Quantum paramagnetic ground states on the honeycomb lattice and field-induced transition to Néel order
R. Ganesh, D. N. Sheng, Young-June Kim, A. Paramekanti
备注：
8 pages, revised longer version of arXiv:1012.0316. Corrected factor of 2 error in Eq.[16], replotted Fig.[4] and revised the critical $J_c/J_1$ needed to stabilize interlayer dimer state. We thank S. V. Isakov for discussions which uncovered this error
Motivated by recent experiments on Bi$_3$Mn$_4$O$_{12}$(NO$_3$), and a broader interest arising from numerical work on the honeycomb lattice Hubbard model, we have studied the effect of a magnetic field on honeycomb lattice spin models with quantum paramagnetic ground states. For a model with frustrating second-neighbor exchange, $J_2$, we use a Lindemann-like criterion within spin wave theory to show that Néel order melts beyond a critical $J_2$. The critical $J_2$ increases with a magnetic field, implying the existence of a field-induced paramagnet-Néel transition over a range of $J_2$. We also study bilayer model using a spin-$S$ generalization of bond operator mean field theory. We show that there is a Néel-dimer transition for various spin values with increasing bilayer coupling, and that the resulting interlayer dimer state undergoes a field induced transition into a state with transverse Néel order. Finally, we study a spin-3/2 model which interpolates between the Heisenberg model and the Affleck-Kennedy-Lieb-Tasaki (AKLT) parent Hamiltonian. Using exact diagonalization, we compute the fidelity susceptibility to locate the Neel-AKLT quantum critical point, obtain the spin gap of the AKLT parent Hamiltonian, and argue that AKLT state also undergoes field-induced Neel ordering.
Recent work shows that a quantum spin liquid can arise in realistic fermionic models on a honeycomb lattice. We study the quantum spin-1/2 Heisenberg honeycomb model, considering couplings J1, J2, and J3 up to third nearest neighbors. We use an unbiased pseudofermion functional renormalization group method to compute the magnetic susceptibility and determine the ordered and disordered states of the model. Aside from antiferromagnetic, collinear, and spiral order domains, we find a large paramagnetic region at intermediate J2 coupling. For larger J2 within this domain, we find a strong tendency…
Quantum phase transitions in the Hubbard model on the honeycomb lattice are investigated in the variational cluster approximation. The critical interaction for the paramagnetic to antiferromagnetic phase transition is found to be in remarkable agreement with a recent large-scale quantum Monte Carlo simulation. Calculated staggered magnetization increases continuously with $U$ and thus we find the phase transition is of a second order. We also find that the semimetal-insulator transition occurs at infinitesimally small interaction and thus a paramagnetic insulating state appears in a wide inter…
We investigate the ground-state phase diagram of a spin-1/2 honeycomb-lattice antiferromagnetic (AF) Heisenberg model with three exchange interactions, $J_{\rm A}$, $J_{\rm B}$, and $J_{\rm C}$ that is realized in a distorted honeycomb-lattice antiferromagnet ${\rm Cu_2 (pymca)_3 (ClO_4)}$. We remeasured the magnetic susceptibility of its polycrystalline sample with special care, and determined the exchange parameters of this material through the comparison with numerical results based on a quantum Monte Carlo (QMC) method. The QMC method also provides a ground-state phase diagram in the $J_{\…
We obtain the phase-diagram of the half-filled honeycomb Hubbard model with density matrix embedding theory, to address recent controversy at intermediate couplings. We use clusters from 2-12 sites and lattices at the thermodynamic limit. We identify a paramagnetic insulating state, with possible hexagonal cluster order, competitive with the antiferromagnetic phase at intermediate coupling. However, its stability is strongly cluster and lattice size dependent, explaining controver- sies in earlier work. Our results support the paramagnetic insulator as being a metastable, rather than a true, i…
Na2Co2TeO6 is a proposed approximate Kitaev magnet, yet its actual magnetic interactions are elusive due to a lack of knowledge on the full excitation spectrum. Here, using inelastic neutron scattering and single crystals, we determine the system's temperature-dependent magnetic excitations over the entire Brillouin zone. Without committing to specific models, we unveil a distinct signature of the third-nearest-neighbor coupling in the spin waves, which signifies the associated distance as an emerging "soft link" in the ordered state. The presence of at least six non-overlapping spin-wave bran…
