The layered compound $α$-RuCl$_3$ is composed of a honeycomb lattice of magnetic Ru$^{3+}$ ions with the $4d^5$ electronic state. We have investigated the magnetic properties of $α$-RuCl$_3$ via magnetization and specific heat measurements using single crystals. It was observed that $α$-RuCl$_3$ undergoes a structural phase transition at $T_{t}\,{\simeq}\,150$ K accompanied by fairly large hysteresis. This structural phase transition is expected to be similar to that observed in closely related CrCl$_3$. The magnetizations and magnetic susceptibilities are strongly anisotropic, which mainly arise from the anisotropic $g$-factors, i.e., $g_{ab}\,{\simeq}\,2.5$ and $g_c\,{\simeq}\,0.4$ for magnetic fields parallel and perpendicular to the $ab$ plane, respectively. These $g$-factors and the obtained entropy indicate that the effective spin of Ru$^{3+}$ is one-half, which results from the low-spin state. Specific heat data show that magnetic ordering occurs in four steps at zero magnetic field. The successive magnetic phase transitions should be ascribed to the competition among exchange interactions. The magnetic phase diagram for $H\,{\parallel}\,ab$ is obtained. We discuss the strongly anisotropic $g$-factors in $α$-RuCl$_3$ and deduce that the exchange interaction is strongly XY-like. $α$-RuCl$_3$ is magnetically described as a three-dimensionally coupled XY-like frustrated magnet on a honeycomb lattice.
Using quantum chemistry calculations we shed fresh light on the electronic structure and magnetic properties of RuCl3, a proposed realization of the honeycomb Kitaev spin model. It is found that the nearest-neighbor Kitaev exchange K is weaker than in 5d5 Ir oxides but still larger than other effective spin couplings. The electronic-structure computations also indicate a ferromagnetic K in the halide, which is supported by a detailed analysis of the field-dependent magnetization. From exact-diagonalization calculations for extended Kitaev-Heisenberg Hamiltonians we additionally find that a tra…
The honeycomb Mott insulator $α$-RuCl$_3$ loses its low-temperature magnetic order by pressure. We report clear evidence for a dimerized structure at $P>1$ GPa and observe the breakdown of the relativistic $j_{\rm eff}$ picture in this regime strongly affecting the electronic properties. A pressure-induced Kitaev quantum spin liquid cannot occur in this broken symmetry state. We shed light on the new phase by broad-band infrared spectroscopy of the low-temperature properties of $α$-RuCl$_{3}$ and ab initio density functional theory calculations, both under hydrostatic pressure.
Novel ground states might be realized in honeycomb lattices with strong spin-orbit coupling. Here we study the electronic structure of $α$-RuCl$_3$, in which the Ru ions are in a d5 configuration and form a honeycomb lattice, by angle-resolved photoemission, x-ray photoemission and electron energy loss spectroscopy supported by density functional theory and multiplet calculations. We find that $α$-RuCl$_3$ is a Mott insulator with significant spin-orbit coupling, whose low energy electronic structure is naturally mapped onto Jeff states. This makes $α$-RuCl$_3$ a promising candidate for the re…
We present high-field electron spin resonance (ESR) studies of the honeycomb-lattice material $α$-RuCl$_3$, a prime candidate to exhibit Kitaev physics. Two modes of antiferromagnetic resonance were detected in the zigzag ordered phase, with magnetic field applied in the $ab$ plane. A very rich excitation spectrum was observed in the field-induced quantum paramagnetic phase. The obtained data are compared with results of recent numerical calculations, strongly suggesting a very unconventional multiparticle character of the spin dynamics in $α$-RuCl$_3$. The frequency-field diagram of the lowes…
