We use Quantum Monte-Carlo methods to study the ground state phase diagram of a S=1/2 honeycomb lattice magnet in which a nearest-neighbor antiferromagnetic exchange J (favoring Néel order) competes with two different multi-spin interaction terms: a six-spin interaction Q_3 that favors columnar valence-bond solid (VBS) order, and a four-spin interaction Q_2 that favors staggered VBS order. For Q_3 ~ Q_2 >> J, we establish that the competition between the two different VBS orders stabilizes Néel order in a large swathe of the phase diagram even when J is the smallest energy-scale in the Hamiltonian. When Q_3 >> (Q_2,J) (Q_2 >> (Q_3,J)), this model exhibits at zero temperature phase transition from the Néel state to a columnar (staggered) VBS state. We establish that the Néel-columnar VBS transition is continuous for all values of Q_2, and that critical properties along the entire phase boundary are well-characterized by critical exponents and amplitudes of the non-compact CP^1 (NCCP^1) theory of deconfined criticality, similar to what is observed on a square lattice. However, a surprising three-fold anisotropy of the phase of the VBS order parameter at criticality, whose presence was recently noted at the Q_2=0 deconfined critical point, is seen to persist all along this phase boundary. We use a classical analogy to explore this by studying the critical point of a three-dimensional XY model with a four-fold anisotropy field which is known to be weakly irrelevant at the three-dimensional XY critical point. In this case, we again find that the critical anisotropy appears to saturate to a nonzero value over the range of sizes accessible to our simulations.
Using large-scale quantum Monte Carlo simulations, we exactly solve a model of Fermions hopping on the honeycomb lattice with cluster charge interactions, which has been proposed as an effective model with possible application to twisted bilayer graphene near half-filling. We find an interaction driven semimetal to insulator transition to an insulating phase consisting of a valence bond solid with Kekulé pattern. Finite size scaling reveals that the phase transition of the semimetal to Kekulé valence bond solid phase is continuous and belongs to chiral XY universality class.
The honeycomb lattice material Li2RuO3 undergoes a dimerization of Ru4+ cations on cooling below 270C, where the magnetic susceptibility vanishes. We use density functional theory calculations to show that this reflects the formation of a 'valence bond crystal', with a strong bond disproportionation. On warming, x-ray diffraction shows that discrete three-fold symmetry is regained on average, and the dimerization apparently disappears. In contrast, local structural measurements using high-energy x-rays, show that disordered dimers survive at the nanoscale up to at least 650C. The high temperat…
High-frequency ESR results on the S=1/2 Heisenberg hexagonal antiferromagnet InCu2/3V1/3O3 are reported. This compound appears to be a rare model substance for the honeycomb lattice antiferromagnet with very weak interlayer couplings. The high-temperature magnetic susceptibility can be interpreted by the S=1/2 honeycomb lattice antiferromagnet, and it shows a magnetic-order-like anomaly at TN=38 K. Although, the resonance field of our high-frequency ESR shows the typical behavior of the antiferromagnetic resonance, the linewidth of our high-frequency ESR continues to increase below TN, while i…
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 use exact quantum Monte Carlo simulations to demonstrate that the Néel ground state of an antiferromagnetic SU(2) spin-$\frac{1}{2}$ Heisenberg model on the honeycomb lattice can be destroyed by a coupling to quantum phonons. We find a clear first-order transition to a valence-bond-solid state with Kekulé order instead of a deconfined quantum critical point. However, quantum lattice fluctuations can drive the transition towards weakly first-order, revealing a tunability of the transition by the retardation of the interaction. In contrast to the one-dimensional case, our phase diagram in the…
We study S=1/2 Heisenberg model on the honeycomb lattice with first and second neighbor antiferromagnetic exchange (J_{1}-J_{2} model), employing exact diagonalization in both S_z=0 basis and nearest neighbor singlet valence bond (NNVB) basis. We find that for 0.2<J_2/J_1<0.3, NNVB basis gives a proper description of the ground state in comparison with the exact results. By analyzing the dimer-dimer as well as plaquette-plaquette correlations and also defining appropriate structure factors, we investigate possible symmetry breaking states as the candidate for the ground state in the frustrated…
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 a spin-1/2 SU(2) model on the honeycomb lattice with nearest-neighbor antiferromagnetic exchange $J$ that favors Néel order, and competing 6-spin interactions $Q$ which favor a valence bond solid (VBS) state in which the bond-energies order at the "columnar" wavevector ${\mathbf K} = (2π/3,-2π/3)$. We present quantum Monte-Carlo evidence for a direct continuous quantum phase transition between Néel and VBS states, with exponents and logarithmic violations of scaling consistent with those at analogous deconfined critical points on the square lattice. Although this strongly suggests a d…
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.