We discover a new type of multiple-$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…
The role of non-local Coulomb correlations in the honeycomb lattice is investigated within cluster dynamical mean field theory combined with finite-temperature exact diagonalization. The paramagnetic semi-metal to insulator transition is found to be in excellent agreement with finite-size determinantal Quantum Monte Carlo simulations and with cluster dynamical mean field calculations based on the continuous-time Quantum Monte Carlo approach. As expected, the critical Coulomb energy is much lower than within a local or single-site formulation. Short-range correlations are shown to give rise to …
Paramagnetic impurities in a quantum spin-liquid can result in Kondo effects with highly unusual properties. We have studied the effect of locally exchange-coupling a paramagnetic impurity with the spin-1/2 honeycomb Kitaev model in its gapless spin-liquid phase. The (impurity) scaling equations are found to be insensitive to the sign of the coupling. The weak and strong coupling fixed points are stable, with the latter corresponding to a noninteracting vacancy and an interacting, spin-1 defect for the antiferromagnetic and ferromagnetic cases respectively. The ground state in the strong coupl…
Phase transition in a honeycomb lattice is studied by the means of the two dimensional Hubbard model and the exact diagonalization dynamical mean field theory at zero temperature. At low energies, the dispersion relation is shown to be a linear function of the momentum. In the limit of weak interactions, the system is in the semi-metal phase. By increasing the on site interaction a semi-metal to insulator transition takes place in the paramagnetic phase. Calculation of double occupancy shows such a phase transition is of the second order. The respective phase transition point and critical on-s…
As a model for the B 2pz bands of MgB$_2$, a half-filled Hubbard model on a honeycomb lattice is studied, and a possibility of an antiferromagnetism (AF) at the ground state is examined by Monte Carlo calculations as well as a random phase approximation method. On a single-layer honeycomb lattice, a paramagnetic to AF phase transition occurs at a finite value of the repulsion energy $U_c/t \simeq 3.6$, due to the loss of the density of states at the fermi level. On a layered honeycomb lattice, however, inter-layer hopping term creates a perfect nesting of the fermi surface, and leads the AF wi…
We study numerically a bosonic analog of the Kitaev honeycomb model, which is a minimal model for $4d^4/5d^4$ quantum magnets with honeycomb lattice geometry. We construct its phase diagram by a combination of Landau theory analysis and quantum Monte Carlo simulations. In particular, we show that the phase boundaries between the paramagnetic state and magnetically ordered states are generically fluctuation-induced first order phase transitions. Our results are potentially applicable to Ru$^{4+}$- and Ir$^{5+}$-based honeycomb magnets.
Motivated by recent experiments on the spin-3/2 frustrated bilayer honeycomb antiferromagnet Bi$_3$Mn$_4$O$_{12}$(NO$_3$), we study the spin-S Heisenberg model on the honeycomb lattice with various additional exchange interactions which frustrate Néel order. Using spin wave theory, exact diagonalization, and bond operator theory, we consider the effects of (i) second-neighbor exchange, (ii) biquadratic exchange for $S = 3/2$ which leads to an AKLT valence bond solid, and (iii) bilayer coupling which leads to an interlayer dimer solid. We show that the resulting paramagnetic states undergo a tr…
Using the density matrix renormalization group, we investigate the $S=1/2$ Heisenberg model on the honeycomb lattice with first- ($J_1$) and second-neighbor ($J_2$) interactions. We are able to study long open cylinders with widths up to 12 lattice spacings. For $J_2/J_1$ near 0.3, we find an apparently paramagnetic phase, bordered by an antiferromagnetic phase for $J_2\lesssim 0.26$ and by a valence bond crystal for $J_2\gtrsim 0.36$. The longest correlation length that we find in this intermediate phase is for plaquette valence bond (PVB) order. This correlation length grows strongly with cy…
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…
The Kitaev-Heisenberg model defined on both honeycomb and triangular lattices has been studied intensively in recent years as a possible model to describe spin-orbital physics in iridium oxides. In the model, there are many phases characteristic for each lattice. However, there is no study how the phases in the two lattices merge each other when geometry changes from honeycomb lattice to triangular lattice. We investigate the ground state of the Kitaev-Heisenberg model defined on the system connecting the honeycomb and triangular lattices, named a honeycomb-triangular lattice. We obtain a grou…
