Re-entrance of Gapless Quantum Spin Liquids Observed in a Newly Synthesized Spin-1/2 Kagome Antiferromagnet $ZnCu_{3}(OH)_{6}SO_{4}$

Quantum spin liquid (QSL) is a novel state of matter with exotic excitations and was theoretically predicted to be realized most possibly in an S=1/2 kagome antiferromagnet. Experimentally searching for the candidate materials is a big challenge in condensed matter physics and only two such candidates were reported so far. Here we report the successful synthesis of a new spin-1/2 kagome antiferromagnet ZnCu3(OH)6SO4. No magnetic ordering is observed down to 50 mK, despite a moderately high Weiss temperature of {\theta}W ~ -79 K. It strongly suggests that the material is a new QSL candidate. Most interestingly, the magnetic specific heat clearly exhibits linear behaviors in two low-temperature regions. Both behaviors exactly correspond to two temperature-independent susceptibilities. These consistently reveal a novel re-entrance phenomenon of gapless QSL state at the lowest temperatures. The findings provide new insights into QSL ground and excited states and will inspire new theoretical and experimental studies.


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Spin frustration describes a situation where spins cannot find an overall orientation configuration to simultaneously satisfy all of the nearest neighbor interactions 1 . In a strongly frustrated spin system, typical long-range magnetic ordering is prohibited and macroscopically degenerate ground states are produced.
The ground state and low-energy excitations of a frustrated spin system have captured the greatest interests in condensed matter physics for several decades since the long-range resonating valence bond (RVB) state was proposed by Anderson, not only due to their relation to high temperature superconductivity, but also due to their remarkable collective phenomena [2][3][4][5] . The spin frustration was considered to be strongest in a spin-1/2 kagome Heisenberg antiferromagnet (KHA), which received extensive theoretical studies and many kinds of novel quantum spin liquid (QSL) ground states were proposed [6][7][8][9][10][11] . On the experimental side, only a few compounds were discovered and reported to show QSL features so far. Experimentally they exhibit Fermi-liquid-like low-energy excitations such as linear temperature dependence of specific heat and/or temperature-independent susceptibility, which were considered to arise from spinons, the fractional particle excitations in a gapless spin liquid [12][13][14][15][16] .
Currently, one of the key issues in the field is to search for new QSL candidates.
Several key factors are essential in searching promising QSL candidates. Magnetic ions with small spins are the first one, due to their strong quantum spin fluctuations at low temperatures. The others are a triangle-based lattice, a lower magnetic dimension and a smaller coordination number, etc. These put strong constraints on potential 4 materials. Spin-1/2 KHA-type compounds meet the strict requirements. So far, only two spin-1/2 kagome antiferromagnets were discovered. One is the vanadium-based organic compound with S=1 interlayer ions 15 . The other one is herbertsmithite ZnCu 3 (OH) 6 Cl 2 [17][18][19][20][21] . The 2D nature of spin lattices in the latter compound may be affected by an effective magnetic coupling between kagome planes, which is induced by anti-site disorder due to a small mixing of magnetic Cu 2+ and non-magnetic Zn 2+ between kagome and interlayer sites. And Dzyaloshinskii-Moriya (DM) interaction, which is a measure of spin-orbit coupling, was found to play a role in the compound 22,23 . materials, but close to that of organic SL ones 5,13 , implying a small spin-orbit coupling in the new compound.
Most surprisingly, as cooling down to 0.6 K, the spin system clearly re-enters into a gapless QSL state with a much raised density of low-energy states, and maintains at least down to 50 mK. The observations seem compatible with the RVB QSL with a "pseudo-Fermi surface" 3,4 . The novel re-entrance of QSL has never been revealed before. It offers a completely new insight into QSL and its low-energy excitations.
Synchrotron X-ray powder diffraction and Rietveld refinement for ZnCu 3 (OH) 6 SO 4 are shown in Fig. 1 X-ray diffraction and combined Rietveld refinements revealed 28 . The crystal structure and ∠CuOCu bond angles are shown in Fig. 1(b). The ∠CuOCu bond angles suggest an antiferromagnetic (AF) coupling-dominated configuration 29,30 . In Fig. 1 We further performed extended magnetic measurements on ZnCu 3 (OH) 6 SO 4 .
