Critical spin liquid at ⅓ magnetization in a spin-½ triangular antiferromagnet

Although magnetically ordered at low temperatures, the spin-½ triangular antiferromagnet Cs₂CuCl₄ exhibits remarkable spin dynamics that strongly suggest proximity to a spin-liquid phase. Here we ask whether a proximate spin liquid may also occur in an applied magnetic field, leaving a similar imprint on the dynamical spin correlations of this material. Specifically, we explore a spatially anisotropic Heisenberg spin-½ triangular antiferromagnet at ⅓ magnetization from a dual vortex perspective, and indeed find a “critical” spin-liquid phase described by quantum electrodynamics in (2+1)-dimensions with an emergent SU(6) symmetry. A number of nontrivial predictions follow for the dynamical spin structure factor in this “algebraic vortex liquid” phase, which can be tested via inelastic neutron scattering. We also discuss how well-studied “up-up-down” magnetization plateaus can be captured within our approach, and further predict the existence of a stable gapless solid phase in a weakly ordered up-up-down state. Finally, we predict several anomalous “roton” minima in the excitation spectrum in the regime of lattice anisotropy where the canted Néel state appears.