Chiral spin liquid and quantum phase diagram of spin- 1 2 J 1 − J 2 − J χ model on the square lattice
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Zhang, Xiao-Tian (ORCID:0000000339451135)↗
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A Dipolar Chiral Spin Liquid on the Breathed Kagome Lattice
Continuous control over lattice geometry, when combined with long-range interactions, offers a powerful yet underexplored tool to generate highly frustrated quantum spin systems. By considering long-range dipolar antiferromagnetic interactions on a breathed Kagome lattice, we demonstrate how these tools can be leveraged to stabilize a chiral spin liquid. We support this prediction with large-scale density-matrix renormalization group calculations and explore the surrounding phase diagram, identifying a route to adiabatic preparation via a locally varying magnetic field. At the same time, we identify the relevant low-energy degrees of freedom in each unit cell, providing a complementary language to study the chiral spin liquid. Finally, we carefully analyze its stability and signatures in finite-sized clusters, proposing direct, experimentally viable measurements of the chiral edge mode in both Rydberg atom and ultracold polar molecule arrays.
Machado↗
Anisotropic Thermal Conductivity Oscillations in Relation to the Putative Kitaev Spin Liquid Phase of α-RuCl 3
In the presence of an external magnetic field, the Kitaev model could host either gapped topological anyons or gapless Majorana fermions. In α-RuCl 3 , the gapped and gapless cases are only separated by a 30° rotation of the in-plane magnetic field vector. The presence or absence of the spectral gap is key for understanding the thermal transport behavior in α-RuCl 3 . Here, we study the anisotropy of the oscillatory features of thermal conductivity in α-RuCl 3 . We examine the oscillatory features of thermal conductivities (κ / / a, κ / / b) with fixed external fields and find distinct behavior for the gapped (B / / a) and gapless (B / / b) scenarios. Furthermore, we track the evolution of thermal resistivity (λ α ) and its oscillatory features with the rotation of in-plane magnetic fields from B / / b to B / / a. The thermal resistivity λ(B, φ) displays distinct rotational symmetries before and after the emergence of the field-induced Kitaev spin liquid phase. These results suggest that oscillatory features of thermal conductivity in α-RuCl 3 are closely linked to the putative Kitaev spin liquid phase and its excitations.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Observation of the spiral spin liquid in a triangular-lattice material
The spiral spin liquid (SSL) is a highly degenerate state characterized by a continuous contour or surface in reciprocal space spanned by a spiral propagation vector. Although the SSL state has been predicted in a number of various theoretical models, very few materials are so far experimentally identified to host such a state. Via combined single-crystal wide-angle and small-angle neutron scattering, we report observation of the SSL in the quasi-two-dimensional delafossite-like AgCrSe 2 . We show that it is a very close realization of the ideal Heisenberg J 1 –J 2 –J 3 frustrated model on the triangular lattice. By supplementing our experimental results with microscopic spin-dynamics simulations, we demonstrate how such exotic magnetic states are driven by thermal fluctuations and exchange frustration.
36 MATERIALS SCIENCE↗
Quasiparticle Interference in Kitaev Quantum Spin Liquids
We study quasiparticle interference (QPI) in the Kitaev quantum spin liquid (QSL) for electrons tunneling into the QSL. The local tunneling conductance around a spin vacancy or localized vison reveals unique features associated with fractionalized Majorana fermions, chargons, and visons. In certain parameter regimes, the single-spinon density of states and momentum dispersion can both be directly extracted from the tunneling conductance. In conclusion, our results suggest that QPI is a promising tool for identifying the Kitaev QSL and its fractionalized excitations.
Anyons↗
Magnetic order and spin liquid behavior in [Mo 3 ] 11+ molecular magnets
Molecular magnets based on [Mo 3 ] 11+ units with one unpaired electron per trimer have attracted recent interest due to the identification of quantum spin liquid candidacy in some family members. Here, we present comprehensive measurements on polycrystalline samples of ZnScMo 3 O 8 , MgScMo 3 O 8 , and Na 3 Sc 2 Mo 5 O 16 with the same Mo 3 O 13 magnetic building blocks. In this work, the crystal structures are characterized with x-ray or neutron powder diffraction and the magnetic ground states are determined by performing ac and dc susceptibility, specific heat, neutron powder diffraction, and muon spin relaxation measurements. Our work indicates that ZnScMo 3 O 8 and MgScMo 3 O 8 have ferromagnetic Curie-Weiss temperatures of 18.5 and 11.9 K, ordered ground states with net moments (low-moment ferromagnetism or canted antiferromagnetism), and zero field ordering temperatures of $T_c$ = 6 K and $T_c$ < 2 K, respectively. On the other hand, Na 3 Sc 2 Mo 5 O 16 hosts a dynamical magnetic ground state with no evidence for magnetic ordering or spin freezing down to 20 mK despite an antiferromagnetic Curie-Weiss temperature of –36.2 K, and therefore is a candidate for quantum spin liquid behavior. By comparing the present results to past work on the same family of materials, we construct a phase diagram which illustrates that the magnetic ground states of these Mo-based molecular magnets are very sensitive to small changes in the nearest-neighbor Mo-Mo distance.
