Magnetostriction and thermal expansion of HoAl3(BO3)4

The magnetostriction and thermal expansion of rare-earth aluminoborate HoAl₃(BO₃)₄ have been studied theoretically. The calculated field and temperature dependences of the multipole moments of the Ho³⁺ ion in HoAl₃(BO₃)₄ made it possible to describe the known experimental data and to predict possible anomalies of thermal expansion. It has been shown that, for the direction of the field B ‖ c, the nonmonotonic character of magnetostriction along the axis a is determined by the multipole moments, the main of which is β _J 〈O ₄ ⁰ 〉. For B ‖ a and B ‖ b, the maximum moments are β _J 〈O ₄ ² 〉and α _J 〈O ₂ ² 〉; their variation with the field and temperature explain well the form of magnetostriction. It has been established that the greater value of magnetostriction Δa/a for B ‖ b than for B ‖ a and the greater value of magnetostriction for the field in the basal plane than for B ‖ c are caused by greater variations in the field of actual multipole moments.     

Layered structure of superfluid4He at supercritical motion

Landau’s criterion plays an important role in the theory of superfluidity. According to this criterion, superfluid motion is possible if \(\tilde \varepsilon \left( p \right) \equiv \varepsilon \left( p \right) + pV > 0\) along the curve of the spectrum?(p) of excitations. For⁴He it means thatv<v _c,v _c≈60 m/sec.v _s is equal to the tangent of the slope to the roton part of the spectrum. The question of what happens to the liquid when this velocity is exceeded, as far as we know, remains unclear. We shall show that for small excesses abovev _c a one-dimensional periodic structure appears in the helium. A wave vector of this structure oriented opposite to the flow and equal toρ _c/h whereρ _c is the momentum at the tangent point. The quantity \(\tilde \varepsilon \left( p \right)\) is the energy of excitation in the liquid moving with velocity v. Inequality of Landau ensures that \(\tilde \varepsilon \) is positive. If \(\tilde \varepsilon \) becomes negative, then the boson distribution function \(n\left( {\tilde \varepsilon } \right)\) becomes negative, indicating the impossibility of thermodynamic equilibrium of the ideal gas of rotons; therefore the interaction between them must be taken into account. The final form of the energy operator is $$\hat H = \int {\left\{ {\hat \psi + \tilde \varepsilon \left( p \right)\hat \psi + \tfrac{g}{2}\hat \psi + \hat \psi + \hat \psi \hat \psi } \right\}} d^3 x, g \sim 2 \cdot 10^{ - 38} erg.cm.$$ Then we can seek the rotonψ-operator in the formψ=ηexp(i p _c r/h), determiningη from the condition that the energy is minimized. The result is (η)²=(v?v _c)ρ _c/g, forv>v _c. The plane waveψ corresponds to a uniform distribution of rotons. It leads, however, to a spatial modulation of the density of the helium, since the density operator \(\hat n\) contains a term which is linear in the operator \(\psi :\hat n = n_0 + \left( {n_0 } \right)^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-0em} 2}} {A \mathord{\left/ {\vphantom {A {\hat \psi \to \hat \psi ^ + }}} \right. \kern-0em} {\hat \psi \to \hat \psi ^ + }}\) ), where |A|²～ρ _c ² /2m?(ρ _c). Finally we find that the density of helium is modulated according to the law $$\frac{{n - n_0 }}{{n_0 }} = \left[ {\frac{{\left| A \right|^2 \left( {\nu - \nu _c } \right)\rho _c }}{{n_0 g}}} \right]^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} \sin \rho _c x \approx 2,6\left[ {\frac{{\nu - \nu _c }}{{\nu _c }}} \right]^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} \sin \rho _c x$$ . This phenomenon can be observed, in principle, in the experiments on scattering ofx-rays in moving helium.     

Spatial dispersion in polariton spectra of CuGaS2 crystals

The unmodulated and wavelength-modulated reflectivity spectra of CuGaS₂ crystals for the polarization E ‖ c, k ⊥ c at 77 and 8 K have been studied. The states n=1, 2, and 3 of A excitons and n=1 and 2 of B and C excitons are established. The luminescence spectra from the surface at k ‖ c and k ⊥ c are obtained. The fine structure of the reflectivity spectra of excitons are analyzed with due regard for the normal and oblique incidence of light onto the crystal surface. The main parameters of the A, B, and C excitonic series are determined such as the energies of the longitudinal and transverse excitons Γ₄ (E ‖ c) for states n=1 and 2, the longitudinal and the transverse mass of excitons in CuGaS 2, and the effective masses of electrons (m _c1*) and holes (m _v1*, m _v2*, m _v3*). It is shown that the mass m _v1* in the upper valence band at k ‖ c equals (0.7–0.8)m ₀ and at k ⊥ c, 1.87m ₀.     

