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We investigate the signature of magnetic surface anisotropy in nanoparticlesin their spin-flip neutron scattering cross section. Taking into account theisotropic exchange interaction, an external magnetic field, a uniaxial or cubicmagnetic anisotropy for the particle's core, and several models for the surfaceanisotropy (N\'eel, conventional, random), we compute the spin-flip small-angleneutron scattering (SANS) cross section from the equilibrium spin structuresobtained using the Landau-Lifshitz equation. The sign of the surface anisotropyconstant, which is related to the appearance of tangential- or radial-like spintextures, can be distinguished from the momentum-transfer dependence of thespin-flip signal. The data cannot be described by the well-known and often-usedanalytical expressions for uniformly magnetized spherical or core-shellparticles, in particular at remanence or at the coercive field. Based on asecond-order polynomial expansion for the magnetization vector field, wedevelop a novel minimal model for the azimuthally-averaged magnetic SANS crosssection. The theoretical expression considers a general magnetizationinhomogeneity and is not restricted to the presence of surface anisotropy. Itis shown that the model describes very well our simulation data as well as morecomplex spin patterns such as vortex-like structures. Only seven expansioncoefficients and some basis functions are sufficient to describe the scatteringbehavior of a very large number of atomic spins.

Signature of surface anisotropy in the spin-flip neutron scattering  cross section of spherical nanoparticles: atomistic simulations and  analytical theory