Spectroscopic evidence for an antisymmetric Dzyaloshinskii-Moriya interaction in natural mineral brochantite Cu₄SO₄(OH)₆

We report the direct observation of a commensurate-ordered antiferromagnetic (AFM) state but incommensurate helical spin dynamics in the natural mineral brochantite Cu₄SO₄(OH)₆ through neutron diffraction and neutron spectroscopy in a magnetic field. We experimentally observe the effect of the Dzyaloshinskii-Moriya (DM) interaction, which elevates the degeneracy of the spin-wave modes shifting them in opposite directions in reciprocal space. We demonstrate that the system has a commensurate AFM ground state, stabilized by the anisotropic symmetric Heisenberg exchange interactions, and quasi-one-dimensional chiral spin dynamics due to the antisymmetric DM interaction. Employing linear spin-wave theory and density-matrix renormalization group calculations, we obtain both the symmetric exchange parameters and the DM vector components from the experimentally measured spin-wave spectra across the entire Brillouin zone. Our work provides detailed insights into the complex dynamics of the spin chain in the presence of DM interaction.