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

Abstract

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-

Range of Magnetic Correlations in Nanocrystalline Soft Magnets

“…By contrast, the field dependence of l C in NC Ni [ Fig. 3(b)] with an average crystallite size of D 49 nm indicates the presence of inhomogeneities in the anisotropy field on a scale smaller than D [4]; l C varies from about 45 nm at 39 mT to 13 nm at 1790 mT. The solid line in Fig.…”

“…As a case study, we determine the applied magnetic field dependence of the magnetic correlation length in NC electrodeposited Co and Ni, and we relate the values of the correlation length to characteristic microstructural length scales and to a prediction from micromagnetics theory. A preliminary study on NC Ni was published in a conference proceedings [4].…”

“…where V denotes the scattering volume, M s is the magni-tude of the magnetization vector Mx, and the function M p x represents the fluctuation of the local magnetization Mx about its position-independent average hMi, i.e., M p x Mx ÿ hMi. For isotropic systems Cr can be related to an experimental magnetic SANS cross section d mag =d according to [4,5] Cr…”

“…For the completely isotropic ferromagnet, at zero or vanishing applied magnetic fields, the parameter a in Eq. (2) takes on the value a 9 and, similarly, a 8 for the nearly saturated, texture-free ferromagnet, where variations of the magnetization are restricted to lie in a plane perpendicular to the applied field [4,5]. We are interested in evaluating a magnetic ''correlation length'' l C , i.e., 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.…”

“…The materials parameters used in the data analysis along with sample characterization (and correlation functions of NC Ni) can be found in Refs. [4,8].…”