Spin tunneling in the Kagom\'e antiferromagnet

TL;DR

This paper investigates quantum spin tunneling in the Kagome antiferromagnet, revealing that tunneling is suppressed for half-odd-integer spins due to interference, and suggesting tunneling influences ground state selection for small integer spins.

Contribution

It provides a detailed calculation of tunneling energies in the Kagome antiferromagnet and uncovers the role of spin parity in tunneling suppression, offering insights into ground state properties.

Findings

Tunneling amplitude is zero for half-odd-integer spins due to destructive interference.

Tunneling may compete with order-from-disorder effects in small integer spins.

Results suggest tunneling could lead to a partially disordered, spin nematic ground state.

Abstract

The collective tunneling of a small cluster of spins between two degenerate ground state configurations of the Kagom\'{e}-lattice quantum Heisenberg antiferromagnet is \mbox{studied}. The cluster consists of the six spins on a hexagon of the lattice. The resulting tunnel splitting energy $\Delta$ is calculated in detail, including the prefactor to the exponential $\exp(- \SSo / \hbar)$. 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 Kagom\'{e} lattice. For small, integer spins, our results suggest that tunneling strongly competes with \mbox{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.