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Gapless quantum spin liquid in the S = 1/2 anisotropic kagome antiferromagnet ZnCu3(OH)6SO4

We have successfully synthesized the new S = 1/2 anisotropic kagome antiferromagnet ZnCu3(OH)6SO4 and determined its structure by synchrotron x-ray diffraction. No magnetic ordering is observed down to 50 mK, despite a moderately high Weiss temperature of Θw ∼ −79 K, indicating that the compound is a new quantum spin liquid (QSL) candidate. A linear temperature dependence of the magnetic heat capacity is found at 6 ∼ 15 K and below 0.6 K. Temperature-independent intrinsic susceptibilities are observed exactly in both temperature ranges. This consistently suggests a gapless QSL below 0.6 K, which may evolve from an unconventional quantum spin state at higher temperatures (6 ∼ 15 K).


Introduction
The ground state and low-energy excitations of a frustrated spin system have attracted a great deal of interest in condensed matter physics [1][2][3][4]. The strongest spin frustration was considered to occur in a S = 1/2 kagome Heisenberg antiferromagnet (KHA), on which extensive theoretical studies were performed and many novel quantum spin liquid (QSL) ground states were proposed [5][6][7][8][9][10]. Fermi-liquid-like low-energy excitations, such as the linear temperature dependence of heat capacity and/or temperature-independent susceptibility, are experimentally observed in most reported QSL candidate compounds. These excitations are attributed to spinons, fractional particle excitations in gapless spin liquids [11][12][13][14].
One of the current key issues in the field is to search for new QSL candidates. Two promising S = 1/2 KHA candidates have been reported so far. One is a vanadium-based organic compound with S = 1 interlayer ions [15,16]. The other one is the famous herbertsmithite ZnCu 3 (OH) 6 Cl 2 [17][18][19][20][21][22]. In the latter compound, a small mixing of magnetic Cu 2+ and nonmagnetic Zn 2+ between kagome and interlayer sites, and the Dzyaloshinskii-Moriya (DM) interaction, which is a measure of spin-orbit coupling, were reported [23].
ZnCu 3 (OH) 6 Cl 2 was synthesized by replacing 25% of Cu 2+ ions in clinoatacamite Cu 4 (OH) 6 Cl 2 (Neel temperature T c ∼ 7.5 K) with Zn 2+ . The site preferences drive Zn 2+ ions to enter interlayer sites and Cu 2+ ions to occupy kagome sites [24][25][26]. In this paper we tried a similar substitution in the recently synthesized brochantite Cu 4 (OH) 6 SO 4 , which has four symmetrically inequivalent Cu sites forming corrugated distorted triangular 2D planes and shows a long-range Neel ordering at 7.5 K [27]. When one of the four Cu sites (Cu4) in Cu 4 (OH) 6 SO 4 was successfully replaced by Zn 2+ , we obtained a new S = 1/2 anisotropic kagome antiferromagnet ZnCu 3 (OH) 6 SO 4 with well magnetically separated corrugated 2D planes. Unlike herbertsmithite, both Cu 2+ and Zn 2+ ions in the new compound are located in the anisotropic kagome planes. For a fixed number of spins in 2D planes, from less-frustrated edgesharing triangular to vertex-sharing kagome lattices, the number of constraints is minimized, and the ground-state degeneracy is maximized [28]. Naturally an obvious suppression of longrange Neel ordering and a much stronger spin frustration should be expected.
Magnetization and heat capacity measurements reveal some exciting features in the compound. No magnetic ordering was observed, even down to 50 mK. The Weiss temperature of Θ w ∼ −79 K gives a degree of spin frustration, f = |Θ w |/T c , [4,28] higher than ∼1580. The two linear temperature-dependent behaviors in magnetic heat capacity exactly correspond to the temperature-independent intrinsic susceptibilities at 6 ∼ 15 K and below 0.6 K. Both the linear heat capacity coefficients (γ) and temperature-independent intrinsic susceptibilities (χ) are proportional to the density of low-energy states, which may be attributed to spinons, electrons or other quasi-particles with a 'pseudo-Fermi surface' [4]. Considering that the compound is a good insulator with a gap of 4.2 eV, the quantum spin state below 0.6 K seems compatible with the resonating valence bond (RVB) QSL with a 'pseudo-Fermi surface' [2,3]. It may evolve from the unusual quantum state at higher temperatures (6 ∼ 15 K) through a rapid crossover, possibly driven by spin-orbit coupling, anisotropic nearest neighboring interactions or other higher order interactions.

