Linear theory of random textures of <Superscript>3</Superscript>He-A in an aerogel

The spatial variation of the orbital part of the order parameter of ³He-A in an aerogel has been represented as random walk of a unit vector l(r) over a sphere under the action of random anisotropy created by the system of strands of the aerogel. The statistical properties of the resulting random texture have been studied. For distances at which the variation of l is much smaller than its magnitude, the average square <δl²> of variation of l has been expressed in terms of the correlation function of the component of the random anisotropy tensor. Under simplifying assumptions on the structure of this correlation function, an analytical dependence of <δl²> on r has been obtained for isotropic and axially anisotropic aerogels. The average values of the squares of the projections of l on the axes of anisotropy for an anisotropic aerogel have been represented in terms of the parameters of the aerogel. The characteristic scale at which the long-range order is broken, as well as the magnitude of global anisotropy sufficient for the recovery of the long-range order, has been numerically estimated within a simple model. The values obtained have been compared to other estimates.     

Magnetization curves of randomly oriented ferromagnetic single-domain nanoparticles with combined symmetry of magnetic anisotropy

The magnetization curves of randomly oriented nanoparticles with combined symmetry of magnetic anisotropy were studied. The composite mode of the Stoner–Wolfarth model has been used. In terms of this model each nanoparticle is characterized by random cubic crystalline magnetic anisotropy and by random uniaxial magnetic anisotropy. The series of simulated magnetization curves have been obtained. Each curve corresponds to different contributions of cubic and uniaxial magnetic anisotropy energy to the full energy of an individual nanoparticle k_u. Within this series we discuss the values of remnant magnetization, coercive force, both initial and maximal susceptibilities as the function of k_u. It is found that the magnetic properties are not monotonous functions of k_u. We discuss the possibility of comparing the calculated magnetization curves with the experimental curves in order to obtain new information on the magnetic constant.     

Theory of first order magnetization processes: Uniaxial anisotropy

The first order magnetization process (FOMP) is associated with the irreversible rotation of the magnetization vector M_s between inequivalent states. The critical field H_cr and the amplitude ΔM of the jump observed in the direction parallel to the applied magnetic field are functions of the anisotropy constants of the crystal. A complete phenomenological analysis is given for the case of uniaxial anisotropy in terms of the first three anisotropy constants K₁, K₂ and K₃, as well as in terms of the anisotropy coefficients χ_2,0, χ_4,0, χ_6,0. Computer plots of the critical parameters and the magnetic phase diagram are given together with an analytical treatment of the problem. The results give a unified view of the FOMP in uniaxial crystals and provide a method for the accurate determination of the anisotropy constants at the temperatures where the phenomenon is present.     

Long-wavelength excitations in a Bose gas at zero temperature

The long-wavelength excitations in a simple model of a dilute Bose gas at zero temperature are investigated from a purely microscopic viewpoint. The role of the interaction and the effects of the condensate are emphasized in a dielectric formulation, in which the response functions are expressed in terms of regular functions that do not involve an isolated single-interaction line nor an isolated single-particle line. Local number conservation is incorporated into the formulation by the generalized Ward identities, which are used to express the regular functions involving the density in terms of regular functions involving the longitudinal current. A perturbation expansion is then developed for the regular functions, producing to a given order in the perturbation expansion an elementary excitation spectrum without a gap and simultaneously response functions that obey local number conservation and related sum rules.Explicit results to the first order beyond the Bogoliubov approximation in a simple one-parameter model are obtained for the elementary excitation spectrum ω_k, the dynamic structure function $\text{S}$(k, ω), the associated structure function $\text{S}$_m(k), and the one-particle spectral function $\text{A}$(k, ω), as functions of the wavevector k and frequency ω. These results display the sharing of the gapless spectrum ω_k by the various response functions and are used to confirm that the sum rules of interest are satisfied. It is shown that ω_k and some of the $\text{S}$_m(k) are not analytic functions of k in the long wavelength limit. The dynamic structure function $\text{S}$(k, ω) can be conveniently separated into three parts: a one-phonon term which exhausts the f sum rule, a backflow term, and a background term. The backflow contribution to the static structure function $\text{S}$₀(k) leads to the breakdown of the one-phonon Feynman relation at order k³. Both $\text{S}$(k, ω) and $\text{A}$(k, ω) display broad backgrounds because of two-phonon excitations. Simple arguments are given to indicate that some of the qualitative features found for various physical quantities in the first-order model calculation might also be found in superfluid helium.     

