Magnetic small-angle neutron scattering by nanocrystalline terbium

Weißmüller, J.; Michels, D.; Michels, Andreas; Wiedenmann, A.; Krill, Carl E.; Sauer, H.; Birringer, R.

doi:10.1016/s1359-6462(01)00774-6

Cited by 3 publications

(7 citation statements)

References 7 publications

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“…For a completely isotropic ferromagnet, at zero or vanishing internal fields, the parameter a in Eq. (2) takes on the value a ¼ 9, and, similarly, a ¼ 8 for the nearly saturated, texture-free ferromagnet, where the variation of the magnetization is confined to the plane perpendicular to the applied field [6] (the value a ¼ 8 for the nearly saturated ferromagnet corrects the erroneous value a ¼ 32/p reported in Ref. [6]).…”

Section: The Correlation Function Of the Spin Misalignmentmentioning

confidence: 72%

“…(2) takes on the value a ¼ 9, and, similarly, a ¼ 8 for the nearly saturated, texture-free ferromagnet, where the variation of the magnetization is confined to the plane perpendicular to the applied field [6] (the value a ¼ 8 for the nearly saturated ferromagnet corrects the erroneous value a ¼ 32/p reported in Ref. [6]). We are interested in evaluating a magnetic "correlation length" l C , that is, a characteristic dimension of regions in which the magnetic moments are coherently misaligned in the same direction relative to the direction of the mean magnetization hMi.…”

Section: The Correlation Function Of the Spin Misalignmentmentioning

confidence: 79%

“…For isotropic systems, C(r) can be related to an experimental magnetic SANS cross-section dS mag /dW [6],…”

Section: The Correlation Function Of the Spin Misalignmentmentioning

confidence: 99%

“…There are various ways for defining and measuring l C , for instance in terms of the initial slope of C(r) (compare Ref. [6]). As a robust measure, which is independent of small oscillations of C at small r, we shall here identify l C with the value of r for which C is decreased to 1/e of the extrapolated value at r ¼ 0.…”

Section: The Correlation Function Of the Spin Misalignmentmentioning

confidence: 99%

“…Moreover, the technique of SANS is capable of resolving the magnetic microstructure in the bulk and on a length scale of a few nanometers, so that SANS may supplement surface sensitive methods such as Kerr-, magnetic forceor Lorentz microscopy. SANS studies do exist on soft magnetic [2][3][4][5] as well as on hard magnetic [6] single-component nc ferromagnets.…”

Section: Introductionmentioning

confidence: 99%

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Measurement of a Magnetic-Field Dependent Correlation Length in Nanocrystalline Ni Using Small-Angle Neutron Scattering

Michels

Weißmüller²,

Erb

et al. 2002

phys. stat. sol. (a)

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We have analyzed magnetic-field dependent small-angle neutron scattering data on nanocrystalline electrodeposited Ni by means of the correlation function of the spin misalignment. The approach yields a correlation length l C of the spin misalignment that is a measure for the characteristic dimension of regions in which the magnetic moments are misaligned coherently into a common direction. We find that l C varies strongly with the applied magnetic field H i with values extending from about 50 nm (larger than the value for uniformly magnetized grains) at small H i to about 10 nm (considerably smaller than the grain size) at large applied fields. IntroductionIn nanocrystalline (nc) ferromagnets the direction and/or the strength of the magnetic anisotropy field changes randomly on a length scale of the order of the average grain size D which is typically about 10 nm. The static magnetic microstructure of nanocrystalline ferromagnets is therefore, compared to their microcrystalline counterparts, highly nonuniform on a nanometer scale, and this inhomogeneity results in a strong elastic magnetic neutron scattering signal at small scattering angles. This fact combined with the recent availability of high-purity, porosity-free electrodeposited nc soft magnets [1], where the ratio of interesting magnetic scattering to nuclear background is favorably high, render such samples attractive for studies by magnetic smallangle neutron scattering (SANS). Moreover, the technique of SANS is capable of resolving the magnetic microstructure in the bulk and on a length scale of a few nanometers, so that SANS may supplement surface sensitive methods such as Kerr-, magnetic forceor Lorentz microscopy. SANS studies do exist on soft magnetic [2][3][4][5] as well as on hard magnetic [6] single-component nc ferromagnets.Here, we present a SANS study of the field dependence of the magnetic microstructure of nc Ni. Our previous analysis of SANS by soft magnets was based on a micromagnetics model which requires the material to be nearly saturated, and which supplies information on the magnetic interactions. Here, we employ a model-independent approach, which ignores the magnetic interactions, but which remains valid far from sa-

