Electron Doping a Kagome Spin Liquid

Herbertsmithite, ZnCu$_3$(OH)$_6$Cl$_2$, is a two dimensional kagom\'{e} 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 $1/3$rd electron doping. Here we report the topochemical synthesis of electron-doped ZnLi$_x$Cu$_3$(OH)$_6$Cl$_2$ from $x$ = 0 to $x$ = 1.8 ($3/5$th per 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.

For decades, the resonance valance bond (RVB), or quantum spin-liquid, state has been theorized to be an intricate part of the mechanism for high temperature superconductivity [1,2]. One geometrically frustrated system, Herbertsmithite ( Fig.1(a)), is considered an ideal spin two dimensional liquid candidate due to its perfectly ordered kagomé lattice of S = 1/2 copper ions, antiferromagnetic interactions with J ≈ −200 K, strong evidence for fractional spin excitations by neutron scattering, and, most recently, convincing indications of a gapped spin-liquid ground state by oxygen-17 NMR [3][4][5][6][7][8]. All of these factors suggest Herbertsmithite is the realization of a quantum spin liquid. Recent predictions expanded upon Andersons theory in DFT calculations of electron doped Herbertsmithite, M x Zn 1−x Cu 3 (OH) 6 Cl 2 , where Ga 3+ or other aliovalent metals replace zinc [9,10]. A trivalent substitution introduces electrons into the material, raising the Fermi level to the Dirac points at x = 1, and giving rise to a rich phase diagram spanning from a frustrated RVB spin liquid (x = 0) to a strongly correlated Dirac metal (x = 1) with possible Mott-Hubbard metal-insulator transitions, charge ordering, ferromagnetism, or superconducting states.
It is challenging to synthesize electron doped Herbertsmithite directly as Cu 1+ will not assume the same distorted octahedral site on the kagomé lattice as Cu 2+ under thermodynamic conditions, and copper(I) hydroxide is thermodynamically unstable towards disproportionation and evolution of hydrogen gas. By using low temperature topochemical techniques, this problem is circumvented by producing a kinetically meta-stable phase [11][12][13][14]. Here we use intercalation of lithium to produce electron doped Herbertsmithite, ZnLi x Cu 3 (OH) 6 Cl 2 with 0 ≤ x ≤ 1.8. Laboratory X-ray powder diffraction (XRPD), Fig.1(b), shows the underlying structure is maintained throughout the doped series. Lithium is not directly detected due to its small X-ray scattering intensity relative to copper and zinc. Any changes in the lattice parameters as a function of doping are small and are within the resolution of the Laboratory X-ray diffractometer (see SI). During Rietveld analysis, CuO and Cu 2 O were tested and are absent from the air-free samples by both XRPD and neutron diffraction. Unlike the air stable parent, the doped samples decomposed readily in air, Fig.1(c), with the most heavily doped samples completely decomposing within hours. This rapid and total decomposition is in agreement with the formation of a reduced copper (Cu 1+ ) hydroxide in the bulk that is prone to decomposition in moisture. The color change from blue to black is also in agreement. As soon as there are any Cu 1+ ions present, there is another possible optical absorption mode: intervalence charge transfer (i.e. Cu 2+ + Cu 1+ → Cu 1+ + Cu 2+ ), or, put another way, a transition from an impurity band in the gap to the conduction band. Such absorption modes are common in mixed valent systems, such as the Cu 1+ -Cu 2+ mixed valence (N 2 H 5 ) 2 Cu 3 Cl 6 [15].
To determine the position of Li within the structure, we carried out neutron powder diffraction of the undoped and maximally Li-doped specimens using the high flux NOMAD diffractometer at the Spallation Neutron Source, Oak Ridge National Laboratory (see SI).
