Disorder-induced spin-liquid-like behavior in kagome-lattice compounds

Quantum spin liquids (QSLs) are an exotic state of matter that is subject to extensive research. However, the relationship between the ubiquitous disorder and the QSL behaviors is still unclear. Here, by performing comparative experimental studies on two kagomé-lattice QSL candidates, ${\mathrm{Tm}}_3{\mathrm{Sb}}_3{\mathrm{Zn}}_2{\mathrm{O}}_{14}$ and ${\mathrm{Tm}}_3{\mathrm{Sb}}_3{\mathrm{Mg}}_2{\mathrm{O}}_{14}$, which are isostructural to each other but with strong and weak structural disorder, respectively, we show unambiguously that the disorder can induce spin-liquid-like features. In particular, both compounds show dominant antiferromagnetic interactions with a Curie-Weiss temperature of $-17.4$ and $-28.7$ K for ${\mathrm{Tm}}_3{\mathrm{Sb}}_3{\mathrm{Zn}}_2{\mathrm{O}}_{14}$ and ${\mathrm{Tm}}_3{\mathrm{Sb}}_3{\mathrm{Mg}}_2{\mathrm{O}}_{14}$, respectively, but remain disordered down to about 0.05 K. Specific-heat results suggest the presence of gapless magnetic excitations characterized by a residual linear term. Magnetic excitation spectra obtained by inelastic neutron scattering (INS) at low temperatures display broad continua. All these observations are consistent with those of a QSL. However, we find in ${\mathrm{Tm}}_3{\mathrm{Sb}}_3{\mathrm{Zn}}_2{\mathrm{O}}_{14}$, which has strong disorder resulting from the random mixing of the magnetic ${\mathrm{Tm}}^{3+}$ and nonmagnetic ${\mathrm{Zn}}^{2+}$, that the low-energy magnetic excitations observed in the specific-heat and INS measurements are substantially enhanced compared to those of ${\mathrm{Tm}}_3{\mathrm{Sb}}_3{\mathrm{Mg}}_2{\mathrm{O}}_{14}$, which has much less disorder. We believe that the effective spins of the ${\mathrm{Tm}}^{3+}$ ions in the ${\mathrm{Zn}}^{2+}/{\mathrm{Mg}}^{2+}$ sites give rise to the low-energy magnetic excitations, and the amount of the occupancy determines the excitation strength. These results provide direct evidence of the mimicry of a QSL caused by disorder.

Figure 1

(a) Schematic crystal structure of ${\mathrm{Tm}}_3{\mathrm{Sb}}_3{\mathrm{Zn}}_2{\mathrm{O}}_{14}$ and ${\mathrm{Tm}}_3{\mathrm{Sb}}_3{\mathrm{Mg}}_2{\mathrm{O}}_{14}$ with $R\overline{3}m$ space group. (b) Top view of the kagomé layer consisting of ${\mathrm{Tm}}^{3+}$ ions at the corners and ${\mathrm{Zn}}^{2+}$ ions at the centers. (c), (d) Rietveld refinement results for the powder x-ray diffraction data for ${\mathrm{Tm}}_3{\mathrm{Sb}}_3{\mathrm{Zn}}_2{\mathrm{O}}_{14}$ and ${\mathrm{Tm}}_3{\mathrm{Sb}}_3{\mathrm{Mg}}_2{\mathrm{O}}_{14}$, respectively. (e), (f) Temperature dependence of magnetic susceptibility for ${\mathrm{Tm}}_3{\mathrm{Sb}}_3{\mathrm{Zn}}_2{\mathrm{O}}_{14}$ and ${\mathrm{Tm}}_3{\mathrm{Sb}}_3{\mathrm{Mg}}_2{\mathrm{O}}_{14}$, respectively, measured under zero-field-cooling (ZFC) and field-cooling (FC) conditions with a magnetic field of 0.1 T from 2 to 300 K. The insets of (e) and (f) show the inverse susceptibility data at low temperatures. The dashed lines are the fits with the Curie-Weiss law.

