⇦Chinese Physics Letters, 2022, Vol. 39, No. 5, Article code 050102Viewpoint Material Search for Quantum Spin Liquids on the Simplest Frustrated Lattice Hui-Ke Jin (金汇可)1* and Yi Zhou (周毅)2,3,4,5* Affiliations 1Department of Physics TQM, Technische Universität München, James-Franck-Straße 1, D-85748 Garching, Germany 2Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China 3Songshan Lake Materials Laboratory, Dongguan 523808, China 4Kavli Institute for Theoretical Sciences, University of Chinese Academy of Sciences, Beijing 100190, China 5CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences, Beijing 100190, China Received 7 April 2022; accepted 15 April 2022; published online 30 April 2022 *Corresponding authors. Email: huike.jin@tum.de; yizhou@iphy.ac.cn Citation Text: Jin H K and Zhou Y 2022 Chin. Phys. Lett. 39 050102    Abstract DOI:10.1088/0256-307X/39/5/050102 © 2022 Chinese Physics Society Article Text The past few decades have witnessed a great endeavor in the search for quantum spin liquids (QSLs).[1–8] This phase of matter, which features long-ranged quantum entanglement and fractionalized spin excitations, is beyond Landau's symmetry-breaking paradigm and is naturally associated with the celebrated idea of resonating valence bond (RVB).[1] What is more, high-temperature superconductivity was proposed to emerge from doping such an RVB state.[2,9] While so far there is still lack of a smoking-gun experimental evidence for identifying a QSL, this exotic phase has been well established theoretically via exactly solvable models together with other analytical and numerical analyses.[6] It is widely accepted that quantum spin fluctuations play a crucial role in the formation of a QSL, and there are several routes to enhance the fluctuations, namely, (i) a small spin quanta $S$, (ii) geometric frustration,[10–13] (iii) competing spin interactions that include nearest-neighbor (NN) anisotropic spin coupling and isotropic (or anisotropic) spin couplings on longer bonds, (iv) charge fluctuations in the vicinity of a Mott transition, and (v) extra degeneracy due to orbital degrees of freedom. The simplest example satisfying (i) and (ii) is the $S=1/2$ antiferromagnet on the triangular lattice, which was proposed as the first QSL candidate by Anderson in 1973.[1] Unfortunately, numerical studies on the antiferromagnetic (AFM) Heisenberg model with NN couplings on a triangular lattice strongly suggested a long-range 120$^{\circ}$ AFM order,[6] thereby falsifying Anderson's original proposal. However, the door to triangular-lattice QSLs is still open because of the last three routes: (iii) competing spin interactions, (iv) charge fluctuations, and (v) orbital degeneracy. On the experimental side, the successful synthesis of the rare-earth compound YbMgGaO$_4$ has aroused a lot of interest in triangular lattices antiferromagnets.[14–26] This insulating compound has triangular layers formed by Yb$^{3+}$ ions, exhibiting spatially isotropic $R\bar{3}m$ symmetry in crystallography.[14] While temperature dependent magnetic susceptibility yields a small AFM Curie–Weiss constant $\theta_{\rm w}\sim -4$ K,[14] various measurements, including specific heat, thermal transport, electron spin resonance, and muon spin relaxation, suggest the absence of spin ordering or freezing down to $T\sim 100$ mK.[14–17] In particular, a continuum of spin excitations has been observed by neutron scattering experiments, broadly distributed in momentum-energy space (0.1–2.0 meV) and indicative of short-range spin correlations.[18] Meanwhile, the Yb$^{3+}$ ions in this compound are slightly displaced by the Mg$^{2+}$–Ga$^{3+}$ mixing in the interleaved double layers. This lattice distortion will introduce considerable bond randomness. Therefore the possibility of a bond glass (or a random spin-singlet state) cannot be ruled out.[21,23,27,28] In comparison with YbMgGaO$_4$, a family of newly discovered rare-earth chalcogenides, AReCh$_2$ (A = alkali, Re = rare earth, and Ch = O, S, Se), provides a more promising platform for searching QSLs on triangular lattices.