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The honeycomb magnet $\alpha-$RuCl$_3$ is a prime candidate material for realizing the Kitaev quantum spin liquid (QSL), but it shows long-range magnetic order at low temperature. Nevertheless, its broad inelastic neutron scattering (INS) response at finite frequency has been interpreted as that of a 'proximate QSL'. A moderate in-plane magnetic field indeed melts the residual zigzag order, giving rise to peculiar intermediate field phases before the high-field polarized state. In INS measurements the low-frequency spin waves disappear, leading to a broad scattering continuum in the field-induced intermediate regime, whose nature is currently under debate. Here, we study the magnetic field dependent spin dynamics of the $K-\Gamma-\Gamma'-$model within a stochastic semiclassical treatment, which incorporates the effect of finite-temperature fluctuations. At temperatures relevant for INS experiments, we show how the excitations of the zigzag phase broaden and that the different intermediate phases all show a similar continuum response. We discuss the implications of our results for experiments and highlight the importance of distinguishing finite temperature fluctuations from genuine quantum fractionalization signatures in frustrated magnets., Comment: 8 + 3 pages. 5 + 4 figures; minor changes and updated figure format

Quantum spin liquids are fascinating phases of matter, hosting fractionalized spin excitations and unconventional long-range quantum entanglement. These exotic properties, however, also render their experimental characterization challenging, and finding ways to diagnose quantum spin liquids is therefore a pertinent challenge. Here, we numerically compute the spectral function of a single hole doped into the half-filled Hubbard model on the triangular lattice using techniques based on matrix product states. At half-filling the system has been proposed to realize a chiral spin liquid at intermediate interaction strength, surrounded by a magnetically ordered phase at strong interactions and a superconducting/metallic phase at weak interactions. We find that the spectra of these phases exhibit distinct signatures. By developing appropriate parton mean-field descriptions, we gain insight into the relevant low-energy features. While the magnetic phase is characterized by a dressed hole moving through the ordered spin background, we find indications of spinon dynamics in the chiral spin liquid. Our results suggest that the hole spectral function, as measured by angle-resolved photoemission spectroscopy, provides a useful tool to characterize quantum spin liquids., 8 pages, 6 figures (published version)

We present a large-scale density matrix renormalization group (DMRG) study of the spin-$1$ SU(3) bilinear-biquadratic model on the square lattice, which was suggested to host a nematic spin liquid state in recent DMRG calculations. We report that this spin liquid appears to strongly compete with a three-sublattice magnetic order. To further study the competition between the two states, and the reason of the emergent nematic spin liquid, we included an additional next-nearest-neighbor SU(3) symmetric interactions along one of the two plaquette diagonal directions. This allows to tune the square-lattice model to the triangular-lattice model. By computing spin correlation functions and various order parameters, we find that the three-sublattice order may develop at infinitesimal additional new coupling, at least within the precision of our study. Compared with the previous findings that the nematic spin liquid is stable in extended parameter regions with additional couplings that respect the lattice symmetries of the square lattice, we argue that here the diagonal couplings, which frustrate the bipartite-lattice structure, rapidly suppress the two-sublattice fluctuations and the three-sublattice order thus wins. This numerical result is consistent with the conjecture that the nematic spin liquid emerges from the competition between two- and three-sublattice fluctuations., 7 pages, 7 figures

Long-range entanglement in quantum spin liquids (QSLs) leads to novel low-energy excitations with fractionalized quantum numbers and (in two dimensions) statistics. Experimental detection and manipulation of these excitations present a challenge particularly in view of diverse candidate magnets. A promising probe of fractionalization is their coupling to phonons. Here, we present Raman scattering results for the $S=1/2$ honeycomb iridate ${\mathrm{Cu}}_{2}{\mathrm{IrO}}_{3}$, a candidate Kitaev QSL with fractionalized Majorana fermions and Ising flux excitations. We observe anomalous low-temperature frequency shift and linewidth broadening of the Raman intensities in addition to a broad magnetic continuum, both of which, as we derive, are naturally attributed to the phonon decaying into itinerant Majoranas. The dynamic Raman susceptibility marks a crossover from the QSL to a thermal paramagnet at $\ensuremath{\sim}120$ K. The phonon anomalies below this temperature demonstrate a strong phonon-Majorana coupling. These results provide evidence of spin fractionalization in ${\mathrm{Cu}}_{2}{\mathrm{IrO}}_{3}$.

Single crystals of the three-dimensional frustrated magnet and spin liquid candidate compound PbCuTe$_2$O$_6$ were grown using both the Travelling Solvent Floating Zone (TSFZ) and the Top-Seeded Solution Growth (TSSG) techniques. The growth conditions were optimized by investigating the thermal properties. The quality of the crystals was checked by polarized optical microscopy, X-ray Laue and X-ray powder diffraction, and compared to the polycrystalline samples. Excellent quality crystals were obtained by the TSSG method. Magnetic measurements of these crystals revealed a small anisotropy for different crystallographic directions in comparison with the previously reported data. The heat capacity of both single crystal and powder samples reveal a transition anomaly around 1 K. Curiously the position and magnitude of the transition are strongly dependent on the crystallite size and it is almost entirely absent for the smallest crystallites. A structural transition is suggested which accompanies the reported ferroelectric transition, and a scenario whereby it becomes energetically unfavourable in small crystallites is proposed., 10 pages, 8 figures

Experimental detection of spin dynamics of the quantum spin liquid phase, which occurs when the quantum fluctuations lead to fractionalized spin states, remains a challenge. In this paper, we illustrate spin-liquid signatures in the geometrically frustrated layered kagome system $\mathrm{YBa}{\mathrm{Co}}_{4\ensuremath{-}x}{\mathrm{Fe}}_{x}{\mathrm{O}}_{7+\ensuremath{\delta}}$ ($x=0$ and $x=0.6$) over a wide temperature range using micro-Raman spectroscopy. The thermal response of the gapped broad band over a high temperature range possibly marks a spin liquid phase in this system. We report the appearance of sharp spectral features in the high temperature regime with unusual thermal behavior for $\mathrm{YBa}{\mathrm{Co}}_{4\ensuremath{-}x}{\mathrm{Fe}}_{x}{\mathrm{O}}_{7+\ensuremath{\delta}}$ ($x=0.6$). Besides, atypical oscillation of a phonon mode frequency with temperature suggests an unconventional electron-lattice coupling in the doped compound via a strong correlation between their lattice vibration and magnetic spin dynamics.

