Magnetic Guinier law

Small-angle scattering of x-rays and neutrons is a routine method for the determination of nanoparticle sizes. The so-called Guinier law represents the low-q approximation for the small-angle scattering curve from an assembly of particles. The Guinier law has originally been derived for nonmagnetic particle-matrix-type systems, and it is successfully employed for the estimation of particle sizes in various scientific domains (e.g., soft matter physics, biology, colloidal chemistry, materials science). An important prerequisite for it to apply is the presence of a discontinuous interface separating particles and matrix. Here, we introduce the Guinier law for the case of magnetic small-angle neutron scattering (SANS) and experimentally demonstrate its applicability for the example of nanocrystalline cobalt. It is well- known that the magnetic microstructure of nanocrystalline ferromagnets is highly nonuniform on the nanometer length scale and characterized by a spectrum of continuously varying long-wavelength magnetization fluctuations, i.e., these systems do not manifest sharp interfaces in their magnetization profile. The magnetic Guinier radius depends on the applied magnetic field, on the magnetic interactions (exchange, magnetostatics), and on the magnetic anisotropy-field radius, which characterizes the size over which the magnetic anisotropy field is coherently aligned into the same direction. In contrast to the nonmagnetic conventional Guinier law, the magnetic version can be applied to fully dense random-anisotropy-type ferromagnets

Microstructural-defect-induced Dzyaloshinskii-Moriya interaction

The antisymmetric Dzyaloshinskii?Moriya interaction (DMI) plays a decisive role for the stabilization and control of chirality of skyrmion textures in various magnetic systems exhibiting a noncentrosymmetric crystal structure. A less studied aspect of the DMI is that this interaction is believed to be operative in the vicinity of lattice imperfections in crystalline magnetic materials, due to the local structural inversion symmetry breaking. If this scenario leads to an effect of sizable magnitude, it implies that the DMI introduces chirality into a very large class of magnetic materials?defect-rich systems such as polycrystalline magnets. Here, we show experimentally that the microstructural-defect-induced DMI gives rise to a polarization-dependent asymmetric term in the small-angle neutron scattering (SANS) cross section of polycrystalline ferromagnets with a centrosymmetric crystal structure. The results are supported by theoretical predictions using the continuum theory of micromagnetics. This effect, conjectured already by Arrott in 1963, is demonstrated for nanocrystalline terbium and holmium (with a large grain-boundary density), and for mechanically deformed microcrystalline cobalt (with a large dislocation density). Analysis of the scattering asymmetry allows one to determine the defect-induced DMI constant, D=0.45±0.07mJ/m2 for Tb at 100K. Our study proves the generic relevance of the DMI for the magnetic microstructure of defect-rich ferromagnets with vanishing intrinsic DMI. Polarized SANS is decisive for disclosing the signature of the defect-induced DMI, which is related to the unique dependence of the polarized SANS cross section on the chiral interactions. The findings open up the way to study defect-induced skyrmionic magnetization textures in disordered materials

Evidence for the formation of nanoprecipitates with magnetically disordered regions in bulk Ni50Mn45In5 Heusler alloys

Shell ferromagnetism is a new functional property of certain Heusler alloys which has been recently observed in $\mathrm{Ni}_{50}\mathrm{Mn}_{45}\mathrm{In}_{5}$. We report the results of a comparative study of the magnetic microstructure of bulk $\mathrm{Ni}_{50}\mathrm{Mn}_{45}\mathrm{In}_{5}$ Heusler alloys using magnetometry, synchrotron x-ray diffraction, and magnetic small-angle neutron scattering (SANS). By combining unpolarized and spin-polarized SANS (POLARIS) we demonstrate that a number of important conclusions regarding the mesoscopic spin structure can be made. In particular, the analysis of the magnetic neutron data suggests that nanoprecipitates with an effective ferromagnetic component form in an antiferromagnetic matrix on field annealing at $700 \, \mathrm{K}$. These particles represent sources of perturbation, which seem to give rise to magnetically disordered regions in the vicinity of the particle-matrix interface. Analysis of the spin-flip SANS cross section via the computation of the correlation function yields a value of $\sim 55 \, \mathrm{nm}$ for the particle size and $\sim 20 \, \mathrm{nm}$ for the size of the spin-canted region.Comment: 11 pages, 8 figure

Magnetic Guinier Law and Uniaxial Polarization Analysis in Small Angle Neutron Scattering

