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The magnetization profile and the related magnetic small-angle neutronscattering cross section of a single spherical nanoparticle with Neel surfaceanisotropy is analytically investigated. We employ a Hamiltonian that comprisesthe isotropic exchange interaction, an external magnetic field, a uniaxialmagnetocrystalline anisotropy in the core of the particle, and the Neelanisotropy at the surface. Using a perturbation approach, the determination ofthe magnetization profile can be reduced to a Helmholtz equation with Neumannboundary condition, whose solution is represented by an infinite series interms of spherical harmonics and spherical Bessel functions. From the resultinginfinite series expansion, we analytically calculate the Fourier transform,which is algebraically related to the magnetic small-angle neutron scatteringcross section. The approximate analytical solution is compared to the numericalsolution using the Landau-Lifshitz equation, which accounts for the fullnonlinearity of the problem.

Magnetic neutron scattering from spherical nanoparticles with Neel surface anisotropy: Analytical treatment