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     

Magnetic inverted photonic crystals: A polarized neutron scattering study

This work is devoted to a small-angle polarized neutron scattering study of the structure and magnetic properties of nickel inverted photonic crystals. Depending on the intensity of the small-angle scattering, diffraction maximums up to fourth-order reflections, which correspond to scattering from the highly ordered structures of the test samples, are observed. Several contributions to the scattering are analyzed: a nuclear contribution; a magnetic contribution; a contribution depending on an external magnetic field; and a nuclear magnetic interference, which shows a correlation between magnetic and nuclear structures. It is found that a magnetization reversal process, which was represented by a standard hysteresis curve, for weak fields was accompanied by both domain formation and coherent magnetization rotation from the field direction to directions caused by geometric structure peculiarities.     

Resolving magnetic and chemical correlations in CoPtCr films using soft X-ray resonant scattering

Resonant small-angle scattering at the 2p levels of 3d transition elements strongly enhances scattering from both magnetic and chemical structure in the plane of thin films, as recently demonstrated for Co/Pt multilayers having perpendicular anisotropy. Here this resonant enhancement is demonstrated for CoPtCr films having in-plane magnetic anisotropy. A simple formalism describing the spectral dependence of the kinematical scattering provides a means to distinguish between magnetic and charge scattering and to probe the chemical segregation processes yielding charge scattering, thereby providing new information about this structure. It is found that correlation lengths of magnetic scattering are roughly 5 times larger than those for chemical scattering in the as-deposited CoPtCr film studied, consistent with significant exchange-coupling between polycrystalline grains.     

Magnetic properties of cobalt nanowires: Study by polarized SANS

Structural and magnetic properties of two-dimensional spatially ordered system of ferromagnetic cobalt nanowires embedded into Al₂O₃ matrix have been studied using polarized small-angle neutron scattering. A comprehensive analysis of contributions to the scattering intensity was carried out, including nonmagnetic (nuclear) contribution, magnetic contribution depending on the magnetic field, and nuclear-magnetic interference indicating the correlation between the magnetic and nuclear structures. Experiments have revealed an anomalously low value of the magnetic contribution as compared to the nuclear one. This behavior is interpreted in terms of low coherence of the magnetic structure caused by the anisotropy of Co crystallites as compared with the large coherency of nuclear structure of nanowires.     

Existence, stability and structure of a hexagonal phase doped with nanoparticles

We describe and study by small-angle X-ray scattering (SAXS) a new type of hybrid system. It is composed of a swollen lyotropic hexagonal phase into the cylinders of which solid magnetic particles of nanometric size have been incorporated. It has been found to be stable for volume fractions of particles up to 2% provided the cylinders are sufficiently large. A unidimensionnal magnetic liquid is thus realized. The structural properties of this colloidal assembly have been investigated by SAXS, and the specific features of the scattering spectra are analysed and interpreted. One of the remarkable results is the evidence of depletion interactions between the particles and the inner walls of the cylinders inside which particles are located. Received: 4 September 1997 / Revised: 14 October 1997 / Accepted: 19 November 1997     

Small-angle neutron scattering of nanocrystalline terbium with random paramagnetic susceptibility

We report magnetic small-angle neutron scattering (SANS) data for the nanocrystalline rare earth metal Terbium in its paramagnetic state. Whereas critical scattering dominates at large momentum transfer, q, the (magnetic-) field response of the scattering at small q arises from the spatial nonuniformity of the paramagnetic susceptibility tensor. The finding of an interrelation between SANS and the susceptibility suggests a way for characterizing the nonuniform magnetic interactions in hard magnets by neutron scattering.     

Square vortex lattice at anomalously low magnetic fields in electron-doped Nd1.85Ce0.15CuO4

We report here on the first direct observations of the vortex lattice in the bulk of electron-doped Nd1.85Ce0.15CuO4 single crystals. Using small-angle neutron scattering, we have observed a square vortex lattice with the nearest neighbors oriented at 45 degrees from the Cu-O bond direction, which is consistent with theories based on the d-wave superconducting gap. However, the square symmetry persists down to unusually low magnetic fields. Moreover, the diffracted intensity from the vortex lattice is found to decrease rapidly with increasing magnetic field.     

