Scale-Free Antiferromagnetic Fluctuations in the $s=1/2$ Kagome Antiferromagnet Herbertsmithite

Neutron spectroscopy and diffuse neutron scattering on herbertsmithite [${\mathrm{ZnCu}}_3(\mathrm{OH}{)}_6{\mathrm{Cl}}_2$], a near-ideal realization of the $s=1/2$ kagome antiferromagnet, reveal the hallmark property of a quantum spin liquid: instantaneous short-ranged antiferromagnetic correlations in the absence of a time-averaged ordered moment. These dynamic antiferromagnetic correlations are weakly dependent of neutron-energy transfer and temperature, and persist up to 25 meV and 120 K. At low energy transfers a shift of the magnetic scattering to low $Q$ is observed with increasing temperature, providing evidence of gapless spinons. It is argued that these observations provide important evidence in favor of resonating-valence-bond theories of (doped) Mott insulators.

Figure 1

(a)  Instantaneous magnetic correlations at 4 K (open circles) and 10 K (filled circles) from $D7$. Data taken at 60 K (not shown) resemble the 10 K data. The solid lines are a guide to the eye. (b) The $Q$ dependence in the dynamic correlations from IN4 and MARI with the energy integration interval indicated in the legend. The dotted line in panel (a) and (b) is the structure factor for dimerlike AF correlations, for the dashed line a single-ion contribution corresponding to the 6% antisite spins in this system is added. (c) The energy and temperature dependence at $Q=1.3{\AA }^{-1}$ from the TOF data.

Figure 2

Inelastic intensity for 3 polarization channels: ${\mathrm{NSF}}_{xx}$ contains phonons and NSF background. ${\mathrm{SF}}_{xx}$ contains $2/3$ of the magnetic intensity and SF background. ${\mathrm{SF}}_{zz}$ contains $1/3$ of the magnetic intensity. Hence, $S_{\mathrm{mag}}/3={\mathrm{SF}}_{xx}-{\mathrm{SF}}_{zz}$. It is seen that magnetic intensity at the maximum at $Q=1.3{\AA }^{-1}$ [${\mathrm{SF}}_{xx}$ in panel (a)] is finite and nearly constant for all covered temperatures (b) and energies (c),(d). Data in (a), (c), and (d) were measured at 2 K.

Figure 3

The scattering cross section $S(Q,ϵ)$ of at 2 K (a) and 120 K (b). The intensity scale is $\mathrm{mb}{\mathrm{sr}}^{-1}{\mathrm{meV}}^{-1}\mathrm{f}.\mathrm{u}{.}^{-1}$. The elastic powder diffraction pattern is also shown in (b). Panel (c) and (d) show respectively $S_{\mathrm{AF}}$ and ${\chi }^{\prime \prime }$. The white band at low $Q$ is a gap between detectors. Some increase in intensity in $S_{\mathrm{AF}}$ is observed at higher energies but this is likely due to the direct beam and larger error bars. As shown in Fig. 4a the increase in intensity is only very small.

Figure 4

(a) The $Q$ dependence in $S_{\mathrm{AF}}(Q,ϵ)$ for a number of energy transfers. (b) The temperature dependence for a number of points in $S(Q,ϵ=4\mathrm{meV})$ and fits to the data using Eq. (2).