Electron spin resonance (ESR) derivative spectrum of ZnCu 3 (OH) 6 SO 4 at 1.8 K is shown in Fig.3(a). The derivative Lorentzian fittings give an average g factor of ~ 2.19. The dc magnetization down to 0.5 K under 1000 Oe is shown in Fig.3(b). The magnetization upturn at low temperatures is caused by the small mixing of Zn and Cu on kagome planes as observed in other inorganic SL candidates. Using the g factor obtained from ESR measurements, we can estimate an effective amount (~ 9%) of quasi-free defects by fitting susceptibilities from 6~15K, which gives a Weiss temperature, θ D ~ -1.16 K (inset of Fig.3(b)). The similar level of quasi-free defects and θ D were also reported in herbertsmithites [32][33][34] . By subtracting the above contributions from quasi-free spins, we obtained bulk susceptibilities dominantly contributed by frustrated (or intrinsic) spins. It allows us to make a simulation of high temperature series expansion (HTSE) 35  Heat capacity experiment is one of the key techniques to probe low-energy excitations. We performed heat capacity measurements down to 50 mK with a dilution 9 refrigerator system. No sharp peak structure is observed ( Fig.4 (a) and (d)), suggesting the absence of long-range spin ordering. A broad peak is observed at several Kelvins and shifts to higher temperatures when applying magnetic fields. It is a typical Schottky anomaly arising from magnetic defects as found in some SL candidates [14][15][16]36 . As shown in Fig.4 (b) Fig.4 (b), may be due to a small coupling between quasi-free spins as suggested in our high magnetic field measurements.
In addition, there is a very small Schottky contribution from hydrogen nuclear spins below 80 mK, which can be seen in the inset of Fig.4 (c) and Fig. 5. The term is centered below 50 mK and its high-energy wing can be exactly simulated by AT -2 , where A ~ 6.6(2)×10 -2 mJKmol -1 , in good accord with κ-(BEDT-TTF) 2 Cu 2 (CN) 3 and The remaining specific heat from 6 to 15 K follows a form of βT 3 +γ 1 T after the Schottky contributions from defect spins are removed, as shown in the plot of C p T -1 versus T 2 in Fig. 4(c), where γ 1 ~ 177 mJK -2 mol -1 and β ~ 1.18 mJK -4 mol -1 12,13 .
Clearly the term βT 3 arises from lattice contributions. In order to confirm this and make further quantitative analyses strictly, we have measured the specific heat up to 10 60 K in both ZnCu 3 (OH) 6 SO 4 and Zn 0.6 Cu 3.4 (OH) 6 SO 4 ( Fig.4 (d)). Due to the structural similarity, their specific heats merge together at high temperatures when lattice contributions become dominant and magnetic specific heat is negligible at T > 45 K. So we can applied the strict Debye function with a Debye temperature ~ 225 K, to fit the lattice specific heat at T > 45 K (Fig.4(d)). Below 20 K, the discrepancy between Debye fitting and T 3 -law is less than 1%, which means that we can safely use βT 3 to fit lattice specific heat at low temperatures (<15 K).
Intrinsic magnetic specific heat from kagome spins is obtained after further subtracting lattice specific heat, as shown in Fig.4(e). Interestingly, two linear behaviors are found with γ 1 ~ 177 mJK -2 mol -1 from 6 ~ 15 K and γ 2 ~ 405 mJK -2 mol -1 below 0.6 K. We further calculated the intrinsic magnetic entropy increase ( Fig. 4(f)). Correspondingly it shows two linear regions and saturates at ~ 40 K, which implies that a ground state with macroscopic degeneracy (~ 63 % residual entropy) is realized in the new compound.
In order to further uncover the underlying physics, we put intrinsic bulk susceptibilities and specific heat together in Fig. 5 15 . In the S=1 triangular antiferromagnet, Ba 3 NiSb 2 O 9 (6H-B) 14 , it can go up to 7 K(0.093θ W ). Due to a smaller spin moment and stronger frustration configuration, for a S=1/2 HKA one can reasonably expect a higher temperature limit, below which gapless QSL overcomes thermal dynamics.
The linear magnetic specific heat suggests the existence of two gapless QSL states in the material [12][13][14][15][16] . Quantitatively, γ and χ in the lower-temperature QSL state are several times larger than those in the higher temperature QSL state. This suggests that the lower temperature QSL state has a larger density of low-energy states than that of higher temperature one. It seems incompatible with valence-bond crystal (VBC) 10 , the gapped Ζ 2 6 and gapless U(1) Dirac 7,8 (where C~T 2 and χ~T) SL ground states of HKA, but compatible with the RVB QSL with a "pseudo-Fermi surface" 3,4 .
What drives the crossover from the higher temperature QSL state to the stable one at lower temperatures? As mentioned above, the magnetic coupling between well-separated neighboring kagome planes, if exists, should be very weak. So it is less possible that the crossover is related to the change of dimension. Moreover, the linear behaviors in specific heat both above and below the crossover, is also hard to be interpreted by the change of dimension 14  In conclusion, we synthesized a new QSL candidate, ZnCu 3 (OH) 6

SO 4 , which has
Cu-1/2 corrugated distorted but well magnetically separated kagome planes. No magnetic ordering is observed even down to 50 mK ( f > 1580). In the temperature ranges of 6 ~15 K and below 0.6 K, intrinsic magnetic specific heat shows a linear temperature dependence and bulk susceptibilities are constants. The facts lead us to an unexpected conclusion that the gapless QSL state at higher temperatures (6 ~ 15 K) re-enters into a QSL state with a larger density of low-energy states at T < 0.6 K, after a crossover possibly driven by spin-orbit coupling. The observations cannot be interpreted by the existing theoretical picture. The present work may lead to a new insight into QSL ground state and its low-energy excitations.