Gapped Spin-1/2 Spinon Excitations in a New Kagome Quantum Spin Liquid Compound Cu₃Zn(OH)₆FBr^*

When subject to strong geometric frustrations, quantum spin systems may achieve paramagnetic ground states dubbed quantum spin liquid (QSL).^[1] It is characterized by the pattern of long-range quantum entanglement that has no classical counterpart.^[2–4] QSL is an unambiguous Mott insulator whose charge gap is not associated with any symmetry breaking.^[1] It is related to the mechanism of high-temperature superconductivity^[1] and the implementation of topological quantum computation.^[5] The underlying principle of QSL, i.e. topological orders due to quantum entanglement,^[3,4] is beyond the Landau symmetry-breaking paradigm^[2] and has been realized in fractional quantum Hall systems,^[6] resulting in fractionalized e/3 charged anyon.^[7,8] Similarly, fractionalized spin-1/2 spinon excitations are allowed in QSL.^[9–12]

Kagome Heisenberg antiferromagnets are promising systems for the pursuit of QSL.^[13–15] For example, herbertsmithite ZnCu₃(OH)₆Cl₂ is a famous kagome system, which displays a number of well-established QSL behaviors.^[16–29] Inelastic neutron scattering measurements have detected continuum of spin excitations^[25] while nuclear magnetic resonance (NMR) measurements suggest a finite gap at low temperature.^[29] However, multiple NMR lines of nuclear spins with $I\gt 1/2$ can not be easily resolved, particularly in the presence of residual interkagome Cu²⁺ spin moments even in high-quality single crystals.^{[20,23,28,29]} Furthermore, although it is commonly accepted that the quantum number of spinons is spin-1/2, no direct evidence has been observed.^[29] Therefore, it is crucial to find new QSL systems to unambiguously demonstrate the spin-1/2 quantum number of spinons.

Recently, barlowite Cu₄(OH)₆FBr has attracted much attention as a new kagome system with minimum disorder.^[30–35] As opposed to herbertsmithite with ABC-stacked kagome planes, barlowite crystallizes in high-symmetry hexagonal rods owing to direct AA kagome stacking. It has also been found that the in-plane Dzyaloshinskii-Moriya interaction in barlowite is an order of magnitude smaller than that in herbertsmithite.^[35] Consequently, the QSL physics has been suggested to be present at relative high temperature. Unfortunately, the material goes through an antiferromagnetic transition at ∼15 K.^[32,35] It has thus been proposed that substituting the interkagome Cu²⁺ sites with non-magnetic ions may suppress the magnetic transition and ultimately lead to a QSL ground state.^{[15,32,34,36]}

In this Letter, we report a new kagome QSL candidate Cu₃Zn(OH)₆FBr. It does not experience any phase transition down to 50 mK, more than three orders lower than the antiferromagnetic Curie-Weiss temperature (∼200 K). ¹⁹F NMR measurements reveal a gapped QSL ground state in Cu₃Zn(OH)₆FBr. The field dependence of the gap implies a zero-field gap 7.5 ± 0.4 K and spin-1/2 quantum number for spin excitations, i.e. spinons.

We have successfully synthesized Cu₃Zn(OH)₆FBr polycrystalline samples by replacing the interkagome Cu²⁺ sites in Cu₄(OH)₆FBr with non-magnetic Zn²⁺. Our thermodynamical (e.g. magnetic susceptibility and specific heat) measurements were carried out on the Physical Properties Measurement Systems (PPMS). The NMR spectra of ¹⁹F with the nuclear gyromagnetic ratio γ = 40.055 MHz/T were obtained by integrating the spin echo as a function of the RF frequency at constant external magnetic fields of 0.914 T, 3 T, 5.026 T and 7.864 T, respectively.

