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

Abstract

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 ${\mathbf{H}}_{p}(\mathbf{x})$, 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 ${\mathbf{H}}_{p}(\mathbf{x})$. 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 ${l}_{C}$ 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 ${l}_{C}({H}_{i})=\mathcal{L}+{l}_{H}({H}_{i})$, where the field-independent quantity $\mathcal{L}$ is on the order of the particle size and ${l}_{H}({H}_{i})$ represents the so-called exchange length of the applied magnetic field.