Electron Doping a Kagome Spin Liquid

Herbertsmithite, ${\mathrm{ZnCu}}_3(\mathrm{OH}{)}_6{\mathrm{Cl}}_2$, is a two-dimensional kagome lattice realization of a spin liquid, with evidence for fractionalized excitations and a gapped ground state. Such a quantum spin liquid has been proposed to underlie high-temperature superconductivity and is predicted to produce a wealth of new states, including a Dirac metal at $1/3$ electron doping. Here, we report the topochemical synthesis of electron-doped ${\mathrm{ZnLi}}_x{\mathrm{Cu}}_3(\mathrm{OH}{)}_6{\mathrm{Cl}}_2$ from $x=0$ to $x=1.8$ ($3/5$ per ${\mathrm{Cu}}^{2+}$). Contrary to expectations, no metallicity or superconductivity is induced. Instead, we find a systematic suppression of magnetic behavior across the phase diagram. Our results demonstrate that significant theoretical work is needed to understand and predict the role of doping in magnetically frustrated narrow band insulators, particularly the interplay between local structural disorder and tendency toward electron localization, and pave the way for future studies of doped spin liquids.

Popular Summary

Despite the discovery of superconductivity over a century ago, the phenomenon still lacks a general theory, particularly in the high-temperature limit (i.e., above 30 K). In 1987, Anderson theorized that a complex magnetic state, known as a quantum spin liquid, could predicate high-temperature superconductivity. In particular, high-temperature superconductivity could be induced by introducing charge carriers into a quantum spin liquid material. However, this prediction has not been experimentally realized to date; no one has been able to successfully chemically dope a quantum spin liquid until now. Here, we introduce electrons by chemically inserting lithium ions into the leading candidate spin liquid, Herbertsmithite, and investigate the doped material using a variety of experimental techniques.

Herbertsmithite, ${\mathrm{ZnCu}}_3(\mathrm{OH}{)}_6{\mathrm{Cl}}_2$, has been studied extensively over the past decade for its magnetically frustrated kagome structure, a lattice of corner-sharing triangles in two-dimensional planes. This structure has been experimentally shown to possess the predicted hallmarks of the spin liquid state such as fractional spin excitations. We intercalate lithium into Herbertsmithite to yield ${\mathrm{ZnLi}}_x{\mathrm{Cu}}_3(\mathrm{OH}{)}_6{\mathrm{Cl}}_2$, where $x$ ranges from 0 to 1.8. We then use x-ray powder diffraction and x-ray photoelectron spectroscopy, among other techniques, to investigate the resulting doped material, which appears to be black. We find that electron doping continuously suppresses the magnetism in the material without the appearance of superconductivity or related metallic phases at temperatures as low as $T=1.8\mathrm{K}$. Additionally, our heat capacity measurements reveal an interesting trend of excess entropy that is consistent with a singlet-triplet excitation of localized electron pairs.

We expect that our findings will pave the way for additional studies of doped spin liquids and revised theories of superconductivity.

Figure 1

Doped herbertsmithite structure. (a) A top-down (along $c$ axis) representation of the parent herbertsmithite copper kagome layer (blue dotted line) with Cu (blue) and O (red), H (white), Zn (gray), and Cl (green) between the kagome layers. The dark and light atoms are located above and below the kagome plane, respectively. (b) The x-ray powder diffraction (XRPD) patterns of the complete series. The gray asterisks represent the presence of Si (internal standard). An image of the blue-green parent material is shown in the lower left-hand corner while a picture of the black doped sample N is shown in the upper left. All doped samples are also black. (c) XRPD data demonstrate the instability of one of the maximally doped samples, sample N, in air ($x=1.8$) as it decomposes in hours into several other phases.

Figure 2

X-ray photoelectron spectroscopy (XPS). (a) Cu $2p$ XP spectra of parent herbertsmithite (black), sample A (magenta), sample N (violet), and Cu metal (gray). The black dashed line indicates locations of satellite peaks in the parent, characteristic of ${\mathrm{Cu}}^{2+}$, which are significantly reduced in the doped samples. (b) The x-ray generated Auger Cu $L_3{M}_{4,5}{M}_{4,5}$ spectra of the same four samples. The black and the gray dotted lines represent the location of the greatest intensity peak for the parent and the copper metal, respectively. The peak shape and binding energy of the doped samples varies significantly from both the parent and the copper metal. (c) A Wagner plot shows the relative chemical shift of the four samples and ${\mathrm{Cu}}^{1+}$ in $\mathrm{Cu}(\mathrm{I}{)}_2\mathrm{O}$ (literature value) [18] by plotting the kinetic energy from the Cu $L_3{M}_{4,5}{M}_{4,5}$ peak on the $y$ axis and the binding energy from the Cu $2p_{3/2}$ peak on the $x$ axis. The chemical shift is sensitive to the polarizability of the chemical environment.