Dislocation structure of intermetallic Ti3Al subjected to high-temperature deformation

Transmission electron microscopy was used to examine the dislocation structure of intermetallic Ti₃Al subjected to deformation at tempertures T = 1073–1273 K. The microstructure of samples subjected to high-temperature deformation is established to contain mobile superdislocations of a and 2c + a types, and single dislocations with Burgers vector [0001] are also observed on the prismatic planes. Possible models of destruction of barriers associated with 2c + a superdislocations on the pyramidal planes are discussed using the results of computer simulations of the structure of a superdislocation core in in Ti₃Al.     

A Novel Series Colorimetric and Off–On Fluorescent Chemosensors for Fe3+ Based on Rhodamine B Derivative

A novel series colorimetric and off–on fluorescent chemosensors (2a, 2b, 2c) were designed and synthesized, which showed reversible and highly selective and sensitive recognition toward Fe³⁺ over other examined metal ions. Upon addition of Fe³⁺, sensors (2a, 2b) exhibit remarkably and 2c exhibits moderate enhanced absorbance intensity and color change from colorless to pink in CH₃OH–H₂O(1:1, v/v). The three compounds (2a, 2b, 2c) may therefore be applicable as rhodamine-based turn-on type fluorescent chemosensors.     

Types of defect ordering in undoped and lanthanum-doped Bi2201 single crystals

Undoped and lanthanum-doped Bi2201 single crystals having a perfect average structure have been comparatively studied by x-ray diffraction. The undoped Bi2201 single crystals exhibit very narrow satellite reflections; their half-width is five to six times smaller than that of Bi2212 single crystals grown by the same technique. This narrowness indicates three-dimensional defect ordering in the former crystals. The lanthanumdoped Bi2201 single crystals with x = 0.7 and T _c = 8–10 K exhibit very broad satellite reflections consisting of two systems (modulations) misoriented with respect to each other. The modulation-vector components of these two modulations are found to be q ₁ = 0.237b* + 0.277c* and q ₂ = 0.238b* + 0.037c*. The single crystals having a perfect average structure and a homogeneous average distribution of doping lanthanum consist of 70-to 80-Å-thick layers that alternate along the c axis and have two different types of modulated superlattice. The crystals having a less perfect average structure also consist of alternating layers, but they have different lanthanum concentrations. The low value of T _c in the undoped Bi2201 single crystals (9.5 K) correlates with three-dimensional defect ordering in them, and an increase in T _c to 33 K upon lanthanum doping can be related to a thin-layer structure of these crystals and to partial substitution of lanthanum for the bismuth positions.     

A theoretical and numerical consideration of the longitudinal and transverse relaxations in the rotating frame

We previously derived a simple equation for solving time-dependent Bloch equations by a matrix operation. The purpose of this study was to present a theoretical and numerical consideration of the longitudinal (R_1ρ = 1/T_1ρ) and transverse relaxation rates in the rotating frame (R_2ρ = 1/T_2ρ), based on this method. First, we derived an equation describing the time evolution of the magnetization vector (M(t)) by expanding the matrix exponential into the eigenvalues and the corresponding eigenvectors using diagonalization. Second, we obtained the longitudinal magnetization vector in the rotating frame (M_1ρ(t)) by taking the inner product of M(t) and the eigenvector with the smallest eigenvalue in modulus, and then we obtained the transverse magnetization vector in the rotating frame (M_2ρ(t)) by subtracting M_1ρ(t) from M(t). For comparison, we also computed the spin-locked magnetization vector. We derived the exact solutions for R_1ρ and R_2ρ from the eigenvalues, and compared them with those obtained numerically from M_1ρ(t) and M_2ρ(t), respectively. There was excellent agreement between them. From the exact solutions for R_1ρ and R_2ρ, R_2ρ was found to be given by R_2ρ = (2R₂ + R₁)/2 − R_1ρ/2, where R₁ and R₂ denote the conventional longitudinal and transverse relaxation rates, respectively. We also derived M_1ρ(t) and M_2ρ(t) for bulk water protons, in which the effect of chemical exchange was taken into account using a 2-pool chemical exchange model, and we compared the R_1ρ and R_2ρ values obtained from the eigenvalues and those obtained numerically from M_1ρ(t) and M_2ρ(t). There was also excellent agreement between them. In conclusion, this study will be useful for better understanding of the longitudinal and transverse relaxations in the rotating frame and for analyzing the contrast mechanisms in T_1ρ- and T_2ρ-weighted MRI.     

