Spin Liquid Candidate Research Articles

Persistent spin dynamics and absence of spin freezing in the H−T phase diagram of the two-dimensional triangular antiferromagnet YbMgGaO4

We report results of muon spin relaxation and rotation ($\mu$SR) experiments on the spin-liquid candidate~YbMgGaO$_{4}$. No static magnetism $\gtrsim 0.003\mu_B$ per Yb ion, ordered or disordered, is observed down to 22~mK, a factor of two lower in temperature than previous measurements. Persistent (temperature-independent) spin dynamics are observed up to 0.20~K and at least 1~kOe, thus extending previous zero-field $\mu$SR results over a substantial region of the $H$-$T$ phase diagram. Knight shift measurements in a 10-kOe transverse field reveal two lines with nearly equal amplitudes. Inhomogeneous muon depolarization in a longitudinal field, previously characterized by stretched-exponential relaxation due to spatial inhomogeneity, is fit equally well with two exponentials, also of equal amplitudes. We attribute these results to two interstitial muon sites in the unit cell, rather than disorder or other spatial distribution. Further evidence for this attribution is found from agreement between the ratio of the two measured relaxation rates and calculated mean-square local Yb$^{3+}$ dipolar fields at candidate muon sites. Zero-field data can be understood as a combination of two-exponential dynamic relaxation and quasistatic nuclear dipolar fields.

Topological theory of Lieb-Schultz-Mattis theorems in quantum spin systems

The Lieb-Schultz-Mattis (LSM) theorem states that a spin system with translation and spin rotation symmetry and half-integer spin per unit cell does not admit a gapped symmetric ground state lacking fractionalized excitations. That is, the ground state must be gapless, spontaneously break a symmetry, or be a gapped spin liquid. Thus, such systems are natural spin-liquid candidates if no ordering is found. In this work, we give a much more general criterion that determines when an LSM-type theorem holds in a spin system. For example, we consider quantum magnets with arbitrary space group symmetry and/or spin-orbit coupling. Our criterion is intimately connected to recent work on the general classification of topological phases with spatial symmetries and also allows for the computation of an "anomaly" associated with the existence of an LSM theorem. Moreover, our framework is also general enough to encompass recent works on "SPT-LSM" theorems where the system admits a gapped symmetric ground state without fractionalized excitations, but such a ground state must still be non-trivial in the sense of symmetry-protected topological (SPT) phases.

Quantum spin liquid candidate YCu3(OH)6Br2[Brx(OH)1−x] (x ≈ 0.51): With an almost perfect kagomé layer

Herbertsmithite ZnCu3(OH)6Cl2 was initially proposed to have a “perfect” model for the S = 1/2 kagomé antiferromagnet, but further investigations have revealed its intrinsic shortcomings arising from serious intersite mixing between Zn2+ and Cu2+ ions. Another system YCu3(OH)6Cl3 with a more perfect kagomé lattice has been developed to minimize intersite mixing, but is adversely affected by common parasitic intergrowth inclusions and surface coating of Cu2(OH)3Cl, which led to ambiguous and contradictory magnetic data. Herein we report a new bromine compound YCu3(OH)6Br2[Brx(OH)1−x] (x ≈ 0.51), which not only inherits the almost perfect kagomé lattice from its chlorine analogue but also eludes the impurities from either inclusion or surface coating, resulting in high quality pure single crystals. Single crystal X-ray diffraction data of the title compound does not support the superstructure model suggested for its chlorine analogue but suggests an incommensurate structure. Magnetic measurements demonstrate that the title compound features a strong antiferromagnetic (AFM) interaction with θcw = −74 K at low temperature and no long-range magnetic order down to 2 K. These results suggest that the title compound is a new promising quantum spin liquid candidate, successfully overcoming the above-mentioned shortcomings of herbertsmithite, kapellasite and YCu3(OH)6Cl3.

