We have numerically calculated the autocorrelation function $C\left(r\right)$ of the spin misalignment by means of micromagnetic theory. $C\left(r\right)$ 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 ${\mathbf{H}}_p\left(\mathbf{x}\right)$, 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 ${\mathbf{H}}_p\left(\mathbf{x}\right)$. 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 $C\left(r\right)$, 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 $l_C\left(H_i\right)=\mathcal{L}+l_H\left(H_i\right)$, where the field-independent quantity $\mathcal{L}$ is on the order of the particle size and $l_H\left(H_i\right)$ represents the so-called exchange length of the applied magnetic field.

• Received 4 May 2010

DOI:https://doi.org/10.1103/PhysRevB.82.024433