We examine the role of spin-orbit coupling in the electronic structure of $α$-RuCl3, in which Ru ions in 4d5 configuration form a honeycomb lattice. The measured optical spectra exhibit a clear optical gap and excitations within the t2g orbitals. The spectra can be described very well with first-principles electronic structure calculations obtained by taking into account both spin orbit coupling and electron correlations. Furthermore, our X-ray absorption spectroscopy measurements at the Ru L-edges exhibit distinct spectral features associated with the presence of substantial spin- orbit coupl…
We report magnetic and thermodynamic properties of single crystal $α$-RuCl$_3$, in which the Ru$^{3+}$ ($4d^5$) ion is in its low spin state and forms a honeycomb lattice. Two features are observed in both magnetic susceptibility and specific heat data; a sharp peak at 7~K and a broad hump near 10-15K. In addition, we observe a metamagnetic transition between 5~T and 10~T. Our neutron diffraction study of single crystal samples confirms that the low temperature peak in the specific heat is associated with a magnetic order with unit cell doubling along the honeycomb (100) direction, which is co…
Muon spin rotation measurements have been performed on a powder sample of a-RuCl3, a layered material which previously has been proposed to be a quantum magnet on a honeycomb lattice close to a quantum spin liquid ground state. Our data reveal two distinct phase transitions at 11 K and 14 K which we interpret as originating from the onset of three-dimensional order and in-plane magnetic order, respectively. We identify, with the help of density functional theory calculations, likely muon stopping sites and combine these with dipolar field calculations to show that the two measured muon rotatio…
Fine-tuning chemistry by doping with transition metals enables new perspectives for exploring Kitaev physics on a two-dimensional (2D) honeycomb lattice of α-RuCl3, which is promising in the field of quantum information protection and quantum computation. The key parameters to vary by doping are both Heisenberg and Kitaev components of the nearest-neighbor exchange interaction between the Jeff = 1/2 Ru3+ spins, depending strongly on the peculiarities of the crystal structure. Here, we successfully grew single crystals of the solid solution series Ru1-xCrxCl3 with Cr3+ ions coupled to the Ru3+ …
We report on the unusual behavior of the in-plane thermal conductivity ($κ$) and torque ($τ$) response in the Kitaev-Heisenberg material $α$-RuCl$_3$. $κ$ shows a striking enhancement with linear growth beyond H = 7 T, where magnetic order disappears, while $τ$ for both of the in-plane symmetry directions shows an anomaly at the same field. The temperature- and field-dependence of $κ$ are far more complex than conventional phonon and magnon contributions, and require us to invoke the presence of unconventional spin excitations whose properties are characteristic of a field-induced spin-liquid …
Hexagonal alpha-Ru trichloride single crystals exhibit a strong magnetic anisotropy and we show that upon applying fields up to 14 T in the honeycomb plane the successive magnetic order at T1 = 14 K and T2 = 8 K could be completely suppressed whereas in the perpendicular direction the magnetic order is robust. Furthermore the field dependence of chi(T) implies coexisting ferro- and antiferromagnetic exchange between in-plane components of Ru^3+-spins, whereas for out-of-plane components a strong antiferromagnetic exchange becomes evident. 101^Ru zero-field nuclear magnetic resonance in the ord…
The pure Kitaev honeycomb model harbors a quantum spin liquid in zero magnetic fields, while applying finite magnetic fields induces a topological spin liquid with non-Abelian anyonic excitations. This latter phase has been much sought after in Kitaev candidate materials, such as $α$-RuCl$_3$. Currently, two competing scenarios exist for the intermediate field phase of this compound ($B=7-10$ T), based on experimental as well as theoretical results: (i) conventional multiparticle magnetic excitations of integer quantum number vs. (ii) Majorana fermionic excitations of possibly non-Abelian natu…
