Synthesis and investigation of precipitated ensembles of magnetic nanoparticles with controlled easy axis orientation

Two samples with immobilized magnetic nanoparticles are synthesized and investigated. The first sample has randomly oriented easy axes of magnetic anisotropy; the second sample has preferentially aligned easy axes, produced via the precipitation of a colloid of ferromagnetic particles in the presence of a magnetic field. It is shown that the precipitation of an aqueous suspension of nanoparticles in the presence of a magnetic field greatly changes the anisotropy of a sample, compared to one prepared by precipitation without a magnetic field. The second sample exhibits a preferential direction of the easy axes of magnetic anisotropy that coincides with the direction of the external magnetic field applied in the drying process of sample preparation.     

Scaling approach to anisotropic magnetic systems statics

Scaling laws are stated for anisotropic magnetic systems, where the anisotropy parameters are either scaled or held fixed. Combining the two ways of scaling, the critical behavior of thermodynamic quantities in anisotropic systems is determined. Particular attention is drawn to the temperature range where the anisotropy becomes important, and to the dependence there of the different quantities on the anisotropy parameters. In a transverse magnetic field the phase transition of an anisotropic magnet takes place along aλ-line. Assuming the singular part of the free enthalpy to depend on the distance from theλ-line, anomalous corrections to the transverse susceptibility and magnetization are calculated. For an experimental verification of many of the results, experiments including a variation of the anisotropy parameters or a finite transverse field are necessary.     

Phase diagram of uniaxial antiferromagnetic particles: Field perpendicular to the easy axis

We consider a spherical uniaxial antiferromagnetic particle in the presence of an external magnetic field perpendicular to its easy axis. The model is described by a classical Heisenberg Hamiltonian including a single-ion uniaxial anisotropy, where the magnetic moments of the particle are represented by continuous spin vectors. We employ mean-field calculations and Monte Carlo simulations to determine the phase diagram of the system. The phase diagram in the plane field versus temperature is obtained for particles with radii ranging from three up to twelve spacing lattice units. We have seen that a particle with more than nine shells behaves as a true thermodynamic system. We find the explicit dependence of the zero temperature critical field and the Néel temperature on the diameter of the particle. At low temperatures, we have also shown that, for particles with three or more shells, the critical field follows a T² law, which is in agreement with the predictions of the spin-wave theory, when the field is perpendicular to the easy axis.     

Collision cascade evolution in media with energy independent scattering: spatial,energy, and angular distribution

The evolution of an ion induced collision cascade in a solid medium is studied by means of a DPl-approximation to the linear transport equation. Infinite medium and half space geometries are considered. Special attention is given to the effect of the anisotropy of the energy independent scattering cross section. We present results on the spatial distribution of particles moving at different energies, and the energy and angle distribution at the target surface. The spatial distributions are found to obey simple scaling laws; the energy and angular distributions are independent of the form of the scattering cross section, unless it is very strongly forward peaked.     

一种新的菲涅耳位相波带片

利用液晶分子取向的电场可控及光学各向异性的特点,设计了一种新型的菲涅耳痊相波带片,这种器件具有制作简单、造价低廉、抗划损的优点。     

Phase diagram of a two-dimensional square lattice of magnetic particles with perpendicular anisotropy

