Dzyaloshinskii–Moriya interaction: How to measure its sign in weak ferromagnetics?

Three experimental techniques sensitive to the sign of the Dzyaloshinskii–Moriya interaction are discussed: neutron diffraction, Mössbauer $\gamma$-ray diffraction, and resonant x-ray scattering. Classical examples of hematite ($\alpha$-Fe$_2$O$_3$) and MnCO$_3$ crystals are considered in detail.