Figures 1(a) and 1(b) depict the crystal structure of Cu₃Zn(OH)₆FBr. Micrometer-size crystals are easily observed by the scanning electron microscope (SEM) (Fig. 1(c)). The refinement of the powder x-ray diffraction pattern (Fig. 1(d)) shows that the material crystallizes in $P{6}_{3}/{mmc}$ space group with Cu²⁺ ions forming a direct stack of undistorted kagome planes separated by non-magnetic Zn²⁺ ions (Figs. 1(a) and (b)) as expected from theoretical calculations.^[34] Cu₃Zn(OH)₆FBr is a charge-transfer insulator and the charge gap between Cu-3d⁹ and O-2p orbitals is around 1.8 eV according to first principles calculations.^[34,37] Powder x-ray diffraction measurements were carried out using Cu ${K}_{\alpha }$ radiation at room temperature. The diffraction data is analyzed by the Rietveld method using the program RIETAN-FP.^[38] All positions are refined as fully occupied with the initial atomic positions taken from Cu₄(OH)₆FBr.^[31] The refined results are summarized in Table 1.

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No phase transition is observed in our thermodynamical measurements (Fig. 2), establishing strong evidence for a QSL ground state in Cu₃Zn(OH)₆FBr. Temperature dependence of magnetic susceptibility under different magnetic fields does not display any magnetic transition down to 2 K as shown in Fig. 2(a). No splitting is detected between the field-cooled (FC) and zero-field-cooled (ZFC) results down to 2 K, indicating the absence of spin glass transition. At high temperature, magnetic susceptibility can be well fitted by the Curie-Weiss law with the Curie temperature and Curie constant as −200 K and 1.57 K $\cdot$ emu/mol, respectively. This indicates a strong antiferromagnetic superexchange interaction $J\sim 17$ meV among Cu²⁺ moments in the kagome planes. The g-factor is estimated to be about g = 2.4, consistent with the g-factor measurements in the Barlowite.^[35] In Fig. 2(b), no visible hysteresis loop is observed in the magnetic field dependence of magnetization at different temperatures. Figure 2(c) is the specific heat measurement at zero field down to 50 mK. The inset shows the magnetic field effect on the specific heat at low temperatures, which exhibits upturn behavior at high field due to nuclear Schottky anomaly.

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There are residual interkagome Cu²⁺ (RIC) moments due to incomplete Zn²⁺ substitution in Cu₃Zn(OH)₆FBr. Few Zn²⁺ exists in kagome planes according to the line shape of NMR spectra (see below for Fig. 3). The energy dispersive x-ray spectroscopy measurements at different locations indicate that the composition is stoichiometric with the atomic ratio between Cu and Zn as 1:0.36. The inductively coupled plasma atomic emission spectroscopy analysis suggests the atomic ratio between Cu and Zn as 1:0.30. From the chemical component analysis, we roughly estimate the concentration of the RIC moments to be ∼10%, comparable to those in herbertsmithite.^[39]

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At low temperatures, RIC moments obscure the intrinsic kagome plane QSL behaviors in the bulk magnetic susceptibility and heat capacity, similar to previous results of herbertsmithite.^[22,39–43] DC susceptibility at low temperatures in 0.1 T magnetic field is fitted by Curie-Weiss behavior with Curie constant and Curie temperature as 0.18 K $\cdot$ emu/mol and −2.9 K, respectively, indicating weak antiferromagetically interacting RIC moments. Under high magnetic fields, the RIC moments freeze and the AC susceptibility drops at low temperatures (see Fig. 2(a)). We also measure T-dependent AC susceptibilities for various frequencies and magnetic fields at low temperatures, see Fig. S7 in the supplementary materials (SM).^[44] The AC susceptibility is independent of frequencies, implying that RIC moments do not develop spin glass freezing down to 2 K. The RIC moments also contribute a shoulder in the specific heat measurements at low temperatures (see Fig. 2(c)). The shoulder is suppressed in magnetic fields, as shown in the inset of Fig. 2(c), along which the RIC moments are polarized, similar to herbertsmithite.^[41]