The ground state of an array of small single-domain magnetic particles having perpendicular anisotropy and forming a square two-dimensional lattice is studied in the presence of a magnetic field. The stability of some basic states with respect to nonuniform perturbations is analyzed in a linear approximation, and analytical model calculations and numerical simulation are used for an analysis. The entire set of states at various anisotropy constants and magnetic fields is considered when a field is normal to the array plane. Two main classes of states are possible for an infinite system, namely, collinear and noncollinear states. For collinear states, the magnetic moments of all particles are normal to the array plane. At a sufficiently high anisotropy, a wide class of collinear states exists. At low fields, a staggered antiferromagnetic order of magnetic moments takes place. An increase in the magnetic field causes an unsaturated state, and this state transforms into a saturated (ferromagnetic) state with a parallel orientation of the magnetic moments of all particles at a sufficiently high field. At a lower anisotropy, the ground state of the system is represented by noncollinear states, which include a complex four-sublattice structure for the components of the magnetic moments in the array plane and a nonzero projection of the magnetic moments of the particles onto the field direction. A phase diagram is plotted for the states of an array of anisotropic magnetic particles in the anisotropy constant-magnetic field coordinates. For a finite array of particles, sample boundaries are shown to play a significant role, which is particularly important for noncollinear states. As a result of the effect of the boundaries at a moderate field or anisotropy, substantially heterogeneous noncollinear states with a heterogeneity size comparable with the sample size can appear in the system.     

On the influence of anisotropy on the magnetic small-angle neutron scattering of superparamagnetic particles

This paper presents a calculation of the magnetic small-angle neutron scattering cross-section resulting from a dilute ensemble of superparamagnetic particles exhibiting uniaxial magnetic anisotropy. We focus on the two experimentally relevant scattering geometries in which the incident neutron beam is perpendicular or parallel to an applied magnetic field, and we discuss several orientations of the anisotropy axes with respect to the field. Magnetic anisotropy has no influence on the magnetic small-angle neutron scattering when the particles are mobile, as is the case e.g. in ferrofluids, but, when the particles are embedded in a rigid non-magnetic matrix and the orientations of the anisotropy axes are fixed, significant deviations compared to the case of negligible anisotropy are expected. For the particluar situation in which the anisotropy axes are parallel to the applied field, closed-form expressions suggest that an effective anisotropy energy or anisotropy-energy distribution can be determined from experimental scattering data. Received 8 November 2001     

Electro-optical study of the correlation between dimensions and polarizability of particles in colloid systems

The applicability of methods of molecular electro-optics for the study of colloid systems is analyzed. It is shown that the basic formulas of molecular electro-optics can be applied for the calculation of electrical and geometric characteristics of particles of colloid size. The basic integral equations describing electro-optical effects in colloid systems are presented to find distributions of particles over their size and polarizability anisotropy. The accuracy of their solutions is evaluated by mathematical simulation. Studying the dichroism induced by an external electric field in aqueous colloids of anisylidenbenzidine and graphite, the polarizability and size distribution functions are found for particles with an “optical weight.” From the resulting distribution functions, the statistical dependences of the polarizability anisotropy of those particles on their size are found and analyzed.     

Magnetic hyperfine splitting in mössbauer spectra of microcrystals

Below the superparamagnetic blocking temperature of a microcrystal the magnetization direction is in general not fixed, but fluctuates in directions close to an easy direction of magnetization. Such fluctuations (collective magnetic excitations) result in a reduction in the magnetic splitting of the Mössbauer spectrum. A low-temperature approximation for this reduction is derived for microcrystals with arbitrary magnetic energy. Moreover, explicit expressions are presented for particles with special types of magnetic anisotropy and for particles exposed to external magnetic fields. The reduction in the magnetic hyperfine field has its maximum value just below the blocking temperature but does not exceed 5–15% in isolated particles with uniaxial anisotropy in zero applied magnetic field. However, ferro- and ferrimagnetic particles, exposed to external magnetic fields, and particles for which exchange anisotropy is predominant, may exhibit any magnetic hyperfine splitting between zero and the saturation value. It is shown that in special cases an assembly of microcrystals in close contact with each other may behave like a spin-glass. We discuss how studies of the magnetic hyperfine splitting ofMössbauer spectra of microcrystals give information of the particle size and the prevailing magnetic anisotropies.     