Rietveld analysis reveals that the previously reported structure accurately models the data of the doped specimens, with the exception of the presence of a pocket of negative scattering in a tetrahedral hole formed by three (OH − ) and one Cl − group, located above and below the copper triangles in the kagomé layer. This is consistent with the presence of Li, which has a negative scattering factor. Although the site is physically small for a Li ion, the connectivity is consistent with a favorable tetrahedral bonding environment for Li. The XRPD studies are also consistent with this model. There are systematic changes in the O-Cu-Cl bond angle and the O-Cu, Cl-Cu, and O-O bond lengths (see SI). As the doping increased, the oxygen atoms move away from the Cu kagomé lattice and spread from one another. In concert, the Cl atom moves away from the kagomé lattice along the c-axis. These combined movements create more space in the Cl-(OH) 3 tetrahedral hole. Further, a similar geometry is found in CuMg 2 Li 0.31 [16], and a stable Rietveld refinement is obtained for the maximally doped sample N, when including Li in that site, with the occupancy refining to ∼0.9 (x = 1.8 (3) per formula unit, see SI). This structure puts the Li ion in close proximity to the Cl atom and appears to form a neutral LiCl dimer along the c-axis with a bond distance of ∼1.4Å.
Such a dimer is consistent with our attempts to intercalate the larger K + ion, which resulted instead in the formation of KCl. Future work is needed to determine if this model is an accurate description of the local atomic structure. In the doped samples, this satellite is greatly reduced due to the filled 3d shell in Cu 1+ preventing this loss transition from occurring [18,19]. If it were purely Robin-Day Class 1 mixed valance (pure Cu 1+ and Cu 2+ sites with no interactions of ground or excited states), we would expect a mixed XPS Signal of Cu 1+ and Cu 2+ with an approximate 2:1 ratio. In this case, however, there must be interactions between neighboring Cu 1+ and Cu 2+ , given the shared hydroxyl bridge, through which we know (from the parent) that adjacent Cu ions interact [20][21][22]. The result is a suppression of the Cu 2+ XPS satellites, even though resistance measurements show the charges must be localized. This model (which has discrete Cu 1+ and Cu 2+ ions, Robin-Day Class 2), would not only suppress the Cu 2+ satellites but also give rise to an optical intervalence charge transfer, which would explain the black color of the material upon even light doping.
Secondly, the photoelectron induced Auger Cu L 3 M 4,5 M 4,5 spectra, Fig.2 [18,19]. Although information on copper oxidation states is lost in a depth profile analysis with ion sputtering, it can be used to determine the chemical composition [24]. As expected from the topochemical synthesis method, a thin surface layer of Li and benzophenone starting material is detected; upon ion sputtering (up to 100 min), the ratio of Cu:Zn:Cl is in agreement with the expected parent Herbertsmithite phase, with Li located throughout (see SI). Despite the introduction of a substantial number of electrons, the material remains insulating: two probe room temperature resistance measurements on cold pressed pellets in a glovebox give a resistance > 2 MΩ for the doped series. Fig.3(a) shows the magnetic susceptibility, χ ≈ M/H, for the ZnLi x Cu 3 (OH) 6 Cl 2 series. For x = 0, the inverse magnetic susceptibility is well-known to be linear at high temperatures and dominated by the kagomé network, with the signal at T < 20 K containing significant contributions from 9 defect Cu 2+ ions on the Zn 2+ site between kagomé layers [5]. We thus performed fits to the Curie-Weiss law in the low temperature (T = 1.8-15 K) and high temperature (T = 100-300 K) regions to extract estimates of the number of spins arising from the intrinsic and excess Cu ions respectively as a function of x. The extracted Curie constants of both the low and high temperature regions decrease linearly with increasing doping level, Fig.4(a).
This systematic decrease is consistent with the reduction of magnetic Cu 2+ (S = 1/2) to non-magnetic Cu 1+ (S = 0). With an x-intercept value of x = 3.3(5), the high temperature extrapolation to zero is also consistent with the known stoichiometry of Herbertsmithite, Zn 0.85 Cu 3.15 (OH) 6 Cl 2 , where x = 3.15 would be necessary to convert all Cu 2+ to Cu 1+ . All of the Weiss temperatures are negative, becoming less negative upon doping (see SI), in agreement with the expectation that the number of spins are reduced in the lattice. The low temperature extrapolation x-intercept value is x = 3.9(9); this is within error equal to that found from the high temperature extrapolation. Any subtle divergence between the high and low temperature x-intercept likely reflects a difference in reducibility of the kagomé compared to the interlayer Cu 2+ ions, since the high temperature paramagnetism includes both the kagomé and interlayer spins, whereas the latter is attributable only to the interlayer defect spins. Given the placement of the Li ions near the kagomé layer, it is no surprise the kagomé layers are more greatly reduced than the interlayer sites. Further, the difference in local coordination (interlayer Cu in O 6 octahedron vs kagomé Cu in O 4 Cl 2 octahedron), would result in a difference in redox potential for Cu 2+ + e − → Cu 1+ between the two sites, so reducing one should be slightly more favorable than reducing the other. Fig.3(b) shows the low temperature heat capacity. There are two regions of significant entropy change as a function of doping: at T ≈ 5 K, the heat capacity of the sample decreases with increasing Li content while at higher temperatures, there is an entropy gain at nonzero x. Qualitatively, the low temperature data can be explained by same mechanism as the magnetization, namely a reduction of the number of spins as Cu 2+ is converted to Cu 1+ .
