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

TL;DR

This paper provides an analytical model for the magnetization profile and neutron scattering cross section of spherical nanoparticles with Neel surface anisotropy, validated against numerical solutions.

Contribution

It introduces an analytical approach to determine the magnetization profile and scattering cross section considering Neel surface anisotropy in spherical nanoparticles.

Findings

Analytical solution derived using perturbation and spherical harmonics.

Comparison shows good agreement with numerical Landau-Lifshitz simulations.

Provides insights into surface anisotropy effects on neutron scattering.

Abstract

The magnetization profile and the related magnetic small-angle neutron scattering cross section of a single spherical nanoparticle with Neel surface anisotropy is analytically investigated. We employ a Hamiltonian that comprises the isotropic exchange interaction, an external magnetic field, a uniaxial magnetocrystalline anisotropy in the core of the particle, and the Neel anisotropy at the surface. Using a perturbation approach, the determination of the magnetization profile can be reduced to a Helmholtz equation with Neumann boundary condition, whose solution is represented by an infinite series in terms of spherical harmonics and spherical Bessel functions. From the resulting infinite series expansion, we analytically calculate the Fourier transform, which is algebraically related to the magnetic small-angle neutron scattering cross section. The approximate analytical solution is compared to the numerical solution using the Landau-Lifshitz equation, which accounts for the full nonlinearity of the problem.