Certain general questions of fast-electron transport II. Kinetic equations and conditions governing the accelerated motion of fast electrons in dielectrics in an electric field

A general kinetic equation for the differential density of fast particles moving in a medium in an external field is derived on the basis of the continuity equation in phase space. An equation is written for the differential flux in the case of fixed target particles. This equation is used to derive equations for fast electrons; account is taken of the coupling of energy-loss and scattering events in an electric field for various particular problems analogous to those studied in the theory of electron transport in the absence of a field. The kinetic equations are used to analyze the conditions governing accelerated motion of electrons in a dielectric in an external electric field in the continuous-deceleration approximation. Account is taken of fluctuations in the energy loss and of multiple scattering. There are two energy ranges of particles moving in a dielectric in which accelerated motion can occur; in the case of an electron beam with a continuous energy spectrum, this acceleration would be accompanied by monochromatization of the beam.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 7–12, February, 1972.     

Mean field phase diagram of the discrete Frenkel-Kontorova model

The mean field phase diagram of the discrete Frenkel-Kontorova model (harmonic chain of particles exposed to a sinusoidal potential) is studied using a fixed irrational value for the ratio of atoms and available sites as a boundary condition. Independent variables are the temperature and the height of the sinusoidal potential. The phase diagram contains two different solid phases, namely an intrinsically pinned incommensurate and an unpinned incommensurate phase. The position of the phase boundary and the nature of the phases are determined. We also investigate the influence of an electric field and the resulting pinning-unpinning transition for fields smaller than the threshold field.     

Interaction between glow discharge plasma and dust particles

The effect of dust particle concentration on gas discharge plasma parameters was studied through development of a self-consistent kinetic model which is based on solving the Boltzmann equation for the electron distribution function. It was shown that an increase in the Havnes parameter causes an increase in the average electric field and ion density, as well as a decrease in the charge of dust particles and electron density in a dust particle cloud. Self-consistent simulations for a wide range of plasma and dust particle parameters produced several scaling laws: these are laws for dust particle potential and electric field as a function of dust particle concentration and radius, and the discharge current density. The simulation results demonstrate that the process of self-consistent accommodation of parameters of dust particles and plasma in condition of particle concentration growth causes a growth in the number of high-energy electrons in plasma, but not to depletion of electron distribution function.     

Analogue of a spin flop phase transition for an array of magnetic moments with dipole interaction

In a two-dimensional array of magnetic moments with planar magnetization and relatively weak anisotropy in the basal plane, a stepwise phase transition is induced by an external magnetic field parallel to the easy axis of the system. This transition is similar to the spin flop phase transition in weakly anisotropic Heisenberg antiferromagnets with the significant difference that it is accompanied by the rearrangement of the sublattice structure of the magnet; i.e., it can be interpreted as a topological transition. The transition should manifest itself for arrays of submicron magnetic particles (magnetic dots) on nonmagnetic substrates, which have recently become the object of intensive research.     

Computation of effective propagation parameters in the optical domain with a finite difference time domain method

The study of optical scattering by heterogeneous media is a complex topic where homogenization is very helpful and rigorous methods are useful. Finite difference time domain (FDTD) method coupled with Monte Carlo process is used to compute the effective parameters of heterogeneous media. Effective parameters based on the coherent field propagation of a beam in the medium are determined in bidimensional geometry and for both polarizations. It is applied to media composed of small particles embedded in an host medium, for relevant ranges of particle sizes and optical constants for both binder and particles. The results are compared to the Maxwell–Garnett and Bruggeman mixing laws and the Foldy–Twersky and Keller perturbative approximations, leading to the assessment of their validity domain.     

Magnetization switching in single-domain particles and a response to a field pulse

An equation in the Gilbert form that describes the motion of the magnetization vector in intense high-frequency magnetic fields is solved numerically. The solution obtained is used to study switching of the magnetization of a single-domain ferromagnetic particle that has the shape of an ellipsoid of revolution and possesses cubic anisotropy from the position parallel to an easy axis to the position normal to this axis. The ranges of amplitudes and frequencies of the magnetic field where magnetization switching is observed are determined. An expression for the response of an ensemble of variously oriented particles is derived. It is shown that a particle ensemble generated by an rf field may serve as a data carrier on which information is written and read out by means of nonlinear and linear ferromagnetic resonances.     

