Magnetic Small-angle Neutron Scattering Research Articles

On the angular anisotropy of the randomly averaged magnetic neutron scattering cross section of nanoparticles.

The magnetic small-angle neutron scattering (SANS) cross section of dilute ensembles of uniformly magnetized and randomly oriented Stoner-Wohlfarth particles is calculated using the Landau-Lifshitz equation. The focus of this study is on the angular anisotropy of the magnetic SANS signal as it can be seen on a two-dimensional position-sensitive detector. Depending on the symmetry of the magnetic anisotropy of the particles (e.g. uniaxial, cubic), an anisotropic magnetic SANS pattern may result, even in the remanent state or at the coercive field. The case of inhomogeneously magnetized particles and the effects of a particle-size distribution and interparticle correlations are also discussed.

Resolving the Complex Spin Structure in Fe-Based Soft Magnetic Nanocrystalline Material by Magnetic Small-Angle Neutron Scattering

Resolving the Complex Spin Structure in Fe-Based Soft Magnetic Nanocrystalline Material by Magnetic Small-Angle Neutron Scattering

Toward Understanding Complex Spin Textures in Nanoparticles by Magnetic Neutron Scattering.

In the quest to image the three-dimensional magnetization structure we show that the technique of magnetic small-angle neutron scattering (SANS) is highly sensitive to the details of the internal spin structure of nanoparticles. By combining SANS with numerical micromagnetic computations we study the transition from single-domain to multidomain behavior in nanoparticles and its implications for the ensuing magnetic SANS cross section. Above the critical single-domain size we find that the cross section and the related correlation function cannot be described anymore with the uniform particle model, resulting, e.g., in deviations from the well-known Guinier law. In the simulations we identify a clear signature for the occurrence of a vortexlike spin structure at remanence. The micromagnetic approach to magnetic SANS bears great potential for future investigations, since it provides fundamental insights into the mesoscale magnetization profile of nanoparticles.

Unraveling Nanostructured Spin Textures in Bulk Magnets

One of the key challenges in magnetism remains the determination of the nanoscopic magnetization profile within the volume of thick samples, such as permanent ferromagnets. Thanks to the large penetration depth of neutrons, magnetic small‐angle neutron scattering (SANS) is a powerful technique to characterize bulk samples. The major challenge regarding magnetic SANS is accessing the real‐space magnetization vector field from the reciprocal scattering data. In this study, a fast iterative algorithm is introduced that allows one to extract the underlying 2D magnetic correlation functions from the scattering patterns. This approach is used here to analyze the magnetic microstructure of Nanoperm, a nanocrystalline alloy which is widely used in power electronics due to its extraordinary soft magnetic properties. It can be shown that the computed correlation functions clearly reflect the projection of the 3D magnetization vector field onto the detector plane, which demonstrates that the used methodology can be applied to probe directly spin textures within bulk samples with nanometer resolution.

Magnetic structure factor of correlated moments in small-angle neutron scattering

The interplay between structural and magnetic properties of nanostructured magnetic materials allows to realize unconventional magnetic effects, which results in a demand for experimental techniques to determine the magnetization profile with nanoscale resolution. Magnetic small-angle neutron scattering (SANS) probes both the chemical and magnetic nanostructure and is thus a powerful technique e.g. for the characterization of magnetic nanoparticles. Here, we show that the conventionally used particle-matrix approach to describe SANS of magnetic particle assemblies, however, leads to a flawed interpretation. As remedy, we provide general expressions for the field-dependent 2D magnetic SANS cross-section of correlated moments. It is shown that for structurally disordered ensembles the magnetic structure factor is in general, and contrary to common assumptions, (i) anisotropic also in zero field, and (ii) that even in saturation the magnetic structure factor deviates from the nuclear one. These theoretical predictions explain qualitatively the intriguing experimental, polarized SANS data of an ensemble of dipolar-coupled iron oxide nanoparticles.