To directly unveil QSL physics in kagome plane, we implement NMR measurements to probe uniform spin susceptibility of kagome Cu²⁺ spin moments in Cu₃Zn(OH)₆FBr. A unique advantage of Cu₃Zn(OH)₆FBr for the NMR measurements is that it contains ¹⁹F. It is known that ²D, ¹⁷O and ³⁵Cl NMR measurements in herbertsmithite are rather difficult due to multiple resonance peaks resulted from nuclear spins I = 1, I = 5/2 and I = 3/2, respectively.^{[20,23,28,29]} In contrast, only one resonance peak needs to be resolved for ¹⁹F with I = 1/2 nuclear spin, as shown in Fig. 3(a). The sharp high-temperature peaks suggest that few ions of Zn²⁺ exist in kagome planes. Moreover, no extra peak due to RIC moments is observed even at low temperatures. The line shape asymmetry may arise from the magnetic anisotropy, e.g. ${g}_{\parallel }/{g}_{\perp }=2.42/2.21$ in Barlowite.^[35] We have also carried out the measurements with different pulse interval (τ) in NMR echo to exclude the possibility of impurity moment contributions in the NMR spectrum.^[44]

In a gapped QSL, the spin susceptibility should become zero at low temperature. The Knight shift is related to the uniform susceptibility χ as ¹⁹K = A_hf χ+ K_chem, where A_hf is the hyperfine coupling constant between the ¹⁹F nuclear spin and the electron spins, and K_chem is the T-independent chemical shift. K_chem = 0.015% is obtained from the ¹⁹K–χ plot at high temperatures as shown in the inset of Fig. 3(b), where χ is the DC susceptibility at B = 3 T. Figure 3(b) shows that the Knight shift drops quickly below ∼30 K. At high temperatures (∼100 K), the Knight shift ¹⁹K has a systematic variation as a function of magnetic field, whose origin is unclear at present and left for future investigation, but we note that such a behavior would not change our results at low temperatures below 30 K. The Knight shift at low fields (0.914 T and 3 T) tends to merge to K_chem at low temperatures, similar to the previous results of herbertsmithite.^[29] The inset of Fig. 3(c) is the Arrhenius plot of ¹⁹K−K_chem, where the low-temperature data can be well fitted by an exponential function $A\exp (-{\rm{\Delta }}/T)$, with A and Δ as fitting parameters for a constant and the gap value, respectively. In the fit, we fixed K_chem = 0.015%.

With elevating the magnetic fields, the gap is suppressed due to Zeeman effect as ${\rm{\Delta }}(B)={\rm{\Delta }}(0)-g{\mu }_{{\rm{B}}}{SB}$, where ${\mu }_{{\rm{B}}}$ is Bohr magneton. From the linear fitting of the field dependence of Δ, we obtain a zero-field gap 7.5 ± 0.4 K and gS = 1.16 ± 0.11. Regarding to g = 2.4 obtained from bulk magnetic susceptibility measurements in Fig. 2(a), gS = 1.16 ± 0.11 confirms a spin quantum number S = 1/2 and g = 2.32 ± 0.22. The spin S = 1/2 quantum number implies fractionalized spinon excitations in the quantum spin liquid compound Cu₃Zn(OH)₆FBr.

Detecting the spin-1/2 quantum number of spin excitations in a QSL state is of great significance. Spin-1/2 spinon excitations have been discussed since the early stage of spin liquid theory,^[9] yet there is no direct experimental confirmation of the spin-1/2 quantum number till now. Our results show that Cu₃Zn(OH)₆FBr has a gapped QSL ground state, consistent with the results in herbertsmithite,^[29] and unambiguously manifest the spin-1/2 quantum number of spinons. It reflects the spin fractionalization in a QSL state when spin rotation symmetry meets topology. Within minimal symmetry (e.g. time reversal symmetry and translational symmetry) assumptions, a gapped kagome QSL should be ${{\mathbb{Z}}}_{2}$-gauge type^[11,12] (i.e. toric code type^[5]) according to the theoretical constraints.^[45]

In conclusion, we have successfully synthesized a new kagome compound Cu₃Zn(OH)₆FBr and its quantum spin liquid ground state is verified in our thermodynamical measurements. Our ¹⁹F NMR data reveals a gapped spin-liquid ground state for Cu₃Zn(OH)₆FBr, similar to previous ¹⁷O NMR results on herbertsmithite. Most importantly, we provide experimental evidence for spin-1/2 quantum number for spin excitations, i.e. spinons. We therefore believe that Cu₃Zn(OH)₆FBr provides a promising platform for future investigations of the topological properties of quantum spin liquid states.

We acknowledge Yongqing Li for discussions on the magnetic susceptibility measurements. We thank Xi Dai and Zhong Fang for useful discussions.