Probing The Spin-Spin Correlator Of Kagome Lattice Heisenberg Antiferromagnets Through Non-linear Optical Harmonic Generation

Antiferromagnetically coupled quantum spins on the Kagome lattice are proposed to realize a spin-liquid ground state where short-range spin correlations exist but symmetry breaking is avoided through frustration and quantum fluctuations. The temperature dependence of the short-range spin-spin correlator is important for understanding the underlying spin Hamiltonian of candidate materials but is typically difficult to measure. Here we show that the non-linear optical response embeds the spin-spin correlator in spin-liquid candidates by performing high harmonic generation experiments on Herbertsmithite and Zn-Barlowite. We find the temperature evolution of the spin correlations of these materials to be in very good agreement with the theoretical prediction for the S = 1/2 Heisenberg Kagome antiferromagnet. These results provide a new route to probing the governing spin Hamiltonian of spin-liquid candidates.