Small-angle neutron scattering modeling of spin disorder in nanoparticles

Magnetic small-angle neutron scattering (SANS) is a powerful technique for investigating magnetic nanoparticle assemblies in nonmagnetic matrices. For such microstructures, the standard theory of magnetic SANS assumes uniformly magnetized nanoparticles (macrospin model). However, there exist many experimental and theoretical studies which suggest that this assumption is violated: deviations from ellipsoidal particle shape, crystalline defects, or the interplay between various magnetic interactions (exchange, magnetic anisotropy, magnetostatics, external field) may lead to nonuniform spin structures. Therefore, a theoretical framework of magnetic SANS of nanoparticles needs to be developed. Here, we report numerical micromagnetic simulations of the static spin structure and related unpolarized magnetic SANS of a single cobalt nanorod. While in the saturated state the magnetic SANS cross section is (as expected) determined by the particle form factor, significant deviations appear for nonsaturated states; specifically, at remanence, domain-wall and vortex states emerge which result in a magnetic SANS signal that is composed of all three magnetization Fourier components, giving rise to a complex angular anisotropy on a two-dimensional detector. The strength of the micromagnetic simulation methodology is the possibility to decompose the cross section into the individual Fourier components, which allows one to draw important conclusions regarding the fundamentals of magnetic SANS.

A neutron diffraction study of the hexagonal Laves phases, Ho(Co0.667Ga0.333)2 and Er(Co0.667Ga0.333)2: Co/Ga site preferences and magnetic structure

RE(Co0.667Ga0.333)2 (RE = Ho, Er) were characterized by neutron powder diffraction (NPD). Rietveld refinement of the NPD data at 280K confirms the hexagonal MgZn2-type structure (P63/mmc), in accordance with the previous XRD results. Co/Ga occupancies on the 2a and 6h sites were refined to be 0.46/0.54(2) and 0.74/0.26(2), respectively, indicating a preference of Ga for the 2a site and of Co for the 6h site. Both materials are ferromagnetic, k = (000), with measureable moments only on the RE sites. The magnetic (Shubnikov) space group is P63/mm′c′ for the Er phase. Co moments refined to values of 0.1–0.3 μB and are effectively zero within 3σ. The Er moment, 6.07(8) μB at 3.5K is parallel to the c axis and this orientation persists up to TC = 18.5K, while the Ho moment has components along both the a and c axes with a total moment of 6.3(1) μB at 3.5K. Both moments are much reduced from the free ion values, 9 μB (Er) and 10 μB (Ho), which is attributed to crystal field effects. In addition, the Ho moment angle with the c axis is strongly temperature dependent, being roughly constant, ~ 24(6)° from T = 29K to ~25K, then increasing with decreasing temperature to 44(1)° at 3.5K. Magnetic small angle neutron scattering (MSANS) was observed over a Q-range from 0.14Å−1 to 0.50Å−1 in both samples. The integrated MSANS of the Er phase peaks near TC, then decreases monotonically with decreasing temperature, behavior typical for a simple ferromagnet. On the other hand, the integrated MSANS for the Ho phase exhibits a weak peak around TC = 31K, followed by a plateau to 25K and a strong increase with decreasing temperatures, which tracks the evolution of the Ho moment angle with the c axis.

Individual-collective crossover driven by particle size in dense assemblies of superparamagnetic nanoparticles

Prussian blue analogues (PBA) ferromagnetic nanoparticles Cs I x Ni II [Cr III (CN)6 ] z ·3(H2O) embedded in CTA+ (cetyltrimethylammonium) matrix have been investigated by magnetometry and magnetic small-angle neutron scattering (SANS). Choosing particle sizes (diameter D = 4.8 and 8.6 nm) well below the single-domain radius and comparable volume fraction of particle, we show that the expected superparamagnetic regime for weakly anisotropic isolated magnetic particles is drastically affected due to the interplay of surface/volume anisotropies and dipolar interactions. For the smallest particles (D = 4.8 nm), magnetocrystalline anisotropy is enhanced by surface spins and drives the system into a regime of ferromagnetically correlated clusters characterized by a temperature-dependent magnetic correlation length L mag which is experimentally accessible using magnetic SANS. For D = 8.6 nm particles, a superparamagnetic regime is recovered in a wide temperature range. We propose a model of interacting single-domain particles with axial anisotropy that accounts quantitatively for the observed behaviors in both magnetic regimes.