The present PhD thesis is devoted to the development of the use of the magnetic small-angle neutron scattering (SANS) technique for analyzing the magnetic microstructures of magnetic materials. The emphasis is on the three aspects: (i) analytical development of the magnetic Guinier law; (ii) the application the magnetic Guinier law and of the generalized Guinier-Porod model to the analysis of experimental neutron data on various magnets such as a Nd-Fe-B nanocomposite, nanocrystalline cobalt, and Mn-Bi rare-earth-free permanent magnets; (iii) development of the theory of uniaxial neutron polarization analysis and experimental testing on a soft magnetic nanocrystalline alloy. The conventional “nonmagnetic” Guinier law represents the low-q approximation for the small-angle scattering curve from an assembly of particles. It has been derived for nonmagnetic particle-matrix-type systems and is routinely employed for the estimation of particle sizes in e.g., soft-matter physics, biology, colloidal chemistry, materials science. Here, the extension of the Guinier law is provided for magnetic SANS through the introduction of the magnetic Guinier radius, which depends on the applied magnetic field, on the magnetic interactions (exchange constant, saturation magnetization), and on the magnetic anisotropy-field radius. The latter quantity characterizes the size over which the magnetic anisotropy field is coherently aligned into the same direction. In contrast to the conventional Guinier law, the magnetic version can be applied to fully dense random-anisotropy-type ferromagnets. The range of applicability is discussed and the validity of the approach is experimentally demonstrated on a Nd-Fe-B-based ternary permanent magnet and on a nanocrystalline cobalt sample. Rare-earth-free permanent magnets in general and the Mn-Bi-based ones in particular have received a lot of attention lately due to their application potential in electronics devices and electromotors. Mn-Bi samples with three different alloy compositions were studied by means of unpolarized SANS and by very small-angle neutron scattering (VSANS). It turns out that the magnetic scattering of the Mn-Bi samples is determined by long-wavelength transversal magnetization fluctuations. The neutron data is analyzed in terms of the generalized Guinier-Porod model and the distance distribution function. The results for the so-called dimensionality parameter obtained from the Guinier-Porod model indicate that the magnetic scattering of a Mn$_{45}$Bi$_{55}$ specimen has its origin in slightly shape-anisotropic structures and the same conclusions are drawn from the distance distribution function analysis. Finally, based on Brown’s static equations of micromagnetics and the related theory of magnetic SANS, the uniaxial polarization of the scattered neutron beam of a bulk magnetic material is computed. The theoretical expressions are tested against experimental data on a soft magnetic nanocrystalline alloy, and both qualitative and quantitative correspondence is discussed. The rigorous analysis of the polarization of the scattered neutron beam establishes the framework for the emerging polarized real-space techniques such as spin-echo small-angle neutron scattering (SESANS), spin-echo modulated small-angle neutron scattering (SEMSANS), and polarized neutron dark-field contrast imaging (DFI), and opens up a new avenue for magnetic neutron data analysis on nanoscaled systems

Magnetic Guinier Law

We introduce the Guinier law for the case of magnetic SANS and provide an analysis of experimental data on a Nd-Fe-B-based nanocomposite and on a rare-earth-free MnBi permanent magnet. The robustness of this novel approach is discussed and the quantities derived are analyzed in the framework of the existing research literature

Uniaxial polarization analysis of bulk ferromagnets: theory and first experimental results

Based on Brown’s static equations of micromagnetics, the uniaxial polarization of the scattered neutron beam of a bulk magnetic material is computed. The approach considers a Hamiltonian that takes into account the isotropic exchange interaction, the antisymmetric Dzyaloshinskii–Moriya interaction, magnetic anisotropy, the dipole–dipole interaction, as well as the effect of an applied magnetic field. In the high-field limit, the solutions for the magnetization Fourier components are used to obtain closed-form results for the spinpolarized SANS (small-angle neutron scattering) cross sections and the ensuing polarization. The theoretical expressions are compared with experimental data on a soft magnetic nanocrystalline alloy. The micromagnetic SANS theory provides a general framework for polarized real-space neutron methods, and it may open up a new avenue for magnetic neutron data analysis on magnetic microstructures

Magnetic Guinier law

Small-angle scattering of X-rays and neutrons is a routine method for the determination of nanoparticle sizes. The so-called Guinier law represents the low-q approximation for the small-angle scattering curve from an assembly of particles. The Guinier law has originally been derived for nonmagnetic particle-matrix-type systems and it is successfully employed for the estimation of particle sizes in various scientific domains (e.g. soft-matter physics, biology, colloidal chemistry, materials science). An important prerequisite for it to apply is the presence of a discontinuous interface separating particles and matrix. Here, the Guinier law is introduced for the case of magnetic small-angle neutron scattering and its applicability is experimentally demonstrated for the example of nanocrystalline cobalt. It is well known that the magnetic microstructure of nanocrystalline ferromagnets is highly nonuniform on the nanometre length scale and characterized by a spectrum of continuously varying long-wavelength magnetization fluctuations, i.e. these systems do not manifest sharp interfaces in their magnetization profile. The magnetic Guinier radius depends on the applied magnetic field, on the magnetic interactions (exchange, magnetostatics) and on the magnetic anisotropy-field radius, which characterizes the size over which the magnetic anisotropy field is coherently aligned into the same direction. In contrast to the nonmagnetic conventional Guinier law, the magnetic version can be applied to fully dense random-anisotropy-type ferromagnets