36 MATERIALS SCIENCE↗
Spin-liquid behavior of the three-dimensional magnetic system Ba 3 NiIr 2 O 9 with S = 1
The quantum spin liquid (QSL) is an exotic phase of magnetic materials where the spins continue to fluctuate without any symmetry breaking down to zero temperature. Among the handful reports of QSL with spin S ≥ 1, examples with magnetic ions on a three-dimensional (3D) magnetic lattice are extremely rare since both larger spin and higher dimension tend to suppress quantum fluctuations. In this work, we offer a new strategy to achieve 3D QSL with high spin by utilizing two types of transition metal ions; both are magnetically active but located at crystallographically inequivalent positions. Furthermore, we design a 3D magnetic system Ba 3 NiIr 2 O 9 consisting of interconnected corner-shared NiO 6 octahedra and face-shared Ir 2 O 9 dimer, both having triangular arrangements in a-b plane. X-ray absorption spectroscopy measurements confirm the presence of Ni 2+ (S = 1). Furthermore, our detailed thermodynamic and magnetic measurements reveal that this compound is a realization of gapless QSL state down to at least 100 mK. Ab initio calculations find a strong magnetic exchange between Ir and Ni sublattices and in-plane antiferromagnetic coupling between the dimers, resulting in dynamically fluctuating magnetic moments.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Superconductivity in the doped quantum spin liquid on the triangular lattice
Abstract Broad interest in quantum spin liquid (QSL) phases was triggered by the notion that they can be viewed as insulating phases with preexisting electron pairs, such that upon light doping they might automatically yield high temperature superconductivity. Yet despite intense experimental and numerical efforts, definitive evidence showing that doping QSLs leads to superconductivity has been lacking. We address the problem of a lightly doped QSL through a large-scale density-matrix renormalization group study of the t - J model on finite-circumference triangular cylinders with a small but nonzero concentration of doped holes. We provide direct evidences that doping QSL can naturally give rise to d -wave superconductivity. Specifically, we find power-law superconducting correlations with a Luttinger exponent, K s c ≈ 1, which is consistent with a strongly diverging superconducting susceptibility, $${\chi }_{sc} \,\sim\, {T}^{-(2\,-\,{K}_{sc})}$$ χ s c ~ T − ( 2 − K s c ) as the temperature T → 0. The spin–spin correlations—as in the undoped QSL state—fall exponentially which suggests that the superconducting pair-pair correlations evolve smoothly from the insulating parent state.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Dynamics of vacancy-induced modes in the non-Abelian Kitaev spin liquid
Here, we study the dynamical response of vacancy-induced quasiparticle excitations in the site-diluted Kitaev spin liquid with a magnetic field. Due to the flux-binding effect and the emergence of dangling Majorana fermions around each spin vacancy, the low-energy physics is governed by a set of vacancy-induced quasi-zero-energy modes. These localized modes result in unique characteristics of the dynamical spin correlation functions, which intriguingly mimic the single-quasiparticle density of states and further exhibit a quasi-zero-frequency peak. By recognizing the potential observability of these local correlation functions via scanning tunneling microscopy (STM), we show how the STM response is sensitive to the local flux configuration, the magnetic field strength, and the vacancy concentration. Constructing a simple model of the localized modes, we also elucidate how the local correlation functions can be interpreted in terms of the hybridization between these modes.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Quantitative investigation of the short-range magnetic correlations in the candidate quantum spin liquid NaYbO 2
Here, we present a neutron diffraction study of NaYbO 2 , a candidate quantum spin-liquid (QSL) compound hosting a geometrically frustrated triangular lattice of magnetic Yb 3+ ions. We observe diffuse magnetic scattering that persists to at least 20 K, demonstrating the presence of short-range magnetic correlations in this system up to a relatively high-energy scale. Using a reverse Monte Carlo and magnetic pair distribution function analysis, we confirm the predominant antiferromagnetic nature of these correlations and show that the diffuse scattering data can be well described by noninteracting layers of Heisenberg or XY spins on the triangular lattice. We rule out Ising spins and short-range-ordered stripe or 120° phases as candidate ground states of NaYbO 2 . These results are consistent with a possible QSL ground state in NaYbO 2 and showcase the benefit of a combined reciprocal- and real-space analysis of materials with short-range magnetic correlations.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Footprints of Kitaev spin liquid in the Fano lineshape of Raman-active optical phonons
We develop a theoretical description of the Raman spectroscopy in the spin-phonon-coupled Kitaev system and show that it can provide observable signatures of fractionalized excitations characteristic of the underlying spin-liquid phase. In particular, we obtain the explicit form of the phonon modes and construct the coupling Hamiltonian based on the D 3d symmetry. We then systematically compute the Raman intensity and show that the spin-phonon coupling renormalizes phonon propagators and generates the salient Fano lineshape. We find that the temperature evolution of the Fano lineshape displays two crossovers, and the low-temperature crossover shows pronounced magnetic-field dependence. We thus identify the observable effect of the Majorana fermions and the Z2 gauge fluxes encoded in the Fano lineshape. Our results are consistent with the phonon Raman scattering experiments in the candidate material α-RuCl 3 .