We theoretically investigate the electronic band structures and magnetic properties of ilmenites with edge-sharing ${\mathrm{IrO}}_{6}$ honeycomb layers, $A{\mathrm{IrO}}_{3}$ with $A= \mathrm{Mg}, \mathrm{Zn}, \mathrm{and} \mathrm{Mn}$, in comparison with a collinear antiferromagnet ${\mathrm{MnTiO}}_{3}$. The compounds with $A= \mathrm{Mg} \mathrm{and} \mathrm{Zn}$ were recently reported in Y. Haraguchi et al., Phys. Rev. Mater. 2, 054411 (2018), while ${\mathrm{MnIrO}}_{3}$ has not been synthesized yet but the honeycomb stacking structure was elaborated in a superlattice with ${\mathrm{MnTiO}}_{3}$ in K. Miura et al., Commun. Mater. 1, 55 (2020). We find that, in contrast to ${\mathrm{MnTiO}}_{3}$, where an energy gap opens in the Ti $3d$ bands by antiferromagnetic ordering of the high-spin $S=5/2$ moments, ${\mathrm{MgIrO}}_{3}$ and ${\mathrm{ZnIrO}}_{3}$ have a gap in the Ir $5d$ bands under the influence of both spin-orbit coupling and electron correlation. Their electronic structures are similar to those in the spin-orbit coupled Mott insulators with the ${j}_{\mathrm{eff}}=1/2$ pseudospin degree of freedom, as found in monoclinic ${A}_{2}{\mathrm{IrO}}_{3}$ with $A=$ Na and Li, which have been studied as candidates for the Kitaev spin liquid. Indeed, we find that the effective exchange interactions between the ${j}_{\mathrm{eff}}=1/2$ pseudospins are dominated by the Kitaev-type bond-dependent interaction and the symmetric off-diagonal interactions. On the other hand, for ${\mathrm{MnIrO}}_{3}$, we show that the local lattice structure is largely deformed, and both Mn $3d$ and Ir $5d$ bands appear near the Fermi level in a complicated manner, which makes the electronic and magnetic properties qualitatively different from ${\mathrm{MgIrO}}_{3}$ and ${\mathrm{ZnIrO}}_{3}$. Our results indicate that the ${\mathrm{IrO}}_{6}$ honeycomb network in the ilmenites $A{\mathrm{IrO}}_{3}$ with $A=$ Mg and Zn would offer a good platform for exotic magnetism by the spin-orbital entangled moments like the Kitaev spin liquid.

The quantum Monte Carlo method on asymptotic Lefschetz thimbles is a numerical algorithm devised specifically for alleviation of the sign problem appearing in the simulations of quantum many-body systems. In this method, the sign problem is alleviated by shifting the integration domain for the auxiliary fields, appearing, for example, in the conventional determinant quantum Monte Carlo method, from real space to an appropriate manifold in complex space. Here, we extend this method to quantum spin models with generic two-spin interactions, by using the Hubbard-Stratonovich transformation to decouple the exchange interactions and the Popov-Fedotov transformation to map the quantum spins to complex fermions. As a demonstration, we apply the method to the Kitaev model in a magnetic field whose ground state is predicted to deliver a topological quantum spin liquid with non-Abelian anyonic excitations. To illustrate how the sign problem is alleviated in this method, we visualize the asymptotic Lefschetz thimbles in complex space, together with the saddle points and the zeros of the fermion determinant. We benchmark our method in the low-temperature region in a magnetic field and show that the sign of the action is recovered considerably and unbiased numerical results are obtained with sufficient precision.

Quantum spin liquids are exotic states of matter that may be realized in frustrated quantum magnets and feature fractionalized excitations and emergent gauge fields. Here, we consider a gapless U(1) spin liquid with spinon Fermi pockets in two spatial dimensions. Such a state appears to be the most promising candidate to describe the exotic field-induced behavior observed in numerical simulations of the antiferromagnetic Kitaev honeycomb model. A similar such state may also be responsible for the recently-reported quantum oscillations of the thermal conductivity in the field-induced quantum paramagnetic phase of $\alpha$-RuCl$_3$. We consider the regime close to a Lifshitz transition, at which the spinon Fermi pockets shrink to small circles around high-symmetry points in the Brillouin zone. By employing renormalization group and mean-field arguments, we demonstrate that interactions lead to a gap opening in the spinon spectrum at low temperatures, which can be understood as a nesting instability of the spinon Fermi surface. This leads to proliferation of monopole operators of the emergent U(1) gauge field and confinement of spinons. While signatures of fractionalization may be observable at finite temperatures, the gapless U(1) spin liquid state with nested spinon Fermi pockets is ultimately unstable at low temperatures towards a conventional long-range-ordered ground state, such as a valence bond solid. Implications for Kitaev materials in external magnetic fields are discussed., Comment: 19 pages, 7 figures, 1 table; v2: added several minor improvements and references

Effective gauge theories based on slave particle construction are widely used to describe quantum number fractionalization in strongly correlated electron systems. However, even setting aside the debates on the confinement issue of the slave particles, there are still significant conflicts between theory and experiment. In particular, a ${T}^{2/3}$ specific heat anomaly has been predicted to be the smoking-gun signature of low-lying gauge fluctuation in a $U(1)$ spin liquid with a large spinon Fermi surface, which has, however, never been observed. Here we show that such an anomaly is actually an artifact of a Gaussian approximation and is absent when the no-double-occupancy constraint on the slave particles is strictly enforced. We also show that projective construction based on slave particle representation provides a unified understanding of the mechanism of spin fractionalization in one- and two-dimensional spin liquids.

Heavy fermion metals typically exhibit unconventional quantum critical point or quantum critical phase at zero temperature due to competition of Kondo effect and magnetism. Previous theories were often based on certain local type of assumptions and a fully consistent explanation of experiments has not been achieved. Here we develop an efficient algorithm for the Schwinger boson approach to explore the effect of spatial correlations on the Kondo lattice and introduce the concept of nonlocal Kondo effect in the quantum critical region with deconfined spinons. We predict a global phase diagram containing a non-Fermi liquid quantum critical phase with a hidden holon Fermi surface and a partially enlarged electron Fermi surface for strong quantum fluctuations while a single quantum critical point for weak quantum fluctuations. This explains the unusual metallic spin liquid recently reported in the frustrated Kondo lattice CePdAl and resolves the Fermi volume puzzle in YbRh$_2$Si$_2$. Our theory highlights the importance of nonlocal physics and provides a unified understanding of heavy fermion quantum criticality., 11 pages, 6 figures

We investigate the low temperature magnetic properties of a $S=\frac{5}{2}$ Heisenberg kagome antiferromagnet, the layered monodiphosphate ${\mathrm{Li}}_{9}{\mathrm{Fe}}_{3}({\mathrm{P}}_{2}{\mathrm{O}}_{7}{)}_{3}({\mathrm{PO}}_{4}{)}_{2}$, using magnetization measurements and $^{31}\mathrm{P}$ nuclear magnetic resonance. An antiferromagnetic-type order sets in at ${T}_{N}=1.3\text{ }\text{ }\mathrm{K}$ and a characteristic magnetization plateau is observed at $1/3$ of the saturation magnetization below ${T}^{*}\ensuremath{\sim}5\text{ }\text{ }\mathrm{K}$. A moderate $^{31}\mathrm{P}$ NMR line broadening reveals the development of anisotropic short-range correlations concomitantly with a gapless spin-lattice relaxation time ${T}_{1}\ensuremath{\sim}{k}_{B}T/\ensuremath{\hbar}S$, which may point to the presence of a semiclassical nematic spin-liquid state predicted for the Heisenberg kagome antiferromagnetic model or to the persistence of the zero-energy modes of the kagome lattice under large magnetic fields.