Figure 3

Physical properties of ${\mathrm{ZnLi}}_x{\mathrm{Cu}}_3(\mathrm{OH}{)}_6{\mathrm{Cl}}_2$ series. (a) The magnetic susceptibility, $\chi \approx M/H$, as a function of temperature for the doped ${\mathrm{ZnLi}}_x{\mathrm{Cu}}_3(\mathrm{OH}{)}_6{\mathrm{Cl}}_2$ series. Black and gray lines are from high-temperature Curie-Weiss analysis of the ${\chi }_0$-corrected inverse magnetic susceptibility (inset). All samples have paramagnetic behavior and a decrease in susceptibility is seen as Li content increases. (b) Heat capacity divided by temperature as a function of temperature under zero field from $T=1.8–20\mathrm{K}$. The low-temperature region systematically decreases with increasing Li content across the series, while at higher temperatures the doped samples have increased entropy. Black and gray lines represent fits to the data.

Figure 4

Magnetization and heat capacity fit parameters. (a) The extracted Curie constants $C$ from the high-temperature (black squares) and low-temperature (red diamonds) Curie-Weiss analysis of the ${\mathrm{ZnLi}}_x{\mathrm{Cu}}_3(\mathrm{OH}{)}_6{\mathrm{Cl}}_2$ series. The dashed lines are a guide to the eye that demonstrate a linear decrease. (b) The Schottky anomaly parameter $A_{\mathrm{HT}}$ (blue circles) from heat capacity fits to the doped herbertsmithite series, which describes the feature in the high-temperature heat capacity data. The blue dashed line and the black dotted line are two different models for singlet trapping in doped herbertsmithite (see SM [15]).

Figure 5

Detailed heat capacity analysis of ${\mathrm{ZnLi}}_x{\mathrm{Cu}}_3(\mathrm{OH}{)}_6{\mathrm{Cl}}_2$ series. (a) High-temperature ($C_p-\gamma$) $T^{-3}$ Schottky analysis of the temperature range $T=1.8–300\mathrm{K}$ for the parent ${\mathrm{ZnCu}}_3(\mathrm{OH}{)}_6{\mathrm{Cl}}_2$ (black), ${\mathrm{ZnLi}}_{0.8}{\mathrm{Cu}}_3(\mathrm{OH}{)}_6{\mathrm{Cl}}_2$ (dark green), and ${\mathrm{ZnLi}}_{0.8}{\mathrm{Cu}}_3(\mathrm{OH}{)}_6{\mathrm{Cl}}_2$ (magenta). The dashed blue line is the high-temperature Schottky anomaly of the extracted values from the zero-field $T=1.8–20\mathrm{K}$ fits. It does a good job of describing the Schottky anomaly we see in the doped samples in the higher-temperature region of the heat capacity. Debye modes (which are a constant at low temperature and fall off at higher temperatures) are not shown for clarity. (b) Simple model fits to field-dependent heat capacity measurements. Top left: the parent ${\mathrm{ZnCu}}_3(\mathrm{OH}{)}_6{\mathrm{Cl}}_2$ (black); top right: ${\mathrm{ZnLi}}_{0.2}{\mathrm{Cu}}_3(\mathrm{OH}{)}_6{\mathrm{Cl}}_2$ (green); bottom left: ${\mathrm{ZnLi}}_{0.8}{\mathrm{Cu}}_3(\mathrm{OH}{)}_6{\mathrm{Cl}}_2$ (blue); bottom right: ${\mathrm{ZnLi}}_{1.2}{\mathrm{Cu}}_3(\mathrm{OH}{)}_6{\mathrm{Cl}}_2$ (red). The data sets go from a dark color at low fields to a lighter color at higher fields. The lines are fits as described in the text.