Anisotropy of conductivity due to warm holes inp-type germanium andp-type silicon

The dependence of the electric conductivity on a d.c. electric field of medium intensity is measured for 3.5 ohm-cmp-type silicon and 0.9 ohm-cmp-type germanium. From these data and the symmetry properties of the cubic crystal lattice the dependence of the conductivity on crystal orientation is determined. Also, an analytical treatment is made for silicon by assuming a model of constant energy surfaces near momentum?k=0 which consists of spheroids of rotational symmetry penetrating each other. The usually accepted model of warped surfaces does not seem to be tractable. The ratio of effective masses parallel and perpendicular to the axis of rotation enters as a parameter which is determined by the experimental value of the conductivity anisotropy. This mass ratio for silicon at 275 °K is 3.25, at 193 °K 4.64 and at 77 °K 37. With germanium the observed anisotropy is stronger than the anisotropy calculated with any finite mass ratio which means that the model is not adequate.     

Ferromagnetic resonance of nonstoichiometric zinc ferrite and cobalt-doped zinc ferrite nanoparticles

Ferromagnetic resonance spectra of zinc ferrite and cobalt doped zinc ferrite nanoparticles, measured at various temperatures, exhibit an invariant point at a given field. This makes it possible to determine the equation relating the resonance field shift to the peak-to-peak linewidth. When particles are frozen in a matrix in a magnetic field, the anisotropy constant of the material can be derived from the angular variation of the resonance field. This procedure is useful to determine the thermal dependence of the anisotropy constant, but is shown to require various freezing temperatures experiments to estimate the accuracy of the deduced anisotropy constant values. It is also shown that the angular dependence of the resonance field is similar for a uniaxial (zinc ferrite) and cubic (zinc ferrite containing 40% cobalt ions) anisotropy. This unexpected result is explained by the weakness of the texturation, leading to a distribution in easy axes directions.     

Magnetic field induced instabilities of a doped lyotropic hexagonal phase

A new anisotropic magnetic fluid is obtained using a colloidal suspension of magnetic particles of nanometric size (ferrofluid) as a component of a swollen lyotropic hexagonal phase. This doped hexagonal system exhibits specific behaviors when submitted to a magnetic field of weak intensity. The field-induced instabilities are described and interpreted; they result from a high anisotropy of the magnetic susceptibility of the medium, which is measured. It is finally shown that the magnetic properties of the doped hexagonal phase allows one a determination of the compression modulus of the system. Received 10 February 1998     

EHD kelvin-helmholtz instability in viscous porous medium permeated with suspended particles

The electrohydrodynamic Kelvin-Helmholtz instability of the plane interface between two uniform, superposed viscous and streaming dielectric fluids permeated with suspended particles through porous medium is considered under the influence of a tangential electric field. In the absence of surface tension, it is found that perturbations transverse to the direction of streaming are unaffected by the presence of both streaming and the tangential electric field, if perturbations in the direction of streaming are ignored. For perturbations in all other directions there exists instability for a certain wavenumber range. In the presence of surface tension, it is found that the instability of this system is suppressed by the presence of the tangential electric field. Both the tangential electric field and the surface tension have stabilizing effects and they are able to suppress Kelvin-Helmholtz instability for small wavelength perturbations. The medium porosity reduces the stability range given in terms of a difference in streaming velocities and the electric field effect, while the suspended particles do not affect the above results.     

Solitons in an easy plane ferromagnet

Dynamical solitons in a uniaxial ferromagnet are considered. The second constant of magnetic anisotropy is taken into account. In the case of easy plane anisotropy the explicit form for the magnetization is found. The dispersion laws for obtained solitons are discussed.