A lower bound for the volume-averaged mean-square magnetostatic stray field

Based on a micromagnetics model, we develop a method through which quantitative information on the volume-averaged mean-square magnetostatic stray field 〈|H ^b _d|²〉 _v due to non-zero divergences of the magnetization M within the bulk of a ferromagnetic body can be obtained by analysis of magnetic-field-dependent small-angle neutron scattering data. In the limit of high applied magnetic field H _a, when the direction of M deviates only sligthly from H _a, we have estimated a lower bound for 〈|H ^b _d|²〉 _v as a function of the external field, and we have applied the method to bulk samples of nanocrystalline electrodeposited Ni and Co and coarse-grained polycrystalline cold-worked Ni. The root-mean-square magnetostatic stray field, which is inherent to a particular magnetic microstructure, shows a pronounced field dependence, with values ranging from about 5 to 50mT. Even at applied fields as large as 1.7T, the quantity μ〈|H ^b _d|²〉^1/2 _v of nanocrystalline Co is still 24mT, which suggests that contributions to the total magnetostatic field originating from the bulk are significant in nanocrystalline ferromagnets; therefore, 〈|H ^b _d|²〉 _v cannot be ignored in the interpretation of e.g. measurements of magnetization or spin-wave resonance. A comparison of 〈|H ^b _d|²〉 _v with the volume-averaged mean-square anisotropy field reveals that both quantities are of comparable magnitude. Received 25 April 2002 Published online 31 October 2002 RID="a" ID="a"e-mail: anmi@nano.uni.saarland.de     

Magnetoconductance of a two-dimensional metal in the presence of spin-orbit coupling

We show that in the metallic phase of a two dimensional electron gas the spin-orbit coupling due to structure inversion asymmetry leads to a characteristic anisotropy in the magnetoconductance. Within the assumption that the metallic phase can be described by a Fermi liquid, we compute the conductivity in the presence of an in-plane magnetic field. Both the spin-orbit coupling and the Zeeman coupling with the magnetic field give rise to two spin subbands, in terms of which most of the transport properties can be discussed. The strongest conductivity anisotropy occurs for Zeeman energies of the order of the Fermi energy corresponding to the depopulation of the upper spin subband. The energy scale associated with the spin-orbit coupling controls the strength of the effect. More in particular, we find that the detailed behavior and the sign of the anisotropy depends on the underlying scattering mechanism. Assuming small angle scattering to be the dominant scattering mechanism our results agree with recent measurement on Si-MOSFET's in the vicinity of the metal-insulator transition. Received 11 July 2001     

On determination of the structural parameters of polydisperse magnetic fluids by small-angle neutron scattering

Factors affecting the determination of the structural parameters of polydisperse particles of typical magnetic fluids (MFs) from small-angle neutron scattering data (SANS), including the possible anisotropy of the particle shape and the residual incoherent background, are analyzed. It is shown that the effect of particle anisotropy on scattering must be considered in combination with the influence of their polydispersity. The relative shift in the MF’s structural parameters caused by particle anisotropy does not exceed 10–20% for particles with an anisotropy parameter which is less than four and becomes insignificant for more anisotropic particles. The main effect of the residual incoherent background of neutron scattering is related to determination of the thickness of the stabilizing shell and the generalized contrast parameter. It is shown that restrictions on the available maximum values of the scattering vector, measured in the experiment, lead to a relative shift in these parameters by up to 10%, while the other structural parameters (the average particle radius and the width of the size distribution) are determined with sufficiently high accuracy (the relative systematic error is 5% or less).     