Anisotropic resonant magnetoplasticity of NaCl crystals in the Earth’s magnetic field

Resonant relaxation of the dislocation structure under the action of crossed magnetic fields, i.e., constant magnetic field of the Earth (B _Earth) and alternating radio-frequency field ( $\tilde B$ ), has been experimentally studied in a series of dielectric (NaCl) crystals with various compositions of impurities under variations in the frequency, direction of the pumping field $\tilde B$ , and orientation of the samples in the Earth’s magnetic field. The frequency dependence of the dislocation path length l(ν) exhibits peaks with various heights (l _max) and resonant frequencies (ν_res). The maximum resonant effect has been observed for dislocations with the direction L orthogonal to the plane of crossed magnetic fields in a configuration of mutually perpendicular vectors {L, $\tilde B$ , B _Earth} belonging, together with sample edges {a, b, c}, to the 〈100〉 system. Variation of the concentration C of calcium impurity in crystals of the NaCl_Ca series only influenced the resonant peak height as $l_{\max } \propto 1/\sqrt C $ . Rotation of the magnetic field $\tilde B$ in the (b, c) plane from direction $\tilde B$ ⊥ B _Earth to $\tilde B$ ∥ B _Earth also did not influence the frequency of the resonance but changed its amplitude. Depending on the crystal type, this influence changed from rather insignificant (in crystals of the NaCl_LOMO series) to complete suppression of the effect for $\tilde B$ ∥ B _Earth (in the NaCl_Nik series). The resonant frequency ν_res is sensitive to orientation of the sample with respect to B _Earth. Upon rotation of the crystal by the angle θ = ∠(c, B _Earth) about the a ⊥ B _Earth edge, the initial peak for dislocations L ‖ a at the crystal orientation θ = 0 and the frequency ν _res ⁰ is replaced by a pair of peaks at frequencies ν_{1, 2} ≈ ν _res ⁰ cosθ_{1, 2}, where θ₁ = 90° ? θ and θ₂ = θ. Previously, these peaks were observed separately in NaCl_Nik crystals for $\tilde B$ ∥ c and $\tilde B$ ∥ b. In the present study, these peaks have been observed simultaneously for both orientations of $\tilde B$ in NaCl_LOMO and NaCl_Ca crystals, where the resonance is not completely suppressed for $\tilde B$ ∥ B _Earth.     

Galvanomagnetic properties of atomically disordered Sr<Subscript>2</Subscript>RuO<Subscript>4</Subscript> single crystals

The effect of neutron-bombardment-induced atomic disorder on the galvanomagnetic properties of Sr₂RuO₄ single crystals has been experimentally studied in a broad range of temperatures (1.7–380 K) and magnetic fields (up to 13.6 T). The disorder leads to the appearance of negative temperature coefficients for both the in-plane electric resistivity (ρ_a) and that along the c axis (ρ_c), as well as the negative magnetoresistance Δρ, which is strongly anisotropic to the magnetic field orientation (H ∥ a and H ∥ c), with the easy magnetization direction along the c axis and a weak dependence on the probing current direction in the low-temperature region. The experimental ρ_a(T) and ρ_c(T) curves obtained for the initial and radiation-disordered samples can be described within the framework of a theoretical model with two conductivity channels. The first channel corresponds to the charge carriers with increased effective masses (～10m _e , where m _e is the electron mass) and predominantly electron-electron scattering, which leads to the quadratic temperature dependences of ρ_a and ρ_c. The second channel corresponds to the charge carriers with lower effective masses exhibiting magnetic scattering at low temperatures, which leads to the temperature dependence of the ρ_{a, c}(T) ∝ 1/T type.     

Dynamic model for alpha particle emission during fission

We investigate the motion of anα-particle in the average time depencent potentialV(R _α ,t) of a fissioning nucleus. The emission process is treated quantum mechanically via a numerical solution of the one-body Schroedinger equation withV(R _α ,t). This solution yields the distribution of initial conditions for classical trajectories describing theα-particles outside the Coulomb barrier. The time and shape dependence ofV(R _α,t) is shown to have significant influence on the observable angle and energy distribution of theα-particles emitted during fission.     