We assess the ground-state phase diagram of the ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ Heisenberg model on the Kagome lattice by employing Gutzwiller-projected fermionic wave functions. Within this framework, different states can be represented, defined by distinct unprojected fermionic Hamiltonians that include hopping and pairing terms, as well as a coupling to local Zeeman fields to generate magnetic order. For ${J}_{2}=0$, the so-called U(1) Dirac state, in which only hopping is present (such as to generate a $\ensuremath{\pi}$-flux in the hexagons), has been shown to accurately describe the exact ground state [Y. Iqbal, F. Becca, S. Sorella, and D. Poilblanc, Phys. Rev. B 87, 060405(R) (2013); Y.-C. He, M. P. Zaletel, M. Oshikawa, and F. Pollmann, Phys. Rev. X 7, 031020 (2017).]. Here we show that its accuracy improves in the presence of a small antiferromagnetic superexchange ${J}_{2}$, leading to a finite region where the gapless spin liquid is stable; then, for ${J}_{2}/{J}_{1}=0.11(1)$, a first-order transition to a magnetic phase with pitch vector $\mathbf{q}=(0,0)$ is detected by allowing magnetic order within the fermionic Hamiltonian. Instead, for small ferromagnetic values of $|{J}_{2}|/{J}_{1}$, the situation is more contradictory. While the U(1) Dirac state remains stable against several perturbations in the fermionic part (i.e., dimerization patterns or chiral terms), its accuracy clearly deteriorates on small systems, most notably on 36 sites where exact diagonalization is possible. Then, on increasing the ratio $|{J}_{2}|/{J}_{1}$, a magnetically ordered state with $\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}$ periodicity eventually overcomes the U(1) Dirac spin liquid. Within the ferromagnetic ${J}_{2}$ regime, evidence is shown in favor of a first-order transition at ${J}_{2}/{J}_{1}=\ensuremath{-}0.065(5)$.

Quantum spin liquids are exotic states of matter that form when strongly frustrated magnetic interactions induce a highly entangled quantum paramagnet far below the energy scale of the magnetic interactions. Three-dimensional cases are especially challenging due to the significant reduction of the influence of quantum fluctuations. Here, we report the magnetic characterization of ${\mathrm{K}}_{2}{\mathrm{Ni}}_{2}({\mathrm{SO}}_{4}{)}_{3}$ forming a three-dimensional network of ${\mathrm{Ni}}^{2+}$ spins. Using density functional theory calculations, we show that this network consists of two interconnected spin-1 trillium lattices. In the absence of a magnetic field, magnetization, specific heat, neutron scattering, and muon spin relaxation experiments demonstrate a highly correlated and dynamic state, coexisting with a peculiar, very small static component exhibiting a strongly renormalized moment. A magnetic field $B\ensuremath{\gtrsim}4\text{ }\text{ }\mathrm{T}$ diminishes the ordered component and drives the system into a pure quantum spin liquid state. This shows that a system of interconnected $S=1$ trillium lattices exhibits a significantly elevated level of geometrical frustration.

Recently, Urai et al. [Phys. Rev. Lett. 124, 117204 (2020)] reported that an antiferromagnetic long-range-ordered state in $\ensuremath{\kappa}$-${(\mathrm{ET})}_{2}\mathrm{Cu}\mathrm{[N}{(\mathrm{CN})}_{2}\mathrm{]Cl}$ changes into a quantum spin liquid via an unconventional spin glass-like state as randomness is introduced by x-ray irradiation. Here, we focused on the spin glass-like state and conducted a detailed investigation into it using $^{13}\mathrm{C}$-NMR measurements on 150-h x-ray-irradiated $\ensuremath{\kappa}$-$({\mathrm{ET})}_{2}\mathrm{Cu}\mathrm{[N(}{\mathrm{CN})}_{2}\mathrm{]Cl}$. We found that the spin glass-like state is composed of two components: the major component inherits the spin structure of nonirradiated $\ensuremath{\kappa}$-$({\mathrm{ET})}_{2}\mathrm{Cu}\mathrm{[N(}{\mathrm{CN})}_{2}\mathrm{]Cl}$, whereas the minor component differs from that of nonirradiated $\ensuremath{\kappa}$-${(\mathrm{ET})}_{2}\mathrm{Cu}\mathrm{[N(}{\mathrm{CN})}_{2}\mathrm{]Cl}$. We also found that in the spin glass-like state, spin moments fluctuate very slowly around stable directions even at low temperatures, which is very likely related to the Griffiths physics.

The magnetic Hamiltonian of the Heisenberg quantum antiferromagnet $\mathrm{Sr}\mathrm{Cu}{\mathrm{Te}}_{2}{\mathrm{O}}_{6}$ is studied by inelastic neutron scattering technique on powder and single-crystalline samples above and below the magnetic transition temperatures at 8 and 2 K. The high-temperature spectra reveal a characteristic diffuse scattering corresponding to a multispinon continuum, confirming the dominant quantum spin chain behavior due to the third neighbor interaction ${J}_{\text{intra}}=4.22$ meV (49 K). The low-temperature spectra exhibit sharper excitations at energies 1.25 meV, which can be explained by considering a combination of weak antiferromagnetic first nearest neighbor interchain coupling ${J}_{1}=0.17$ meV ($1.9$ K) and even weaker ferromagnetic second nearest neighbor ${J}_{2}=\ensuremath{-}0.037$ meV ($\ensuremath{-}0.4$ K) or a weak ferromagnetic ${J}_{2}=\ensuremath{-}0.11$ meV ($\ensuremath{-}1.3$ K) and antiferromagnetic ${J}_{6}=0.16$ meV ($1.85$ K), giving rise to the long-range magnetic order and spin-wave excitations at low energies. These results suggest that $\mathrm{Sr}\mathrm{Cu}{\mathrm{Te}}_{2}{\mathrm{O}}_{6}$ is a highly one-dimensional Heisenberg system with three mutually perpendicular spin chains coupled by a weak ferromagnetic ${J}_{2}$ in addition to the antiferromagnetic ${J}_{1}$ or ${J}_{6}$, presenting a contrasting scenario from the highly frustrated hyper-hyperkagome lattice (equally strong antiferromagnetic ${J}_{1}$ and ${J}_{2}$) found in the isostructural quantum spin liquid candidate $\mathrm{Pb}\mathrm{Cu}{\mathrm{Te}}_{2}{\mathrm{O}}_{6}$ .