Methods
ZnCu 3 (OH) 6 6 SO 4 with a scanning electron microscope-x-ray energy dispersive spectrometer (SEM-EDX, JEOL JSM-6700F). Synchrotron x-ray diffractions (XRD) and x-ray absorption fine structure (XAFS) spectra were performed in the diffraction station (4B9A) of Beijing Synchrotron Radiation Facility (BSRF). The powder sample of ∼200 mg for synchrotron XRD was pressed into the 1 cm × 1 cm × 1.5 mm square groove of a glass slide. A tape evenly coated with the powder sample, ∼10 mg, was used for synchrotron XAFS. The General Structure Analysis System (GSAS) program was used for Rietveld refinements [29]. The ultraviolet/visible (UV/VIS) absorption spectrum for ZnCu 3 (OH) 6 SO 4 was measured using a PerkinElmer Lambda 950 with a deuterium lamp. The powder sample, ∼10 mg, was tightly and evenly clamped by two quartz slides for the UV/VIS absorption experiment. High-pulsed-field (up to 42 T) magnetization measurements were performed at Wuhan Pulsed High Magnetic Field Center (WHMFC). Magnetization and heat capacity measurements above 2 K were made with Quantum Design MPMS and PPMS, respectively. Magnetization measurements between 2 K and 0.5 K were made with a Quantum Design SQUID with a 3 He system. Heat capacities between 3.6 K and 50 mK were measured using a Quantum Design PPMS with a dilution refrigerator system, on a 1.7 mg dye-pressed pellet of ZnCu 3 (OH) 6 SO 4 . The international system of units (SI) is used.

Results
Synchrotron x-ray powder diffraction and Rietveld refinement for ZnCu 3 (OH) 6 SO 4 are shown in figure 1(a). No additional peak is observed, indicating negligible impurity phases in the sample. ZnCu 3 (OH) 6 SO 4 has a monoclinic structure with the space group P 21/a, a = 13.0606 (12) Å, b = 9.8697(10) Å, c = 6.0882(6) Å, and β = 103.6071(24) o , similar to the parent Cu 4 (OH) 6 SO 4 [27]. One of the four inequivalent Cu sites (Cu4) in Cu 4 (OH) 6 SO 4 is dominantly replaced (∼78%) by Zn (see the supplementary information), as synchrotron resonant XRD, XAFS and combined Rietveld refinements revealed [30]. The ∠CuOCu bond angles characterizing nearest neighboring exchange couplings [27,31,32] are shown in figure 1(b). In figures 1(b) and (c), two non-equivalent chains along the c-axis can be clearly seen. Edgesharing copper octahedrons (CuO 6 ) line up along the first chain (A), and the other chain (B) is an alternate alignment of zinc planes (ZnO 4 ) and copper octahedrons (CuO 6 ). The chains are AB-stacked along the b-axis to form corrugated kagome planes with 6% distortions of Cu-Cu bonds ( figure 1(d)). The corrugated Cu 2+ S = 1/2 kagome planes are well magnetically separated by non-magnetic SO 4 tetrahedrons (figure 1(e)). As a building block of kagome lattices, each spin triangle consists of three non-equivalent nearest Cu 2+ ions, suggesting anisotropic spin interactions. Refinements give a ∼8% site disorder between Cu 2+ and Zn 2+ , which is further confirmed by magnetization and heat capacity measurements (see below).