Aging effect in CaLaBa{Cu1???xFex}3O7???�� with 0 �� x �� 0.07 studied by M?ssbauer spectroscopy

In this work, we study the long-term aging effect caused by Fe atoms in the superconductor CaLaBa{Cu_1???xFe_x}₃O_7????? with 0 ?? x ?? 0.07. XRD confirms that this system has a YBCO-like structure. The critical temperature (T_c) is strongly affected by aging and depends on the amount of Fe in the structure. Room temperature Mössbauer spectroscopy reveals the presence of the typical species A, B?CB ??, C and new species E ?? and F. Interestingly; A, which corresponds to the Fe^3?+? atom located in the Cu(1) of the chains with spin S _z = 3/2, shows a drastic reduction which means migration to the species B, B ?? and C. Species B and B ?? correspond to the Fe^3?+? in the Cu(2) site forming planar quasi-octahedral and planar square pyramidal, while the C specie is a square pyramidal with O(5) respectively (spin S_z = 3/2 in all these cases). Aging causes loss of superconductivity in the samples with 5 and 7% of iron content.     

Magnetic properties of the Nd0.95Dy0.05Fe3(BO3)4 ferroborate with small substitution in the rare-earth element subsystem

The magnetic properties of a substituted Nd_0.95Dy_0.05Fe₃(BO₃)₄ ferroborate single crystal with competing Nd-Fe and Dy-Fe exchange interactions are studied experimentally and theoretically. A spontaneous spin-reorientation transition is detected near T = 4.3 K, and anomalies are observed in the low-temperature magnetization curves along trigonal axis c and in basal plane ab. The measured properties and the detected effects are interpreted in terms of a general theoretical approach, which is based on the molecular field approximation and crystal field calculations for a rare-earth ion. The experimental temperature dependences of the initial magnetic susceptibility in the range 2–300 K, the anomalies in the magnetization curves for B ‖ c and B ⊥ c in fields up to 1.5 T, and the field and temperature dependences of magnetization in fields up to 9 T are described. The effect of small substitution in the rare-earth subsystem on the magnetic properties is analyzed. The crystal field parameters and the parameters of the R-Fe and Fe-Fe exchange interactions are determined from the experimental data.     

Nuclear magnetic resonance in noncollinear antiferromagnet Mn3Al2Ge3O12

The ⁵⁵Mn nuclear magnetic resonance spectrum of noncollinear 12-sublattice antiferromagnet Mn₃Al₂Ge₃O₁₂ has been studied in the frequency range of 200–640 MHz in the external magnetic field H ‖ [001] at T = 1.2 K. Three absorption lines have been observed in fields less than the field of the reorientation transition H _c at the polarization h ‖ H of the rf field. Two lines have been observed at H > H _c and h ⊥ H. The spectral parameters indicate that the magnetic structure of manganese garnet differs slightly from the exchange triangular 120-degree structure. The anisotropy of the spin reduction and (or) weak antiferromagnetism that are allowed by the crystal symmetry lead to the difference of ≈3% in the magnetization of sublattices in the field H < H _c. When the spin plane rotates from the orientation perpendicular to the C ₃ axis to the orientation perpendicular to the C ₄ axis, all magnetic moments of the electronic subsystem decrease by ≈2% from the average value in the zero field.     

Bivariate distributions in statistical spectroscopy studies: III. Non interacting particle strength densities for one-body transition operators

In statistical spectroscopy, it was shown by French et al. (Ann. Phys., N.Y. 181, 235 (1988)) that the bivariate strength densities take a convolution form with the non interacting particle (NIP) strength density being convoluted with a spreading bivariate Gaussian due to interactions. Leaving aside the question of determining the parameters of the spreading bivariate Gaussian, one needs good methods for constructing the NIP bivariate strength densitiesI _O ^h (E,E′) (h is a one-body hamiltonian andO is a transition operator) in large shell model spaces. A formalism for constructingI _O ^h is developed for one-body transition operators by using spherical orbits and spherical configurations. For rapid construction and also for applying the statistical theory in large shell model spacesI _O ^h is decomposed into partial densities defined by unitary orbit configurations (unitary orbit is a set of spherical orbits). Trace propagation formulas for the bivariate momentsM _rs with r+s ≤2 of the partial NIP strength densities, which will determine the Gaussian representation, are derived. In a large space numerical example with Gamow-Tellerβ ^? transition operator, the superposition of unitary orbit partial bivariate Gaussian densities is shown to give a good representation of the exact NIP strength densities. Trace propagation formulas forM _rs with r+<—4 are also derived inm-particle scalar spaces which are useful for many purposes.     