We investigate a microscopic origin of nonreciprocal magnon that is distinct from the Dzyaloshinskii-Moriya interaction in a honeycomb antiferromagnet. The key ingredient is a symmetric anisotropic exchange interaction depending on the bond direction, which results in a valley-type nonreciprocal magnon excitations under the staggered antiferromagnetic ordering. Furthermore, we find this type of nonreciprocal magnon exhibits a peculiar magnetic-field response; the nonreciprocal direction can be manipulated by the in-plane rotating magnetic field. The obtained results can be accounted for the em…
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…
Motivated by the recent numerical simulations for doped $t$-$J$ model on the honeycomb lattice, we study superconductivity of singlet and triplet pairing on the honeycomb lattice Hubbard model. We show that a superconducting state with coexisting spin-singlet and spin-triplet pairings is induced by the antiferromagnetic order near half filling. The superconducting state we obtain has a topological phase transition that separates a topologically trivial state and a nontrivial state with Chern number two. Possible experimental realization of such a topological superconductivity is also discussed…
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.
The topological properties of massive and massless fermionic quasiparticles have been intensively investigated over the past decade in topological materials without magnetism. Recently, the bosonic analogs of such quasiparticles arising from spin waves have been reported in the two-dimensional (2D) honeycomb lattice ferromagnet/antiferromagnet and the 3D antiferromagnet. Here we use time-of-flight inelastic neutron scattering to study spin waves of the S = 1 honeycomb lattice antiferromagnet BaNi2(AsO4)2, which has a zig-zag antiferromagnetic (AF) ground state identical to that of the Kitaev q…
We theoretically propose possible magnetism-induced negative thermal expansion in honeycomb-lattice antiferromagnets with edge-sharing networks of $MX_6$ octahedra where $M$ and $X$ are transition-metal and ligand ions, respectively. In this crystal structure, the nearest-neighbor exchange interaction is composed of two competing contributions, i.e., the antiferromagnetic contribution from a direct 180$^\circ$ $M$-$M$ bond and the ferromagnetic contribution from 90$^\circ$ $M$-$X$-$M$ bonds, amplitudes of which have different bond-length dependence. Numerical analysis of the spin-lattice model…
Using the coupled cluster method we study the phase diagram of the spin-1/2 Heisenberg antiferromagnet on a honeycomb lattice with nearest-neighbor exchange coupling $J_{1}>0$ and frustrating next-nearest-neighbor coupling $J_{2} \equiv xJ_{1}>0$. In the range $0<x<1$ we find four phases exhibiting respectively Néel, 6-spin plaquette, staggered dimer, and Néel-II orderings, with quantum critical points at $x_{c_{1}} \approx 0.207(3), x_{c_{2}} \approx 0.385(10)$, and $x_{c_{3}} \approx 0.65(5)$. The transitions at $x_{c_{1}}$ and $x_{c_{3}}$ appear to be continuous (and hence deconfined) ones,…
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 …
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.
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 present a comprehensive computational study of the phase diagram of the frustrated S=1/2 Heisenberg antiferromagnet on the honeycomb lattice, with second-nearest (J2) and third-neighbor (J3) couplings. Using a combination of exact diagonalizations of the original spin model, of the Hamiltonian projected into the nearest neighbor short range valence bond basis, and of an effective quantum dimer model, as well as a self-consistent cluster mean-field theory, we determine the boundaries of several magnetically ordered phases in the region J2,J3\in [0,1], and find a sizable magnetically disorder…
It is shown that the semimetallic state of the two-dimensional honeycomb lattice with a point-like Fermi surface is unstable towards a canted antiferromagnetic insulator upon application of an in-plane magnetic field. This instability is already present at the mean-field level; the magnetic field shifts the up- and the down-spin cones in opposite directions thereby generating a finite density of states at the Fermi surface and a perfect nesting between the up- and the down-spin Fermi sheets. This perfect nesting triggers a canted antiferromagnetic insulating state. Our conclusions, based on me…
Using variational wave functions and Monte Carlo techniques, we study the antiferromagnetic Heisenberg model with first-neighbor $J_1$ and second-neighbor $J_2$ antiferromagnetic couplings on the honeycomb lattice. We perform a systematic comparison of magnetically ordered and nonmagnetic states (spin liquids and valence-bond solids) to obtain the ground-state phase diagram. Néel order is stabilized for small values of the frustrating second-neighbor coupling. Increasing the ratio $J_2/J_1$, we find strong evidence for a continuous transition to a nonmagnetic phase at $J_2/J_1 \approx 0.23$. C…
