Heat Transport in Herbertsmithite: Can a Quantum Spin Liquid Survive Disorder?

One favorable situation for spins to enter the long-sought quantum spin liquid (QSL) state is when they sit on a kagome lattice. No consensus has been reached in theory regarding the true ground state of this promising platform. The experimental efforts, relying mostly on one archetypal material ${\mathrm{ZnCu}}_3{(\mathrm{OH})}_6{\mathrm{Cl}}_2$, have also led to diverse possibilities. Apart from subtle interactions in the Hamiltonian, there is the additional degree of complexity associated with disorder in the real material ${\mathrm{ZnCu}}_3{(\mathrm{OH})}_6{\mathrm{Cl}}_2$ that haunts most experimental probes. Here we resort to heat transport measurement, a cleaner probe in which instead of contributing directly, the disorder only impacts the signal from the kagome spins. For ${\mathrm{ZnCu}}_3{(\mathrm{OH})}_6{\mathrm{Cl}}_2$, we observed no contribution by any spin excitation nor obvious field-induced change to the thermal conductivity. These results impose strong constraints on various scenarios about the ground state of this kagome compound: while certain quantum paramagnetic states other than a QSL may serve as natural candidates, a QSL state, gapless or gapped, must be dramatically modified by the disorder so that the kagome spin excitations are localized.

Figure 1

Schematics of the $ABC$-stacked and $AA$-stacked kagome planes of magnetic ${\mathrm{Cu}}^{2+}$ ions (blue spheres) separated by nonmagnetic ${\mathrm{Zn}}^{2+}$ ions (gray spheres) in (a) ${\mathrm{ZnCu}}_3{(\mathrm{OH})}_6{\mathrm{Cl}}_2$ and (b) ${\mathrm{Cu}}_3\mathrm{Zn}(\mathrm{OH}{)}_6\mathrm{FBr}$, respectively. The two sources of disorder for both compounds are shown only in (a) for ${\mathrm{ZnCu}}_3{(\mathrm{OH})}_6{\mathrm{Cl}}_2$ and highlighted with red circles.

Figure 2

The specific heat $C$ of ${\mathrm{ZnCu}}_3{(\mathrm{OH})}_6{\mathrm{Cl}}_2$ in various applied magnetic fields. Inset: Enlarged view of the low-temperature part of the zero-field specific heat. The solid line shows the fitting as in Ref. [23], representing the contribution from the dynamical spin fluctuations associated with the impurity spins. See Sec. I in the Supplemental Material [64] for more details.

Figure 3

The thermal conductivity $\kappa$ of ${\mathrm{ZnCu}}_3{(\mathrm{OH})}_6{\mathrm{Cl}}_2$ (sample 1) in various applied magnetic fields. The solid line in (a) represents a fit to the zero-field data below 0.35 K by $\kappa /T=a+b{T}^{\alpha -1}$. The inset in (a) schematically depicts the setup for thermal conductivity measurements, where the four leads in connection with the heater, the thermometers at the higher- and lower-temperature end, and the heat sink are shown. The heat current $J$ flows along the path from the heater to the sink. Note that for each silver wire, the silver paint was applied on all possible surfaces to achieve better thermal contact. The inset in (b) shows the relative direction of $J$, the direction of the applied magnetic field $H$, and the crystallographic axes of a kagome lattice. $J$ is parallel to $a^{*}$ (i.e., perpendicular to $a$) for ${\mathrm{ZnCu}}_3{(\mathrm{OH})}_6{\mathrm{Cl}}_2$ (sample 1). The field dependence of $\kappa /T$ at representative temperatures is shown in (c).