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

TL;DR

This study investigates the kagome lattice compound Cu$_3$(HOTP)$_2$, revealing it hosts a quantum spin liquid state with no magnetic order down to 50 mK, supported by muon spin relaxation and theoretical modeling.

Contribution

It provides experimental evidence of a quantum spin liquid in Cu$_3$(HOTP)$_2$ and introduces a Z$_2$-linear Dirac model for its spin excitations.

Findings

No magnetic ordering down to 50 mK

Presence of spin fluctuations consistent with QSL

Close proximity to a quantum critical point

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.