The Kitaev model predicts that quantum spin liquids (QSLs) will form at low temperatures under certain special conditions, and materials hosting the QSL state are frequently sought. The layered honeycomb lattice material α-RuCl3 has emerged as a prime candidate for displaying the Kitaev QSL state. Here we describe a new polymorph of RuI3 with a layered honeycomb lattice structure, synthesized at moderately high pressures and stable under ambient conditions. Preliminary characterization reveals metallic, paramagnetic behavior, the absence of long-range magnetic order down to 0.35 K and an unusu…
We report a muon spin rotation/relaxation ($μ$SR) study of single-crystalline samples of the $α$-RuCl$_3$ honeycomb magnet, which is presumed to be a model compound for the Kitaev-Heisenberg interaction. It is inferred from magnetic susceptibility and specific-heat measurements that the present samples exhibit successive magnetic transitions at different critical temperatures $T_{\rm N}$ with decreasing temperature, eventually falling into the $T_{\rm N}=7$ K antiferromagnetic (7 K) phase that has been observed in only single-crystalline specimens with the least stacking fault. Via $μ$SR measu…
Spin $\frac{1}{2}$ honeycomb materials have gained substantial interest due to their exotic magnetism and possible application in quantum computing. However, in all current materials out-of-plane interactions are interfering with the in-plane order, hence a true 2D magnetic honeycomb system is still of demand. Here, we report the exfoliation of the magnetic semiconductor $α$-RuCl$_3$ into the first halide monolayers and the magnetic characterization of the spin $\frac{1}{2}$ honeycomb arrangement of turbostratically stacked RuCl$_3$ monolayers. The exfoliation is based on a reductive lithiatio…
The magnetic insulator $α$-RuCl$_{3}$ is a promising candidate to realize Kitaev interactions on a quasi-2D honeycomb lattice. We perform extensive susceptibility measurements on single crystals of $α$-RuCl$_{3}$, including angle-dependence of the in-plane longitudinal and transverse susceptibilities, which reveal a unidirectional anisotropy within the honeycomb plane. By comparing the experimental results to a high-temperature expansion of a Kitaev-Heisenberg-$Γ$ spin Hamiltonian with bond anisotropy, we find excellent agreement with the observed phase shift and periodicity of the angle-resol…
Recently, there have been increasingly hot debates on whether there exists a quantum spin liquid in the Kitaev honeycomb magnet $α$-RuCl$_3$ in high magnetic field. To investigate this issue, we perform the ultralow-temperature thermal conductivity measurements on the single crystals of $α$-RuCl$_3$ down to 80 mK and up to 9 T. Our experiments clearly show a field-induced phase transition occurring at $H_c$ $\approx$ 7.5 T, above which the zigzag magnetic order is completely suppressed. The minimum of thermal conductivity at 7.5 T is attributed to the strong scattering of phonons by the magnet…
A quantum spin-liquid might be realized in $α$-RuCl$_{3}$, a honeycomb-lattice magnetic material with substantial spin-orbit coupling. Moreover, $α$-RuCl$_{3}$ is a Mott insulator, which implies the possibility that novel exotic phases occur upon doping. Here, we study the electronic structure of this material when intercalated with potassium by photoemission spectroscopy, electron energy loss spectroscopy, and density functional theory calculations. We obtain a stable stoichiometry at K$_{0.5}$RuCl$_3$. This gives rise to a peculiar charge disproportionation into formally Ru$^{2+}$ (4$d^6$) a…
