Correlation functions of the spin misalignment in magnetic small-angle neutron scattering

We have numerically calculated the autocorrelation function C(r) of the spin misalignment by means of micromagnetic theory. C(r) depends sensitively on the details of the underlying magnetic microstructure and can be determined by Fourier inversion of magnetic small-angle neutron scattering data. The model system which we consider consists of a single isolated spherical nanoparticle that is embedded in an infinitely extended matrix. The particle is uniquely characterized by its magnetic anisotropy field Hp(x), whereas the matrix is assumed to be otherwise anisotropy-field free. In the approach-to-saturation regime, we have computed the static response of the magnetization to different spatial profiles of Hp(x). Specifically, we have investigated the cases of a uniform particle anisotropy, uniform core shell, linear increase, and exponential and power-law decay. From the magnetization profiles and the associated C(r), we have extracted the correlation length lc of the spin misalignment, and we have compared the applied-field dependence of this quantity with semiquantitative theoretical predictions. We find that for practically all of the considered models for the anisotropy field (except the core-shell model) the field dependence of the spin-misalignment fluctuations is quite uniquely reproduced by lc(Hi)=L+lh(Hi), where the field-independent quantity L is on the order of the particle size and lh(Hi) represents the so-called exchange length of the applied magnetic field.