A prominent feature of quantum spin liquids is fractionalization of the spin degree of freedom. Fractionalized excitations have their own dynamics in different energy scales, and hence, affect finite-temperature ($T$) properties in a peculiar manner even in the paramagnetic state harboring the quantum spin liquid state. We here present a comprehensive theoretical study of the spin dynamics in a wide $T$ range for the Kitaev model on a honeycomb lattice, whose ground state is such a quantum spin liquid. In this model, the fractionalization occurs to break up quantum spins into itinerant matter …
Bi3Mn4O12(NO3), in which the Mn4+ ions carry S=3/2, is the first honeycomb lattice system that shows no long-range magnetic order. Using neutron scattering, we have determined that short-range antiferromagnetic correlations develop at low temperatures. Applied magnetic fields induce a magnetic transition, in which the short-range order abruptly expands into a long-range order.
An exact solution (incomplete) of the ground-state problem for an Ising model in an external field on a 3D honeycomb zigzag-ladder lattice with two types of sites is found. It is shown that the geometrical frustration due to the presence of triangle elements leads to the emergence of a variety of magnetic phases. The majority of these are partially disordered (highly degenerate). The theoretical results are used to explain the sequence of experimentally observed phase transitions in the honeycomb zigzag-ladder magnets and to predict the appearance of new phases.
We study the ground-state phase diagram of the quantum $J_1-J_2$ model on the honeycomb lattice by means of an entangled-plaquette variational ansatz. Values of energy and relevant order parameters are computed in the range $0\le {J_2}/{J_1} \le 1$. The system displays classical order for ${J_2}/{J_1}\lesssim 0.2$ (Néel), and for $J_2/J_1 \gtrsim 0.4$ (collinear). In the intermediate region, the ground-state is disordered. Our results show that the reduction of the half-filled Hubbard model to the model studied here does not yield accurate predictions.
We present an antiferromagnetic quantum spin-1/2 model on honeycomb lattice. It has two parts, one of which is the usual nearest-neighbor Heisenberg model. The other part is a certain multiple spin interaction term, introduced by us, which is exactly solvable for the ground state. Without the Heisenberg part, the model has an exact threefold degenerate dimer ground state. This exact ground state is also noted to exist for the general spin-S case. For the spin-1/2 case, we further carry out the triplon analysis in the ground state, to study the competition between the Heisenberg and the multipl…
We report low-temperature (down to $\sim$5 K) Raman signatures of the recently discovered intercalated honeycomb magnet Ag$_3$LiIr$_2$O$_6$, a putative Kitaev quantum spin liquid (QSL) candidate. The Kitaev QSL is predicted to host Majorana fermions as its emergent elementary excitations through a thermal fractionalization of entangled spins $S = 1/2$. We observe evidence of this fractionalization in the low-energy magnetic continuum whose temperature evolution harbours signatures of the predicted Fermi statistics obeyed by the itinerant Majorana quasiparticles. The magnetic Raman susceptibili…
In extended Kitaev models on the honeycomb lattice, off-diagonal interactions (e.g. the $Γ, Γ^{'}$ terms) give rise to non-Kitaev quantum spin liquid (QSL) and several magnetically ordered phases. In the present work, we dope holes to the system and study the resultant $t$-$K$-$Γ$-$Γ^{'}$ model by mean field theory. The interplay between the charge and spin degrees of freedom results in a rich phase diagram. Similar to doped cuprates, superconductors, pseudogap phases, fermi liquid, strange metal and paramagnetic phase are generated. What is different is that, more than one superconducting pha…
We study the ground-state (gs) phase diagram of the frustrated spin-1/2 $J_{1}$-$J_{2}$-$J_{3}$ antiferromagnet with $J_{2} = J_{3} =κJ_1$ on the honeycomb lattice, using coupled-cluster theory and exact diagonalization methods. We present results for the gs energy, magnetic order parameter, spin-spin correlation function, and plaquette valence-bond crystal (PVBC) susceptibility. We find a Néel antiferromagnetic (AFM) phase for $κ< κ_{c_{1}} \approx 0.47$, a collinear striped AFM phase for $κ> κ_{c_{2}} \approx 0.60$, and a paramagnetic PVBC phase for $κ_{c_{1}} \lesssim κ\lesssim κ_{c_{2}}$. …
