Spin liquid properties of the kagome material Cu${}_3$(HOTP)${}_2$

Abstract

The metal-organic-framework (MOF) compound Cu${}_3$(HOTP)${}_2$, a.k.a. Cu${}_3$(HHTP)${}_2$, is a small-gap semiconductor containing a kagome lattice of antiferromagnetically coupled $S$=1/2 Cu${}^{\mathrm{II}}$ spins with intra-layer nearest-neighbor exchange coupling $J\sim$ 2 K. The intra-layer $J$ value obtained from DFT+U calculations is shown to match with the experimental value for reasonable values of U. Muon spin relaxation confirms no magnetic ordering down to 50~mK and sees spin fluctuations diffusing on a 2D lattice, consistent with a quantum spin liquid (QSL) ground state being present within highly decoupled kagome layers. Reduction of the spin diffusion rate on cooling from the paramagnetic region to the low-temperature QSL region reflects quantum entanglement. It is also found that the layers become more strongly decoupled in the low-temperature QSL region. Comparison of results for the spin diffusion, magnetic susceptibility and specific heat in the QSL region suggests close proximity to a quantum critical point and a large density of low energy spinless electronic excitations. A Z${}_2$-linear Dirac model for the spin excitations of the QSL is found to provide the best match with experiment.

14 pages