻¹;C=3.45B andξ=600 cm⁻¹.     

Thermal conductivity of crystalline fullerite C60 in the simple cubic phase

The behavior of the thermal conductivity k(T) of bulk faceted fullerite C₆₀ crystals is investigated at temperatures T=8–220 K. The samples are prepared by the gas-transport method from pure C₆₀, containing less than 0.01% impurities. It is found that as the temperature decreases, the thermal conductivity of the crystal increases, reaches a maximum at T=15–20 K, and drops by a factor of ∼2, proportional to the change in the specific heat, on cooling to 8 K. The effective phonon mean free path λ _p, estimated from the thermal conductivity and known from the published values of the specific heat of fullerite, is comparable to the lattice constant of the crystal λ _p∼d=1.4 nm at temperatures T>200 K and reaches values λ_p∼50d at T<15 K, i.e., the maximum phonon ranges are limited by scattering on defects in the volume of the sample in the simple cubic phase. In the range T=25−75 K the observed temperature dependence k(T) can be described by the expression k(T)∼exp(Θ/bT), characteristic for the behavior of the thermal conductivity of perfect nonconducting crystals at temperatures below the Debye temperature Θ (Θ=80 K in fullerite), where umklapp phonon-phonon scattering processes predominate in the volume of the sample. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 8, 651–656 (25 April 1997)     

Optical absorption spectrum of Cr3+ in natural ruby

Two sharp line-like bands calledN andR lines on the red side, a close doublet (B lines) on the violet side and two broad bands are observed for natural ruby. At liquid air temperature the splitting ofR line was found and also three sharp-bands calledR, R′ andB lines are identified with spin-forbidden transitions of² E,² T ₁ and² T ₂. The two broad bands calledU band andY band are assigned accordingly to the spin-allowed transitions⁴ T ₂ and⁴ T ₁ respectively. The observed bands of natural ruby have been attributed to Cr³⁺ ion in an octahedral environment with trigonal distortion. The crystal field parameters which gave a good fit to the observed band positions areB=732 cm⁻¹,C=4.25B,Dq=1830 cm⁻¹,V=−1996 cm⁻¹ andλ=34 cm⁻¹.     

Effect of polarization on population transfer in H2 by stimulated Raman transition with partially overlapping laser pulses

Polarization effects on population transfer by stimulated Raman transition using overlapping time dependent pump and Stokes laser pulses from the ground X ¹Σ _g ^/+ (v _g=0, J _g=1) level of H₂ to the final X ¹Σ _g ^/+ (v _f=1, J _f=1) level via the intermediate B ¹Σ _u ^/+ (v _i=14, J _i=0,2), C ¹Π _u ^/+ (v _i=3, J _i=2) and C ¹Π _u ^/− (v _i=3, J _i=1) levels have been theoretically investigated by applying the density matrix formalism. We have studied in detail the dependence of the population transfer on time delay between two pulses for the cases of on-resonance excitations considering linear parallel and same-sense circular polarizations of the fields. The pump and Stokes fields are taken as having Gaussian pulse shapes with peak intensities I _P ^/0 (I _S ^/0 )=2 × 10⁶ and 1 × 10⁷ W/cm². Density matrix equations have been solved for each value of the magnetic quantum number M _g(0, ±1) of the initial ground level taking into account the M _g dependence of the Rabi frequencies. M _g — averaged population transfer to the final level has also been calculated. For resonance excitations to the B(14, 0) or C(3, 1) levels, appreciable population transfer is achieved for intuitive pulse order for some particular values of M _g and M _i (magnetic quantum number of the resonant intermediate level) depending on the nature of polarizations. The calculated values of M _g — averaged population transfer for the two cases of polarizations show that for on-resonance excitation to the B(14, 0) or the C(3, 1) level, linear parallel polarization of the laser fields yield more transfer efficiency whereas for resonance excitation to the B(14, 2) level, larger population transfer results from the same-sense circular polarizations. For resonance excitation to the C(3, 2) level, M _g — averaged population is found to be almost polarization independent. The calculations for the six-level H₂ system reveal some interesting features of polarization effects on the population transfer efficiency.     

Crystal electric field excitations in ferromagnetic CeTX compounds

A ferromagnetic ground state was identified for the compounds CeCuGe (T_C=10 K), CeCuSi (T_C=15 K) [F. Yang, et al., J. Appl. Phys. 69 (1991) 4705] and CeAuGe (T_C=10 K) [R. Pottgen, J. Magn. Magn. Mater. 152 (1996) 196]. The observed saturation magnetic moment values at low temperatures for all three compounds are considerably less than the theoretically expected value g_JJ=2.14μ_B for the free Ce³⁺ ion involving the entire six-fold J=5/2 multiplet, and thus provide a first indication of partial lifting of the f-electron level degeneracy in these compounds. Specific heat data yield crystal electric field (CEF) excitation energies (Δ_Sch) equivalent to 140 K for CeCuGe, 110 K for CeCuSi and 280 K for CeAuGe. To confirm the presence of CEF excitations directly, we have carried out inelastic neutron scattering (INS) measurements on all three compounds, using the HET spectrometer at ISIS Facility. Here, we present a detailed analysis of the INS spectra of CeCuSi on the basis of a CEF model and the detailed analysis of the INS of the other two compounds will be reported elsewhere.     

Investigation of thermal expansion,phase diagrams,and barocaloric effect in the (NH4)2WO2F4 and (NH4)2MoO2F4 oxyfluorides

The thermal expansion along the principal crystallographic axes of the (NH₄)₂WO₂F₄ and (NH₄)₂MoO₂F₄ oxyfluorides has been studied. The anomalous behavior of α _i (T) due to the phase transitions has been revealed at T ₁ = 271.4 K and T ₂ ≈ 180 K for the molybdate and at T ₁ = 201.5 K and T ₂ ≈ 161 K for the tungstate. The quantities dT/dp and dT/dσ _i , which characterize the dependence of the phase transition temperatures on the hydrostatic and uniaxial pressures, have been determined from analyzing the results of studies of the thermal expansion and heat capacity with the use of the Pippard relations. The p-T and α _i -T phase diagrams reflect different characters of the influence of the pressure on the stability of the initial and distorted phases of the oxyfluorides. The magnitudes of the extensive and intensive barocaloric effects determined in the vicinity of the structural phase transitions are as follows: ΔS _BCE varies from approximately −10 to −17 J/mol K and ΔT _AD ≈ 8−17 K for the molybdate and ΔS _BCE varies from approximately −10 to −17 J/mol K and ΔT _AD ≈ 8−13 K for the tungstate.     

Asymptotic Properties of Solutions to 3-Particle Schrödinger Equations

We construct a generalized Fourier transformation ℱ(λ) associated with the 3-body Schr?dinger operator H=−Δ+Σ ^a V ^a (x ^a ) and characterize all solutions of (H−λ)u= 0 in the Agmon–H?rmander space ℬ^* as the image of ℱ(λ)^*. These stationary solutions admit asymptotic expansions in ℬ^* in terms of spherical waves associated with scattering channels. Received: 20 September 2000 / Accepted: 20 May 2001