Quantum spin liquid is a disordered magnetic state with fractional spin excitations. Its clearest example is found in an exactly solved Kitaev honeycomb model where a spin flip fractionalizes into two types of anyons, quasiparticles that are neither fermions nor bosons: a pair of gauge fluxes and a Majorana fermion. Here we demonstrate this kind of fractionalization in the Kitaev paramagnetic state of the honeycomb magnet $α$-RuCl$_3$. The spin-excitation gap measured by nuclear magnetic resonance consists of the predicted Majorana fermion contribution following the cube of the applied magneti…
The ground state phase diagram of the dimerized spin-1/2 XX honeycomb model in presence of a transverse magnetic field (TF) is known. With the absence of the magnetic field, two quantum phases, namely, the Néel and the dimerized phases have been identified. Moreover, canted Néel and the paramagnetic (PM) phases also emerge by applying the magnetic field. In this paper, using two complementary numerical exact techniques, Lanczos exact diagonalization, and Density matrix renormalization group (DMRG) methods, we study this model by focusing on the quantum correlations, the concurrence, and the qu…
Lattice Wigner crystal states stabilized by long-range Coulomb interactions have recently been realized in two-dimensional moiré materials. We employ large-scale unrestricted Hartree-Fock techniques to unveil the magnetic phase diagrams of honeycomb lattice Wigner crystals. For the three lattice filling factors with the largest charge gaps, n = 2/3, 1/2, 1/3, the magnetic phase diagrams contain multiple phases, including ones with non-collinear and non-coplanar spin arrangements. We discuss magnetization evolution with external magnetic field, which has potential as an experimental signature o…
We investigate the ground-state properies of the $K-Γ$ model on a honeycomb lattice using series expansions and numerical exact diagonalizations, where the model includes Kitaev ($K$) and symmetric off-diagonal ($Γ$) interactions. Starting from the weakly interacting dimers on the specific bond, we strengthen the interdimer interactions to the isotropically interacting system. We show that depending on $Γ$ and $K$, the dimer state survives up to the isotropically interacting system, where the phase transition occurs, or obeys a phase transition to a magnetically ordered state at an anisotropic…
In this paper we analyze the groundstate and finite-temperature properties of a frustrated Heisenberg $J_1-J_2$ model on a honeycomb lattice by employing the Schwinger boson technique. The phase diagram and spin gap as functions of ${J}_{2}/{J}_{1}$ are presented, showing that the exotic spin liquid phase lies in $0.21<{J}_{2}/{J}_{1} <0.43$. The temperature and magnetic-field dependences of specific heat, magnetic susceptibility and Knight shift are also presented. We find the spin liquid state is robust with respect to external magnetic field. These results provide clear information characte…
We study the Hubbard model on the honeycomb lattice in the vicinity of the quantum critical point by means of a multiband formulation of the Dual Fermion approach. Beyond the strong local correlations of the dynamical mean field, critical fluctuations on all length scales are included by means of a ladder diagram summation. Analysis of the susceptibility yields an estimate of the critical interaction strength of the quantum phase transition from a paramagnetic semimetal to an antiferromagnetic insulator, in good agreement to other numerical methods. We further estimate the crossover temperatur…
Temperature evolution of the spin correlation and excitation spectrum is investigated for a Kitaev model defined on a decorated honeycomb lattice by using the quantum Monte Carlo simulation in the Majorana fermion representation. The ground state of this quantum spin model is given by two kinds of chiral spin liquids: one is topologically trivial with Abelian anyon excitations, and the other is topologically nontrivial with non-Abelian anyon excitations. While lowering temperature, the model exhibits several crossovers in the paramagnetic state, which originate from the fractionalization of qu…
It is shown that the unique sign structure of the ground state of the Hubbard model on honeycomb lattice, which is shown to be insensitive to the trapped $Z_{2}$ gauge flux when the system is defined on a torus, may cause the absence of topological degeneracy on this bipartite system. Examples of variational Mott insulating state on the honeycomb lattice are given to illustrate the close relation between the sign structure of the ground state and the (absence of) topological degeneracy.
