Exchange-stiffness constant in cold-worked and nanocrystalline Ni measured by elastic small-angle neutron scattering

We present a new method for determining the exchange-stiffness constant A of a ferromagnetic bulk material by field-dependent elastic small-angle neutron scattering (SANS). In the limit of high applied magnetic field H, for which the scattering volume is a single magnetic domain and the magnetization is nearly aligned with the direction of the applied field, a combination of micromagnetics theory with neutron scattering formalism suggests closed-form expressions for the differential scattering cross section as a function of the scattering vector and of H. Based on these results it is suggested that the exchange-stiffness constant can be extracted from experimental SANS data recorded as a function of H. At ambient temperature we have applied this method to polycrystalline cold-worked Ni and nanocrystalline electrodeposited Ni, finding exchange-stiffness constants of (8.2±0.2)×10−12 and (7.6±0.3)×10−12  J/m, respectively. Measurement at 5 K yields a value of (9.2±0.2)×10−12 J/m for the nanocrystalline sample, a temperature dependence that agrees qualitatively with data in the literature. In addition to the value of A, the technique supplies information on the spatial structure of the magnetic anisotropy field.