Persistent spin dynamics in the pressurized spin-liquid candidate YbMgGaO4

Single-crystal x-ray diffraction, density-functional band-structure calculations, and muon spin relaxation ($\mu$SR) are used to probe pressure evolution of the triangular spin-liquid candidate YbMgGaO$_4$. The rhombohedral crystal structure is retained up to at least 10 GPa and shows a nearly uniform compression along both in-plane and out-of-plane directions, whereas local distortions caused by the random distribution of Mg$^{2+}$ and Ga$^{3+}$ remain mostly unchanged. The $\mu$SR data confirm persistent spin dynamics up to 2.6 GPa and down to 250 mK with no change in the muon relaxation rate. Longitudinal-field $\mu$SR reveals power-law behavior of the spin-spin autocorrelation function, both at ambient pressure and upon compression.

Crystal structure reconstruction in the surface monolayer of the quantum spin liquid candidate α-RuCl3

α-RuCl3, a layered 2D material, was recently identified as a promising candidate for realizing a Kitaev quantum spin liquid. However one fundamental property, the crystal structure, has not been well resolved yet due to difficulty of bulk diffraction techniques caused by layer stacking faults. Furthermore, the surface relaxation of monolayer-level thin films is completely unknown yet. In this report, surface sensitive low energy electron diffraction technique with µm selectivity (µ-LEED) combined with dynamical LEED analysis were used to reveal the detailed crystal structure of the surface monolayer of α-RuCl3. A surface structural distortion that breaks the inversion symmetry of the ideal bulk structure was revealed. To be specific, we found the surface Cl sub-lattice is buckled with one Cl atom approximately 0.16 Å below the other two Cl atoms, in the unit cell. The Ru atomic layer shows an even larger buckling of approximately 0.31 Å. Through density functional theory (DFT) calculations, we suggested that this surface distortion may be induced by Cl-vacancies that are inevitable in this material system. Inversion symmetry breaking in this material could have a significant impact on the 2D Kitaev interaction for both, interfaces with other 2D materials, such as graphene and future monolayer devices.

Crystal Growth of Spin-frustrated Ba4Nb0.8Ir3.2O12: A Possible Spin Liquid Material

Polycrystalline Ba4NbIr3O12 has recently been shown to be a promising spin liquid candidate. We report an easy and reliable method to grow millimeter-sized single crystals of this trimer based spin liquid candidate material with the actual stoichiometry of Ba4Nb0.8Ir3.2O12. The growth of large crystals is achieved using BaCl2 as flux. The crystals show hexagonal plate-like habit with edges up to 3 mm in length. The structure is confirmed by single crystal X-ray diffraction and is found to be the same as of previously reported phase Ba12Nb2.4Ir9.6O36 [Ba4Nb0.8Ir3.2O12], indeed with a mixed occupancy of Nb/Ir at 3a site. The magnetic and calorimetric study on the individual single crystals confirms the possibility of a spin liquid state consistent with a recent report on a polycrystalline sample

Impurity moments conceal low-energy relaxation of quantum spin liquids

We scrutinize the magnetic properties of $\kappa$-(BEDT-TTF)$_2$Hg(SCN)$_2$Cl through its first-order metal-insulator transition at $T_{\rm CO}=30$ K by means of $^1$H nuclear magnetic resonance (NMR). While in the metal we find Fermi-liquid behavior with temperature-independent $(T_1T)^{-1}$, the relaxation rate exhibits a pronounced enhancement when charge order sets in. The NMR spectra remain unchanged through the transition and no magnetic order stabilizes down to 25 mK. Similar to the isostructural spin-liquid candidates $\kappa$-(BEDT-TTF)$_2$Cu$_2$(CN)$_3$ and $\kappa$-(BEDT-TTF)$_2$Ag$_2$(CN)$_3$, $T_1^{-1}$ acquires a dominant maximum (here around 5 K). Field-dependent experiments identify the low-temperature feature as a dynamic inhomogeneity contribution that is typically dominant over the intrinsic relaxation but gets suppressed with magnetic field.