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 show that the spin-density wave state on the partially filled honeycomb and triangular lattices is preempted by a paramagnetic phase that breaks an emergent Z_4 symmetry of the system, associated with the four inequivalent arrangements of spins in the quadrupled unit cell. Unlike other emergent paramagnetic phases in itinerant and localized-spin systems, this state preserves the rotational symmetry of the lattice but breaks its translational symmetry, giving rise to a super-lattice structure that can be detected by scanning tunneling microscopy. This emergent phase also has distinctive sign…
A spin-1/2 Heisenberg model on honeycomb lattice is investigated by doing triplon analysis and quantum Monte Carlo calculations. This model, inspired by Cu$_2$(pymca)$_3$(ClO$_4$), has three different antiferromagnetic exchange interactions ($J_A$, $J_B$, $J_C$) on three different sets of nearest-neighbour bonds which form a kagome superlattice. While the model is bipartite and unfrustrated, its quantum phase diagram is found to be dominated by a quantum paramagnetic phase that is best described as a spin-gapped hexagonal-singlet state. The Néel antiferromagnetic order survives only in a small…
The unusual ground state and thermodynamic properties of spin-1/2 two-leg honeycomb (HC) spin ladder are systematically studied by jointly utilizing various analytical and numerical methods. The HC spin ladder is found to exhibit behaviors dramatically different from those of the conventional square spin ladder. A strong relevant term nJ and a half saturation magnetization plateau that can be attributed to the formation of diluted dimer states are observed in the HC ladder, both of which are absent in the square ladder. The ground state phase diagram of the HC spin ladder is identified, and th…
We calculated the phase diagram of the Kondo-Heisenberg model on two-dimensional honeycomb lattice with both nearest-neighbor and next-nearest-neighbor antiferromagnetic spin exchanges, to investigate the interplay between RKKY and Kondo interactions at presence of magnetic frustration. Within a mean-field decoupling technology in slave-fermion representation, we derived the zero-temperature phase diagram as a function of Kondo coupling $J_k$ and frustration strength $Q$. The geometrical frustration can destroy the magnetic order, driving the original antiferromagnetic (AF) phase to non-magnet…
We classify the order parameters on the honeycomb lattice using the SO(4) symmetry of the Hubbard model. We will focus on the topologically nontrivial quantum spin Hall order and spin triplet superconductor, which together belong to the (3, 3) representation of the SO(4). Depending on the microscopic parameters, this (3, 3) order parameter has two types of ground states with different symmetries: type A, the ground state manifold is [S^2xS^2]/Z_2; and type B, with ground state manifold SO(3)xZ_2. We demonstrate that phase A is adjacent to a Z_2xZ_2 topological phase with mutual semion statisti…
Motivated by the absence of both spin freezing and a cooperative Jahn-Teller effect at the lowest measured temperatures, we study the ground state of Ba3CuSb2O9. We solve a general spin-orbital model on both the honeycomb and the decorated honeycomb lattice, revealing rich phase diagrams. The spin-orbital model on the honeycomb lattice contains an SU(4) point, where previous studies have shown the existence of a spin-orbital liquid with algebraically decaying correlations. For realistic parameters on the decorated honeycomb lattice, we find a phase that consists of clusters of nearest-neighbou…
We present a family of two-dimensional frustrated quantum magnets solely based on pure nearest-neighbor Heisenberg interactions which can be solved quasi-exactly. All lattices are constructed in terms of frustrated quantum cages containing a chiral degree of freedom protected by frustration. The ground states of these models are dubbed ultimate quantum paramagnets and exhibit an extensive entropy at zero temperature. We discuss the unusual and extensively degenerate excitations in such phases. Implications for thermodynamic properties as well as for decoherence free quantum computation are dis…