Magnetic properties in silica-coated CoFe2O4 nanoparticles: Quantitative test for a theory of single-domain particles with cubic anisotropy

We report magnetic properties of silica-coated CoFe₂O₄ nanoparticles (about 32 nm) in a wide temperature range (4-700 K). Coating CoFe₂O₄ nanoparticles with amorphous silica yields an assembly of noninteracting single-domain particles with cubic magnetocrystalline anisotropy. We find that the reduced remanence is about 0.81-0.82 at low temperatures (?100 K), very close to the theoretical prediction (0.83) for cubic anisotropy. The room-temperature anisotropy constant K₁ inferred from the data is also in quantitative agreement with the bulk value (1.8×¹⁰⁶ erg/cm³). The current work thus provides a quantitative test for a theory of noninteracting single-domain particles with cubic anisotropy.     

New theoretical results about the anisotropy of the secondary emission of Al(001) and Al(110)

The source function giving the number of electrons acquiring the energy E and the direction of propagation Ω at the depth z in a target of aluminium submitted to a bombardment of electrons of an energy of 350 eV is evaluated by a Monte Carlo calculation. This source function is used to study the anisotropy of the secondary electron emission. The influences of the depth dependence and of the anisotropy of the source function on the anisotropy of the secondary electron emission on Al(001) and Al(110) are negligible. These results are considered as an evidence that the observed anisotropy in the emitted beam is due to electron final state effects.     

Bulk magnetization study of a DyNi5 single crystal

Magnetization and susceptibility measurements were performed on a single crystal of DyNi₅ along the three main symmetry axes of the ortho-hexagonal cell. Below its ordering temperature (T_c = 11.6 K), b and c are respectively the easy and hard magnetization axes. The strong anisotropy originates from the crystalline electric field acting on the 4f electrons of the Dy³⁺ ions. A small magnetization is induced on nickel atoms by the applied field and the exchange interactions with the dysprosium atoms. The crystal field parameters, the molecular field coefficients and the susceptibility of nickel atoms are determined from the experimental data.     

Magnetic properties of erbium iron garnet in high magnetic fields up to 150kOe

The magnetic properties of single crystals of erbium iron garnet (ErIG) were studied in applied fields up to 150kOe between 1.4 and 300K. At low temperature, the macroscopic easy direction of the bulk magnetization is [100]; below the compensation temperature (80±2K), the magnetization presents non-linear field evolution. On the assumption of an isolated ground doublet, the anisotropy constantsK _i (i=1,2) of ErIG are given byK _i (Er)+K _i (YIG); theK _i are calculated as a function of theG andg tensor components. It is worthwhile noting that theK _i (Er) are strongly temperature dependent; so at low temperature the anisotropy of the garnet is determined by the rare earth ions, while in the 50 K regionK ₁(Er) becomes comparable toK ₁(YIG) with the opposite sign which results in a very weak anisotropy of the garnet. Above 50 K,K ₁(YIG) is predominant and the Fe³⁺ ions determine the garnet anisotropy.     

The τ lepton as a laboratory for quantum chromodynamics

Decays of the τ lepton provide a clean environment to study hadron dynamics in an energy regime dominated by resonances. Inclusive spectral functions are the basis for quantum chromodynamics (QCD) analyses, providing a most accurate determination of the strong coupling constant and quantitative information on nonperturbative contributions. The τ vector spectral function is used together with e⁺e⁻ data in order to compute vacuum polarization integrals arising in the calculations of the anomalous magnetic moment of the muon and the running of the electromagnetic coupling constant. To cite this article: M. Davier, A. Höcker, C. R. Physique 3 (2002) 1223–1233.     