We study the field-induced magnetization processes of extended Heisenberg-Kitaev models on the honeycomb lattice, taking into account off-diagonal and longer-range exchange interactions, using a combination of Monte-Carlo simulations, classical energy minimization, and spin-wave theory. We consider a number of different parameter sets, previously proposed to describe the magnetic behavior of $α$-RuCl$_3$ and Na$_2$IrO$_3$ with their antiferromagnetic zigzag ground states. By classifying these parameter sets, we reveal the existence of three distinct mechanisms to stabilize zigzag states, which…
The honeycomb Kitaev model in a magnetic field is a source of a topological quantum spin liquid with Majorana fermions and gauge flux excitations as fractional quasiparticles. We present experimental results for the thermal Hall effect of the material $α$-RuCl$_{3}$ which recently emerged as a prime candidate for realizing such physics. At temperatures above long-range magnetic ordering $T\gtrsim T_N\approx8$ K, we observe with an applied magnetic field $B$ perpendicular to the honeycomb layers a sizeable positive transversal heat conductivity $κ_{xy}$ which increases linearly with $B$. Upon r…
The low-temperature magnetic phases in the layered honeycomb lattice material $α$-RuCl$_3$ have been studied as a function of in-plane magnetic field. In zero field this material orders magnetically below 7 K with so-called zigzag order within the honeycomb planes. Neutron diffraction data show that a relatively small applied field of 2 T is sufficient to suppress the population of the magnetic domain in which the zigzag chains run along the field direction. We found that the intensity of the magnetic peaks due to zigzag order is continuously suppressed with increasing field until their disapp…
$α$-RuCl$_3$ is a Mott insulator with a honeycomb lattice with strong spin-orbit coupling. We report dielectric measurements on $α$-RuCl$_3$ single crystals under field. At zero field, the dielectric constant, $ε$, drops rapidly when cooled through the magnetic transition temperature T$_N$. With increasing field, the onset of the drop in $ε$ tracks the T$_N$. Such behavior is absent with field above a critical value H$_c$ ~ 7.5 T, indicating the onset of a quantum phase transition. Our data suggest that the dielectric constant can be used as a probe of magnetic ordering in $α$-RuCl$_3$, and $α…
Motivated by recent reports of a field-induced intermediate phase (IP) in the antiferromagnetic honeycomb Kitaev model that may be a spin liquid whose nature is distinct from the Kitaev Z2 phase, we present a detailed numerical study on the nature and dynamical response (such as dynamical spin-structure factors and resonant inelastic x-ray scattering intensities) of this field-induced IP and neighboring phases in a family of Kitaev-based models related by hidden symmetries and duality transformations. We further show that the same field-induced IP can appear in models relevant for $α$-RuCl${_3…
Frustrated bilayer quantum magnets have attracted attention as flat-band spin systems with unconventional thermodynamic properties. We study the low-temperature properties of a frustrated honeycomb-lattice bilayer spin-$\frac{1}{2}$ isotropic ($XXX$) Heisenberg antiferromagnet in a magnetic field by means of an effective low-energy theory using exact diagonalizations and quantum Monte Carlo simulations. Our main focus is on the magnetization curve and the temperature dependence of the specific heat indicating a finite-temperature phase transition in high magnetic fields.
The Kitaev material $α$-RuCl$_3$ is among the most prominent candidates to host a quantum spin-liquid state endowed with fractionalized excitations. Recent experimental and theoretical investigations have separately revealed the importance of both the magnetoelastic coupling and the magnetic anisotropy, in dependence of the applied magnetic field direction. In this combined theoretical and experimental research, we investigate the anisotropic magnetic and magnetoelastic properties for magnetic fields applied along the main crystallographic axes as well as for fields canted out of the honeycomb…