Spin Structures of Textured and Isotropic Nd-Fe-B-Based Nanocomposites: Evidence for Correlated Crystallographic and Spin Textures

We report the results of a comparative study of the magnetic microstructure of textured and isotropic $\mathrm{Nd}_2\mathrm{Fe}_{14}\mathrm{B}/\alpha$-$\mathrm{Fe}$ nanocomposites using magnetometry, transmission electron microscopy, synchrotron x-ray diffraction, and, in particular, magnetic small-angle neutron scattering (SANS). Analysis of the magnetic neutron data of the textured specimen and computation of the correlation function of the spin misalignment SANS cross section suggests the existence of inhomogeneously magnetized regions on an intraparticle nanometer length scale, about $40-50 \, \mathrm{nm}$ in the remanent state. Possible origins for this spin disorder are discussed: it may originate in thin grain-boundary layers (where the materials parameters are different than in the $\mathrm{Nd}_2\mathrm{Fe}_{14}\mathrm{B}$ grains), or it may reflect the presence of crystal defects (introduced via hot pressing), or the dispersion in the orientation distribution of the magnetocrystalline anisotropy axes of the $\mathrm{Nd}_2\mathrm{Fe}_{14}\mathrm{B}$ grains. X-ray powder diffraction data reveal a crystallographic texture in the direction perpendicular to the pressing direction -- a finding which might be related to the presence of a texture in the magnetization distribution, as inferred from the magnetic SANS data.

Third-order effect in magnetic small-angle neutron scattering by a spatially inhomogeneous medium

Magnetic small-angle neutron scattering (SANS) is a powerful tool for investigating nonuniform magnetization structures inside magnetic materials. Here, we consider a ferromagnetic medium with weakly inhomogeneous uniaxial magnetic anisotropy, saturation magnetization, and exchange stiffness, and derive, to second order in the amplitudes of the inhomogeneities, the micromagnetic solutions for the equilibrium magnetization textures. Further, we compute the corresponding magnetic SANS cross section up to the third order. For the special case of scattering geometry where the incident neutron beam is perpendicular to the applied magnetic field, twice the cross section along the direction orthogonal to both the field and the neutron beam cancels the cross section along the field direction in the second order. This cancellation does not depend on the defect shape and amplitudes of the exchange inhomogeneities. Hence, such a cross-section difference has only a third-order contribution in the amplitudes of the inhomogeneities. It provides a separate gateway for a deeper analysis of the sample's magnetic structure. We derive and analyze analytical expressions for the dependence of this difference on the scattering-vector magnitude for the case of spherical Gaussian inhomogeneities.

Micromagnetic simulation of magnetic small-angle neutron scattering from two-phase nanocomposites

The recent development of a micromagnetic simulation methodology—suitable for multiphase magnetic nanocomposites—permits the computation of the magnetic microstructure and of the associated magnetic small-angle neutron scattering (SANS) cross section of these materials. In this review we summarize results on the micromagnetic simulation of magnetic SANS from two-phase nanocomposites. The decisive advantage of this approach resides in the possibility to scrutinize the individual magnetization Fourier contributions to the total magnetic SANS cross section, rather than their sum, which is generally obtained from the experiment. The procedure furnishes unique and fundamental information regarding magnetic neutron scattering from nanomagnets.

Theory of magnetic small-angle neutron scattering of two-phase ferromagnets

Based on micromagnetic theory we have derived analytical expressions for the magnetic small-angle neutron scattering (SANS) cross section of a two-phase particle-matrix-type ferromagnet. The approach---valid close to magnetic saturation---provides access to several features of the spin structure such as perturbing magnetic anisotropy and magnetostatic fields. Depending on the applied magnetic field and on the magnitude $H_p$ of the magnetic anisotropy field relative to the magnitude $\Delta M$ of the jump in the longitudinal magnetization at the particle-matrix interface, we observe a variety of angular anisotropies in the magnetic SANS cross section. In particular, the model explains the "clover-leaf"-shaped angular anisotropy which was previously observed for several nanostructured magnetic materials, and it provides access to the magnetic interaction parameters such as the average exchange-stiffness constant. It is also shown that the ratio $H_p / \Delta M$ decisively determines the asymptotic power-law exponent and the range of spin-misalignment correlations.

