Dynamic Scaling in the Susceptibility of the Spin-$\frac{1}{2}$ Kagome Lattice Antiferromagnet Herbertsmithite

The spin-$\frac{1}{2}$ kagome lattice antiferromagnet herbertsmithite, ${\mathrm{ZnCu}}_3(\mathrm{OH}{)}_6{\mathrm{Cl}}_2$, is a candidate material for a quantum spin liquid ground state. We show that the magnetic response of this material displays an unusual scaling relation in both the bulk ac susceptibility and the low energy dynamic susceptibility as measured by inelastic neutron scattering. The quantity $\chi T^{\alpha }$ with $\alpha \simeq 0.66$ can be expressed as a universal function of $H/T$ or $\omega /T$. This scaling is discussed in relation to similar behavior seen in systems influenced by disorder or by the proximity to a quantum critical point.

Figure 1

(a) The in-phase component of the ac susceptibility, measured at 100 Hz with an oscillating field of 17 Oe. (b) A scaled plot of the ac susceptibility data measured at nonzero applied field, plotted as ${\chi }_{\mathrm{ac}}^{\prime }{T}^{\alpha }$ with $\alpha =0.66$ on the $y$ axis and ${\mu }_{B}H/k_{B}T$ on the $x$ axis. Inset: A scaled plot of the dc magnetization, showing $M{T}^{-0.34}$ vs ${\mu }_{B}H/k_{B}T$.

Figure 2

(a) Neutron scattering structure factor $S(\omega )$, measured using the Disk Chopper Spectrometer integrated over wave vectors $0.5\le Q\le 1.9{\AA }^{-1}$. (b) The local dynamic susceptibility ${\chi }^{\prime \prime }(\omega )$, determined as described in the text. Uncertainties where indicated in this article are statistical in origin and represent 1 standard deviation.

Figure 3

The quantity ${\chi }^{\prime \prime }(\omega )T^{\alpha }$ with $\alpha =0.66$ plotted against $\hslash \omega /k_{B}T$ on a log-log scale. The data collapse onto a single curve. The lines are fits as described in the text.