We show how Oshikawa's theorem for the Fermi surface volume of the Kondo lattice can be extended to the $\mathrm{SU}(N)$ symmetric case. By extending the theorem, we can show that the mechanism of Fermi surface expansion seen in the large $N$ mean-field theory is directly linked to the expansion of the Fermi surface in a spin-$\frac{1}{2}$ Kondo lattice. This linkage enables us to interpret the expansion of the Fermi surface in a Kondo lattice as a fractionalization of the local moments into heavy electrons. Our method allows extension to a pure U(1) spin liquid, where we find the volume of the spinon Fermi surface by applying a spin twist, analogous to Oshikawa's, [Phys. Rev. Lett. 84, 3370 (2000)] flux insertion. Lastly, we discuss the possibility of interpreting the ${\mathrm{FL}}^{*}$ phase characterized by a small Fermi surface in the absence of symmetry breaking, as a nontopological coexistence of such a U(1) spin liquid and an electronic Fermi liquid.

Doping of quantum spin liquid (QSL) insulators by electron or hole leads to intriguing phase transitions to metallic and superconducting states. The barlowite family with geometrically perfect $S=1/2$ kagome planes and tunable interkagome coupling is an emerging platform to realize spin-ordered, valence bond crystal, QSL states. Theoretical investigations on electron doping revealed localized states in the band gap of barlowite unlike metallicity in cuprate (${\mathrm{Nd}}_{2}\mathrm{Cu}{\mathrm{O}}_{4}$). We present successful anchoring of phase-pure barlowite crystallites onto reduced graphene oxide (rGO). The resulting barlowite-rGO system was found to be an electrical semiconductor with Arrhenius activation energy of 0.07 eV. Semiconducting properties of the barlowite-rGO system were further modulated with retention of structural integrity. We have attributed such a transformation of electrical transport response to plausible electron doping thereby making charge-doping experiments on barlowite and its analogs propitious.

In the pseudospin-$\frac{1}{2}$ honeycomb Mott insulators with strong spin-orbit coupling, there are two types of bond-dependent exchange interactions, named Kitaev ($K$) and $\Gamma$, leading to strong frustration. While the ground state of the Kitaev model is a quantum spin liquid with fractionalized excitations, the ground state of the $\Gamma$ model remains controversial. In particular, the phase diagram of the $K\Gamma$ model with ferromagnetic $K$ and antiferromagnetic $\Gamma$ interactions has been intensively studied because of its relevance to candidate materials such as $\alpha$-RuCl$_{3}$. Numerical studies also included the effects of tuning the bond strengths, i.e., $z$-bond strength different from the other bonds. However, no clear consensus on the overall phase diagram has been reached yet. Here we study the classical $K\Gamma$ model with the anisotropic bond strength using Monte Carlo simulations to understand the emerging phases out of competition between the two frustrated limits. We also address how the anisotropic bond strength affects the phase diagram and strength of quantum fluctuations. We found various large unit cell phases due to the competing frustrations, and analyzed their intrinsic degeneracy based on the symmetry of the Hamiltonian. Using the linear spin wave theory we showed that the anisotropic bond strength enhances quantum fluctuations in the $\Gamma$-dominant regime where a small reduced moment is observed. The implications of our findings in relation to the quantum model are also discussed., Comment: 11 pages, 16 figures. journal version with minor changes

Recent experiments suggest a quantum spin liquid ground state in the material ${\mathrm{PbCuTe}}_{2}{\mathrm{O}}_{6}$, where $S=1/2$ moments are coupled by antiferromagnetic Heisenberg interactions into a three-dimensional structure of corner sharing triangles dubbed the hyper-hyperkagome lattice. It exhibits a richer connectivity, and thus likely a stronger geometric frustration, than the relatively well studied hyperkagome lattice. Here, we investigate the possible quantum spin liquids in the $S=1/2$ hyper-hyperkagome magnet using the complex fermion mean field theory. Extending the results of a previous projective symmetry group analysis, we identify only two ${\mathbb{Z}}_{2}$ spin liquids and a $U(1)$ spin liquid that are compatible with the hyper-hyperkagome structure. The $U(1)$ spin liquid has a spinon Fermi surface. For the ${\mathbb{Z}}_{2}$ spin liquids, one has a small excitation gap, while the other is gapless and proximate to the $U(1)$ spin liquid. We show that the gapped and gapless spin liquids can in principle be distinguished by heat capacity measurements. Moreover, we calculate the dynamical spin structure factors of all three spin liquids and find that they highly resemble the inelastic neutron scattering spectra of ${\mathrm{PbCuTe}}_{2}{\mathrm{O}}_{6}$. Implications of our work to the experiments, as well as its relations to the existing theoretical studies, are discussed.

The Kitaev model realizes a quantum spin liquid where the spin excitations are fractionalized into itinerant Majorana fermions and localized ${\mathbb{Z}}_{2}$ vortices. Quantum entanglement between the fractional excitations can be utilized for decoherence-free topological quantum computation. Of particular interest is the anyonic statistics realized by braiding the vortex excitations under a magnetic field. Despite the promising potential, the practical methodology for creation and control of the vortex excitations remains elusive thus far. Here we theoretically propose how one can create and move the vortices in the Kitaev spin liquid. We find that the vortices are induced by a local modulation of the exchange interaction; especially, the local Dzyaloshinskii-Moriya (symmetric off-diagonal) interaction can create vortices most efficiently in the (anti)ferromagnetic Kitaev model, as it effectively flips the sign of the Kitaev interaction. We test this idea by performing the ab initio calculation for the candidate material $\ensuremath{\alpha}\text{\ensuremath{-}}\mathrm{Ru}{\mathrm{Cl}}_{3}$ through the manipulation of the ligand positions that breaks the inversion symmetry and induces the local Dzyaloshinskii-Moriya interaction. We also demonstrate a braiding of vortices by adiabatically and successively changing the local bond modulations.

We build and probe a $\mathbb{Z}_2$ spin liquid in a programmable quantum device, the D-Wave DW-2000Q. Specifically, we observe the classical 8-vertex and 6-vertex (spin ice) states and transitions between them. To realize this state of matter, we design a Hamiltonian with combinatorial gauge symmetry using only pairwise-qubit interactions and a transverse field, i.e., interactions which are accessible in this quantum device. The combinatorial gauge symmetry remains exact along the full quantum annealing path, landing the system onto the classical 8-vertex model at the endpoint of the path. The output configurations from the device allows us to directly observe the loop structure of the classical model. Moreover, we deform the Hamiltonian so as to vary the weights of the 8 vertices and show that we can selectively attain the classical 6-vertex (ice) model, or drive the system into a ferromagnetic state. We present studies of the classical phase diagram of the system as function of the 8-vertex deformations and effective temperature, which we control by varying the relative strengths of the programmable couplings, and we show that the experimental results are consistent with theoretical analysis. Finally, we identify additional capabilities that, if added to these devices, would allow us to realize $\mathbb{Z}_2$ quantum spin liquids on which to build topological qubits., 6 pages, 5 figures

