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

摘要

A simple model considering grain-size distribution is proposed based on the random anisotropy model. When the maximum grain size (D{sub}m) is less than the exchange correlation length and induced anisotropies are sufficiently small, the effective magnetic anisotropy constant () is given by using a distribution function (f(D)) for the grain size (D) as ≈ K{sub}1{sup}4{∫(D{sup}3f(D)dD) (D from 0 to D{sub}m)}{sup}2/(φ{sup}6A{sub}c{sup}3), where K{sub}1 is the magnetocrystalline anisotropy constant, φ is a parameter which reflects both the symmetry of and the total spin rotation angle over the exchange-correlated coupling chain and A{sub}c is the exchange stiffness constant. The log-normal distribution function reproduces well the observed grain-size distribution and yields ≈ K{sub}1{sup}4 {sup}6 exp(6σ{sub}D{sup}2)/(φ{sup}6A{sub}c{sup}3), where is the mean grain size and σ{sub}D is the geometric standard deviation for the distribution. This result satisfies the well-known {sup}6 law. However, increases with increasing σ{sub}D even if 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 (H{sub}c ∝ /J{sub}s, where J{sub}s 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 H{sub}c 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 H{sub}c.