Helimagnons in a chiral ground state of the pyrochlore antiferromagnets

The Goldstone mode in a helical magnetic phase, also known as the helimagnon, is a propagating mode with a highly anisotropic dispersion relation. Here we study theoretically the magnetic excitations in a complex chiral ground state of pyrochlore antiferromagnets such as spinel CdCr₂O ₄ and itinerant magnet YMn₂. We show that the effective theory of the soft modes in the helical state possesses a symmetry similar to that of smectic liquid crystals. An overall agreement is obtained between experiments and our dynamics simulations with realistic model parameters. By exactly diagonalizing the linearized Landu-Lifshitz equation in various commensurate limits of the spiral order, we find a low-energy dispersion relation characteristic of the helimagnons. Our calculation thus reveals the first example of helimagnon excitations in geometrically frustrated spin systems.