Magnetic small-angle neutron scattering by a nanocrystalline ferromagnet with anisotropic exchange interaction

TL;DR

This paper develops a micromagnetic framework for magnetic SANS in nanocrystalline ferromagnets that includes anisotropic exchange interactions, revealing new angular features in the scattering cross section.

Contribution

It introduces a general tensor-based model for anisotropic exchange in magnetic SANS, extending classical approaches to include symmetric exchange anisotropy effects.

Findings

Derivation of analytical SANS response functions for hexagonal exchange symmetry.

Identification of new angular harmonics due to anisotropic exchange.

Framework enables quantification of exchange anisotropy in experiments.

Abstract

A micromagnetic framework for magnetic small-angle neutron scattering (SANS) is presented that accounts for weak symmetric anisotropic exchange in centrosymmetric nanocrystalline ferromagnets. The exchange interaction is expressed via a general fourth-rank tensor decomposed into isotropic and deviatoric parts. We start with the exchange energy and effective field, assuming weakly fluctuating in space saturation magnetization, solve micromagnetic problem to find spatial distribution of local magnetization vector and compute the averaged (over random orientations of nanocrystals) SANS cross sections. The isotropic part reproduces the classical Heisenberg-type SANS response, while non-zero deviatoric part of the exchange tensor gives rise to new angular harmonics in the magnetic SANS cross section. As a specific example, analytical response functions for an exchange tensor with hexagonal symmetry in perpendicular and parallel scattering geometries are derived. The results provide a basis for identifying and quantifying symmetric exchange anisotropy in magnetic SANS experiments.