We have synthesized three samples with Zn = 0, 0.6 and 1.0. All of the samples are good insulators with a room-temperature resistance higher than 20 MΩ. The UV/VIS absorption spectrum of ZnCu 3 (OH) 6 SO 4 gives a large band gap Eg of ∼4.2 eV. the dc susceptibilities are shown in figure 2(a). The high temperature (150 ∼ 300 K) Currie-Weiss fitted parameters are summarized in table 1. The Lande g factors, obtained from the fitted Curie constants, are in accord with the typical value of Cu 2+ [23]. The magnetizations under zero field cooling (ZFC) and field cooling (FC, 100 Oe) are shown in figure 2(b). A clear splitting between FC and ZFC in Cu 4 (OH) 6 SO 4 occurs around T c ∼ 7.5 K, indicating a long-range Neel transition [27] and a moderate degree of spin frustration f = |Θ w |/T c ∼ 13 for parent triangular lattices [4]. The transition temperature is suppressed to 3.5 K in Zn 0.6 Cu 3.4 (OH) 6 SO 4 and f is pushed up to ∼26. The splitting in the partially Zn-substituted compound could originate from an AF or a spinglass transition [33]. The splitting completely disappears in ZnCu 3 (OH) 6 SO 4 . Further magnetization and heat capacity measurements (see below) indicate that no magnetic transition is found, even down to 50 mK (f > 1580). This demonstrates that strong spin frustration in brochantite systems is successfully realized through non-magnetic ion substitution.
Magnetization measurements were made under high pulsed magnetic fields (up to 42 T) at 4.2 K and static fields (up to 6 T) at 0.5 K (figures 3(a) and (b)). Magnetization saturation occurs ∼20 T at 4.2 K and ∼4.5 T at 0.5 K, respectively [16,34]. Above the saturation fields, the magnetizations exhibit a linear field-dependence with the slopes of χ up (4.2 K) ∼ 0.08 cm 3 mol −1 and χ up (0.5 K) ∼ 0.26 cm 3 mol −1 . By subtracting the linear contributions (χ up H ), ∼8% quasifree spins can be consistently estimated at both temperatures, in agreement with the above refinement results. The quasi-free spins are often attributed to magnetic defects due to a small Zn-Cu mixing [34,35]. Disordered magnetic defects Cu 2+ (Cu4) and the integrated staggered  magnetization around kagome nonmagnetic defects Zn 2+ can contribute to these quasi-free spins [36]. The magnetizations from defect spins can be well described by Brillouin functions at 4.2 K and 0.5 K, except for a small overshooting at low fields, which suggests that defect spins are somehow coupled rather than completely free [16,34]. Schottky contributions to the zero-field heat capacity from quasi-free defect spins become negligible at 7 ∼ 15 K (see also below, Δ 0T /k B ≪ 7 K). Thus the total heat capacity can be safely decomposed into lattice and intrinsic (magnetic or electronic) contributions. Figure 3(c) shows the zero-field heat capacity from 7 to 15 K, which can be well fitted with a T term plus a T 3 term: C p = βT 3 + γ 1 T, where β ∼ 1.18(1) mJ K −4 mol −1 and γ 1 ∼ 1 77(1) mJ K −2 mol −1 . The T 3 term comes from lattice vibrations (see below), while the linear term is generally attributed to gapless QSL with a 'pseudo-Fermi surface' or electronic specific heat. Physically, the linear heat capacity corresponds to the temperature-independent susceptibility (χ 1 ) in the same temperature range [4]. Therefore, the measured susceptibility can be decomposed into two parts: the intrinsic susceptibility χ 1 and the contributions from the magnetic defects χ def = C def / (T-Θ def ) [34,37,38] (inset of figure 3(c)). It gives ∼9% weakly coupled rather than completely free S = 1/2 defect spins with a Weiss temperature Θ def ∼ −1.16(1) K [34,37,38]. By subtracting the magnetic defect contributions from the total susceptibilities, we further obtain bulk susceptibilities dominantly contributed by frustrated spins (figure 3(d)). With cooling down, a broad hump of bulk susceptibilities develops around |Θ w |, suggesting a short-range magnetic correlation in kagome planes [37,38]. Bulk susceptibilities are nearly temperatureindependent with χ 1 ∼ 0.068 cm 3 mol −1 from 6 to 15 K, and they quickly rise with further cooling down. A blurred but still visible maximum χ 2 ∼ 0.27 cm 3 mol −1 is reached below 0.6 K (inset of figure 3(d)). The slopes χ up (4.2 K) and χ up (0.5 K) extracted from figures 3(a) and (b) are in good agreement with the bulk susceptibilities. This indicates that our data analysis is selfconsistent and bulk susceptibilities are contributed by intrinsic magnetic excitations. By applying an S = 1/2 KHA high-temperature series expansion (HTSE) simulation to the high temperature part (>150 K) of the measured susceptibilities with g ∼ 2.20 ( figure 3(d)), an average effective antiferromagnetic coupling can be estimated to be J eff ∼ 65 K [14,38,39].