Cubic harmonic analysis of magnetic anisotropy measurements on single crystal HoxTb1−xFe2 laves phase compounds

Room temperature magnetic anisotropy measurements have been made on a series of low anisotropy Ho_xTb_1?xFe₂ compounds, with 0.826 < x < 0.908, using torque magnetometry techniques. An analysis of the data using the conventional expansion of anisotropy energy in terms of the direction cosines proved inadequate because of the presence of higher order contributions to the anisotropy. When these contributions were included in the expansion, non unique anisotropy constants were obtained which were not consistent with the predictions of the single ion model. An analysis of the data using an expansion of the anisotropy in terms of an orthonormal set of functions, namely the cubic harmonics developed by Mueller and Priestly, proved more successful. The results showed that the two lowest order anisotropy constants, κ₄ and κ₆, both varied linearly with holmium concentrations as predicted by the single ion model; however, κ₈, the next higher order term, was not consistent with the predicted behavior. The origin of this contribution is believed to be related to the magnetostriction.     

BaTiO3晶体结构及弹性的分子动力学模拟

有效的势函数是分子动力学模拟的关键. 引入了一种势函数,该势函数的特点是运用参数r_eff计算原子间的静电作用. 通过分子动力学方法模拟得到了BaTiO₃晶体立方相、四方相结构的对关联函数和X射线衍射谱,计算得出了它们的晶格常数及弹性常数. 模拟结果与实验结果符合较好.该势函数可以有效地模拟BaTiO₃晶体的热学和力学性能. 关键词： 分子动力学模拟 势函数 3铁电晶体')" href="#">BaTiO₃铁电晶体     

Magnetic phase transition in Heisenberg antiferromagnetic films with easy-axis single-ion anisotropy

The staggered susceptibility of spin-1 and spin-3/2 Heisenberg antiferromagnet with easy-axis single-ion anisotropy on the cubic lattice films consisting of n=2, 3, 4, 5 and 6 interacting square lattice layers is studied by high-temperature series expansions. Sixth order series in J/k_BT have been obtained for free-surface boundary conditions. The dependence of the Néel temperature on film thickness n and easy-axis anisotropy D has been investigated. The shifts of the Néel temperature from the bulk value can be described by a power law n^−λ with a shift exponent λ, where λ is the inverse of the bulk correlation length exponent. The effect of easy-axis single-ion anisotropy on shift exponent of antiferromagnetic films has been studied. A comparison is made with related works. The results obtained are qualitatively consistent with the predictions of finite-size scaling theory.     

Crystal field measurement for Tb3+ in gold

The crystal field parameters for 0.01 at.% Tb³⁺ in gold have been determined by gamma-ray anisotropy measurements as a function of magnetic field. The values of the parameters are X = 0.90 ± 0.01 and W = -0.19 ± 0.002 K.     

Molecular dynamics simulations on local structure and diffusion in liquid TixAl1−x alloys

The microscopic structure and dynamics of liquid Ti_xAl_1-x alloys together with pure liquid Ti and Al metals were investigated by means of molecular dynamics simulations. This work gives the structural properties, including pair-correlation function, bond-angle distribution function, HA and Voronoi indices, and their composition dependence. The dynamical properties have also been studied. The calculated pair-correlation function, bond-angle distribution function, and HA and Voronoi indices suggest that the stoichiometric composition Ti_0.75Al_0.25 exhibits a different local structure order compared with other concentrations, which help us understand the appearance of the minimum diffusion coefficient at this composition. These results indicate that the mobility of atoms strongly depends on their atomic local structure.     