Insertion of small anisotropic clay particles in swollen lamellar or sponge phases of nonionic surfactant

we have established experimentally the region of existence of smectic and sponge lyotropic microstructures in the presence of synthetic hydrophilic clay particles. Taking into account the adsorption isotherm, we determined the extension of the single-phase regions by visual inspection and looking at low-q behaviour of the small-angle neutron scattering. Conditions of stability such as geometric constraints associated with fluctuation quenching are discussed. Received 11 December 2000 and Received in final form 11 April 2001     

Nanoparticle chain-like formation in electrical double-layered magnetic fluids evidenced by small-angle X-ray scattering

Small-angle X-ray scattering (SAXS) was performed on a series of Electric Double-Layered Magnetic Fluids (EDL-MF) composed of ferrite type-- CoFe₂O₄, MnFe₂O₄, ZnFe₂O₄, NiFe₂O₄ and CuFe₂O₄--nanoparticles of different crystalline sizes ( D _XR ranging from 40 to 139?, as determined by X-ray diffraction). The information concerning the scattering objects was obtained through the analysis of the distance distribution function p(r) and of the size distribution function D(R), both retrieved from SAXS data. The results show that EDL-MF, in the absence of an applied magnetic field, are composed of small magnetic particle aggregates in solution. These agglomerates are elongated in one direction (chain-like) with the longest dimension varying from 240 to 330?. The cross-section size is of the order of D _XR. The data also demonstrate that the maximum dimension of these aggregates is independent of the ferrite type. On the other hand, the number of aggregated magnetic particles is nanoparticle-size-dependent. Accordingly, larger ferrite-type nanoparticles as those with D _XR = 139? form aggregates composed of 2-3 magnetic particles, whereas smaller ones with D _XR 40? form agglomerates of about 6 magnetic particles in solution. As the nanoparticle size is reduced, it might increase the particle surface defects. Such occurrence would affect the particle surface charge density, which could reduce the electrostatic screening, favoring the agglomeration phenomenon. Received 28 February 2000 and Received in final form 28 August 2000     

On neutron depolarization in magnetized media

The neutron depolarization in magnetized samples is considered as a result of scattering in the case of arbitrary orientations between the incident polariztion, the sample field and the direction of polarization analysis. It is shown that the depolarization is determined by the small-angle magnetic scattering within the angular beam width and by an additional contribution arising from the spin-dependent scattering outside the passing beam. The latter follows from the consideration of the interference between the scattered and the transmitted beams. Special attention is paid to the analysis of several measuring regimes for the depolarization and its dependence on neutron wavelength. The depolarization in multidomain ferromagnets is considered.     

Angular dependence of magnetoresistivity in c-oriented MgB thin film

The anisotropy of MgB₂ is still under debate: its value, strongly dependent on the kind of sample and on the measuring method, ranges between 1.2 and 13. In this work we present our results on MgB₂ c-oriented superconducting thin film. To evaluate the anisotropy, we followed two different approaches. Firstly, magnetoresistivity was measured as a function of temperature at selected magnetic fields applied both parallel and perpendicular to the c-axis; secondly, we measured magnetoresistivity at selected temperatures and magnetic fields, varying the angle θ between the magnetic field and the c-axis. The anisotropy estimated from the ratio between the upper critical fields parallel and perpendicular to the c-axis and the one obtained in the framework of the scaling approach within the anisotropic Ginzburg-Landau theory are different but show a similar trend in the temperature dependence. Some differences in the upper critical field and in its anisotropy of our film with respect to single crystals are emphasized: some of these aspects can be accounted for by an analysis of upper critical fields within a two-band model in presence of disorder and/or crystallographic strain. Received 12 July 2002 / Received in final form 17 September 2002 Published online 29 November 2002     

Small-angle polarized neutron scattering study of spherical Fe16N2 nano-particles for magnetic recording tape

We have performed small-angle polarized neutron scattering experiments of spherical Fe₁₆N₂ nano-particles, which are potential candidate materials for high density magnetic recording tape. The results were analyzed based on a core-shell model, and we evaluated the magnetic structure of the particles. The correlation between the magnetic structure and magnetic stability of the particles were discussed in terms of high density recordings.     

