Magnetic Guinier law

Andreas Michels, Artem Malyeyev, Ivan Titov, Dirk Honecker, Robert Cubitt, Elizabeth Blackburn, Kiyonori Suzuki

Research output: Contribution to journalArticleResearchpeer-review

4 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)136-142
Number of pages7
Issue number1
Publication statusPublished - Jan 2020


  • anisotropy
  • ferromagnets
  • Guinier law
  • magnetic materials
  • magnetic scattering
  • micromagnetics
  • nanoscience
  • small-angle neutron scattering

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