Heat capacity measurements down to 50 mK were performed to probe low-energy excitations. No sharp peak structure is observed ( figure 4(a)), suggesting the absence of longrange spin ordering. The broad peak at several Kelvins shifts to higher temperatures when applying magnetic fields. It is a typical Schottky anomaly arising from magnetic defects, as often found in some SL candidates [13,14,16,40]. The difference between 0 T and 12 T data can be well modeled by Zeeman splitting for S = 1/2 spins ( figure 4(b)). The Schottky term can be written as f d [C sch (Δ H1 )-C sch (Δ H2 )]/T, where C sch (Δ H ) is the heat capacity from an S = 1/2 spin with an energy splitting Δ H , and f d is the fraction of doublets per formula. The fitted f d (∼0.184 (2)) gives 6.1(1) % defect spins. The value is a little smaller than ∼8% given by the above refinements and magnetization measurements. A similar discrepancy is also found in ZnCu 3 (OH) 6 Cl 2 [34,37,40,41] and remains an open question. For free spins, Δ H is expected to exactly follow Zeeman splitting with g ∼ 2.20 (inset of figure 4(b)). The slight difference may be due to a small coupling between quasi-free spins, as suggested in magnetization measurements. The zero-field splitting, Δ 0T /k B ∼ 1.4 K, confirms that defect spins are weakly coupled rather than completely free. It explains why the Schottky anomaly is still observed under zero field around ∼0.6 K ( figure 4(a)). It should be noted that a tiny Schottky contribution from hydrogen nuclear spins appears below 80 mK (figures 4(a) and (d)). The term is centered below 50 mK and its high-temperature wing can be well simulated by AT −2 (figure 4(d)), where A ∼ 6.6(2) × 10 −2 mJ K mol −1 , in good accord with κ-(BEDT-TTF) 2 Cu 2 (CN) 3 and EtMe 3 Sb[Pd (dmit) 2 ] 2 [11,12].
We have measured the heat capacity up to 60 K for ZnCu 3 (OH) 6 SO 4 and Zn 0.6 Cu 3.4 (OH) 6 SO 4 ( figure 4(c)). Lattice contributions become dominant and the magnetic heat capacity is negligible at T > 45 K. Both heat capacities merge together due to the structural similarity. We apply the original Debye function with a Debye temperature ∼225 K, to fit the lattice heat capacity at T > 45 K ( figure 4(c)). Below 20 K, the discrepancy between standard Debye fitting and the T 3 -law is less than 1%, suggesting that we can safely use βT 3 to fit the lattice heat capacity at low temperatures (<15 K). This allows us to extract the intrinsic magnetic heat capacity after subtracting lattice contributions and the part contributed by magnetic defects, as shown in figure 4(d). Interestingly, two linear behaviors with γ 1 ∼ 177(1) mJ K −2 mol −1 and γ 2 ∼ 405(4) mJ K −2 mol −1 appear at 6 ∼ 15 K and below 0.6 K, respectively. We further calculate the intrinsic magnetic entropy increase ΔS m from 50 mK to 50 K (inset of figure 4(c)), which gives a ∼63(3)% residual entropy of the total Cu 2+ contributions. The residual entropy reflects the unfreezable part of the total degree of freedom of spins, and clearly suggests a ground state with macroscopic degeneracy in the new compound.

