Helical Spin Dynamics in Commensurate Magnets: a Study on Brochantite, Cu$_4$SO$_4$(OH)$_6$

TL;DR

This study investigates the complex helical spin dynamics in the mineral brochantite, revealing the effects of Dzyaloshinskii-Moriya interactions and magnetic frustration through neutron scattering and theoretical modeling.

Contribution

It provides the first detailed experimental and theoretical analysis of incommensurate helical spin dynamics in brochantite, highlighting the role of DM interactions and magnetic frustration.

Findings

Observation of incommensurate helical spin dynamics in brochantite

Quantification of symmetric exchange and DM interaction parameters

Identification of the mechanism stabilizing the AFM ground state

Abstract

We report the direct observation of a commensurate-ordered antiferromagnetic (AFM) state but incommensurate helical spin dynamics in the natural mineral brochantite Cu$_4$SO$_4$(OH)$_6$ through neutron diffraction and neutron spectroscopy measurements. Inelastic neutron scattering measurements reveal magnon-like excitations with considerable dispersion along the c-axis and almost flat branches in other principal directions, indicating the strong one-dimensional character of the magnetic correlations. We experimentally observe the effect of the uniform Dzyaloshinskii-Moriya (DM) interaction, which elevates the degeneracy of the spin-wave modes shifting them in opposite directions in reciprocal space. 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, we were able to construct an effective Heisenberg Hamiltonian. We quantify both the symmetric exchange parameters and the DM vector components in Cu$_4$SO$_4$(OH)$_6$ and determine the mechanism of the magnetic frustration. Our work provides detailed insights into the complex dynamics of the spin chain in the presence of uniform DM interaction.