Figure 2

(a), (b) Crystal-electric-field (CEF) excitations below 40 meV for ${\mathrm{Tm}}_3{\mathrm{Sb}}_3{\mathrm{Zn}}_2{\mathrm{O}}_{14}$ and ${\mathrm{Tm}}_3{\mathrm{Sb}}_3{\mathrm{Mg}}_2{\mathrm{O}}_{14}$, respectively, measured at 1.6 K on TAIPAN spectrometer. Green and black arrows in (a) indicate the positions of CEF transitions at 1.6 and 18.5 meV caused by ${\mathrm{Tm}}^{3+}$ at the Zn(1) sites, and 4.5, 24.8, and 33.5 meV caused by ${\mathrm{Tm}}^{3+}$ at the original sites for ${\mathrm{Tm}}_3{\mathrm{Sb}}_3{\mathrm{Zn}}_2{\mathrm{O}}_{14}$. Black solid line represents the convolution with two Gaussian functions denoted by dashed lines. Arrows in (b) indicate the positions of CEF transitions at 4, 23.5, and 33.5 meV for ${\mathrm{Tm}}_3{\mathrm{Sb}}_3{\mathrm{Mg}}_2{\mathrm{O}}_{14}$. (c), (d) $\mathit{Q}$-dependence intensities of the CEF levels for ${\mathrm{Tm}}_3{\mathrm{Sb}}_3{\mathrm{Zn}}_2{\mathrm{O}}_{14}$ and ${\mathrm{Tm}}_3{\mathrm{Sb}}_3{\mathrm{Mg}}_2{\mathrm{O}}_{14}$, respectively. Solid lines indicate that the intensities of the CEF excitations follow the magnetic form factor of ${\mathrm{Tm}}^{3+}$ ion well with $I\propto {\left|f\left(\mathit{Q}\right)\right|}^2$. $I$ and $\left|f\right(\mathit{Q}\left)\right|$ denote excitation intensity measured and magnetic form factor of ${\mathrm{Tm}}^{3+}$ ion, respectively. Errors represent one standard deviation throughout the paper.

Figure 3

(a), (b) Specific heat results of ${\mathrm{Tm}}_3{\mathrm{Sb}}_3{\mathrm{Zn}}_2{\mathrm{O}}_{14}$ and ${\mathrm{Tm}}_3{\mathrm{Sb}}_3{\mathrm{Mg}}_2{\mathrm{O}}_{14}$ at ultralow temperatures. The specific heat of nonmagnetic references ${\mathrm{La}}_3{\mathrm{Sb}}_3{\mathrm{Zn}}_2{\mathrm{O}}_{14}$ and ${\mathrm{La}}_3{\mathrm{Sb}}_3{\mathrm{Mg}}_2{\mathrm{O}}_{14}$ are also shown. Solid lines are the fits with Debye model as $C_{\mathrm{p}}\sim T^3$ for the nonmagnetic compounds. Insets show the low-temperature $C_{\mathrm{p}}/T\text{vs}{T}^2$. Dashed lines are the linear fits. (c), (d) Magnetic specific heat ($C_{\mathrm{m}}$) results of ${\mathrm{Tm}}_3{\mathrm{Sb}}_3{\mathrm{Zn}}_2{\mathrm{O}}_{14}$ and ${\mathrm{Tm}}_3{\mathrm{Sb}}_3{\mathrm{Mg}}_2{\mathrm{O}}_{14}$ after subtracting the contribution from the lattice using nonmagnetic reference compounds ${\mathrm{La}}_3{\mathrm{Sb}}_3{\mathrm{Zn}}_2{\mathrm{O}}_{14}$ and ${\mathrm{La}}_3{\mathrm{Sb}}_3{\mathrm{Mg}}_2{\mathrm{O}}_{14}$, respectively.

Figure 4

Inelastic neutron scattering spectra of ${\mathrm{Tm}}_3{\mathrm{Sb}}_3{\mathrm{Zn}}_2{\mathrm{O}}_{14}$ (a)–(c) and ${\mathrm{Tm}}_3{\mathrm{Sb}}_3{\mathrm{Mg}}_2{\mathrm{O}}_{14}$ (e)–(g) measured on PELICAN spectrometer [68]. (d) shows the wave-vector $\mathit{Q}$-dependence of the energy-integrated intensity of ${\mathrm{Tm}}_3{\mathrm{Sb}}_3{\mathrm{Zn}}_2{\mathrm{O}}_{14}$ and ${\mathrm{Tm}}_3{\mathrm{Sb}}_3{\mathrm{Mg}}_2{\mathrm{O}}_{14}$. The energy and $\mathit{Q}$ range are marked with the dashed rectangular in (a) and (e). Because the signals for ${\mathrm{Tm}}_3{\mathrm{Sb}}_3{\mathrm{Mg}}_2{\mathrm{O}}_{14}$ are too weak, to visualize the $\mathit{Q}$ dependence of the intensity in (d), we used the 60-K data as the background and subtracted it. Solid lines are guides to the eye.

Figure 5

Energy dependence of the integrated neutron scattering intensity in the $\mathit{Q}$ range between 0.6 to 1.4 ${\AA }^{-1}$ for ${\mathrm{Tm}}_3{\mathrm{Sb}}_3{\mathrm{Zn}}_2{\mathrm{O}}_{14}$ (a) and ${\mathrm{Tm}}_3{\mathrm{Sb}}_3{\mathrm{Mg}}_2{\mathrm{O}}_{14}$ (b). Solid lines are guides to the eye. Dashed lines represent the instrumental resolutions. Elastic neutron scattering data for (c) ${\mathrm{Tm}}_3{\mathrm{Sb}}_3{\mathrm{Zn}}_2{\mathrm{O}}_{14}$ and (d) ${\mathrm{Tm}}_3{\mathrm{Sb}}_3{\mathrm{Mg}}_2{\mathrm{O}}_{14}$, obtained by integrating the intensity in an energy window of $[-0.1,0.1]$ meV. The data were collected on a time-of-flight spectrometer PELICAN at various temperatures.