Discussion
The linear heat capacity coefficient at 0.05 ∼ 0.6 K (γ 2 ) is comparable to those of other inorganic QSL candidates such as Ba 3 NiSb 2 O 9 (6H-B) and ZnCu 3 (OH) 6 Cl 2 (table 2). At such low temperatures, the linear term is reasonably attributed to a gapless QSL with a 'pseudo-Fermi surface', considering that the compound is a good insulator [4]. The picture seems compatible with the RVB QSL with a 'pseudo-Fermi surface' [2,3] rather than a valence-bond crystal (VBC) [9], the gapped Z 2 [5] and gapless U(1) Dirac [6,7] (where C ∼ T 2 and χ ∼ T) SL ground states of HKA.
The linear behavior at higher temperatures (6 ∼ 15 K) is a little more complicated to understand, as the temperature range seems relatively high for QSL compared with other QSL candidates (table 2). One possibility is the effect of thermal fluctuations. We have also tried βT 3 + aT 2 to fit the heat capacity under 0 T at the temperature region (not shown here). But it fails to follow the experimental data. The temperature-independent susceptibilities (χ 1 ) observed in the same temperature range (figure 4(d)) are also hard to understand in terms of classical thermal spin fluctuations. Another possibility is electronic origin, which should correspond to a weak Pauli paramagnetism in nature. The linear coefficient (γ 1 ) seems too large for a conventional metal, in which the typical Sommerfeld coefficient ranges from 0.1 to 10 mJ K −2 mol −1 . One may argue that it may be caused by a large effective electron mass. The smaller Wilson ratio at 6 ∼ 15 K, R W = 4π 2 k B 2 χ/(3 g 2 μ 0 μ B 2 γ) ∼ 1.9 also looks consistent with this possibility. However, the linear term rising from electrons is nearly zero considering that the compound is a good insulator with a large gap of ∼4.2 eV and that the density of free electrons is extremely low.
On the other hand, the temperature range of 6 ∼ 15 K is still very low (<0.19 |Θ w |) compared with |Θ w | or J eff . As a result, quantum spin fluctuations may be strong enough to overcome classical thermal spin fluctuations, and a QSL state still possibly survives [4]. Both γ and χ below 0.6 K are several times larger than those at 6 ∼ 15 K. This indicates that the density of low-energy quantum states are much enhanced as cooling down. We can further compare Wilson ratios in both temperature ranges, which are considered to be a quantitative description on the importance of spin-orbit coupling [4]. They are R W1 ∼ 1.9 and R W2 ∼ 3.2 in the higherand lower-T regions, respectively. The remarkable increase of R W at low temperatures suggests an enhanced importance of spin-orbit coupling. This becomes possible because the high-order interactions, such as spin-orbit coupling and anisotropic nearest neighboring exchange interaction, may stand out due to the gradual suppression of thermal spin fluctuations at low temperatures. Hence it may result in an enhanced density of low-energy quantum states below 0.6 K in ZnCu 3 (OH) 6 SO 4 . The unconventional behaviors at 6 ∼ 15 K may be also caused by other unknown magnetic or quasi-particle excitations with a 'pseudo-Fermi surface'. To unravel the underlying physics, further theoretical and experimental studies are required in the future.

Conclusion
In conclusion, we have synthesized a new QSL candidate ZnCu 3 (OH) 6 SO 4 , which has corrugated but well-magnetically-separated S = 1/2 kagome planes. No magnetic ordering is observed, even down to 50 mK (f > 1580). The linear temperature dependence of the intrinsic magnetic heat capacity is observed in the ranges of 6 ∼ 15 K and below 0.6 K, while the corresponding bulk susceptibilities are temperature-independent. The observations suggest that a gapless QSL appears at low temperatures (T < 0.6 K), which may evolve from an unconventional quantum spin state at 6 ∼ 15 K with much enhanced density of low-energy states. The understanding of the present observations brings new challenges for the existing theoretical scenarios and is expected to yield new insights into QSL.