[29,30] This family shares the same $R\bar{3}m$ space group with YbMgGaO$_4$, but has a simpler crystal structure, so it has more chances to avoid the crucial random disorder issue. Furthermore, the relatively larger NN AFM exchange in the sub-family NaYbCh$_2$, $\theta_{\rm w}\sim -10$ K, is expected to conquer unavoidable lattice disorder, at least partially. In consistence with these considerations, magnetic susceptibility and specific heat measurements on the representative member, NaYbS$_2$, display no magnetic transition down to $T\sim 50$ mK, implying a QSL state. Moreover, the rich diversity of this family allows us to carry out comparative studies. In addition to the long-sought QSL, the exciting advantages stem from the family of rare-earth chalcogenides AReCh$_2$, also facilitate the studies of other phenomena. Indeed, an insulator to metal phase transition has been observed in NaYbSe$_2$ under a critical pressure $\sim$59 GPa.[31] In the insulating phase, the low temperature resistance can be fitted by Mott's variable range hopping model, $R(T)=R_{0}\exp[(T_0/T)^{1/(d+1)}]$, with the dimensionality $d=2$. As the pressure increases, the QSL candidate becomes a complete metallic state at $\sim$75 GPa, and a non-Fermi liquid is indicated by the transport $R(T)=R_{0}+AT^{n}$ with $n\sim 1$ under this pressure. Above $75$ GPa, the power $n$ gradually increases with pressure and reaches the Fermi liquid value $n=2$ at $126$ GPa. Interestingly, when the pressure exceeds $\sim$103 GPa, a sudden drop of $R(T)$ takes place at low temperatures. For instance, a maximum drop by $\sim$6% occurs at $\sim$8 K under $126$ GPa, the highest pressure realized in the experiment. This small fraction of the $R(T)$ drop was attributed to the emergence of superconductivity. Certainly, it would be a fragile superconductor, if its existence was confirmed. Finally, we would like to make a few comments on other vital ingredients to QSLs, namely, (iii) competing spin couplings, (iv) charge fluctuations, and (v) orbital degeneracy, as mentioned above. First, we believe that competing spin couplings widely exist in all the rare-earth compounds, which is indispensable for an $S=1/2$ (or $J=1/2$) QSL on triangular lattices. Second, charge fluctuations will manifest and give rise to significant multiple-spin exchanges in the vicinity of a Mott transition. Third, orbital degeneracy is known to provide a mechanism to enhance quantum fluctuations,[32] and recent theoretical studies suggest a nematic spin-orbital liquid state on triangular lattice.[33] With all these essential ingredients in mind, one can draw up a “road map” for the future QSL material searching. References Resonating valence bonds: A new kind of insulator?The Resonating Valence Bond State in La2CuO4 and SuperconductivityAn End to the Drought of Quantum Spin LiquidsSpin liquids in frustrated magnetsQuantum spin liquids: a reviewQuantum spin liquid statesA Field Guide to Spin LiquidsQuantum spin liquidsDoping a Mott insulator: Physics of high-temperature superconductivityTheory of the frustration effect. II. Ising spins on a square latticeGapless quantum spin liquid ground state in the two-dimensional spin-1/2 triangular antiferromagnet YbMgGaO4Rare-Earth Triangular Lattice Spin Liquid: A Single-Crystal Study of YbMgGaO 4 Absence of Magnetic Thermal Conductivity in the Quantum Spin-Liquid Candidate YbMgGaO 4 Muon Spin Relaxation Evidence for the U(1) Quantum Spin-Liquid Ground State in the Triangular Antiferromagnet YbMgGaO 4 Evidence for a spinon Fermi surface in a triangular-lattice quantum-spin-liquid candidateIn situ click chemistry generation of cyclooxygenase-2 inhibitorsCrystalline Electric-Field Randomness in the Triangular Lattice Spin-Liquid YbMgGaO 4 Continuous excitations of the triangular-lattice quantum spin liquid YbMgGaO4Spin-Glass Ground State in a Triangular-Lattice Compound YbZnGaO 4 Hierarchy of Exchange Interactions in the Triangular-Lattice Spin Liquid YbMgGaO 4 Structural absorption by barbule microstructures of super black bird of paradise feathersSelective measurements of intertwined multipolar orders: Non-Kramers doublets on a triangular latticePartial Up-Up-Down Order with the Continuously Distributed Order Parameter in the Triangular Antiferromagnet TmMgGaO 4 Disorder-Induced Mimicry of a Spin Liquid in YbMgGaO 4 Valence Bonds in Random Quantum Magnets: Theory and Application to YbMgGaO 4 Rare-Earth Chalcogenides: A Large Family of Triangular Lattice Spin Liquid Candidates NaYbS 2 : A planar spin- 1 2 triangular-lattice magnet and putative spin liquidMott Transition and Superconductivity in Quantum Spin Liquid Candidate NaYbSe2Quantum Melting of Magnetic Order due to Orbital FluctuationsUnveiling a critical stripy state in the triangular-lattice SU(4) spin-orbital model
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