Although magnetically ordered at low temperatures, the spin-$\frac{1}{2}$ triangular antiferromagnet ${\mathrm{Cs}}_2\mathrm{Cu}{\mathrm{Cl}}_4$ 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-$\frac{1}{2}$ triangular antiferromagnet at $\frac{1}{3}$ 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.

• Received 10 February 2007

DOI:https://doi.org/10.1103/PhysRevB.75.144411