Spiral spin-liquids are correlated paramagnetic states with degenerate propagation vectors forming a continuous ring or surface in reciprocal space. On the honeycomb lattice, spiral spin-liquids present a novel route to realize emergent fracton excitations, quantum spin liquids, and topological spin textures, yet experimental realizations remain elusive. Here, using neutron scattering, we show that a spiral spin-liquid is realized in the van der Waals honeycomb magnet FeCl$_3$. A continuous ring of scattering is directly observed, which indicates the emergence of an approximate U(1) symmetry i…
We investigate ground state and finite temperature properties of the half-filled Hubbard model on a honeycomb lattice using quantum monte carlo and series expansion techniques. Unlike the square lattice, for which magnetic order exists at T=0 for any non-zero $U$, the honeycomb lattice is known to have a semi-metal phase at small $U$ and an antiferromagnetic one at large $U$. We investigate the phase transition at T=0 by studying the magnetic structure$and compressibility using quantum monte carlo simulations and by calculating the sublattice magnetization, uniform susceptibility, spin-wave an…
We study the ground-state (gs) phase diagram of the frustrated spin-1/2 $J_{1}$--$J_{2}$ antiferromagnet with $J_{2}=κJ_1>0$ ($J_{1}>0$) on the honeycomb lattice, using the coupled-cluster method. We present results for the ground-state energy, magnetic order parameter and plaquette valence-bond crystal (PVBC) susceptibility. We find a paramagnetic PVBC phase for $κ_{c_1}<κ<κ_{c_2}$, where $κ_{c_1} \approx 0.207 \pm 0.003$ and $κ_{c_2} \approx 0.385 \pm 0.010$. The transition at $κ_{c_1}$ to the Néel phase seems to be a continuous deconfined transition (although we cannot exclude a very narrow…
The crystal structure, magnetic ground state, and the temperature dependent microscopic spin-spin correlations of the frustrated honeycomb lattice antiferromagnet Na2Co2TeO6 have been investigated by powder neutron diffraction. A three dimensional (3D) long-range antiferromagnetic ordering has been found below TN ~ 24.8 K. The magnetic ground state, determined to be zigzag antiferromagnet [k = (1/2 0 0)], occurs due to the competing exchange interactions up to third nearest neighbors within the honeycomb lattice. The exceptional existence of a limited magnetic correlation length along the c ax…
We synthesize and study single crystals of the layered honeycomb lattice Mott insulators Na2RuO3 and Li2RuO3 with magnetic Ru4+(4d4) ions. The newly found Na2RuO3 features a nearly ideal honeycomb lattice and orders antiferromagnetically at 30 K. Single-crystals of Li2RuO3 adopt a honeycomb lattice with either C2/m or more distorted P21/m below 300 K, depending on detailed synthesis conditions. We find that Li2RuO3 in both structures hosts a well-defined magnetic state, in contrast to the singlet ground state found in polycrystalline Li2RuO3. A phase diagram generated based on our results unco…
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…
An effective model in the isolated dimer limit of the Kitaev-type model on a decorated honeycomb lattice is investigated at finite temperature. The ground state of this model is exactly shown to be a chiral spin liquid with spontaneous breaking of time reversal symmetry. We elaborate the finite-temperature phase diagram by using the mean-field approximation and Monte Carlo simulation. We find that the phase transition between the high-temperature paramagnetic phase and the low-temperature chiral spin liquid phase is always of second order in the Monte Carlo results, although a tricritical poin…
Motivated by the observation of a disordered spin ground state in the $S=3/2$ material Bi$_3$Mn$_4$O$_{12}$NO$_3$, we study the ground state properties and excitation spectra of the $S=3/2$ (and for comparison $S=1/2$) bilayer Heisenberg model on the honeycomb lattice, with and without frustrating further neighbor interactions. We use series expansions around the Néel state to calculate properties of the magnetically ordered phase. Furthermore, series expansions in $1/λ=J_1/J_{\perp}$, where $J_1$ is an in-plane exchange constant and $J_\perp$ is the exchange constant between the layers are us…