To more quantitatively describe the changes, we parameterized the temperature-dependent data as a function of composition and applied magnetic field with the model: The γT term captures the linear contribution to the specific heat from the spin liquid (either intrinsic or due to defect spins). The phonon contribution is described by the β 3 T 3 and β 5 T 5 terms [25]. These phonon terms were calculated based on the field fit to the parent. The terms were then held constant for the remaining series at , β  Fig.5(a). Upon doping, A HT (Fig.4(b)) sharply increases then begins to gradually decrease.
This model also fits to the field dependent heat capacity, shown in Fig.5(b). Similar to the zero field data, the phonon terms, β 3 T 3 and β 5 T 5 , were calculated based on the field fit to the parent and held constant at the above values for the remaining series. The parameters γ, A HT , and ∆ HT were shared across fields for each sample and each sample was refined independently until convergence. These constraints yielded results consistent with the zero field fits. All the fits clearly demonstrate the field dependence of the low temperature feature which is consistent with a contribution from the magnetic interlayer Cu 2+ . The low temperature magnetization measurements, sensitive to the interlayer Cu on the Zn site, indicate that these interlayer Cu atoms are also systematically reduced as a function of doping. If these Cu impurities give rise to the finite γ, it is expected that γ would also be reduced with doping as observed. Alternately, if the γT term describes the spin liquid contribution to the heat capacity, a systematic decrease in this value could be explained by the reduction of the spin liquid nature of the material as electrons are introduced into the system. More interestingly, the high temperature Schottky anomaly shows no field dependence and reproduces the trend seen in the zero field data. Direct assignment of the heat capacity terms to specific origins is future work, but it is promising that a single model recapitulates data across temperatures, fields, and composition.
This experimental data is in good agreement with two models for singlet trapping as a function of doping; a Monte Carlo simulation of the trapping of neighboring singlets by Cu 1+ defects (blue dashed line Fig.4(b)) and a calculation of singlet trapping by localized electrons on Cu triangles in the kagomé lattice (black dotted line) (see SI). Since the magnitude of the gap is on the same order as the expected singlet-triplet gap energy in isolated valence bonds in Herbertsmithite [26], it is alluring to interpret the growth in high temperature specific heat as arising due to the trapping of valence bonds into a glass or solid-like state. However, further work is needed to exclude other possibilities, such as a localized oscillator mode arising from the inserted Li ions. The singlet trapping models are also in agreement with the magnetization data. Every intercalated Li atom reduces one Cu atom, removing its spin contribution and yielding a one-to-one relationship. So upon doping, the Curie constant will linearly go to zero, in agreement with the experimental data.
In conclusion, we have successfully introduced electrons into the prototypical kagomé quantum spin liquid Herbertsmithite. Despite the predictions, the doping of this system did not lead to metallicity or superconductivity down to T = 1.8 K. The magnetic field, temperature, and composition dependent specific heat all fit remarkably well to a single model.
What are the precise physical origins responsible for this behavior? It is plausible that the location of the inserted Li ions provides a sufficiently strong disorder potential that Anderson localization is never overcome, irrespective of electron count, but other explanations cannot be ruled out [27] [28]. The interesting physics is the following: why does charge doping this spin liquid not change it into a metal? The lower connectivity, with the 2-D kagomé lattice connects to four magnetic neighbors (n = 4) as compared to six magnetic neighbors of a 2-D triangular lattice (n = 6), may also play a role in the doped series behavior. Previous pressure and doping studies on higher connectivity frustrated geometries, such as organic triangular lattice κ-(ET) 2 Cu 2 (CN) 3 [29], Na x CoO 2 [30], and Na 4