We study bond and spin correlations of the nearest-neighbour resonating valence bond (RVB) wavefunction for a SU($2$) symmetric $S=1/2$ antiferromagnet on the honeycomb lattice. We find that spin correlations in this wavefunction are short-ranged, while the bond energy correlation function takes on an oscillatory power-law form $D(\vec{r}) \sim \cos({\mathbf Q}\cdot {\vec{r}}) /|{\vec{r}}|^{η_w(2)}$, where ${\mathbf Q} = (2π/3, -2π/3)$ is the wavevector corresponding to "columnar" valence-bond solid order on the honeycomb lattice, and $η_w(2) \approx 1.49(3)$. We use a recently introduced larg…
We present a spin-rotation-invariant Green-function theory for the dynamic spin susceptibility in the spin-1/2 antiferromagnetic Heisenberg model on a stacked honeycomb lattice. Employing a generalized mean-field approximation for arbitrary temperatures, the thermodynamic quantities (two-spin correlation functions, internal energy, magnetic susceptibility, staggered magnetization, N'eel temperature, correlation length) and the spin-excitation spectrum are calculated by solving a coupled system of self-consistency equations for the correlation functions. The temperature dependence of the magnet…
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…
The spin$-1/2$ Heisenberg antiferromagnet on the honeycomb bilayer lattice is shown to display a rich variety of semiclassical and genuinely quantum phases, controlled by the interplay between intralayer frustration and interlayer exchange. Employing a complementary set of techniques, comprising spin rotationally invariant Schwinger boson mean field theory, bond operators, and series expansions we unveil the quantum phase diagram, analyzing low-energy excitations and order parameters. By virtue of Schwinger bosons we scan the complete range of exchange parameters, covering both long range orde…
The spin-3/2 Heisenberg antiferromagnet on the bilayer honeycomb lattice is a minimal model to describe the magnetic behavior of Bi$_3$Mn$_4$O$_{12}$(NO$_3$). We study this model with frustrating inter-layer second-neighbor couplings, taking into account quantum and thermal fluctuations. We use a path integral formulation in terms of coherent states to describe the low energy physics of the model. We show that for a particular point in the parameter space, close to the experimental estimated couplings, a continuum classical degeneracy is lifted by both quantum and thermal fluctuations, and a c…
The semimetal to antiferromagnet quantum phase transition of the Hubbard model on the honeycomb lattice has come to the forefront in the context of the proposal that a semimetal to spin liquid transition can occur before the transition to the antiferromagnetic phase. To study the semimetal to antiferromagnet transition, we generalize the two-particle self-consistent (TPSC) approach to the honeycomb lattice (a structure that can be realized in graphene for example). We show that the critical interaction strength where the transition occurs is $U_c/t=3.79\pm 0.01$ quite close to the value $U_c/t…
We present an antiferromagnetic quantum spin-1/2 model on honeycomb lattice. It has two parts, one of which is the usual nearest-neighbor Heisenberg model. The other part is a certain multiple spin interaction term, introduced by us, which is exactly solvable for the ground state. Without the Heisenberg part, the model has an exact threefold degenerate dimer ground state. This exact ground state is also noted to exist for the general spin-S case. For the spin-1/2 case, we further carry out the triplon analysis in the ground state, to study the competition between the Heisenberg and the multipl…
We propose the existence of a symmetry-protected topological Dirac nodal line (DNL) magnonic phase in layered honeycomb collinear antiferromagnets even in the presence of spin-orbit Dzyaloshinskii-Moriya interaction. We show that the magnon spin Nernst effect, predicted to occur in strictly two-dimensional (2D) honeycomb collinear antiferromagnets cancels out in the layered honeycomb collinear antiferromagnets. In other words, the magnon spin Nernst effect in each 2D antiferromagnetic layer cancels out the succeeding layer. Hence, the Berry curvature vanish in the entire Brillouin zone due to …
We carried out inelastic neutron scattering experiments on a buckled honeycomb lattice antiferromagnet Ba$_{2}$NiTeO$_{6}$ exhibiting a stripe structure at a low temperature. Magnetic excitations are observed in the energy range of $\hbar ω\lesssim 10$ meV having an anisotropy gap of 2 meV at 2 K. We perform spin-wave calculations to identify the spin model. The obtained microscopic parameters are consistent with the location of the stripe structure in the classical phase diagram. Furthermore, the Weiss temperature independently estimated from a bulk magnetic susceptibility is consistent with …