We use the coupled cluster method (CCM) to study a frustrated spin-$\frac{1}{2}$ $J_{1}$--$J_{2}$--$J_{1}^{\perp}$ Heisenberg antiferromagnet on a bilayer honeycomb lattice with $AA$ stacking. Both nearest-neighbor (NN) and frustrating next-nearest-neighbor antiferromagnetic (AFM) exchange interactions are present in each layer, with respective exchange coupling constants $J_{1}>0$ and $J_{2} \equiv κJ_{1} > 0$. The two layers are coupled with NN AFM exchanges with coupling strength $J_{1}^{\perp}\equiv δJ_{1}>0$. We calculate to high orders of approximation within the CCM the zero-field trans…
Layered antiferromagnetic spin density wave (LAF) state is one of the plausible ground states of charge neutral Bernal stacked bilayer graphene. In this paper, we use determinant quantum Monte Carlo method to study the effect of the electric field on the magnetic order in bilayer Hubbard model on a honeycomb lattice. Our results qualitatively support the LAF ground state found in the mean field theory. The obtained magnetic moments, however, are much smaller than what are estimated in the mean field theory. As electric field increases, the magnetic order parameter rapidly decreases.
The electronic ground state in many iridate materials is described by a complex wave-function in which spin and orbital angular momenta are entangled due to relativistic spin-orbit coupling (SOC). Such a localized electronic state carries an effective total angular momentum of $J_{eff}=1/2$. In materials with an edge-sharing octahedral crystal structure, such as the honeycomb iridates Li2IrO3 and Na2IrO3, these $J_{eff}=1/2$ moments are expected to be coupled through a special bond-dependent magnetic interaction, which is a necessary condition for the realization of a Kitaev quantum spin liqui…
Kitaev's honeycomb spin-liquid model and its proposed realization in materials such as $α$-RuCl$_3$, Li$_2$IrO$_3$ and Na$_2$IrO$_3$ continue to present open questions about how the dynamics of a spin-liquid are modified in the presence of non-Kitaev interactions as well as the presence of inhomogeneities. Here we use $^{23}$Na nuclear magnetic resonance to probe both static and dynamical magnetic properties in single crystal Na$_2$IrO$_3$. We find that the NMR shift follows the bulk susceptibility above 30 K but deviates from it below; moreover below $T_N$ the spectra show a broad distributio…
We study the low-temperature heat transport of Nd_3Ga_5SiO_{14}, which is a spin-liquid candidate, to probe the nature of ground state and the effect of magnetic field on the magnetic properties. The thermal conductivity (κ) shows a purely phononic transport in zero field. The external magnetic field along the c axis induces a dip-like behavior of κ(H), which can be attributed to a simple paramagnetic scattering on phonons. However, the magnetic field along the ab plane induces another step-like decrease of κ. This kind of κ(H) behavior is discussed to be related to a field-induced partial ord…
Kitaev quantum spin liquid, massively quantum entangled states, is so scarce in nature that searching for new candidate systems remains a great challenge. Honeycomb heterostructure could be a promising route to realize and utilize such an exotic quantum phase by providing additional controllability of Hamiltonian and device compatibility, respectively. Here, we provide epitaxial honeycomb oxide thin film Na3Co2SbO6, a candidate of Kitaev quantum spin liquid proposed recently. We found a spin glass and antiferromagnetic ground states depending on Na stoichiometry, signifying not only the import…
In this paper, we investigate the ground-state phase diagram of the $S=1/2$ Heisenberg-$Γ$ model on a honeycomb lattice by dimer series expansion and exact diagonalization. We focus on the effects of the anisotropy of the interactions; by tuning the coupling constants, the system changes between the isolated dimer and the spin-chain models. We find that, in the spin-chain limit, there are three kinds of states: a Tomonaga-Luttinger liquid and two magnetically long-range-ordered states. All three states become two-dimensional long-range ordered states by the infinitesimal interchain interaction…