Vortex lattice studies in CeCoIn5 with H is orthogonal to c

We present small angle neutron scattering studies of the vortex lattice (VL) in CeCoIn5 with magnetic fields applied parallel (H) to the antinodal [100] and nodal [110] directions. For H is parallel to [100], a single VL orientation is observed, while a 90° reorientation transition is found for H is parallel to [110]. For both field orientations and VL configurations we find a distorted hexagonal VL with an anisotropy, Γ=2.0±0.05. The VL form factor shows strong Pauli paramagnetic effects similar to what have previously been reported for H is parallel to [001]. At high fields, above which the upper critical field (H(c2)) becomes a first-order transition, an increased disordering of the VL is observed.     

Experimental study of quasi-elastic scattering of ultracold neutrons

Ultracold neutrons (UCN) are lost from traps if they are quasi-elastically scattered from the wall with an energy gain sufficient to exceed the Fermi potential for the wall. Possible mechanisms of a quasi-elastic energy transfer are, for instance, scattering from hydrogen diffusing in an impurity surface layer or on surface waves at a liquid wall. Using two different experimental methods at the UCN source of the Institut Laue-Langevin we have investigated both the energy-gain and the energy-loss side of quasi-elastic UCN scattering on Fomblin grease coated walls. For Fomblin oil and similar new types of oil we report up-scattering data as a function of temperature and energy transfer. These low-temperature oils may be used in an improved measurement of the neutron lifetime, which requires extremely low wall reflection losses. Received 13 March 2002 Published online 31 July 2002     

Dynamical molecular disorder and diffuse scattering in an alkane/urea incommensurate inclusion compound

The diffraction pattern of n-alkane/urea inclusion compounds is known to contain a broad diffuse scattering related to the molecular form factor of the alkane species, indicating individual rotational and/or translational disorder of these molecules. Inelastic coherent neutron scattering reveals for the first time the entirely dynamical character of the alkane molecular disorder around room temperature. This observation fully agrees with a recent model of the coherent scattering cross section of totally uncorrelated motions. In the ordered phase this diffuse scattering remains, but elastic, and very low energy molecular vibrational modes are evidenced. These observations are discussed in relation with previous incoherent neutron scattering results. Received 9 February 2001 and Received in final form 1st August 2001     

First-order reorientation transition of the flux-line lattice in CaAlSi

The flux-line lattice in CaAlSi has been studied by small-angle neutron scattering. A well-defined hexagonal flux-line lattice is seen just above H(c1) in an applied field of only 54 Oe. A 30° reorientation of this vortex lattice has been observed in a very low field of 200 Oe. This reorientation transition appears to be first-order and could be explained by nonlocal effects. The magnetic field dependence of the form factor is well-described by a single penetration depth of λ=1496(1) ? and a single coherence length of ξ=307(1) ? at 2 K. At 1.5 K, the penetration depth anisotropy is γ(λ)=2.7(1), with the field applied perpendicular to the c axis, and agrees with the coherence length anisotropy determined from critical field measurements.     

Vesicle-to-micelle transition induced by grafted diblock copolymers

We study by small-angle neutron scattering the vesicle-to-micelle transition induced by anchoring diblock copolymers on the surfactant membranes. Vesicles are made using the ternary system SDS (sodium dodecyl sulfate)/octanol/PS-POE (polystyrene-polyoxyethylene), chosen as a model of more complex biological systems. The anchored polymer chains destabilize the membranes and lead to the formation of mixed polymer-surfactant micelles. We show that there is no influence of the polymer mass on the membranes destabilization. We compare this experimental result with recent theoretical predictions concerning the polymer-grafted membranes. We have a good agreement with predictions involving membrane curvature effects, and also with predictions focusing on more local deformations of membranes created by the grafted chains. Received 12 June 2001 and Received in final form 18 March 2002     

Dipolar interactions in ferromagnetic thin films

We introduce a discrete model describing the motion of a zigzag domain wall in a disordered ferromagnet with in-plane magnetization, driven by an external magnetic field. The main ingredients are dipolar interactions and anisotropy. We investigate the dynamic hysteresis by analyzing the effects of external field frequency on the coercive field by Monte Carlo simulations. Our results are in good agreement with experiments on Fe/GaAs films reported in literature, and we conclude that dynamic hysteresis in this case can be explained by a single propagating domain wall model without invoking domain nucleation.     

