Investigating the spin dynamics of the non-collinear magnetic phase of 3.5\% Ga-doped CuFeO$_2$*

We examine the evolution of the non-collinear phase of a hexagonal lattice antiferromagnet to help understand the inelastic neutron scattering measurements for the multiferroic ground state of 3.5\% Ga-doped CuFeO$_2$. With the complex ground state stabilized by the displacement of the oxygen atoms, the multiferroic coupling is explained by the predicted ``spin-driven'' model. By comparing the observed and calculated spectrum of spin excitations for multiple spin configurations, we conclude that the magnetic ground state is a distorted screw-type spin configuration with a distribution of turn angles produced by lattice distortions.