A lower bound for the volume-averaged mean-square magnetostatic stray field

Abstract

Based on a micromagnetics model, we develop a method through which quantitative information on the volume-averaged mean-square magnetostatic stray field �| H b| 2 � v due to non-zero divergences of the magnetization M within the bulk of a ferromagnetic body can be obtained by analysis of magnetic-field- dependent small-angle neutron scattering data. In the limit of high applied magnetic field Ha, when the direction of M deviates only sligthly from Ha, we have estimated a lower bound for �| H b| 2 � v as a function of the external field, and we have applied the method to bulk samples of nanocrystalline electrodeposited Ni and Co and coarse-grained polycrystalline cold-worked Ni. The root-mean-square magnetostatic stray field, which is inherent to a particular magnetic microstructure, shows a pronounced field dependence, with values ranging from about 5 to 50 mT. Even at applied fields as large as 1. 7T , the quantityµ0�| H b| 2 � 1/2 v of nanocrystalline Co is still 24 mT, which suggests that contributions to the total magnetostatic field originating from the bulk are significant in nanocrystalline ferromagnets; therefore, �| H b| 2 � v cannot be ignored in the interpretation of e.g. measurements of magnetization or spin-wave resonance. A comparison of �| H b| 2 � v with the volume-averaged mean-square anisotropy field reveals that both quantities are of comparable magnitude.