We present an analytical study of the exchange interactions between pseudospin one-half $d^{5}$ ions in honeycomb lattices with edge-shared octahedra. Various exchange channels involving Hubbard U, charge-transfer excitations, and cyclic exchange are considered. Hoppings within $t_{2g}$ orbitals as well as between $t_{2g}$ and $e_g$ orbitals are included. Special attention is paid to the trigonal crystal field $Δ$ effects on the exchange parameters. The obtained exchange Hamiltonian is dominated by ferromagnetic Kitaev interaction K within a wide range of $Δ$. It is found that a parameter regi…
We report the discovery of an intriguing pressure-driven phase transformation in the layered Kitaev-material $α$-RuCl$_3$. By analyzing both the Bragg scattering as well as the diffuse scattering of high-quality single crystals, we reveal a collective reorganization of the layer stacking throughout the crystal. Importantly, this transformation also effects the structure of the RuCl$_3$ honeycomb layers, which acquire a high trigonal symmetry with a single Ru--Ru distance of 3.41Å and a single Ru--Cl--Ru bond angle of 92.8°. Hydrostatic pressure therefore allows to tune the structure of $α$-RuC…
New frustrated antiferromagnetic compounds CuRE2Ge2O8 (RE=Pr, Nd, Sm, Eu) have been investigated using high-resolution x-ray diffraction, magnetic and heat capacity measurements. These systems show different magnetic lattices depending on rare-earth element. The nonmagnetic Eu compound is a S=1/2 two-dimensional triangular antiferromagnetic lattice oriented in the ac plane with geometrical frustration. On the other hand, the Pr, Nd, and Sm compounds show a three-dimensional honeycomb-tunnel-like lattice made of RE^3+ running along the a axis with the characteristic behavior of frustrated antif…
Using exact diagonalization calculations, we investigate the ground-state phase diagram of the hard-core Bose-Hubbard-Haldane model on the honeycomb lattice. This allows us to probe the stability of the Bose-metal phase proposed in Varney et al (2011 Phys. Rev. Lett. 107 077201), against various changes in the originally studied Hamiltonian.
The Kitaev quantum spin liquid (KSL) is a theoretically predicted state of matter whose fractionalized quasiparticles are distinct from bosonic magnons, the fundamental excitation in ordered magnets. The layered honeycomb antiferromagnet $α$-RuCl$_3$ is a KSL candidate material, as it can be driven to a magnetically disordered phase by application of an in-plane magnetic field, with $H_c \sim 7$ T. Here we report a detailed characterization of the magnetic excitation spectrum of this material by high-resolution time-domain terahertz (THz) spectroscopy. We observe two sharp magnon resonances wh…
In spite of flourishing studies on the topology of spin waves, a generic framework to classify and compute magnon band topology in non-collinear magnets is still missing. In this work we provide such a theory framework, by mapping an arbitrary linear spin wave into a local free-fermion Hamiltonian with exactly the same spectrum, symmetry implementation and band topology, which allows for a full classification and calculation on any topological properties of magnon bands. We apply this fermionization approach to honeycomb Kitaev magnet $α$-RuCl$_3$, and show the existence of topologically prote…
We present initial Raman spectroscopy experiments on exfoliated flakes of $α$-RuCl$_3$, from tens of nm thick down to single layers. Besides unexpectedly finding this material to be air stable, in the thinnest layers we observe the appearance with decreasing temperature of a symmetry-forbidden mode in crossed polarization, along with an anomalous broadening of a mode at 164 cm$^{-1}$ that is known to couple to a continuum of magnetic excitations. This may be due to an enhancement of magnetic fluctuations and evidence for a distorted honeycomb lattice in single- and bi-layer samples.
