Small-angle neutron scattering signatures of magnetic hopfions

Magnetic hopfions are three-dimensional localized magnetic topological solitons which can exist in the bulk of magnetic materials. Based on a Ritz model for magnetic hopfions in a chiral magnet, the unpolarized magnetic small-angle neutron scattering (SANS) cross section, the spin-flip scattering cross section, and the chiral function (characterizing the imbalance between the two spin-flip scattering amplitudes) are computed here analytically, while the real-space correlation function is obtained numerically. Features of these functions, specific to magnetic hopfions, are discussed. Our results enable the SANS method to be used for the detection of magnetic hopfions.