Small-angle neutron scattering study of magnetic ordering and inhomogeneity across the martensitic phase transformation in Ni50−xCoxMn40Sn10alloys

The Heusler-derived multiferroic alloy Ni${}_{50\ensuremath{-}x}$Co${}_{x}$Mn${}_{40}$Sn${}_{10}$ has recently been shown to exhibit, at just above room temperature, a highly reversible martensitic phase transformation with an unusually large magnetization change. In this work the nature of the magnetic ordering above and below this transformation has been studied in detail in the critical composition range $x$ $=$ 6--8 via temperature-dependent (5--600 K) magnetometry and small-angle neutron scattering (SANS). We observe fairly typical paramagnetic to long-range-ordered ferromagnetic phase transitions on cooling to 420--430 K, with the expected critical spin fluctuations, followed by first-order martensitic phase transformations to a nonferromagnetic state below 360--390 K. The static magnetization reveals complex magnetism in this low-temperature nonferromagnetic phase, including a Langevin-like field dependence, distinct spin freezing near 60 K, and significant exchange bias effects, consistent with superparamagnetic blocking of ferromagnetic clusters of nanoscopic dimensions. We demonstrate that these spin clusters, whose existence has been hypothesized in a variety of martensitic alloys exhibiting competition between ferromagnetic and antiferromagnetic exchange interactions, can be directly observed by SANS. The scattering data are consistent with a liquidlike spatial distribution of interacting magnetic clusters with a mean center-to-center spacing of 12 nm. Considering the behavior of the superparmagnetism, cooling-field and temperature-dependent exchange bias, and magnetic SANS, we discuss in detail the physical form and origin of these spin clusters, their intercluster interactions, the nature of the ground-state magnetic ordering in the martensitic phase, and the implications for our understanding of such alloy systems.

Small-angle Neutron Scattering with One-dimensional Polarization Analysis

Magnetic small-angle neutron scattering (SANS) is a widely used technique for the investigation of nanoscale inhomogeneities in the magnetic microstructure of bulk materials [1,2]. However, up to now, magnetic SANS was almost exclusively utilized with an unpolarized or a polarized incident neutron beam – denoted as SANSPOL – and an analysis of the spin state of the neutron after the scattering process is generally not performed. Due to recent progress in the development of efficient 3He spin filters [3], it has only now become possible to perform routinely one-dimensional (longitudinal or uniaxial) neutron-polarization analysis (so-called POLARIS) in a SANS experiment, for instance, at V4 at HZB [4], at beamline NG3 at NIST [5–7], or at the instrument D22 at the ILL [8,9]. The principle of operation of such an analyzing device relies on the spin-dependent absorption of neutrons by a nuclear-spin-polarized gas of 3He atoms. Essentially, the decisive advantages of 3He spin filters as compared to other polarizing/analyzing devices are (i) that they can be used over a rather broad wavelength band (from cold to thermal to hot neutrons) and (ii) that they allow for a rather large phase space (neutron-energy transfer and scattering angle) to be covered.

The use of magnetic small angle neutron scattering for the detection of flow profiles in magnetic fluids

We have investigated the possibility of using magnetic small angle neutron scattering (MSANS) to detect the flow pattern of flow in concentrated magnetic fluids. It has been shown that the anisotropy of the scattering pattern can be determined with appropriate accuracy allowing to identify changes of the anisotropy induced by different flow states. These changes can be used as a measure for flow characteristics in the fluids. In this paper we present the general idea and an experimental demonstration of the concept using a simple convective flow pattern.

Microstructural characterisation of F82H-mod. steel using small-angle neutron scattering

Small-angle neutron scattering (SANS) measurements have been carried out on samples of F82H-mod. martensitic steel submitted to different treatments: (a) hardening, (b) tempering and (c) ageing. Size distribution functions referable to the precipitates, formed during the different treatments are obtained both for nuclear and magnetic SANS components. The results, discussed making reference to transmission electron microscopy (TEM) observations and microhardness measurements, show that while samples of groups (a) and (c) exhibit a stable microstructure, marked differences are detected varying the tempering temperature, especially at 550°C (where a fine precipitation is observed) and for temperatures higher than 850°C (formation of delta ferrite).

Segregation and speromagnetic order in amorphous Tb0.18Si0.82 detected by neutron scattering at small and large angles

Abstract Amorphous Tb0.18Si0.82 has been investigated at low temperatures by neutron diffraction (ND) and small angle neutron scattering (SANS). Below the magnetic ordering temperature, magnetic ND rings are observable between the nuclear rings, but no magnetic SANS is detectable at low q (q = 4π sin θ/γ) values where nuclear SANS is intense. From these observations and the comparison with the antiferromagnetic order in crystalline TbSi1.67 alloy, a phase segregation and a speromagnetic order in amorphous Tb0.18Si0.82 with magnetic moment values of about 4μB/Tb and compensation of the magnetic moments over very small distances are proposed.