Multiplet structure of P-excitons in CuBr due to valence band degeneracy

The two-photon absorption spectrum of CuBr shows a fourfold energy splitting of the 2P- and 3P-excitons of the Z_1,2 series. The splitting results from d-like contributions to the kinetic energy of the hole (Γ_δ) which lead to a coupling between angular momentum and hole spin. The energy splitting allows to determine the spherical and cubic parameters μ and δ of the reduced exciton mass. The results are compared with corresponding values of an existing band structure calculation.     

Far-infrared spectra of ring compounds. XII. Far-infrared spectra,ring-puckering vibration,and molecular conformation of some analogs of bicyclo(3.1.0.)hexane

The far-infrared spectra of bicyclo(3.1.0.)hexane, 3-oxabicyclo(3.1.0.)hexane, and 3,6-dioxabicyclo(3.1.0.)hexane exhibit series of Q branches in the frequency range 250–125 cm^?1, like those observed for 6-oxabicyclo(3.1.0.)hexane (cyclopentene oxide) by Carreira and Lord (J. Chem. Phys.51, 2735 (1969)). The Q branches are interpreted as single quantum jumps of a one-dimensional ring-puckering vibration governed by a potential function of the form V(cm^?1) = A(Z⁴ + BZ² + CZ³), where Z is a reduced ring-puckering coordinate.The potential parameters for bicyclo(3.1.0.)hexane are A, 24.31 cm^?1; B, 26.67; C, 9.63; for 3-oxabicyclo(3.1.0.)hexane, 27.77 cm^?1, 20.63, 7.84; and for 3,6-dioxabicyclo(3.1.0.)hexane, 25.25 cm^?1, 17.23, 7.33. They were determined by an iterative least-squares fit to the observed four, seven, and nine Q branches, respectively. These potential functions all have only a single minimum, implying a single stable conformation. The dipole moment, μ_rms, for 3,6-dioxabicyclo(3.1.0.)hexane in benzene solution was determined to be 2.50 D, clearly indicating that the stable conformation is the boat form. The boat conformation had been determined to be the stable form for cyclopentene oxide from a microwave study by Lafferty (J. Mol. Spectrosc.36, 84 (1970)). There is no direct evidence for the preferred conformation of the remaining two molecules but consideration of torsional interactions about the 1–2 and 4–5 bonds as well as the similarity of the spectra and potential functions for these molecules suggests that the boat conformation is the stable form of all of these molecules.     

Photo-induced bias of the hysteresis loop in ferrites at room temperature with long-time memory

New photo-magnetic effects with an indefinitely long-time memory are found at room temperature in the epitaxial Mg_0.75Mn_0.21Co_0.04Fe₂O₄ ferrite film. Illumination of the ferrimagnetic material with low-intensity (0.4 W cm⁻²) circularly polarized light with or without a static magnetic field in the Faraday effect geometry results in a number of nonlinear effects in both space and time. In a uniform crystal with cubic symmetry, the long-lived photo-induced magnetization (PIM) with a unidirectional anisotropy appears along the direction of the incoming light. The effects depend on a combination of magnetic field H and the helicity of circularly polarized light σ. Two combinations H⁺,σ⁺ and H⁻,σ⁻ lead to a photo-induced unidirectional anisotropy with a shift of the hysteresis loop along an applied field and a change in loop parameters. The loop contracts by a factor of two, the shift of the mid-point H_sh increases by factor of five surpassing the coercivity H_c, the coercivity H_c1 and remanence M_r1 (for decreasing applied field) reverse the sign, increasing by 9 Oe and reducing by a factor of 4.5, respectively. The effects cannot be erased by a conventional demagnetization (using an AC current that is reduced to zero amplitude), but can be removed using an illumination with two other combinations (H⁺,σ⁻ and H⁻,σ⁺) as well as by heating at temperatures higher than the Curie temperature. This long-lived room-temperature memory effect may arise from the formation of complex photo-induced defects including photo-induced magnetic polarons. The possible mechanisms responsible for the appearance of a room-temperature photo-induced unidirectional anisotropy with a long-lived memory are discussed. These new photo-magnetic effects may find an application in magneto-optical memory devices.