Phase diagram and thermal Hall conductivity of the spin-liquid Kekulé-Kitaev model

In this work we study the phase diagram of Kekul\'{e}-Kitaev model. The model is defined on a honeycomb lattice with bond dependent anisotropic exchange interactions making it exactly solvable in terms of Majorana representation of spins in close analogy to the Kitaev model. However, the energy spectrum of Majorana fermions has a multi-band structure characterized by Chern numbers 0, $\pm$1, and $\pm2$. We obtained the phase diagram of the model in the plane of exchange couplings and in the presence of a magnetic field and found chiral topological and trivial spin-liquid ground states. In the absence of magnetic field most part of the phase diagram is a trivial gapped phase continuously connected to an Abelian phase, while in the presence of the magnetic field a topological phase arises. Furthermore, motivated by recent thermal measurements on the spin-liquid candidate $\alpha$-RuCl$_{3}$, we calculated the thermal Hall conductivity at different regimes of parameters and temperatures and found the latter is quantized over a wide range of temperatures.

Symmetric spin liquids on the stuffed honeycomb lattice

We use a projective symmetry group analysis to determine all symmetric spin liquids on the stuffed honeycomb lattice Heisenberg model. This lattice interpolates between honeycomb, triangular and dice lattices, always preserving hexagonal symmetry, and it already has one spin liquid candidate, TbInO$_3$, albeit with strong spin-orbit coupling not considered here. In addition to the stuffed honeycomb lattice itself, we gain valuable insight into potential spin liquids on the honeycomb and triangular lattices, as well as how they might be connected. For example, the sublattice pairing state proposed on the honeycomb lattice connects to the uniform spinon Fermi surface that may be relevant for the triangular lattice with ring exchange, while there are no spin liquids competitive on both the $J_1-J_2$ honeycomb and triangular lattice limits. In particular, we find three stuffed honeycomb descendants of the U(1) Dirac spin liquid widely believed to be found on the $J_1-J_2$ triangular lattice. We also discuss how spin liquids near the honeycomb limit can potentially explain the physics of LiZn$_2$Mo$_3$O$_8$.

Frustrated Magnetism in Triangular Lattice TlYbS2 Crystals Grown via Molten Flux.

The triangular lattice compound TlYbS2 was prepared as large single crystals via a molten flux growth technique using sodium chloride. Anisotropic magnetic susceptibility measurements down to 0.4 K indicate a complete absence of long-range magnetic order. Despite this lack of long-range order, short-range antiferromagnetic interactions are evidenced through broad transitions, suggesting frustrated behavior. Variable magnetic field measurements reveal metamagnetic behavior at temperatures ≤2 K. Complex low temperature field-tunable magnetic behavior, in addition to no observable long-range order down to 0.4 K, suggest that TlYbS2 is a frustrated magnet and a possible quantum spin liquid candidate.

Topological thermal Hall effect of magnetic monopoles in the pyrochlore U(1) spin liquid

"Magnetic monopole" is an exotic quantum excitation in pyrochlore U(1) spin liquid, and its emergence is purely of quantum origin and has no classical analogue. We predict topological thermal Hall effect (TTHE) of "magnetic monopoles" and present this prediction through non-Kramers doublets. We observe that, when the external magnetic field polarizes the Ising component of the local moment, internally this corresponds to the induction of emergent dual U(1) gauge flux for the "magnetic monopoles". The motion of "magnetic monopoles" is then twisted by the induced dual gauge flux. This emergent Lorentz force on "magnetic monopoles" is the fundamental origin of TTHE. Therefore, TTHE would be a direct evidence of the "monopole"-gauge coupling and the emergent U(1) gauge structure in pyrochlore U(1) spin liquid. Our result does not depend strongly on our choice of non-Kramers doublets for our presentation, and can be well extended to Kramers doublets. Our prediction can be readily tested among the pyrochlore spin liquid candidate materials. We give a detailed discussion about the expectation for different pyrochlore magnets.

Valence bond phases of herbertsmithite and related copper kagome materials

Recent evidence from magnetic torque, electron spin resonance, and second harmonic generation indicate that the prototypical quantum spin liquid candidate, herbertsmithite, has a symmetry lower than its x-ray refined trigonal space group. Here, we consider known and possible distortions of this mineral class, along with related copper kagome oxides and fluorides, relate these to possible valence bond patterns, and comment on their relevance to the physics of these interesting materials.

