No abstract

Small-angle neutron scattering (SANS) is one of the most important techniques for microstructure determination, being utilized in a wide range of scientific disciplines, such as materials science, physics, chemistry, and biology. The reason for its great significance is that conventional SANS is probably the only method capable of probing structural inhomogeneities in the bulk of materials on a mesoscopic real-space length scale, from roughly 1 − 300 nm. Moreover, the exploitation of the spin degree of freedom of the neutron provides SANS with a unique sensitivity to study magnetism and magnetic materials at the nanoscale. As such, magnetic SANS ideally complements more real-space and surface-sensitive magnetic imaging techniques, e.g., Lorentz transmission electron microscopy, electron holography, magnetic force microscopy, Kerr microscopy, or spinpolarized scanning tunneling microscopy. In this review article we summarize the recent applications of the SANS method to study magnetism and magnetic materials. This includes a wide range of materials classes, from nanomagnetic systems such as soft magnetic Fe-based nanocomposites, hard magnetic Nd−Fe−B-based permanent magnets, magnetic steels, ferrofluids, nanoparticles, and magnetic oxides, to more fundamental open issues in contemporary condensed matter physics such as skyrmion crystals, noncollinar magnetic structures in noncentrosymmetric compounds, magnetic/electronic phase separation, and vortex lattices in type-II superconductors. Special attention is paid not only to the vast variety of magnetic materials and problems where SANS has provided direct insight, but also to the enormous progress made regarding the micromagnetic simulation of magnetic neutron scattering.

No abstract

In ferromagnets with a nonuniform magnetocrystalline and/or magnetoelastic anisotropy, such as nanocrystalline ͑nc-͒ or cold-worked ͑cw-͒ polycrystalline materials, the static magnetic microstructure gives rise to strong elastic magnetic small-angle neutron scattering ͑SANS͒. The paper explores a method for analyzing field-dependent SANS data from such materials in terms of a model based on the theory of micromagnetics. Samples of cw Ni and of electrodeposited nc Ni and nc Co were characterized by x-ray scattering and magnetometry, and were investigated by SANS both with and without polarization of the neutron beam. The variation of the differential scattering cross section with the scattering vector and with the applied magnetic field is well described by the model. Also, experimental results for the exchange stiffness constant A and for the spin-wave stiffness constant D obtained from the analysis are found to agree with literature data obtained by inelastic neutron scattering on single-crystal specimens. The model supplies an ''anisotropy field scattering function'' that contains information on the magnitude of the magnetic anisotropy in the material, and on the characteristic length scales on which the anisotropy changes direction. The results suggest that the anisotropy may be strongly nonuniform in each crystallite, possibly due to twinning, and that some magnetic moments in the Ni samples are strongly pinned at defects.

We summarize recent theoretical and experimental work in the field of magnetic small-angle neutron scattering (SANS) of bulk ferromagnets. The response of the magnetization to spatially inhomogeneous magnetic anisotropy and magnetostatic stray fields is computed using linearized micromagnetic theory, and the ensuing spin-misalignment SANS is deduced. Analysis of experimental magnetic-field-dependent SANS data of various nanocrystalline ferromagnets corroborates the usefulness of the approach, which provides important quantitative information on the magnetic-interaction parameters such as the exchange-stiffness constant, the mean magnetic anisotropy field, and the mean magnetostatic field due to jumps ΔM of the magnetization at internal interfaces. Besides the value of the applied magnetic field, it turns out to be the ratio of the magnetic anisotropy field Hp to ΔM, which determines the properties of the magnetic SANS cross-section of bulk ferromagnets; specifically, the angular anisotropy on a two-dimensional detector, the asymptotic power-law exponent, and the characteristic decay length of spin-misalignment fluctuations. For the two most often employed scattering geometries where the externally applied magnetic field H0 is either perpendicular or parallel to the wave vector k0 of the incoming neutron beam, we provide a compilation of the various unpolarized, half-polarized (SANSPOL), and uniaxial fully-polarized (POLARIS) SANS cross-sections of magnetic materials.

No abstract

We report on the recently developed technique of magnetic-field-dependent small-angle neutron scattering (SANS), with attention to bulk ferromagnets exhibiting random magnetic anisotropy. In these materials, the various magnetic anisotropy fields (magnetocrystalline, magnetoelastic, and/or magnetostatic in origin) perturb the perfectly parallel spin alignment of the idealized ferromagnetic state. By varying the applied magnetic field, one can control one of the ordering terms which competes with the above-mentioned perturbing fields. Experiments which explore the ensuing reaction of the magnetization will therefore provide information not only on the field-dependent spin structure but, importantly, on the underlying magnetic interaction terms. This strategy, which underlies conventional studies of hysteresis loops in magnetometry, is here combined with magnetic SANS. While magnetometry generally records only a single scalar quantity, the integral magnetization, SANS provides access to a vastly richer data set, the Fourier spectrum of the response of the spin system as a function of the magnitude and orientation of the wave vector. The required data-analysis procedures have recently been established, and experiments on a number of magnetic materials, mostly nanocrystalline or nanocomposite metals, have been reported. Here, we summarize the theory of magnetic-field-dependent SANS along with the underlying description of random anisotropy magnets by micromagnetic theory. We review experiments which have explored the magnetic interaction parameters, the value of the exchange-stiffness constant as well as the Fourier components of the magnetic anisotropy field and of the magnetostatic stray field. A model-independent approach, based on the experimental autocorrelation function of the spin misalignment, provides access to the characteristic length of the spin misalignment. The field dependence of this quantity is in quantitative agreement with the predictions of micromagnetic theory. Experiments on nanocomposite ferromagnets reveal that the jump of the magnetization at internal phase boundaries leads to a significant magnetostatic perturbing field, with an unusual 'clover-leaf' SANS pattern as the experimental signature. Furthermore, SANS experiments have been used to monitor the orientation of magnetic domains as well as the length scale of intradomain spin misalignment.

No abstract