In $α$-RuCl$_3$, an external magnetic field applied within the honeycomb plane can induce a transition from a magnetically ordered state to a disordered state that is potentially related to the Kitaev quantum spin liquid. In zero field, single crystals with minimal stacking faults display a low-temperature state with in-plane zigzag antiferromagnetic order and a three-layer periodicity in the direction perpendicular to the honeycomb planes. Here, we present angle-dependent magnetization, ac susceptibility, and thermal transport data that demonstrate the presence of an additional intermediate-f…
$α$-RuCl$_3$ has attracted enormous attention since it has been proposed as a prime candidate to study fractionalized magnetic excitations akin to Kitaev's honeycomb-lattice spin liquid. We have performed a detailed specific-heat investigation at temperatures down to $0.4$ K in applied magnetic fields up to $9$ T for fields parallel to the $ab$ plane. We find a suppression of the zero-field antiferromagnetic order, together with an increase of the low-temperature specific heat, with increasing field up to $μ_0H_c\approx 6.9$ T. Above $H_c$, the magnetic contribution to the low-temperature spec…
We present first-principles results on the magnetoelastic coupling in $α$-RuCl$_3$ and uncover a striking dependence of the magnetic coupling constants on strain effects. Different magnetic interactions are found to respond very unequally to variations in the lattice, with the Kitaev interaction being the most sensitive. Exact diagonalization results on our magnetoelastic model reproduce recent measurements of the structural Grüneisen parameter and explain the origin of the negative magnetostriction of $α$-RuCl$_3$, disentangling contributions related to different anisotropic interactions and …
We discover a new type of multiple-$q$ state, "ripple state", in a frustrated honeycomb-lattice Heisenberg antiferromagnet under magnetic fields. The ground state has an infinite ring-like degeneracy in the wavevector space, exhibiting a cooperative paramagnetic state, "ring-liquid" state. We elucidate that the system exhibits the ripple state as a new low-temperature thermodynamic phase via a second-order phase transition from the ring-liquid state, keeping the ring-like spin structure factor. The spin texture in real space looks like a "water ripple" and can induce a giant electric polarizat…
We consider the spin-$1/2$ XY frustrated antiferromagnetic Heisenberg honeycomb model. There is an unclear intermediate region in the ground state phase diagram of the model. The most recognized phases are the quantum spin-liquid (QSL) and the antiferromagnetic Ising ordering. From the viewpoint of the quantum correlations, the QSL phase is expected to be entangled. Motivated by this fact, we have calculated the concurrence, the quantum discord (QD), and the entanglement entropy, by using numerical Lanczos and density matrix renormalization group (DMRG) methods. Our results explicitly show tha…
Raman scattering has been employed to investigate lattice and magnetic excitations of the honeycomb Kitaev material $α$-RuCl$_3$ and its Heisenberg counterpart CrCl$_3$. Our phonon Raman spectra give evidence for a first-order structural transition from a monoclinic to a rhombohedral structure for both compounds. Significantly, only $α$-RuCl$_3$ features a large thermal hysteresis, consistent with the formation of a wide phase of coexistence. In the related temperature interval of $70-170$ K, we observe a hysteretic behavior of magnetic excitations as well. The stronger magnetic response in th…
Using the density-matrix renormalization group, we determine the phase diagram of the spin 1/2 Heisenberg antiferromagnet on a honeycomb lattice with a nearest neighbor interaction J1 and a frustrating, next-neighbor exchange J2. As frustration increases, the ground state exhibits Neel, plaquette and dimer orders, with critical points at J2/J1 = 0.22 and 0.35. We observe that both the spin gap and the corresponding order parameters vanish continuously at both the critical points, indicating the presence of deconfined quantum criticality.
We calculate the two-magnon Raman scattering spectra in antiferromagnetic phases of several frustrated spin models defined on the honeycomb lattice. These include the Néel antiferromagnetic phase of a $J_1$-$J_2$-$J_3$ model and the stripe phase of the Heisenberg-Kitaev model. We show that both the magnetic frustration and the anisotropy of interactions may significantly affect the Raman spectra. We further discuss the implications of our results to the magnetic excitations of the iron-based compound BaFe$_2$Se$_2$O and show how the magnetic interactions can be extracted from fit to the Raman …