We study theoretically the nonlinear optical response of Tomonaga-Luttinger spin liquid in the context of terahertz (THz) two-dimensional coherent spectroscopy (2DCS). Using the gapless phase of the XXZ-type spin chain as an example, we show that its third-order nonlinear magnetic susceptibilities $\chi^{(3)}_{+--+}$ and $\chi^{(3)}_{-++-}$ exhibit photon echo, where $\pm$ refers to the left/right-hand circular polarization with respect to the $S^z$ axis. The photon echo arises from a ``lensing'' phenomenon in which the wave packets of fractional excitations move apart and then come back toward each other, amounting to a refocusing of the excitations' world lines. Renormalization group irrelevant corrections to the fixed point Hamiltonian result in dispersion and/or damping of the wave packets, which can be sensitively detected by lensing and consequently the photon echo. Our results thus unveil the strength of THz-2DCS in probing the dynamical properties of the collective excitations in a prototypical gapless many-body system., Comment: 16 pages, 8 figures; minor revisions

Recent numerical simulations find a possible chiral spin-liquid state in the intermediate coupling regime of the triangular lattice Hubbard model. Here we provide a simple picture for its origin in terms of a bosonic resonating valence bond (RVB) description. More specifically, we show that such a chiral spin-liquid state can be understood as a quantum disordered tetrahedral spin state stabilized by the four spin ring exchange coupling, which suppresses the order-by-disorder effect toward a stripy spin state. Such a chiral spin-liquid state features a spin Berry phase of $\frac{\ensuremath{\pi}}{2}$ per triangle. However, we show that the topological property of such a state is totally missed in the Schwinger boson mean-field description as a result of the lack of boson rigidity caused by the no double occupancy constraint.

Here, the authors report the discovery of novel types of U(1) and \ensuremath{\mathbb{Z}}${}_{2}$ quantum spin liquids on the pyrochlore lattice through a projective symmetry group classification. The classification highlights a special type of U(1) spin liquid, possessing an unusual symmetry-protected gapless multi-nodal-line structure in the spinon bands. The effect of gauge fluctuations for such a nodal structure is discussed. The leading contributions to the low-temperature specific heat are calculated, providing a clear experimental diagnostic of this U(1) spin liquid.

We develop a microscopic theory for plasmon excitations of $\text{graphene}/\ensuremath{\alpha}\text{\ensuremath{-}}\mathrm{Ru}{\mathrm{Cl}}_{3}$ heterostructures. Within a Kondo-Kitaev model with various interactions, a heavy Fermi liquid hosting flat bands emerges in which the itinerant electrons of graphene effectively hybridize with the fractionalized fermions of the Kitaev quantum spin liquid. We find novel correlated plasmon bands induced by the interplay of flat bands and interactions and argue that our theory is consistent with the available experimental data on $\text{graphene}/\ensuremath{\alpha}\text{\ensuremath{-}}\mathrm{Ru}{\mathrm{Cl}}_{3}$ heterostructures. We predict novel plasmon branches beyond the long-wavelength limit and discuss the implications for probing correlation phenomena in other flat band systems.

Ca$_{10}$Cr$_7$O$_{28}$ is a novel spin-$1/2$ magnet exhibiting spin liquid behaviour which sets it apart from any previously studied model or material. However, understanding Ca$_{10}$Cr$_7$O$_{28}$ presents a significant challenge, because the low symmetry of the crystal structure leads to very complex interactions, with up to seven inequivalent coupling parameters in the unit cell. Here we explore the origin of the spin-liquid behaviour in Ca$_{10}$Cr$_7$O$_{28}$, starting from the simplest microscopic model consistent with experiment - a Heisenberg model on a single bilayer of the breathing-kagome (BBK) lattice. We use a combination of classical Monte Carlo (MC) simulation and (semi-)classical Molecular Dynamics (MD) simulation to explore the thermodynamic and dynamic properties of this model, and compare these with experimental results for Ca$_{10}$Cr$_7$O$_{28}$. We uncover qualitatively different behaviours on different timescales, and argue that the ground state of Ca$_{10}$Cr$_7$O$_{28}$ is born out of a slowly-fluctuating "spiral spin liquid", while faster fluctuations echo the U(1) spin liquid found in the kagome antiferromagnet. We also identify key differences between longitudinal and transverse spin excitations in applied magnetic field, and argue that these are a distinguishing feature of the spin liquid in the BBK model.

We propose a unified scheme to identify phase transitions out of the $\mathbb{Z}_2$ Abelian topological order, including the transition to a non-Abelian chiral spin liquid. Using loop gas and and string gas states [H.-Y. Lee, R. Kaneko, T. Okubo, N. Kawashima, Phys. Rev. Lett. 123, 087203 (2019)] on the star lattice Kitaev model as an example, we compute the overlap of minimally entangled states through transfer matrices. We demonstrate that, similar to the anyon condensation, continuous deformation of a $\mathbb{Z}_2$-injective projected entangled-pair state (PEPS) also allows us to study the transition between Abelian and non-Abelian topological orders. We show that the charge and flux anyons defined in the Abelian phase transmute into the $\sigma$ anyon in the non-Abelian topological order. Furthermore, we show that contrary to the claim in [Phys. Rev. B 101, 035140 (2020)], both the LG and SG states have infinite correlation length in the non-Abelian regime, consistent with the no-go theorem that a chiral PEPS has a gapless parent Hamiltonian., Comment: 9 pages, 9 figures, published version

The Kitaev quantum spin liquid has been among the most intensively studied states of matter but there has been no clear-cut materials realization of it. This absence is largely because all existing honeycomb lattices are inherently distorted and disordered, which inevitably amplifies the competing Heisenberg interaction in the Kitaev-Heisenberg model, leading to an unwanted antiferromagnetic state. This work reports a new, undistorted honeycomb iridate NaxIrO${}_{3}$, where all evidence indicates that the elusive Kitaev spin liquid may finally be within reach.

Magnetic-field-induced phase transitions are investigated in the frustrated gapped quantum paramagnet Rb2Cu2Mo3O12 through dielectric and calorimetric measurements on single-crystal samples. It is clarified that the previously reported dielectric anomaly at 8 K in powder samples is not due to a chiral spin liquid state as has been suggested, but rather to a tiny amount of a ferroelectric impurity phase. Two field-induced quantum phase transitions between paraelectric and paramagnetic and ferroelectric and magnetically ordered states are clearly observed. It is shown that the electric polarization is a secondary order parameter at the lower-field (gap closure) quantum critical point but a primary one at the saturation transition. Having clearly identified the magnetic Bose-Einstein condensation (BEC) nature of the latter, we use the dielectric channel to directly measure the critical divergence of BEC susceptibility. The observed power-law behavior is in very good agreement with theoretical expectations for three-dimensional BEC. Finally, dielectric data reveal magnetic presaturation phases in this compound that may feature exotic order with unconventional broken symmetries., Physical Review Research, 3 (3), ISSN:2643-1564

