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Third-order effect in magnetic small-angle neutron scattering by a spatially inhomogeneous medium

Magnetic small-angle neutron scattering (SANS) is a powerful tool for investigating nonuniform magnetization structures inside magnetic materials. Here, considering a ferromagnetic medium with weakly inhomogeneous uniaxial magnetic anisotropy, saturation magnetization, and exchange stiffness, we derive the second-order (in the amplitude of the inhomogeneities) micromagnetic solutions for the equilibrium magnetization textures and compute the corresponding magnetic SANS cross sections up to the next, third order. We find that in the case of perpendicular scattering (the incident neutron beam is perpendicular to the applied magnetic field) if twice the cross section along the direction orthogonal to both the field and the neutron beam is subtracted from the cross section along the field direction, the result has only a third-order contribution (the lower-order terms are canceled). This difference does not depend on the amplitude of the exchange inhomogeneities and provides a separate gateway for a deeper analysis of the sample's magnetic structure. We derive and analyze analytical expressions for the dependence of this combination on the scattering-vector magnitude for the case of spherical Gaussian inhomogeneities.