Microphase separation in Pr0.67Ca0.33MnO3 by small-angle neutron scattering

We have evidenced by small-angle neutron scattering at low temperature the coexistence of ferromagnetism (F) and antiferromagnetism (AF) in Pr0.67Ca0.33MnO3. The results are compared to those obtained in Pr0.80Ca0.20MnO3 and Pr0.63Ca0.37MnO3, which are F and AF, respectively. Quantitative analysis shows that the small-angle scattering is not due to a mesoscopic mixing but to a nanoscopic electronic and magnetic "red cabbage" structure, in which the ferromagnetic phase exists in the form of thin layers in the AF matrix (stripes or 2D "sheets").     

X-ray studies of the domain formation in rocks under blasting

Quartz plates placed in concrete are used to model the rock blasting procedure. Quartz fragments resulted from blasting are studied by small-angle X-ray scattering. Obtained grains in the quartz fragments are approximately 200–220 nm in size. The samples are discovered to contain low-dimensional (linear) components; the further the sample is from the explosion center, the coarser the grains are in it. Superlattice parameters of the studied fragments are estimated. It is suggested that domain boundaries in the sample quartz fragments are linear objects, such as dislocation walls.     

Microscopic mechanisms of electric-field-induced alignment of block copolymer microdomains

We investigate the microscopic mechanisms responsible for microdomain alignment in block copolymer solutions exposed to an electric field. Using time-resolved synchrotron small-angle x-ray scattering, we reveal two distinct processes, i.e., grain boundary migration and rotation of entire grains, as the two dominant microscopic mechanisms. The former dominates in weakly segregating systems, while the latter is predominant in strongly segregated systems. The kinetics of the processes are followed as a function of polymer concentration and temperature and are correlated to the solution viscosity.     

Small-angle approximation for an ion beam in an external electromagnetic field

A small-angle approximation method is formulated for a curvilinear ion beam propagating in an electromagnetic field. The effects of particle velocity scatter and multiple elastic scattering on the beam path in a magnetic field, the electric field of a cylindrical capacitor, and mutually orthogonal electric and magnetic fields are considered. An analytical model for beam power compression is developed.     

Onset of long-range ferromagnetic order in a system of ferromagnetic particles with giant magnetic moments

Magnetic, x-ray, and small-angle neutron scattering data obtained for the decomposed alloy Cu₆₄Mn₉Al₂₇ are used to show that the onset of long-range ferromagnetic order in a system of small superparamagnetic grains dissolved in a nonmagnetic matrix is attributable to cooperative ordering of their magnetic moments. Zh. éksp. Teor. Fiz. 114, 1848–1858 (November 1998)     

Combined neutron and synchrotron studies of magnetic films

We discuss specular reflectivity and off-specular scattering of neutrons and X-rays from magnetic films. Both these techniques are capable of providing information about the morphology of the chemical and magnetic roughness and the magnetic domain structure. The use of neutrons with polarization analysis enables the spatial distribution of different vector components of the magnetization to be determined, and the use of resonant magnetic X-ray scattering enables magnetization in a compound system to be determined element-selectively. Thus both these methods provide powerful and complementary new probes for studying magnetism at the nanoscopic level in a variety of systems such as those exhibiting exchange bias, giant magnetoresistance, spin injection, etc. We shall illustrate with an example of both techniques applied to an exchange bias system consisting of a single crystal of antiferromagnetic FeF₂ capped with a ferromagnetic Co film, and discuss what has been learned about how exchange bias works in such a system.     

Longitudinal polarization analysis in small-angle neutron scattering

Due to recent progress in the development of ³He spin filters, it has only now become possible to perform routinely longitudinal (one-dimensional) neutron-spin analysis (POLARIS) in small-angle neutron scattering (SANS) experiments. It is the purpose of this article to provide a brief introduction into the technique and to discuss first experimental data. In particular, for the most common scattering geometry where the applied magnetic (guide) field is perpendicular to the incident neutron beam, we write down the equations for the non-spin-flip and spin-flip SANS cross sections of a bulk ferromagnet, and we discuss the various angular anisotropies and asymmetries along with some selected experimental results on an FeCr based soft magnetic nanocrystalline alloy. In particular, we show that the analysis of the spin-flip data allows one to obtain the magnitude-squares of the three vector (Fourier) components of the magnetization.     