While the Heisenberg model for magnetic Mott insulators on planar lattice structures is comparatively well understood in the case of transition metal ions, the intrinsic spin-orbit entanglement of $4f$ magnetic ions on such lattices shows fascinating new physics largely due to corresponding strong anisotropies both in their single-ion and their exchange properties. We show here that the Yb delafossites, containing perfect magnetic ${\mathrm{Yb}}^{3+}$ triangular lattice planes with pseudospin $s=\frac{1}{2}$ at low temperatures, are an ideal platform to study these phenomena. Competing frustrated interactions may lead to an absence of magnetic order associated to a gapless spin liquid ground state with a huge linear specific heat exceeding that of many heavy fermions, whereas the application of a magnetic field induces anisotropic magnetic order with successive transitions into different long-range ordered structures. In this comparative study, we discuss our experimental findings in terms of a unified crystal-field and exchange model. We combine electron paramagnetic resonance (EPR) experiments and results from neutron scattering with measurements of the magnetic susceptibility, isothermal magnetization up to full polarization, and specific heat to determine the relevant model parameters. The impact of the crystal field is discussed as well as the symmetry-compatible form of the exchange tensor, and we give explicit expressions for the anisotropic $g$ factor, the temperature dependence of the susceptibility, the exchange-narrowed EPR linewidth, and the saturation field.

In a recent study [Phys. Rev. X 10, 021042 (2020)], we showed using large-scale density matrix renormalization group (DMRG) simulations on infinite cylinders that the triangular lattice Hubbard model has a chiral spin liquid phase. In this work, we introduce hopping anisotropy in the model, making one of the three distinct bonds on the lattice stronger or weaker compared with the other two. We implement the anisotropy in two inequivalent ways, one which respects the mirror symmetry of the cylinder and one which breaks this symmetry. In the full range of anisotropy, from the square lattice to weakly coupled one-dimensional chains, we find a variety of phases. Near the isotropic limit we find the three phases identified in our previous work: metal, chiral spin liquid, and 120$^\circ$ spiral order; we note that a recent paper suggests the apparently metallic phase may actually be a Luther-Emery liquid, which would also be in agreement with our results. When one bond is weakened by a relatively small amount, the ground state quickly becomes the square lattice N\'{e}el order. When one bond is strengthened, the story is much less clear, with the phases that we find depending on the orientation of the anisotropy and on the cylinder circumference. While our work is to our knowledge the first DMRG study of the anisotropic triangular lattice Hubbard model, the overall phase diagram we find is broadly consistent with that found previously using other methods, such as variational Monte Carlo and dynamical mean field theory., Comment: v3: Added data regarding incommensurate spiral order using flux insertion, 20 pages, 6 figures, plus 23 pages (35 figures) Supplemental Material; v2: Slightly increased parameter space resolution for largest cylinder; v1: 19 pages, 6 figures, plus 22 pages (34 figures) Supplemental Material

Alkali metal rare-earth chalcogenide $ARECh2$ (A=alkali or monovalent metal, RE=rare earth, Ch=O, S, Se, Te), is a large family of quantum spin liquid (QSL) candidates we discovered recently. Unlike $YbMgGaO4$, most members in the family except for the oxide ones, have relatively small crystalline electric-field (CEF) excitation levels, particularly the first ones. This makes the conventional Curie-Weiss analysis at finite temperatures inapplicable and CEF excitations may play an essential role in understanding the low-energy spin physics. Here we considered an effective magnetic Hamiltonian incorporating CEF excitations and spin-spin interactions, to accurately describe thermodynamics in such a system. By taking $NaYbSe2$ as an example, we were able to analyze magnetic susceptibility, magnetization under pulsed high fields and heat capacity in a systematic and comprehensive way. The analysis allows us to produce accurate anisotropic exchange coupling energies and unambiguously determine a crossover temperature ($\sim$25 K in the case of $NaYbSe2$), below which CEF effects fade away and pure spin-spin interactions stand out. We further validated the effective picture by successfully explaining the anomalous temperature dependence of electron spin resonance (ESR) spectral width. The effective scenario in principle can be generalized to other rare-earth spin systems with small CEF excitations., 7 pages, 4 figures + Supplementary Information

We show that gapless spin liquids, which are potential candidates to describe the ground state of frustrated Heisenberg models in two dimensions, become trivial insulators on cylindrical geometries with an even number of legs. In particular, we report calculations for Gutzwiller-projected fermionic states on strips of square and kagome lattices. By choosing different boundary conditions for the fermionic degrees of freedom, both gapless and gapped states may be realized, the latter ones having a lower variational energy. The direct evaluation of static and dynamical correlation functions, as well as overlaps between different states, allows us to demonstrate the sharp difference between the ground-state properties obtained within cylinders or directly in the two-dimensional lattice. Our results shed light on the difficulty to detect bona fide gapless spin liquids in such cylindrical geometries., 9 pages, 10 figures

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 $S\ensuremath{\ge}$ 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. We design a 3D magnetic system ${\mathrm{Ba}}_{3}{\mathrm{NiIr}}_{2}{\mathrm{O}}_{9}$ consisting of interconnected corner-shared ${\mathrm{NiO}}_{6}$ octahedra and face-shared ${\mathrm{Ir}}_{2}{\mathrm{O}}_{9}$ dimer, both having triangular arrangements in a-b plane. X-ray absorption spectroscopy measurements confirm the presence of ${\mathrm{Ni}}^{2+}$ ($S=1)$. 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.

The spin-orbit entangled nature of the magnetic moments in Kitaev materials is expected to give rise to a quantum spin liquid (QSL) state with fractional excitations. Using resonant inelastic x-ray scattering under a magnetic field, here the authors map the excitation spectra of $\ensuremath{\beta}$-Li${}_{2}$IrO${}_{3}$. They observe a dichotomy between a magnon-like response at low energies, originating from intertwined field-induced ground states, and a multi-spinon-like continuum at higher energies, originating from pairwise excitations of long-lived Majorana fermions of the proximate QSL.

We point out that there are two different chiral spin liquid states on the triangular lattice and discuss the conducting states that are expected on doping them. These states labeled CS1 and CS2 are associated with two distinct topological orders with different edge states, although they both spontaneously break time reversal symmetry and exhibit the same quantized spin Hall conductance. While CSL1 is related to the Kalmeyer-Laughlin state, CSL2 is the $\nu =4$ member of Kitaev's 16 fold way classification. Both states are described within the Abrikosov fermion representation of spins, and the effect of doping can be accessed by introducing charged holons. On doping CSL2, condensation of charged holons leads to a topological d+id superconductor. However on doping CSL1 , in sharp contrast , two different scenarios can arise: first, if holons condense, a chiral metal with doubled unit cell and finite Hall conductivity is obtained. However, in a second novel scenario, the internal magnetic flux adjusts with doping and holons form a bosonic integer quantum Hall (BIQH) state. Remarkably, the latter phase is identical to a $d+id$ superconductor. In this case the Mott insulator to superconductor transition is associated with a bosonic variant of the integer quantum Hall plateau transition for the holon. We connect the above two scenarios to two recent numerical studies of doped chiral spin liquids on triangular lattice. Our work clarifies the complex relation between topological superconductors, chiral spin liquids and quantum criticality ., Comment: 20 pages, 8 figures, added App F on spin liquid to superconductor transition and corrected typos