36 MATERIALS SCIENCE↗
Sound attenuation in the hyperhoneycomb Kitaev spin liquid
In recent years, it has been shown that the phonon dynamics may serve as an indirect probe of fractionalization of spin degrees of freedom. Furthermore we propose that the sound attenuation measurements allows for the characterization and identification of the Kitaev quantum spin liquid on the hyperhoneycomb lattice, which is particularly interesting since the strong Kitaev interaction was observed in the the hyperhoneycomb magnet β–Li 2 IrO 3 . To this end we consider the low-temperature scattering between acoustic phonons and gapless Majorana fermions with nodal-line band structure. Here, we find that the sound attenuation has a characteristic angular dependence, which is explicitly shown for the high-symmetry planes at temperatures below the flux energy gap.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Synthesis and anisotropic magnetism in quantum spin liquid candidates A YbSe 2 ( A = K and Rb)
The quantum spin liquid (QSL) state in rare-earth triangular lattices has attracted much attention recently due to its potential application in quantum computing and communication. Here, we report the single-crystal growth synthesis, crystal structure characterizations, and magnetic properties of AYbSe 2 (A = K and Rb) compounds. The x-ray diffraction analysis shows that AYbSe 2 (A = K and Rb) crystallizes in a trigonal space group, R-3m (No. 166) with Z = 3. AYbSe 2 possesses a two-dimensional (2D) Yb–Se–Yb layered structure formed by edged-shared YbSe 6 octahedra. The magnetic properties are highly anisotropic for both title compounds, and no long-range order is found down to 0.4 K, revealing the possible QSL ground state in these compounds. The isothermal magnetization exhibits a one-third magnetization plateau when the magnetic fields are applied in the ab-plane. Heat capacity is performed along both ab-plane and c axis and features the characteristic dome for triangular magnetic lattice compounds as a function of magnetic fields. Due to the change in the interlayer and intralayer distance of Yb 3+ , the dome shifts to low fields from KYbSe 2 to RbYbSe 2 . All these results indicate that the AYbSe 2 family presents unique frustrated magnetism close to the possible QSL and noncollinear spin states.
