This expression for ${\tilde{M}}_y$ follows from Eq. (25) in Ref. [23] by setting the Dzyaloshinskii-Moriya interaction length equal to zero ($l_{\mathrm{D}}=0$), assuming the scattering geometry where the applied magnetic field is perpendicular to the incident neutron beam ($q_x=0$), and noting that ${\tilde{M}}_z=M_{\mathrm{s}}{\tilde{I}}_{\mathrm{m}}$, $q_y{q}_z/q^2=\sin \theta \cos \theta$, and $q_y^2/q^2={\sin }^2\theta$ (in the notation of Ref. [23]).

Equation (2) is valid in the approach-to-saturation regime, when the governing micromagnetic expressions can be linearized. For a detailed derivation, see Ref. [23], which considers the effect of the Dzyaloshinskii-Moriya interaction on the elastic magnetic SANS cross section and the chiral function.

A statistically isotropic polycrystalline magnetic material may be characterized by random variations of the magnitude and direction of the magnetic anisotropy field, e.g., from one crystallite to another. In our experiment, a large external magnetic field is applied, which gives rise to a longitudinal ($z$) magnetization component that is close to the saturation value. For this scenario, the expectation values of the two transversal components of the anisotropy field vanish. Consequently, when averaging the $\tilde{N}{\tilde{M}}_y$ term in Eq. (1) [using Eq. (2)] over the directions of the anisotropy field, the $\tilde{N}{\tilde{H}}_{\mathrm{p}y}$ term vanishes, and only the averages over $\tilde{N}{\tilde{M}}_z$ remain.