The pyrochlore magnet ${\mathrm{Tb}}_{2}{\mathrm{Ti}}_{2}{\mathrm{O}}_{7}$ shows a lack of magnetic order to low temperatures and is considered to be a quantum spin liquid candidate. We perform time-domain THz spectroscopy on high-quality ${\mathrm{Tb}}_{2}{\mathrm{Ti}}_{2}{\mathrm{O}}_{7}$ crystals and study the low-energy excitations as a function of [111] magnetic field with high energy resolution. The low-energy crystal-field excitations change their energies anomalously under magnetic field. Despite several sharp field-dependent changes, we show that the material's spectrum can be described not by phase transitions but by field-dependent hybridization between the low-energy crystal-field levels. We highlight the strong coupling between spin and lattice degrees of freedom in ${\mathrm{Tb}}_{2}{\mathrm{Ti}}_{2}{\mathrm{O}}_{7}$ as evidenced by the magnetic-field tunable crystal-field environment. Calculations based on single ion physics with field-induced symmetry reduction of the crystal-field environment can reproduce our data.

We report the synthesis and initial characterization of ${\mathrm{Ba}}_{6}{\mathrm{Y}}_{2}{\mathrm{Rh}}_{2}{\mathrm{Ti}}_{2}{\mathrm{O}}_{17\ensuremath{-}\ensuremath{\delta}}$, a previously unreported material, to the best of our knowledge, with a hexagonal symmetry structure. Face-sharing $\mathrm{Rh}{\mathrm{O}}_{6}$ octahedra form triangular planes of ${\mathrm{Rh}}_{2}{\mathrm{O}}_{9}$ dimers that are widely separated in the perpendicular direction. The material displays a small effective magnetic moment, due to the Rh ions present, and a negative Curie-Weiss temperature. The charge transport and optical band gaps are very similar, near 0.16 eV. A large upturn in the heat capacity at temperatures below 1 K, suppressed by applied magnetic fields larger than ${\ensuremath{\mu}}_{0}\mathrm{H}=2\phantom{\rule{0.16em}{0ex}}\mathrm{T}$, is observed. A large T-linear term in the specific heat ($\ensuremath{\gamma}=166\phantom{\rule{0.16em}{0ex}}\mathrm{mJ}/{\mathrm{mol}\phantom{\rule{0.16em}{0ex}}\mathrm{f}.\mathrm{u}\phantom{\rule{0.16em}{0ex}}\mathrm{K}}^{2}$) is seen, although the material is insulating at low temperatures. These results suggest the possibility of a spin liquid ground state in this material.

We propose a local detection scheme for the Majorana zero mode (MZM) carried by a vison in Kitaev's chiral spin liquid (CSL) using scanning tunneling microscopy (STM). The STM introduces a single Majorana into the system through hole-charge injection and the Majorana interacts with the MZM to form a stable composite object. We derive the exact analytical expression of single-hole Green's function in the Mott insulating limit of Kitaev's model, and show that the differential conductance has split peaks, as a consequence of resonant tunneling through the vison-hole composite. The peak splitting turns out comparable to the Majorana gap in CSL, well within the reach of experimental observation.

We study the impact of trimerization (breathing) of the nearest-neighbor (NN) exchange on the planar XY spin-1/2 ferromagnet on the kagome lattice, including additional four-site ring exchange. For uniform NN exchange, this model has previously been shown to transit from a long-range ordered ferromagnet into a Z2 quantum spin liquid by virtue of the ring exchange. Using quantum Monte-Carlo calculations, based on the stochastic series expansion, we present results for the spin stiffness, the quantum phase diagram, the longitudinal static, as well as the transverse dynamic structure factor. Our results corroborate 3D XY universality also at finite trimerization and suggest a simple continuation of the quantum critical point of the uniform case into a line in terms of rescaled exchange parameters. Moreover, at any trimerization and in the ordered phase the elementary excitations can be understood very well in terms of linear spin wave theory, while beyond the critical line, in the spin liquid phase we find signatures of spinon continua., 9 pages, 8 figures

We address the ground-state properties of the long-standing and much-studied three-dimensional quantum spin liquid candidate, the $S=\frac{1}{2}$ pyrochlore Heisenberg antiferromagnet. By using SU(2) density-matrix renormalization group (DMRG), we are able to access cluster sizes of up to 128 spins. Our most striking finding is a robust spontaneous inversion symmetry breaking, reflected in an energy density difference between the two sublattices of tetrahedra, familiar as a starting point of earlier perturbative treatments. We also determine the ground-state energy, ${E}_{0}/{N}_{\text{sites}}=\ensuremath{-}0.490(6)J$, by combining extrapolations of DMRG with those of a numerical linked cluster expansion. These findings suggest a scenario in which a finite-temperature spin liquid regime gives way to a symmetry-broken state at low temperatures.

The search for an ideal Kitaev spin liquid candidate with anyonic excitations and long-range entanglement has motivated the synthesis of a new family of intercalated Kitaev magnets such as ${\mathrm{H}}_{3}\mathrm{Li}{\mathrm{Ir}}_{2}{\mathrm{O}}_{6}$, ${\mathrm{Cu}}_{2}\mathrm{Ir}{\mathrm{O}}_{3}$, and ${\mathrm{Ag}}_{3}\mathrm{Li}{\mathrm{Ir}}_{2}{\mathrm{O}}_{6}$. The absence of a susceptibility peak and a two-step release of the magnetic entropy in these materials have been proposed as evidence of proximity to the Kitaev spin liquid. Here we present a comparative study of the magnetic susceptibility, heat capacity, and muon spin relaxation ($\ensuremath{\mu}\mathrm{SR}$) between two samples of ${\mathrm{Ag}}_{3}\mathrm{Li}{\mathrm{Ir}}_{2}{\mathrm{O}}_{6}$ in the clean and disordered limits. In the disordered limit, the absence of a peak in either susceptibility or heat capacity and the lack of zero-field muon precession in the $\ensuremath{\mu}\mathrm{SR}$ signal give the impression of a proximate spin liquid state. However, in the clean limit, peaks are resolved in both susceptibility and heat capacity, and spontaneous oscillations appear in the $\ensuremath{\mu}\mathrm{SR}$ signal, confirming long-range antiferromagnetic order in the ground state. The $\ensuremath{\mu}\mathrm{SR}$ oscillations fit to a Bessel function, characteristic of incommensurate order, as reported in the parent compound $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{Li}}_{2}\mathrm{Ir}{\mathrm{O}}_{3}$. Our results clarify the role of structural disorder in the intercalated Kitaev magnets.