Fate of the peak effect in a type-II superconductor: multicriticality in the Bragg-Glass transition

We have used small-angle neutron scattering (SANS) and ac magnetic susceptibility to investigate the global magnetic field H vs temperature T phase diagram of a Nb single crystal in which a first-order transition of Bragg-glass melting (disordering), a peak effect, and surface superconductivity are all observable. It was found that the disappearance of the peak effect is directly related to a multicritical behavior in the Bragg-glass transition. Four characteristic phase boundary lines have been identified on the H-T plane: a first-order line at high fields, a mean-field-like continuous transition line at low fields, and two continuous transition lines associated with the onset of surface and bulk superconductivity. All four lines are found to meet at a multicritical point.     

Nuclear-resonance beamline at ESRF

Summary The Nuclear-Resonance Beamline at ESRF is dedicated to the excitation of nuclear levels by synchrotron radiation. The source of radiation and optical elements are optimized to provide an intense, highly monochromatic, collimated and stable X-ray beam of small cross-section at the M?ssbauer transition energies between 6 keV and 30 keV. The set-up of the beamline allows to perform studies in diffraction, small-angle scattering, forward scattering and incoherent scattering. Equipment is available to maintain the sample at variable temperature and magnetic field. Fast detectors and timing electronics serve to separate the delayed nuclear scattering from the ?prompt? electronic scattering and to measure the time spectra of nuclear radiation with sub-nanosecond resolution. The general layout and the parameters of the beamline are reported. Typical domains of applications are discussed and illustrated by first experimental results. Paper presented at ICAME-95, Rimini, 10–16 September 1995.     

Study of quasi-two- and three-dimensional ordered porous structures by means of small-angle X-ray scattering in the grazing incidence geometry

The structure of surface layers of thin metal inverse opals has been studied first by the grazing-incidence small-angle X-ray scattering technique. Contributions of the form factor and structure factor to the small-angle diffraction pattern have been separated using a numerical model of the scattering process. The complementary use of the small-angle X-ray scattering and grazing-incidence small-angle X-ray scattering techniques has provided independent information about the bulk and surface properties of the samples and allowed a type of defect in the investigated structures to be determined. The measurement results have been verified by atomic force microscopy.

     

Self-assemblies of magnetic nanoparticles and di-block copolymers: Magnetic micelles and vesicles

Magnetic nanocomposites are obtained by the self-assembly in water of polypeptide-based di-block copolymers polybutadiene-b-poly(glutamic acid) combined with hydrophobic γ-Fe₂O₃ nanoparticles. These hybrid supramolecular objects are either—(3D) spherical micelles filled with a hydrophobic ferrofluid at a concentration as high as 45 vol% or—hollow vesicles with a (2D) magnetic membrane. In this last case, the organic amphiphile copolymers are able to confine the hydrophobic nanoparticles within the thin layer of polybutadiene blocks. We probe these objects by atomic force microscopy, by small-angle neutron scattering (SANS) and by light scattering. Furthermore, anisotropic SANS data bring the experimental evidence of the capability to modify the shape of the mineralized membranes in response to a magnetic field intensity as low as 290 G.     

Neutron decoherence imaging for visualizing bulk magnetic domain structures

Here we introduce a novel neutron imaging method, which is based on the effect that the spatial coherence of the neutron wave front can be changed through small-angle scattering of neutrons at magnetic domain walls in the specimen. We show that the technique can be used to visualize internal bulk magnetic domain structures that are difficult to access by other techniques. The method is transferable to a wide variety of specimens, extendable to three dimensions, and well suited for investigating materials under the influence of external parameters, as, e.g., external magnetic field, temperature, or pressure.     

Characterization of Nanoparticles by Scattering Techniques

Basic principles and applications of different scattering techniques (including static and dynamic light scattering (SLS and DLS), small-angle X-ray scattering (SAXS), wide-angle X-ray diffraction (WAXD) and small-angle neutron scattering (SANS)) on the characterization of nanoparticles are reviewed in this paper. By choosing a suitable scattering technique or a combination of different techniques for nanoparticle characterization, the particles' molecular weight, radius of gyration, hydrodynamic radius, size distribution, shape and internal structure as well as interparticle interactions of nanoparticles, can be determined. Examples including some sophisticated colloidal systems are presented.