Random singlet state in Ba5CuIr3O12 single crystals

We study the thermodynamic and high-magnetic-field properties of the magnetic insulator Ba$_5$CuIr$_3$O$_{12}$, which shows no magnetic order down to 2 K consistent with a spin liquid ground state. While the temperature dependence of the magnetic susceptibility and the specific heat shows only weak antiferromagnetic correlations, we find that the magnetization does not saturate up to a field of 59 Tesla, leading to an apparent contradiction. We demonstrate that the paradox can be resolved, and all of the experimental data can be consistently described within the framework of random singlet states. We demonstrate a generic procedure to derive the exchange coupling distribution $P(J)$ from the magnetization measurements and use it to show that the experimental data is consistent with the power-law form $P(J)\sim J^{-\alpha}$ with $\alpha \approx 0.6 $. Thus, we reveal that high-magnetic-field measurements can be essential to discern quantum spin liquid candidates from disorder dominated states that do not exhibit long-range order.

Dynamical and thermal magnetic properties of the Kitaev spin liquid candidate \u03b1-RuCl3

What is the correct low-energy spin Hamiltonian description of alpha-RuCl_{3}? The material is a promising Kitaev spin liquid candidate, but is also known to order magnetically, the description of which necessitates additional interaction terms. The nature of these interactions, their magnitudes and even signs, remain an open question. In this work we systematically investigate dynamical and thermodynamic magnetic properties of proposed effective Hamiltonians. We calculate zero-temperature inelastic neutron scattering (INS) intensities using exact diagonalization, and magnetic specific heat using a thermal pure quantum states method. We find that no single current model satisfactorily explains all observed phenomena of alpha-RuCl_{3}. In particular, we find that Hamiltonians derived from first principles can capture the experimentally observed high-temperature peak in the magnetic specific heat, while overestimating the magnon energy at the zone center. In contrast, other models reproduce important features of the INS data, but do not adequately describe the magnetic specific heat. To address this discrepancy we propose a modified ab initio model that is consistent with both magnetic specific heat and low-energy features of INS data.

Absence of magnetic ordering in the spin liquid candidate Ca3Cu2GeV2O12

Typically, quantum spin liquid candidates can be found in materials with a combination of geometrical frustration along with low spin. Due to its spin of S = 1/2 the copper (II) ion is often present in the discussion on spin liquid candidates. The solid state compound Ca3Cu2GeV2O12 is a material that crystallizes in the garnet structure (s.g. #230, Ia-3d), where 3D frustration is known to occur. Heat capacity has shown a lack of magnetic ordering down to 0.35 K, confirmed with low temperature neutron diffraction to 0.07 K. This system displays a Weiss temperature of −0.93(1) K indicating net antiferromagnetic interactions and significant J1–J2 competition causing frustration. Using both neutron and x-ray diffraction along with heat capacity and magnetometry, the work presented here shows Ca3Cu2GeV2O12 has potential as a new spin liquid candidate.

Pressure-Tuned Interactions in Frustrated Magnets: Pathway to Quantum Spin Liquids?

Quantum spin liquids are prime examples of strongly entangled phases of matter with unconventional exotic excitations. Here, strong quantum fluctuations prohibit the freezing of the spin system. On the other hand, frustrated magnets, the proper platforms to search for the quantum spin liquid candidates, still show a magnetic ground state in most of the cases. Pressure is an effective tuning parameter of structural properties and electronic correlations. Nevertheless, the ability to influence the magnetic phases should not be forgotten. We review experimental progress in the field of pressure-tuned magnetic interactions in candidate systems. Elaborating on the possibility of tuned quantum phase transitions, we further show that chemical or external pressure is a suitable parameter in these exotic states of matter.