Commensurate and incommensurate states of a spin density wave in a quasi-two-dimensional system with an anisotropic energy spectrum in an external magnetic field of arbitrary direction relative to magnetization

A theory of thermodynamic properties of a spin density wave (SDW) in a quasi-two-dimensional system (with a preset impurity concentration x) is constructed. We choose an anisotropic dispersion relation for the electron energy and assume that external magnetic field H has an arbitrary direction relative to magnetic moment M _Q . The system of equations defining order parameters M _Q ^z , M _Q ^σ , M _z , and M ^σ is constructed and transformed with allowance for the Umklapp processes. Special cases when H ‖ M _Q and H ⊥ M _Q (H _Z H ^σ = 0) are considered in detail as well as cases of weak fields H of arbitrary direction. The condition for the transition of the system to the commensurate and incommensurate states of the SDW is analyzed. The concentration dependence of magnetic transition temperature T _M is calculated, and the components of the order parameter for the incommensurate phase are determined. The phase diagram (T,~x) is constructed. The effect of the magnetic field on magnetic transition temperature T _M is analyzed for H _Z H ^σ = 0, and longitudinal magnetic susceptibility χ‖ is calculated; this quantity demonstrates the temperature dependence corresponding to a system with a gap for x < x _c and to a gapless state for x > x _c . In the immediate vicinity of the critical impurity concentration (x ～ x _c ), the temperature dependence of the magnetic susceptibility acquires a local maximum. The effect of anisotropy of the electron energy spectrum on the investigated physical quantities is also analyzed.     

Some estimates for magnetic fluctuations in a turbulent medium

A new integral relationship between the fluctuations b(r, t) of a magnetic field and its mean B ₀(r, t) is derived for the steady-state magnetic field in a turbulent medium. This formula provides the estimate 〈b?curlb〉=?B ₀?curlB ₀. Simultaneously, the coefficient of amplification of the mean magnetic field α effect) is obtained: α=(η+β)B ₀? curlB ₀/B ₀ ² . The formula for α allows for a decrease in this coefficient owing to the back action of the magnetic field on the turbulent velocity field. It is shown that the Zel’dovich’s estimate 〈 b ²〉?β/η B ₀ ² for two-dimensional turbulence holds for magnetic fields at the instant the fluctuations 〈a ²〉 of the vector potential, rather than 〈b ²〉, reach a maximum. Here, η and β are the ohmic (molecular) and turbulent diffusion coefficients, respectively. This estimate is refined with allowance made for the fact that the condition for diffusion approximation itself relates the β, b, and B ₀ quantities to each other.     

Stimulated multiphoton emission from exciton Bose condensate

The coherent recombination of several (N) Bose-condensed excitons with simultaneous creation of N photons is considered. Due to the momentum conservation law, the total momentum of created photons is zero because of the zero momentum of excitons in Bose condensate. This requirement, in conjunction with the fact that the photon wavenumbers are fixed and equal to approximately E _g /c (E _g is the semiconductor gap and c is the speed of light), determines the mutual orientation of the wavevectors of emitted photons. This can be seen from the photon angular correlation in the experiments with several appropriately oriented detectors operating in the time-coincidence mode. It is shown that, if these processes are induced by N? 1 external laser beams (each with wavevector k _i ), then a unidirectional radiation with recoil wavevector k=?∑_i k _i should emerge from the exciton system. The intensities of coherent three-and four-exciton recombination are estimated for the exciton system in Cu₂O.     

Localization in the ground state of the ising model with a random transverse field

We study the zero-temperature behavior of the Ising model in the presence of a random transverse field. The Hamiltonian is given by $$H = - J\sum\limits_{\left\langle {x,y} \right\rangle } {\sigma _3 (x)\sigma _3 (y) - \sum\limits_x {h(x)\sigma _1 (x)} } $$ whereJ>0,x,y∈Z ^d, σ₁, σ₃ are the usual Pauli spin 1/2 matrices, andh={h(x),x∈Z ^d} are independent identically distributed random variables. We consider the ground state correlation function 〈σ₃(x)σ₃(y)〉 and prove:

1. Letd be arbitrary. For anym>0 andJ sufficiently small we have, for almost every choice of the random transverse fieldh and everyx∈Z ^d, that $$\left\langle {\sigma _3 (x)\sigma _3 (y)} \right\rangle \leqq C_{x,h} e^{ - m\left| {x - y} \right|} $$ for ally∈Z ^d withC _{x h} <∞.
2. Letd≧2. IfJ is sufficiently large, then, for almost every choice of the random transverse fieldh, the model exhibits long range order, i.e., $$\mathop {\overline {\lim } }\limits_{\left| y \right| \to \infty } \left\langle {\sigma _3 (x)\sigma _3 (y)} \right\rangle > 0$$ for anyx∈Z ^d.