Spin tunneling in the kagomé antiferromagnet

The collective tunneling of a small cluster of spins between two degenerate ground-state configurations of the kagomé-lattice quantum Heisenberg antiferromagnet is studied. The cluster consists of the six spins on a hexagon of the lattice. The resulting tunnel-splitting energy Δ is calculated in detail, including the prefactor to the exponential exp(-scrS₀/ħ). This is done by setting up a coherent-spin-state path integral in imaginary time and evaluating it by the method of steepest descent. The hexagon tunneling problem is mapped onto a much simpler tunneling problem, involving only one collective degree of freedom, which can be treated by known methods. It is found that for half-odd-integer spins, the tunneling amplitude and the tunnel-splitting energy are exactly zero, because of destructive interference between symmetry-related (+) instanton and (-) instanton tunneling paths. This destructive interference is shown to occur also for certain larger loops of spins on the kagome$aa— lattice. For small, integer spins, our results suggest that tunneling strongly competes with in-plane order-from-disorder selection effects; it constitutes a disordering mechanism that might drive the system into a partially disordered ground state, related to a spin nematic.