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

摘要

Based on a micromagnetics model, we develop a method through which quantitative information on the volume-averaged mean-square magnetostatic stray field <|H_d~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 H_a, when the direction of M deviates only sligthly from H_a, have estimated a lower bound for <|H_d~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 quantity μ_0 <|H_d~b|~2>_v~(1/2) 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_d~b|~2>_v cannot be ignored in the interpretation of e.g. measurements of magnetization or spin-wave resonance. A comparison of <|H_d~b|~2>_v with the volume-averaged mean-square anisotropy field reveals that both quantities are of comparable magnitude.