Spatial magnetization profile in spherical nanomagnets with surface anisotropy: Green's function approach

TL;DR

This paper develops a semi-analytical Green's function method to determine the spatial magnetization profile in spherical nanomagnets considering surface anisotropy, aiding experimental characterization of nanomagnet assemblies.

Contribution

It introduces a novel semi-analytical approach to compute magnetization profiles in spherical nanomagnets with surface anisotropy using Green's functions.

Findings

Derived a semi-analytical expression for magnetization distribution

Averaged the profile over solid angles for experimental comparison

Predicted effects of size and surface anisotropy on magnetization configurations

Abstract

We consider a single spherical nanomagnet and investigate the spatial magnetization profile $\mathbf{m}\left(\mathbf{r}\right)$ in the continuum approach, using the Green's function formalism. The energy of the (many-spin) nanomagnet comprises an isotropic exchange interaction, a uniaxial anisotropy in the core and N\'eel's surface anisotropy, and an external magnetic field. We derive a semi-analytical expression for the magnetization vector field $\mathbf{m}\left(\mathbf{r}\right)$ for an arbitrary position $\mathbf{r}$ within and on the boundary of the nanomagnet, as a solution of a homogeneous Helmholtz equation with inhomogeneous Neumann boundary conditions. ... For a more plausible comparison with experiments, e.g. using the technique of small-angle magnetic neutron scattering, we have averaged over the direction solid angle and derived the spatial profile in terms of the distance $r$. We believe that the predictions of the present study could help to characterize and understand the effects of size and surface anisotropy on the magnetization configurations in nanomagnet assemblies such as arrays of well-spaced platelets.