Heat transport of the kagome Heisenberg quantum spin liquid candidate ${\mathrm{YCu}}_3{\left(\mathrm{OH}\right)}_{6.5}{\mathrm{Br}}_{2.5}$: Localized magnetic excitations and a putative spin gap

The spin-1/2 kagome Heisenberg antiferromagnet is generally accepted as one of the most promising two-dimensional models to realize a quantum spin liquid state. Previous experimental efforts were almost exclusively on only one archetypal material, the herbertsmithite ${\mathrm{ZnCu}}_3{\left(\mathrm{OH}\right)}_6{\mathrm{Cl}}_2$, which unfortunately suffers from the notorious orphan spin problem caused by magnetic disorders. Here, we turn to ${\mathrm{YCu}}_3{\left(\mathrm{OH}\right)}_{6.5}{\mathrm{Br}}_{2.5}$, recently recognized as another host of a globally undistorted kagome ${\mathrm{Cu}}^{2+}$ lattice free from orphan spins, and thus a more feasible system for studying the intrinsic kagome quantum spin liquid physics. Our high-resolution low-temperature thermal conductivity measurements yield a vanishingly small residual linear term of $\kappa /T$ ($T\to 0$), and thus clearly rule out itinerant gapless fermionic excitations. An unusual scattering of phonons grows exponentially with temperature, suggesting thermally activated phonon-spin scattering and hence a gapped magnetic excitation, consistent with a ${\mathbb{Z}}_2$ quantum spin liquid ground state. Additionally, an analysis of the magnetic field impact on the thermal conductivity reveals a field closing of the spin gap, while the excitations remain localized.

Figure 1

(a) Lattice structure of YCOB. Although the antisite mixing of ${\mathrm{OH}2}^{-}/{\mathrm{Br}2}^{-}$ pushes 70% of ${\mathrm{Y}}^{3+}$ away from its ideal position and imposes quenched exchange randomness on the kagome bonds, as illustrated in (b), the space group of $P\overline{3}m1$ and thus the globally regular kagome lattice of ${\mathrm{Cu}}^{2+}$ remains intact [28]. The black lines show the unit cell.

Figure 2

Low-temperature thermal conductivity of YCOB crystals without magnetic field. (a) $\kappa /T\left(T\right)$ curves of three single crystals. (b) $\kappa /T\left(T\right)$ curve of sample No. 1 as a representative case, plotted in log-log scale. The dashed red line highlights its linear dependence at the low-temperature limit. The data deviate downward from this linear behavior above a temperature $T^{*}\sim 230$ mK marked by the arrow. (c) The fit parameters' residual linear term (${\kappa }_0/T$, left axis) and exponent ($\alpha$, right axis) of all three samples. The red error bar indicates the typical resolution of ${\kappa }_0/T$ of our system ($\sim 5\mu {\mathrm{W}\mathrm{K}}^{-2}{\mathrm{cm}}^{-1}$).

Figure 3

Field impact on the thermal conductivity of YCOB. (a) The $\kappa /T$ curves at different fields. Increasing magnetic field suppresses the $\kappa /T$ curve monotonically, and this effect is discernible at lower temperatures in higher fields. The dashed line represents the putative phononic thermal conductivity ${\kappa }_{\text{fit}}$ (see text). The inset depicts the difference of ${\kappa }_{\text{fit}}$ and $\kappa$ measured at different fields. (b) The solid color circles (left axis) represent the relative change of $\kappa$ according to the field change at different temperatures. For the $T=820$ mK curve, data collected with field ramped up (larger red circles) and down (smaller magenta circles) match perfectly, excluding hysteresis effects. The open squares (right axis) show the relative field change of the magnetic specific heat, adapted from Ref. [28].

Figure 4

Exponential and power-law fits to the temperature dependence of ${\tau }_p/{\tau }_{ps}$ (see text) for one sample at (a) zero field, and (b) high field. The data are plot in log-log scale to better evaluate the fit results. (c) The gap size estimated from the acceptable exponential fits at different fields of sample No. 1 ($\blacksquare$, red), sample No. 2 ($•$, blue), and sample No. 3 ($⧫$, green) [35]. The gray region marks the temperature range over which the fits were performed. The dashed line is a guide to the eye (see text).