Gapped spin-1/2 spinon excitations in a new kagome quantum spin liquid compound Cu$_3$Zn(OH)$_6$FBr

TL;DR

This study presents evidence of gapped spin-1/2 spinon excitations in a new kagome quantum spin liquid compound, demonstrating spin fractionalization and topological order through low-temperature magnetic measurements.

Contribution

The paper reports the discovery of a new kagome quantum spin liquid compound exhibiting spin fractionalization and a low-temperature spin gap, with experimental evidence supporting topological order.

Findings

No phase transition down to 50 mK.

Observation of a low-temperature spin gap.

Magnetic field dependence consistent with spinon excitations.

Abstract

We report a new kagome quantum spin liquid candidate Cu$_3$Zn(OH)$_6$FBr, which does not experience any phase transition down to 50 mK, more than three orders lower than the antiferromagnetic Curie-Weiss temperature ($\sim$ 200 K). A clear gap opening at low temperature is observed in the uniform spin susceptibility obtained from $^{19}$F nuclear magnetic resonance measurements. We observe the characteristic magnetic field dependence of the gap as expected for fractionalized spin-1/2 spinon excitations. Our experimental results provide firm evidence for spin fractionalization in a topologically ordered spin system, resembling charge fractionalization in the fractional quantum Hall state.

Tables

Table 1. Table 1: Structure parameters of Cu 3 Zn(OH) 6 FBr at room temperature. Space group P ​ 6 3 / m ​ m ​ c 𝑃 subscript 6 3 𝑚 𝑚 𝑐 P6_{3}/mmc ; a = b = 6.6678 ​ ( 2 ) 𝑎 𝑏 6.6678 2 a=b=6.6678(2) Å, c = 9.3079 ​ ( 3 ) 𝑐 9.3079 3 c=9.3079(3) Å.

Site	$w$	$x$	$y$	$z$	$B$ (Å2)
Cu	$6g$	0.5	0	0	1.48(6)
Zn	$2d$	1/3	2/3	3/4	1.93(8)
Br	$2c$	2/3	1/3	3/4	1.99(5)
F	$4b$	0.0	0.0	3/4	0.34(2)
O	$12k$	0.1887	0.8113(5)	0.9021(7)	2.22(2)
H	$12k$	0.1225	0.8775	0.871	1.0

Full text

When subject to strong geometric frustrations, quantum spin systems may achieve paramagnetic ground states dubbed quantum spin liquid (QSL) Anderson (1987). It is characterized by the pattern of long-range quantum entanglement that has no classical counterpart Wen (2004); Kitaev and Preskill (2006); Levin and Wen (2006). QSL is an unambiguous Mott insulator whose charge gap is not associated with any symmetry breaking Anderson (1987). It is related to the mechanism of high-temperature superconductivity Anderson (1987) and the implementation of topological quantum computation Kitaev (2003). The underlying principle of QSL, i.e. topological orders due to quantum entanglement Kitaev and Preskill (2006); Levin and Wen (2006), is beyond the Landau symmetry-breaking paradigm Wen (2004) and has been realized in fractional quantum Hall systems Tsui et al. (1982), resulting in fractionalized $e/3$ charged anyon Laughlin (1983); de Picciotto et al. (1997). Similarly, fractionalized spin-1/2 spinon excitations are allowed in QSL Kivelson et al. (1987); Read and Chakraborty (1989); Read and Sachdev (1991); Wen (1991).

Kagome Heisenberg antiferromagnets are promising systems for the pursuit of QSL Lee (2008); Balents (2010); Norman (2016). For example, herbertsmithite ZnCu3(OH)6Cl2 is a famous kagome system, which displays a number of well-established QSL behaviors Shores et al. (2005); Helton et al. (2007); Mendels et al. (2007); Zorko et al. (2008); Imai et al. (2008); de Vries et al. (2009); Helton et al. (2010); Imai et al. (2011); Jeong et al. (2011); Han et al. (2012a, b, 2011, a); Imai et al. (2008); Olariu et al. (2008); Fu et al. (2015). Inelastic neutron scattering measurements have detected continuum of spin excitations Han et al. (2012a) while nuclear magnetic resonance (NMR) measurements suggest a finite gap at low temperature Fu et al. (2015). However, multiple NMR lines of nuclear spins with $I>1/2$ can not be easily resolved, particularly in the presence of residual interkagome Cu2+ spin moments even in high-quality single crystals Imai et al. (2008); Olariu et al. (2008); Imai et al. (2011); Fu et al. (2015). Furthermore, although it is commonly accepted that the quantum number of spinons is spin-1/2, no direct evidence has been observed Fu et al. (2015). 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 Elliot and Cooper (2010); Elliot et al. (2014); Han et al. (2014); Jeschke et al. (2015); Liu et al. (2015a); Han et al. (2016a). 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 Han et al. (2016a). Consequently, the QSL physics has been suggested to be present at relative high temperature. Unfortunately, the material goes through an antiferromagnetic transition at $\sim 15$ K Han et al. (2014, 2016a). 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 Han et al. (2014); Liu et al. (2015a); Guterding et al. (2016); Norman (2016).

