Random Anisotropy Model for Nanocrystalline Soft Magnetic Alloys with Grain-Size Distribution

Teruo Bitoh, Akihiro Makino, Akihisa Inoue, Tsuyoshi Masumoto

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44 Citations (Scopus)


A simple model considering grain-size distribution is proposed based on the random anisotropy model. When the maximum grain size (Dm) is less than the exchange correlation length and induced anisotropies are sufficiently small, the effective magnetic anisotropy constant («K 1») is given by using a distribution function (f(D)) for the grain size (D) as «K1» ≈ K1 4{∫0Dm D3 f(D)dD} 2/(φ6Ac3), where K1 is the magnetocrystalline anisotropy constant, φ is a parameter which reflects both the symmetry of «K1» and the total spin rotation angle over the exchange-correlated coupling chain and Ac is the exchange stiffness constant. The log-normal distribution function reproduces well the observed grain-size distribution and yields «K 1» ≈ K14 «D»6 exp(6σD2)/(φ6Ac 3), where «D» is the mean grain size and σ D is the geometric standard deviation for the distribution. This result satisfies the well-known «D»6 law. However, «K1» increases with increasing σD even if «D» is constant. Our model has been extended by taking into account the effect of the coherent induced anisotropies on the exchange correlation length. The coercivity (Hc ∝ «K 1»/Js where Js, is the saturation magnetization) of the nanocrystalline Fe-Nb-B(-P-Cu) alloys with different grain-size distribution have been calculated. Our model explains well the dependence of Hc on the grain-size distribution. These results suggest that one should pay attention on not only the mean grain size but also on the grain-size distribution since the inhomogeneity of the grain size increases Hc.

Original languageEnglish
Pages (from-to)2011-2019
Number of pages9
JournalMaterials Transactions
Issue number10
Publication statusPublished - 2003 Oct
Externally publishedYes


  • Grain-size distribution
  • Nanocrystalline soft magnetic alloy
  • Random anisotropy model
  • Structural inhomogeneity

ASJC Scopus subject areas

  • Materials Science(all)
  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering


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