Quantum spin liquids in the absence of spin-rotation symmetry: application to Herbertsmithite

Abstract: It has been suggested that the nearest-neighbour (NN) antiferromagnetic Heisenberg (HAF) model on the Kagome lattice may be a good starting point to understand the quantum spin-liquid (QSL) behaviour discovered in Herbertsmithite. We investigate possible QSL phases in the presence of experimentally relevant spin-rotation symmetry-breaking perturbations such as Dzyaloshinskii-Moriya and Ising interactions, as well as second-neighbour antiferromagnetic Heisenberg interactions. We use the projective symmetry group analysis within the slave-fermion framework of QSL phases and systematically classify possible QSLs in the presence of these perturbations. The dynamical spin-structure factor for relevant QSLs is computed and their effects are studied. Our calculations reveal dispersive features in the spin structure factor embedded in a generally diffuse background due to the existence of fractionalized S=1/2 excitations called spinons. For two of the previously proposed $Z_2$ states, the dispersive features are almost absent, and diffuse scattering dominates over a large energy window throughout the Brillouin zone. This resembles the structure factor observed in recent inelastic neutron scattering experiments on singlet crystals of Herbertsmithite. Furthermore, one of the $Z_2$ states with the spin structure factor with mostly diffuse scattering is gapped, and it may be adiabatically connected to the gapped QSL state observed in recent DMRG calculations for the NN HAF. The above perturbations are found to enhance the diffuse nature of the spin structure factor and reduce the momentum dependencies of the spin gap. We also calculate the electron spin resonance absorption spectra that further characterize the role of spin-rotation symmetry breaking perturbations, and can shed more light into the nature of the ground state in Herbertsmithite.