From magnetic order to quantum disorder: a $\mu$SR study of the Zn-barlowite series of $S={\frac{1}{2}}$ kagom\'e antiferromagnets, Zn$_{x}$Cu$_{4-x}$(OH)$_{6}$FBr

TL;DR

This study uses muon spectroscopy and density-functional theory to investigate how zinc substitution in Zn-barlowite affects magnetic order, revealing a transition from magnetic order to a quantum disordered state indicative of a quantum spin liquid.

Contribution

It provides the first detailed muon spectroscopy analysis of the Zn-barlowite series, identifying the suppression of magnetic order with increasing Zn content and the emergence of a quantum disordered ground state.

Findings

Long-range magnetic order in parent compound at 15 K.

Persistence of magnetic fluctuations down to 50 mK in Zn-rich samples.

Crossover from static to dynamic magnetic ground state at x>0.5.

Abstract

We report a comprehensive muon spectroscopy study of the Zn-barlowite series of $S={\frac{1}{2}}$ kagom\'e antiferromagnets, Zn$_x$Cu$_{4-x}$(OH)$_{6}$FBr, for $x=0.00$ to $0.99(1)$. By combining muon spin relaxation and rotation measurements with state-of-the-art density-functional theory muon-site calculations, we observe the formation of both $\mu$--F and $\mu$--OH complexes in Zn-barlowite. From these stopping sites, implanted muon spins reveal the suppression of long-range magnetic order into a possible quantum spin liquid state upon increasing concentration of Zn-substitution. In the parent compound ($x=0$), static long-range magnetic order below $T_{\mathsf{N}}=15$ K manifests itself in the form of spontaneous oscillations in the time-dependent muon asymmetry signal consistent with the dipolar fields expected from the calculated muon stopping sites and the previously determined magnetic structure of barlowite. Meanwhile, in the $x=1.0$ end-member of the series---in which antiferromagnetic kagom\'e layers of Cu$^{2+}$ $S={\frac{1}{2}}$ moments are decoupled by diamagnetic Zn$^{2+}$ ions---we observe that dynamic magnetic moment fluctuations persist down to at least 50 mK, indicative of a quantum disordered ground state. We demonstrate that this crossover from a static to dynamic magnetic ground state occurs for compositions of Zn-barlowite with $x>0.5$, which bears resemblance to dynamical behaviour of the widely studied Zn-paratacamite series that contains the quantum spin liquid candidate herbertsmithite.