Thermal Conductivity of the Quantum Spin Liquid Candidate EtMe3Sb[Pd(dmit)2]2 : No Evidence of Mobile Gapless Excitations

The thermal conductivity $\kappa$ of the quasi-2D organic spin-liquid candidate EtMe$_3$Sb[Pd(dmit)$_2$]$_2$ (dmit-131) was measured at low temperatures, down to 0.07 K. We observe a vanishingly small residual linear term $\kappa_0/T$, in $\kappa/T$ vs $T$ as $T \to 0$. This shows that the low-energy excitations responsible for the sizeable residual linear term $\gamma$ in the specific heat $C$, seen in $C/T$ vs $T$ as $T \to 0,$ are localized. We conclude that there are no mobile gapless excitations in this spin liquid candidate, in contrast with a prior study of dmit-131 that reported a large $\kappa_0/T$ value [Yamashita et al., Science 328, 1246 (2010)]. Our study shows that dmit-131 is in fact similar to $\kappa$-(BEDT-TTF)$_2$Cu$_2$(CN)$_3$, another quasi-2D organic spin-liquid candidate where a vanishingly small $\kappa_0/T$ and a sizeable $\gamma$ are seen. We attribute heat conduction in these organic insulators without magnetic order to phonons undergoing strong spin-phonon scattering, as observed in several other spin-liquid materials.

Absence of Magnetic Thermal Conductivity in the Quantum Spin Liquid Candidate EtMe_{3}Sb[Pd(dmit)_{2}]_{2}.

We present the ultralow-temperature specific heat and thermal conductivity measurements on single crystals of triangular-lattice compound EtMe_{3}Sb[Pd(dmit)_{2}]_{2}, which has long been considered as a gapless quantum spin liquid candidate. In specific heat measurements, a finite linear term is observed, consistent with the previous work [S. Yamashita etal., Nat. Commun. 2, 275 (2011)NCAOBW2041-172310.1038/ncomms1274]. However, we do not observe a finite residual linear term in the thermal conductivity measurements, and the thermal conductivity does not change in a magnetic field of 6T. These results are in sharp contrast to previous thermal conductivity measurements on EtMe_{3}Sb[Pd(dmit)_{2}]_{2} [M. Yamashita etal., Science 328, 1246 (2010)SCIEAS0036-807510.1126/science.1188200], in which a huge residual linear term was observed and attributed to highly mobile gapless excitations, likely the spinons of a quantum spin liquid. In this context, the true ground state of EtMe_{3}Sb[Pd(dmit)_{2}]_{2} has to be reconsidered.

Signatures for spinons in the quantum spin liquid candidate Ca10Cr7O28

We present new experimental low-temperature heat capacity and detailed dynamical spin-structure factor data for the quantum spin liquid candidate material Ca$_{10}$Cr$_7$O$_{28}$. The measured heat capacity shows an almost perfect linear temperature dependence in the range $0.1$ K $\lesssim T\lesssim0.5$ K, reminiscent of fermionic spinon degrees of freedom. The spin structure factor exhibits two energy regimes of strong signal which display rather different but solely diffuse scattering features. We theoretically describe these findings by an effective spinon hopping model which crucially relies on the existence of strong ferromagnetically coupled triangles in the system. Our spinon theory is shown to naturally reproduce the overall weight distribution of the measured spin structure factor. Particularly, we argue that various different observed characteristic properties of the spin structure factor and the heat capacity consistently indicate the existence of a spinon Fermi surface. A closer analysis of the heat capacity at the lowest accessible temperatures hints towards the presence of weak $f$-wave spinon pairing terms inducing a small partial gap along the Fermi surface (except for discrete nodal Dirac points) and suggesting an overall $\mathbb{Z}_2$ quantum spin liquid scenario for Ca$_{10}$Cr$_7$O$_{28}$.

Dirac Spin Liquid on the Spin-1/2 Triangular Heisenberg Antiferromagnet.

We study the spin liquid candidate of the spin-1/2 J_{1}-J_{2} Heisenberg antiferromagnet on the triangular lattice by means of density matrix renormalization group (DMRG) simulations. By applying an external Aharonov-Bohm flux insertion in an infinitely long cylinder, we find unambiguous evidence for gapless U(1) Dirac spin liquid behavior. The flux insertion overcomes the finite size restriction for energy gaps and clearly shows gapless behavior at the expected wave vectors. Using the DMRG transfer matrix, the low-lying excitation spectrum can be extracted, which shows characteristic Dirac cone structures of both spinon-bilinear and monopole excitations. Finally, we confirm that the entanglement entropy follows the predicted universal response under the flux insertion.