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Section: The Correlation Function Of the Spin Misalignmentmentioning

confidence: 72%

Section: The Correlation Function Of the Spin Misalignmentmentioning

confidence: 79%

“…For isotropic systems, C(r) can be related to an experimental magnetic SANS cross-section dS mag /dW [6],…”

Section: The Correlation Function Of the Spin Misalignmentmentioning

confidence: 99%

Section: The Correlation Function Of the Spin Misalignmentmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Measurement of a Magnetic-Field Dependent Correlation Length in Nanocrystalline Ni Using Small-Angle Neutron Scattering

Michels

Weißmüller²,

Erb

et al. 2002

phys. stat. sol. (a)

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Small-angle neutron scattering

Modern Techniques for Characterizing Magnetic Materials

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Abstract. Small Angle Neutron Scattering (SANS) is a technique that enables to probe the 3-D structure of materials on a typical size range lying from ∼ 1 nm up to ∼ a few 100 nm, the obtained information being statistically averaged on a sample whose volume is ∼ 1 cm 3 . This very rich technique enables to make a full structural characterization of a given object of nanometric dimensions (radius of gyration, shape, volume or mass, fractal dimension, specific area. . . ) through the determination of the form factor as well as the determination of the way objects are organized within in a continuous media, and therefore to describe interactions between them, through the determination of the structure factor. The specific properties of neutrons (possibility of tuning the scattering intensity by using the isotopic substitution, sensitivity to magnetism, negligible absorption, low energy of the incident neutrons) make it particularly interesting in the fields of soft matter, biophysics, magnetic materials and metallurgy. In particular, the contrast variation methods allow to extract some informations that cannot be obtained by any other experimental techniques. This course is divided in two parts. The first one is devoted to the description of the principle of SANS: basics (formalism, coherent scattering/incoherent scattering, notion of elementary scatterer), form factor analysis (I(q→0), Guinier regime, intermediate regime, Porod regime, polydisperse system), structure factor analysis (2 nd Virial coefficient, integral equations, characterization of aggregates), and contrast variation methods (how to create contrast in an homogeneous system, matching in ternary systems, extrapolation to zero concentration, Zero Averaged Contrast). It is illustrated by some representative examples. The second one describes the experimental aspects of SANS to guide user in its future experiments: description of SANS spectrometer, resolution of the spectrometer, optimization of spectrometer configurations, optimization of sample characteristics prior to measurements (thickness, volume, hydrogen content. . . ), standards measurements to be made and principle of data reduction.Résumé. (La Diffusion de Neutrons aux petits angles (DNPA) est une technique permettant de sonder la structure 3-D de matériaux sur une gamme typique de taille comprise entre ∼1 nm) et ∼ quelques 100 nm, les informations obtenues étant statistiquement moyennées sur la taille de l'échantillon dont le volume est d'environ 1 cm 3 . C'est une technique très puissante car elle permet de faire une caractérisation complète de la structure d'un objet donné de dimensions nanométriques (rayon de giration, forme, volume, masse, dimension fractale, surface spécifique. . . ) grâce à la détermination du facteur de forme, ainsi que la détermination de la manière dont les objets sont organisés au sein d'un milieu continu, et donc de décrire les interactions entre les objets, par la détermination du facteur de structure. Les propriétés spécifiques de neutrons (possibilité de modul...

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Range of Magnetic Correlations in Nanocrystalline Soft Magnets

Michels

Viswanath²,

Barker

et al. 2003

Phys. Rev. Lett.

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We have obtained the magnetic field dependence of static ferromagnetic correlations in nanocrystalline electrodeposited Co and Ni by means of the correlation function of the spin misalignment, determined from small-angle neutron scattering data. The approach yields a correlation length l(C), which is a measure for the spatial extent of inhomogeneities in the magnetization distribution. The correlation length depends strongly on the applied magnetic field with values ranging from 94 nm in nanocrystalline Co at low fields to about 15 nm at saturation. The results for l(C) indicate that in Co the main source of nonuniformity in the spin system is the anisotropy field of each individual crystallite, whereas in nanocrystalline Ni the main sources of spin disorder originate from twin faults or from the defect cores of grain boundaries.

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Magnetic small-angle neutron scattering by nanocrystalline terbium

Cited by 3 publications

References 7 publications

Measurement of a Magnetic-Field Dependent Correlation Length in Nanocrystalline Ni Using Small-Angle Neutron Scattering

Measurement of a Magnetic-Field Dependent Correlation Length in Nanocrystalline Ni Using Small-Angle Neutron Scattering

Small-angle neutron scattering

Range of Magnetic Correlations in Nanocrystalline Soft Magnets

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