36 MATERIALS SCIENCE↗
Four-Spin Terms and the Origin of the Chiral Spin Liquid in Mott Insulators on the Triangular Lattice
At strong repulsion, the triangular-lattice Hubbard model is described by s=1/2 spins with nearest-neighbor antiferromagnetic Heisenberg interactions and exhibits conventional 120° order. Using the infinite density matrix renormalization group and exact diagonalization, we study the effect of the additional four-spin interactions naturally generated from the underlying Mott-insulator physics of electrons as the repulsion decreases. Although these interactions have historically been connected with a gapless ground state with emergent spinon Fermi surface, we find that, at physically relevant parameters, they stabilize a chiral spin liquid (CSL) of Kalmeyer-Laughlin (KL) type, clarifying observations in recent studies of the Hubbard model. Finally, we present a self-consistent solution based on a mean-field rewriting of the interaction to obtain a Hamiltonian with similarities to the parent Hamiltonian of the KL state, providing a physical understanding for the origin of the CSL.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Phonon dynamics in quantum spin liquid and valence bond crystal states in the barlowite family of kagome magnets
The barlowite [Cu 4 (OD) 6 FBr] family of materials is characterized by antiferromagnetic spin-1/2 kagome layers and are believed to host interesting ground states of quantum magnetism. Substituting the interlayer sites with zinc ions yields Zn-barlowite (Zn 𝑥 Cu 4−𝑥 (OD) 6 FBr, 𝑥 ≈ 0.80) which is a strong candidate to have a quantum spin liquid (QSL) state. Experimentally distinguishing between valence bond crystal (VBC) and QSL states in the absence of magnetic ordering can prove challenging as both states exhibit similar average spin-spin correlations. Using high-resolution inelastic x-ray scattering with 1.4 meV energy resolution, we probe acoustic phonons in these structurally similar materials at various temperatures. Our measurements uncover robust differences possibly driven by different spin-phonon physics in VBC and QSL states, particularly at the 𝑀-point Brillouin zone boundary. Over a large 𝑇=[15,200] K temperature range, where neither material undergoes magnetic ordering nor a structural transition, we observe phonon softening in Zn-barlowite in contrast to a hardening of the same phonon in barlowite. Further, these results indicate that acoustic phonons in the barlowite system can be used to study and possibly distinguish between QSL and disordered VBC states in quantum magnets.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Pressure tuning of Kitaev spin liquid candidate Na 3 Co 2 SbO 6
The search for Kitaev’s quantum spin liquid in real materials has recently expanded with the prediction that honeycomb lattices of divalent, high-spin cobalt ions could host the dominant bond-dependent exchange interactions required to stabilize the elusive entangled quantum state. The layered honeycomb Na 3 Co 2 SbO 6 has been singled out as a leading candidate provided that the trigonal crystal field acting on Co 3d orbitals, which enhances non-Kitaev exchange interactions between $J$ eff = $\frac{1}{2}$ spin-orbital pseudospins, is reduced. Here we show that applied pressure leads to anisotropic compression of the layered structure, significantly reducing the trigonal distortion of CoO 6 octahedra. Ferromagnetic correlations between pseudospins are enhanced in the spin-polarized (3 Tesla) phase up to about 60 GPa. Higher pressures drive a high-spin to low-spin transition destroying the $J$ eff = $\frac{1}{2}$ moments required to map the spin Hamiltonian into Kitaev’s model. The spin transition strongly suppresses the low-temperature magnetic susceptibility and appears to stabilize a paramagnetic phase driven by frustration. The possible emergence of frustrated magnetism of localized $S$ = $\frac{1}{2}$ moments opens the door for exploration of novel magnetic quantum states in compressed honeycomb lattices of divalent cobaltates.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Spin liquid state in a rare-earth hyperkagome lattice
We report quantum fluctuations enhanced by frustration and subtle interplay between competing degrees of freedom offer an ideal ground to realize novel states with fractional quantum numbers in quantum materials that defy standard theoretical paradigms. Quantum spin liquid (QSL) is a highly entangled state wherein frustration-induced strong quantum fluctuations preclude symmetry-breaking phase transitions down to zero temperature without any order parameter. Experimental realizations of QSL in quantum materials with spin dimensionality greater than one is very rare. Here, we present our thermodynamic, nuclear magnetic resonance, muon spin relaxation, and inelastic neutron scattering studies of a rare-earth hyperkagome compound Li 3 Yb 3 Te 2 O 12 in which Yb 3+ ions constitute a three-dimensional spin lattice without any detectable disorder. Our comprehensive experiments evince neither signature of magnetic ordering nor spin freezing down to 38 mK that suggest the realization of dynamic liquid-like ground state in this antiferromagnet. The ground state of this material is interpreted by a low energy J eff = 1/2 degrees of freedom with short-range spin correlations. The present results demonstrate a viable basis to explore spin-orbit driven enigmatic correlated quantum states in a class of rare-earth-based three-dimensional frustrated magnets that may open avenues in theoretical and experimental search for spin liquids.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Linear resistivity and Sachdev-Ye-Kitaev (SYK) spin liquid behavior in a quantum critical metal with spin-1/2 fermions
Significance In “Planckian metals,” electrons dissipate energy at the fastest possible rate allowed by the fundamental laws of quantum mechanics, resulting in a linear temperature dependence of their electrical resistivity. Although observed for a number of quantum materials, this phenomenon lacks a general theoretical understanding and is often considered as one of the prominent fundamental questions in condensed matter physics. Here, we show that Planckian dissipation and a behavior consistent with the “marginal Fermi liquid” phenomenology emerge in the quantum critical regime separating a Mott insulating spin glass and a Fermi liquid. By establishing this behavior in an explicit model solvable by state-of-the-art computational methods, our theory paves the way toward a deeper understanding of Planckian or “strange” metals.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