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 ($\sim$ 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 $7.5\pm 0.4$ 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 $\gamma=40.055$ 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.

Figure 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 $P6_{3}/mmc$ space group with Cu2+ ions forming a direct stack of undistorted kagome planes separated by non-magnetic Zn2+ ions (Fig. 1 (a) and (b)) as expected from theoretical calculations Liu et al. (2015a). Cu3Zn(OH)6FBr is a charge-transfer insulator and the charge gap between Cu-3$d^{9}$ and O-2$p$ orbitals is around 1.8 eV according to first principles calculations Liu et al. (2015b, a). 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 Rietveld (1969). All positions are refined as fully occupied with the initial atomic positions taken from Cu4(OH)6FBr Elliot et al. (2014). The refined results are summarized in Table 1.

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 Han et al. (2016a). 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.

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 in 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 $\sim 10\%$, comparable to those in herbertsmithite Freedman et al. (2010).

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 Bert et al. (2007); de Vries et al. (2008); Helton et al. (2010); Freedman et al. (2010); Han et al. (2016b); Kelly et al. (2016). 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.S 7 in the supplementary materials (SM) sup . 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 supressed in magnetic fields, as shown in the inset of Fig. 2 (c), along which the RIC moments are polarized, similar to herbertsmithite de Vries et al. (2008).

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 Imai et al. (2008); Olariu et al. (2008); Imai et al. (2011); Fu et al. (2015). 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 Zn2+ exists 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. $g_{\|}/g_{\perp}=2.42/2.21$ in Barlowite Han et al. (2016a). We have also carried out the measurements with different pulse interval ($\tau$) in NMR echo to exclude the possibility of impurity moment contributions in the NMR spectrum sup .

In a gapped QSL, the spin susceptibility should become zero at low temperature. The Knight shift is related to the uniform susceptibility $\chi$ as ${}^{19}K=A_{\text{hf}}\chi+K_{\text{chem}}$, where $A_{\text{hf}}$ is the hyperfine coupling constant between the 19F nuclear spin and the electron spins and $K_{\text{chem}}$ is the $T$-independent chemical shift. $K_{\text{chem}}=0.015\%$ is obtained from ${}^{19}K$-$\chi$ plot at high temperatures as shown in the inset of Fig. 3 (b), where $\chi$ is DC susceptibility at $B=3$ T. Figure 3 (b) shows that the Knight shift drops quickly below $\sim 30$ K. At high temperatures ($\sim 100$ K), Knight shift ${}^{19}K$ 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 $K_{\text{chem}}$ at low temperatures, similar to previous results of herbertsmithite Fu et al. (2015). The inset of Fig. 3 (c) is the Arrhenius plot of ${}^{19}K-K_{\text{chem}}$, where the low-temperature data can be well fitted by an exponential function $A\exp(-\Delta/T)$, with $A$ and $\Delta$ as fitting parameters for a constant and the gap value, respectively. In the fit, we fixed $K_{\text{chem}}=0.015\%$.

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

Detecting 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 Kivelson et al. (1987), 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 results in herbertsmithite Fu et al. (2015) 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 Read and Sachdev (1991); Wen (1991) (i.e. toric code type Kitaev (2003)) according to the theoretical constraints Zaletel and Vishwanath (2015).

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. We acknowledge fundings from the National Key Research and Development Program of China under Grant Nos. 2016YFA0300502, 2016YFA0300503, 2016YFA0300604, 2016YF0300300 and 2016YFA0300802, the National Natural Science Foundation of China under Grant Nos. 11421092, 11474330, 11574359, 11674406, 11374346 and 11674375, National Basic Research Program of China (973 Program) No. 2015CB921304, the National Thousand-Young-Talents Program of China, the Strategic Priority Research Program (B) of the Chinese Academy of Sciences under Grant No. XDB07020000, XDB07020200 and XDB07020300. The work in Utah is supported by DOE-BES under No. DE-FG02-04ER46148.