Motivated by a recent inelastic neutron scattering experiment on ${\mathrm{YbMgGaO}}_{4}$, I study the homogeneous spin model on the triangular lattice using the cluster mean-field theory and exact diagonalization. Phase diagrams with and without magnetic field are computed. The results show that the magnetic field can induce the phase transition from the spin liquid state (or the stripe state) to the ${120}^{\ensuremath{\circ}}$ antiferromagnetic state. These phase transitions are suppressed by the next-nearest-neighbor exchange interaction ${J}_{2}/{J}_{1}$ and vanish as ${J}_{2}/{J}_{1}g0.11$. I analyze a parameter space at ${J}_{2}/{J}_{1}=0.1$, where a field induced phase transition can occur, and find that the deviation of the theoretical spin excitation energy from the experimental data is only about 0.054. These results imply that an effective homogeneous spin model still applies to ${\mathrm{YbMgGaO}}_{4}$.

Neutron spectroscopy on the classical triangular-lattice frustrated antiferromagnet $h$-${\mathrm{YMnO}}_{3}$ reveals diffuse, gapless magnetic excitations present both far below and above the ordering temperature. The correlation length of the excitations increases as the temperature approaches zero, bearing a strong resemblance to critical scattering. We model the dynamics in the ordered and correlated disordered phase as critical spin correlations in a two-dimensional magnetic state. We propose that our findings may provide a general framework to understand features often attributed to classical spin liquids.

We present the ultralow-temperature specific-heat and thermal-conductivity measurements on single crystals of the triangular rare-earth lattice material $\mathrm{KBaYb}{({\mathrm{BO}}_{3})}_{2}$. Our experiments show the absence of long-range magnetic order down to 50 mK, giving the possibility of a quantum spin liquid ground state in this frustrated compound. Furthermore, no signature of spin freezing is observed down to 50 mK in the ac susceptibility measurements. However, no notable contributions from gapless magnetic excitations, but only a Schottky anomaly is observed in the specific-heat data. The ultralow-temperature thermal-conductivity data show that the residual linear term at zero field is negligible, and the thermal conductivity is insensitive to the magnetic field up to 9 T. The ground state of this frustrated triangular rare-earth lattice material is discussed.

We present a microscopic study of a doped quantum spin liquid candidate, the hyperkagome ${\mathrm{Na}}_{3}{\mathrm{Ir}}_{3}{\mathrm{O}}_{8}$ compound, by using $^{23}\mathrm{Na}$ NMR. We determine the intrinsic behavior of the uniform q = 0 susceptibility via shift measurements and the dynamical response by probing the spin-lattice relaxation rate. Throughout the studied temperature range, the susceptibility is consistent with a semimetal behavior, though with electronic bands substantially modified by correlations. Remarkably, the antiferromagnetic fluctuations present in the insulating parent compound ${\mathrm{Na}}_{4}{\mathrm{Ir}}_{3}{\mathrm{O}}_{8}$ survive in the studied compound. The spin dynamics are consistent with ${120}^{\ensuremath{\circ}}$ excitation modes displaying short-range correlations.

The magnetic ground state of $\mathrm{Co}{\mathrm{Al}}_{2}{\mathrm{O}}_{4}$ has been a controversial issue because the ratio of nearest- (${J}_{1}$) to next-nearest-neighbor (${J}_{2}$) exchange interactions in the diamond lattice is close to the boundary between a spiral spin liquid and a long-range ordered antiferromagnetic ground state. Recently, Ghara et al. reported a linear magnetoelectric effect in a polycrystalline $\mathrm{Co}{\mathrm{Al}}_{2}{\mathrm{O}}_{4}$ and attributed it to a long-range magnetic order. However, the magnetic ground state and the easy axis anisotropy remained unsolved. Here we propose the easy magnetic axis direction by comparing the results of magnetoelectric measurements in a high-quality single crystal with phenomenological calculations. From the value of polarization ratio $P||[1\text{\ensuremath{-}}10]$ measured under magnetic field applied along $H||[1\text{\ensuremath{-}}10]$ and $H||[001]$, we determined that the magnetic easy axis is along [111]. The single ion contribution of the magnetic ions located at the noncentrosymmetric environment is responsible for the magnetoelectric effect similar to that observed in other $A$-site magnetic spinel oxides, ${\mathrm{Co}}_{3}{\mathrm{O}}_{4}$, $\mathrm{Mn}{B}_{2}{\mathrm{O}}_{4}$ ($B=\mathrm{Al},\phantom{\rule{0.16em}{0ex}}\mathrm{Ga}$).

The quasi two-dimensional Mott insulator $\alpha$-RuCl$_3$ is proximate to the sought-after Kitaev quantum spin liquid (QSL). In a layer of $\alpha$-RuCl$_3$ on graphene the dominant Kitaev exchange is further enhanced by strain. Recently, quantum oscillation (QO) measurements of such $\alpha$-RuCl$_3$ / graphene heterostructures showed an anomalous temperature dependence beyond the standard Lifshitz-Kosevich (LK) description. Here, we develop a theory of anomalous QO in an effective Kitaev-Kondo lattice model in which the itinerant electrons of the graphene layer interact with the correlated magnetic layer via spin interactions. At low temperatures a heavy Fermi liquid emerges such that the neutral Majorana fermion excitations of the Kitaev QSL acquire charge by hybridising with the graphene Dirac band. Using ab-initio calculations to determine the parameters of our low energy model we provide a microscopic theory of anomalous QOs with a non-LK temperature dependence consistent with our measurements. We show how remnants of fractionalized spin excitations can give rise to characteristic signatures in QO experiments., Comment: 4.5 pages, 3 figures, supplementary material included

Thermodynamics of the Kitaev honeycomb magnet $\ensuremath{\alpha}\text{\ensuremath{-}}\mathrm{Ru}{\mathrm{Cl}}_{3}$ is studied for different directions of in-plane magnetic field using measurements of the magnetic Gr\"uneisen parameter ${\mathrm{\ensuremath{\Gamma}}}_{B}$ and specific heat $C$. We identify two critical fields ${B}_{c}^{\mathrm{AF}1}$ and ${B}_{c}^{\mathrm{AF}2}$ corresponding, respectively, to a transition between two magnetically ordered states and the loss of magnetic order toward a quantum paramagnetic state. The ${B}_{c}^{\mathrm{AF}2}$ phase boundary reveals a narrow region of magnetic fields where inverse melting of the ordered phase may occur. No additional transitions are detected above ${B}_{c}^{\mathrm{AF}2}$ for any direction of the in-plane field, although a shoulder anomaly in ${\mathrm{\ensuremath{\Gamma}}}_{B}$ is observed systematically at $8--10\phantom{\rule{0.16em}{0ex}}\mathrm{T}$ . Large field-induced entropy effects imply additional low-energy excitations at low fields and/or strongly field-dependent phonon entropies. Our results establish universal features of $\ensuremath{\alpha}\text{\ensuremath{-}}\mathrm{Ru}{\mathrm{Cl}}_{3}$ in high magnetic fields and challenge the presence of a field-induced Kitaev spin liquid in this material.