We show that the honeycomb Heisenberg antiferromagnet with $J_1/2=J_2=J_3$, where $J_{1/2/3}$ are first-, second- and third-neighbour couplings respectively, forms a classical spin liquid with pinch-point singularities in the structure factor at the Brillouin zone corners. Upon dilution with non-magnetic ions, fractionalised degrees of freedom carrying $1/3$ of the free moment emerge. Their effective description in the limit of low-temperature is that of spins randomly located on a triangular lattice, with a frustrated interaction of long-ranged logarithmic form. The XY version of this magnet …
We study the zero-temperature ($T=0$) ground-state (GS) properties of a frustrated spin-half $J^{XXZ}_{1}$--$J^{XXZ}_{2}$ model on the honeycomb lattice with nearest-neighbor and next-nearest-neighbor interactions with exchange couplings $J_{1}>0$ and $J_{2} \equiv κJ_{1}>0$, respectively, using the coupled cluster method. Both interactions are of the anisotropic $XXZ$ type. We present the $T=0$ GS phase diagram of the model in the ranges $0 \leq Δ\leq 1$ of the spin-space anisotropy parameter and $0 \leq κ\leq 1$ of the frustration parameter. A possible quantum spin-liquid region is identifie…
The combination of electronic correlation and spin-orbit coupling is thought to precipitate a variety of highly unusual electronic phases in solids, including topological and quantum spin liquid states. We report a Raman scattering study that provides evidence for unconventional excitations in $α$-RuCl$_3$, a spin-orbit coupled Mott insulator on the honeycomb lattice. In particular, our measurements reveal unusual magnetic scattering, typified by a broad continuum. The temperature dependence of this continuum is evident over a large scale compared to the magnetic ordering temperature, suggesti…
In the present paper we present some new data supporting the existence of a spin-disordered phase in the Heisenberg model on the honeycomb lattice with antiferromagnetic interactions up to third neighbors along the line J2=J3, predicted in [Phys. Rev. B 83, 094506 (2011)]. We use the Schwinger boson technique followed by a mean field decoupling and exact diagonalization for small systems to show the existence of an intermediate phase with a spin gap and short range Néel correlations in the strong quantum limit (S=1/2).
The material $α$-RuCl$_3$, with a two-dimensional Ru-honeycomb sublattice, has attracted considerable attention because it may be a realization of the Kitaev quantum spin liquid (QSL). Recently, a new honeycomb material, $α$-RuI$_3$, was prepared under moderate high-pressure and it is stable under ambient conditions. However, different from $α$-RuCl$_3$, $α$-RuI$_3$ was reported to be a paramagnetic metal without long-range magnetic order down to $0.35$ K. Here, the structural and electronic properties of the quasi-two-dimensional $α$-RuI$_3$ are theoretically studied. First, based on first-pr…
In the present paper we study the phase diagram of the Heisenberg model on the honeycomb lattice with antiferromagnetic interactions up to third neighbors along the line $J_2=J_3$ that include the point $J_2=J_3=J_1/2$, corresponding to the highly frustrated point where the classical ground state has macroscopic degeneracy. Using the Linear Spin-Wave, Schwinger boson technique followed by a mean field decoupling and exact diagonalization for small systems we find an intermediate phase with a spin gap and short range Néel correlations in the strong quantum limit (S=1/2). All techniques provide …
The layered honeycomb magnet alpha-RuCl3 has been proposed as a candidate to realize a Kitaev spin model with strongly frustrated, bond-dependent, anisotropic interactions between spin-orbit entangled jeff=1/2 Ru4+ magnetic moments. Here we report a detailed study of the three-dimensional crystal structure using x-ray diffraction on untwinned crystals combined with structural relaxation calculations. We consider several models for the stacking of honeycomb layers and find evidence for a crystal structure with a monoclinic unit cell corresponding to a stacking of layers with a unidirectional in…
We study the frustrated Heisenberg model on the bilayer honeycomb lattice. The ground-state energy and spin gap are calculated, using different bosonic representations at mean field level and numerical calculations, to explore different sectors of the phase diagram. In particular we make use of a bond operator formalism and series expansion calculations to study the extent of dimer inter-layer phase. On the other hand we use the Schwinger boson method and exact diagonalization on small systems to analyze the evolution of on-layer phases. In this case we specifically observe a phase that presen…