Electron-atomic-hydrogen “elastic" scattering in the presence of a laser field

Laser-assisted electron-atomic-hydrogen “elastic" scattering is studied in the first Born approximation. The initial and final states of projectile electron are described by the Volkov wavefunctions; the dressed state of target described by a time-dependent perturbative wavefunction in soft photon approximation. The laser modified cross-sections are calculated in two distinct geometries for laser polarization either parallel or perpendicular to the incident direction of electron. The numerical results shows that the multiphoton cross-sections oscillate by a few orders over the whole scattering angular region. The results for a parallel geometry oscillate more frequently in the intermediate angles; while the results for a perpendicular geometry oscillate more frequently in the forward and backward angles. At large scattering angles, the sum rule of Kroll and Watson is noticeably violated. The laser modification on summed total cross-section increases with field strength, but decreases with field frequency and polarization deviation from the incident direction. Received 18 October 2001 and Received in final form 26 December 2001     

Quasi-free Compton scattering and the polarizabilities of the neutron

Differential cross-sections for quasi-free Compton scattering from the proton and neutron bound in the deuteron have been measured using the Glasgow/Mainz photon tagging spectrometer at the Mainz MAMI accelerator together with the Mainz [48]cm ;SPMOslash; × [64]cm NaI(Tl) photon detector and the G?ttingen SENECA recoil detector. The data cover photon energies ranging from [200]MeV to [400]MeV at θ^LAB _γ = 136.2^°. Liquid deuterium and hydrogen targets allowed direct comparison of free and quasi-free scattering from the proton. The neutron detection efficiency of the SENECA detector was measured via the reaction p(γ,π⁺ n). The “free” proton Compton scattering cross-sections extracted from the bound proton data are in reasonable agreement with those for the free proton which gives confidence in the method to extract the differential cross-section for free scattering from quasi-free data. Differential cross-sections on the free neutron have been extracted and the difference of the electromagnetic polarizabilities of the neutron has been determined to be α_n - β_n = 9.8±3.6(stat)^+2.1 _-1.1(syst)±2.2(model) in units of [10^-4]fm ³. In combination with the polarizability sum α_n + β_n = 15.2±0.5 deduced from photoabsorption data, the neutron electric and magnetic polarizabilities, α_n = 12.5±1.8(stat)^+1.1 _-0.6(syst)±1.1(model) and β_n = 2.7±1.8(stat)^+0.6 _-1.1(syst)±1.1(model) are obtained. The backward spin polarizability of the neutron was determined to be γ⁽ⁿ⁾ _π = (58.6±4.0)×10^-4 fm ⁴. Received: 21 August 2002 / Accepted: 16 October 2002 / Published online: 11 February 2003 RID="a" ID="a"Part of the Doctoral Thesis. RID="b" ID="b"Present address: Physikalisch-Technische Bundesanstalt, Bundesallee 100, D-38116 Braunschweig. RID="a" ID="a"Part of the Doctoral Thesis. RID="b" ID="b"Present address: Physikalisch-Technische Bundesanstalt, Bundesallee 100, D-38116 Braunschweig. RID="c" ID="c"Part of the Habilitation Thesis. RID="d" ID="d"e-mail: schumacher@physik2.uni-goettingen.de Communicated by Th. Walcher     

Structure of colloidal complexes obtained from neutral/poly- electrolyte copolymers and oppositely charged surfactants

