Chiral magnetism and helimagnons in a pyrochlore antiferromagnet

Recent neutron scattering measurements on the spinel CdCr₂O ₄ revealed a rare example of helical magnetic order in geometrically frustrated pyrochlore antiferromagnet. The spin spiral characterized by an incommensurate wave vector Q=2π(0,δ,1) with δ≈0.09 is accompanied by a tetragonal distortion. Here we conduct a systematic study on the magnetic ground state resulting from the interplay between the Dzyaloshinskii-Moriya interaction and further neighbor exchange couplings, two of the most important mechanisms for stabilizing incommensurate spin orders. We compute the low-energy spin-wave spectrum based on a microscopic spin Hamiltonian and find a dispersion relation characteristic of the helimagnons. By numerically integrating the Landau-Lifshitz-Gilbert equation with realistic model parameters, an overall agreement between experiment and the numerical spectrum, lending further support to the view that a softened optical phonon triggers the magnetic transition and endows the lattice a chirality.