We study the phase diagram of the frustrated XY model on the honeycomb lattice by using accurate correlated wave functions and variational Monte Carlo simulations. Our results suggest that a spin-liquid state is energetically favorable in the region of intermediate frustration, intervening between two magnetically ordered phases. The latter ones are represented by classically ordered states supplemented with a long-range Jastrow factor, which includes relevant correlations and dramatically improves the description provided by the purely classical solution of the model. The construction of the …
We examine the effects of quantum fluctuations on a classical spin liquid state in the fully-frustrated honeycomb lattice Bose Hubbard model using quantum Monte Carlo simulations. Frustration is induced explicitly in the model by modulating the sign of the interaction spatially around each lattice hexagon. A superfluid to Mott insulating quantum phase transition can be induced by varying the relative strength of the classical interaction and quantum hopping. In the cases where the interaction has a regular spatial modulation, hopping promotes a phase transition to a symmetry-broken valence-bon…
Heat transport mediated by Majorana edge modes in a magnetic insulator leads to a half-integer thermal quantum Hall conductance, which has recently been reported for the two-dimensional honeycomb material $α$-RuCl$_3$. While the conventional electronic Hall effect requires a perpendicular magnetic field, we find that this is not the case in $α$-RuCl$_3$. Strikingly, the thermal Hall plateau appears even for a magnetic field with no out-of-plane components. The field-angular variation of the quantized thermal Hall conductance has the same sign structure of the topological Chern number, which is…
We study the spin-1/2 Heisenberg antiferromagnet on a bilayer honeycomb lattice including interlayer frustration. Using a set of complementary approaches, namely Schwinger bosons, dimer series expansion, bond operators, and exact diagonalization, we map out the quantum phase diagram. Analyzing ground state energies and elementary excitation spectra, we find four distinct phases, corresponding to three collinear magnetic long range ordered states, and one quantum disordered interlayer dimer phase. We detail, that the latter phase is adiabatically connected to an "exact" singlet product ground s…
We study the Hubbard model on the frustrated honeycomb lattice with nearest-neighbor $t_1$ and second nearest-neighbor hopping $t_2$, which is isomorphic to the bilayer triangle lattice, using the SU(2)-invariant slave boson theory. We show that the Coulomb interaction $U$ induces antiferromagnetic (AF) chiral spin-density wave ($χ$-SDW) order in a wide range of $κ=t_2/t_1$ where both the two-sublattice AF order at small $κ$ and the decoupled three-sublattice 120$^\circ$ order at large $κ$ are strongly frustrated, leading to three distinct phases with different anomalous Hall responses. We fin…
The pursuit of quantum spin liquid (QSL) in the Kitaev honeycomb magnets has drawn intensive attention recently. In particular, $α$-RuCl$_3$ has been widely recognized as a promising candidate for the Kitaev QSL. Although the compound exhibits an antiferromagnetic order under zero field, it is believed to be endowed with fractionalized excitations, and can be driven to the QSL phase by magnetic fields. Here, based on a realistic $K$-$J$-$Γ$-$Γ'$ model for $α$-RuCl$_3$ [1], we exploit the exponential tensor renormalization group approach to explore the phase diagram of the compound under magnet…
Highly frustrated spin systems represent a central and challenging problem in condensed mater physics. To this problem, we introduce an algorithm based on mixed projected entangled pair states (m-PEPS), which is a novel type of tensor network. We use the famous Kitaev model on an infinite honeycomb lattice, which can be solved exactly, as a benchmark. With very limited parameters and finite scaling, our calculation results are in good agreement with the exact results, indicating the efficiency of our algorithm. After presenting the benchmark, we investigate the Kitaev-Heisenberg model, which w…
We present comprehensive electron spin resonance (ESR) studies of in-plane oriented single crystals of $α$-RuCl$_3$, a quasi-two-dimensional material with honeycomb structure, focusing on its high-field spin dynamics. The measurements were performed in magnetic fields up to 16 T, applied along the [110] and [100] directions. Several ESR modes were detected. Combining our findings with recent inelastic neutron- and Raman-scattering data, we identify most of the observed excitations. Most importantly, we show that the low-temperature ESR response beyond the boundary of the magnetically ordered r…