We report on the phase behavior and scattering properties of colloidal complexes made from block copolymers and surfactants. The copolymer is poly(sodium acrylate)-b-poly(acrylamide), hereafter abbreviated as PANa-PAM, with molecular weight 5000 g/mol for the first block and 30000 g/mol for the second. In aqueous solutions and neutral pH, poly(sodium acrylate) is a weak polyelectrolyte, whereas poly(acrylamide) is neutral and in good-solvent conditions. The surfactant is dodecyltrimethylammonium bromide (DTAB) and is of opposite charge with respect to the polyelectrolyte block. Combining dynamical light scattering and small-angle neutron scattering, we show that in aqueous solutions PANa-PAM diblocks and DTAB associate into colloidal complexes. For surfactant-to-polymer charge ratios Z lower than a threshold (Z(C) approximately 0.3), the complexes are single surfactant micelles decorated by few copolymers. Above the threshold, the colloidal complexes reveal an original core-shell microstructure. We have found that the core of typical radius 100-200 A is constituted from densely packed surfactant micelles connected by the polyelectrolyte blocks. The outer part of the colloidal complex is a corona and is made from the neutral poly(acrylamide) chains. Typical hydrodynamic sizes for the whole aggregate are around 1000 A. The aggregation numbers expressed in terms of numbers of micelles and copolymers per complex are determined and found to be comprised between 100-400, depending on the charge ratio Z and on the total concentration. We have also shown that the sizes of the complexes depend on the exact procedure of the sample preparation. We propose that the driving mechanism for the complex formation is similar to that involved in the phase separation of homopolyelectrolyte/surfactant systems. With copolymers, the presence of the neutral blocks prevents the macroscopic phase separation from occurring.     

Nuclear-matter distributions of halo nuclei from elastic proton scattering in inverse kinematics

Proton-nucleus elastic scattering at intermediate energies, a well-established method for probing nuclear-matter density distributions of stable nuclei, was applied for the first time to exotic nuclei. This method is demonstrated to be an effective means for obtaining accurate and detailed information on the size and radial shape of halo nuclei. Absolute differential cross-sections for small-angle scattering were measured at energies near 700 MeV/u for the neutron-rich helium isotopes ⁶He and ⁸He, and more recently for the lithium isotopes ⁶Li, ⁸Li, ⁹Li and ¹¹Li, using He and Li beams provided by the fragment separator FRS at GSI Darmstadt. Experiments were performed in inverse kinematics using the hydrogen-filled ionization chamber IKAR which served simultaneously as target and recoil-proton detector. For deducing nuclear-matter distributions, differential cross-sections calculated with the aid of the Glauber multiple-scattering theory, using various parametrizations for the nucleon density distributions as input, were fitted to the experimental cross-sections. The results on nuclear-matter radii and matter distributions are presented, and the significance of the data for a halo structure is discussed. Nuclear-matter distributions obtained for ⁶He and ⁸He conform with the concept that both nuclei compose of α-particle like cores and significant neutron halos. The matter distribution in ¹¹Li exhibits, as expected from previous reaction cross-section studies with nuclear targets, the by far most extended halo component of all nuclei being investigated. In addition the present data allow a quantitative comparison of the structure of the He and Li isobares of either the mass number A = 6 or A = 8. The measured differential cross-sections have also been used for probing density distributions as predicted from various microscopic calculations. A few examples are presented. Received: 21 March 2002 / Accepted: 16 May 2002 / Published online: 31 October 2002 RID="a" ID="a"e-mail: p.egelhof@gsi.de     

Magnetic anisotropy and domain patterns in electrodeposited cobalt nanowires

The magnetic anisotropy and domain structure of electrodeposited cylindrical Co nanowires with length of 10 or 20 μm and diameters ranging from 30 to 450 nm are studied by means of magnetization and magnetic torque measurements, as well as magnetic force microscopy. Experimental results reveal that crystal anisotropy either concurs with shape anisotropy in maintaining the Co magnetization aligned along the wire or favours an orientation of the magnetization perpendicular to the wire, hence competing with shape anisotropy, depending on whether the diameter of the wires is smaller or larger than a critical diameter of 50 nm. This change of crystal anisotropy, originating in changes in the crystallographic structure of Co, is naturally found to strongly modify the zero (or small) field magnetic domain structure in the nanowires. Except for nanowires with parallel-to-wire crystal anisotropy (very small diameters) where single-domain behaviour may occur, the formation of magnetic domains is required to explain the experimental observations. The geometrical restriction imposed on the magnetization by the small lateral size of the wires proves to play an important role in the domain structures formed. Received 14 September 2000