By using a variational Monte Carlo technique based upon Gutzwiller-projected fermionic states, we investigate the dynamical structure factor of the antiferromagnetic $S=1/2$ Heisenberg model on the honeycomb lattice, in presence of first-neighbor ($J_1$) and second-neighbor ($J_2$) couplings, for ${J_2 < 0.5 J_1}$. The ground state of the system shows long-range antiferromagnetic order for ${J_2/J_1 \lesssim 0.23}$, plaquette valence-bond order for ${0.23 \lesssim J_2/J_1 \lesssim 0.36}$, and columnar dimer order for ${J_2/J_1 \gtrsim 0.36}$. Within the antiferromagnetic state, a well-defined …
In this paper we present a detailed study of the antiferromagnetic classical Heisenberg model on a bilayer honeycomb lattice in a highly frustrated regime in presence of a magnetic field. This study shows strong evidence of entropic order-by-disorder selection in different sectors of the magnetization curve. For antiferromagnetic couplings $J_1=J_x=J_p/3$, we find that at low temperatures there are two different regions in the magnetization curve selected by this mechanism with different number of soft and zero modes. These regions present broken $Z_2$ symmetry and are separated by a not fully…
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 $κ_{c_{1}} \lesssim κ\lesssim κ_{c_{2}}$. …
Using the density matrix renormalization group (DMRG) on wide cylinders, we study the phase diagram of the spin-1/2 XY model on the honeycomb lattice, with first-neighbor ($J_1 = 1$) and frustrating second-neighbor ($J_2>0$) interactions. For the intermediate frustration regime $0.22\lesssim J_2\lesssim0.36$, we find a surprising antiferromagnetic Ising phase, with ordered moments pointing along the z axis, despite the absence of any S_z_z interactions in the Hamiltonian. Surrounding this phase as a function of $J_2$ are antiferromagnetic phases with the moments pointing in the $x-y$ plane for…
In our previous work, we identify the Sublattice-Pairing State (SPS) in Schwinger-fermion representation as the spin liquid phase discovered in recent numerical study on a honeycomb lattice. In this paper, we show that SPS is identical to the zero-flux $Z_2$ spin liquid in Schwinger-boson representation found by Wang\cite{Wang2010} by an explicit duality transformation. SPS is connected to an \emph{unusual} antiferromagnetic ordered phase, which we term as chiral-antiferromagnetic (CAF) phase, by an O(4) critical point. CAF phase breaks the SU(2) spin rotation symmetry completely and has three…
The magnetic properties of the two-dimensional, S=1 honeycomb antiferromagnet BaNi$_2$V$_2$O$_8$ have been comprehensively studied using DC susceptibility measurements and inelastic neutron scattering techniques. The magnetic excitation spectrum is found to be dispersionless within experimental resolution between the honeycomb layers, while it disperses strongly within the honeycomb plane where it consists of two gapped spin-wave modes. The magnetic excitations are compared to linear spin-wave theory allowing the Hamiltonian to be determined. The first- and second-neighbour magnetic exchange i…
Antiferromagnetic and ferro/ferrimagnetic orders are typically exclusive in nature, thus, their co-existence in atomic-scale proximity is expected only in heterostructures. Breaking this paradigm and broadening the range of unconventional magnetic states, we report here on an atomic-scale hybrid spin state, which is stabilized in three-dimensional crystals of the polar antiferromagnet Co$_2$Mo$_3$O$_8$ by magnetic fields applied perpendicular to the \emph{Co} honeycomb layers and possesses a spontaneous in-plane ferromagnetic moment. Our microscopic spin model, capturing the observed field dep…
For temperatures T well above the ordering temperature T*=3.0+-0.2K the magnetic properties of the metal-organic material Mn[C10H6(OH)(COO)]2x2H20 built from Mn^2+ ions and 3-hydroxy-2-naphthoic anions can be described by a S=5/2 quantum antiferromagnet on a distorted honeycomb lattice with two different nearest neighbor exchange couplings J2 \approx 2J1 \approx 1.8K. Measurements of the magnetization M(H,T) as a function of a uniform external field H and of the uniform zero field susceptibility χ(T) are explained within the framework of a modified spin-wave approach which takes into account t…
The honeycomb antiferromagnet under a triaxial strain is studied using the quantum Monte Carlo simulation. The strain dimerizes the exchange couplings near the corners, thus destructs the antiferromagnetic order therein. The antiferromagnetic region is continuously reduced by the strain. For the same strain strength, the exact numerical results give a much smaller antiferromagnetic region than the linear spin-wave theory. We then study the strained $XY$ antiferromagnet, where the magnon pseudo-magnetic field behaves quite differently. The $0$th Landau level appears in the middle of the spectru…
We theoretically propose a family of $f$-electron based magnets that realizes Kitaev-type bond-dependent anisotropic interactions. Based on {\it ab initio} calculations, we show that $A_2$PrO$_3$ ($A$: alkali metals) crystalize in a triclinic structure with honeycomb layers of edge-sharing PrO$_6$ octahedra. Each Pr$^{4+}$ cation has a $4f$ electron in the $Γ_7$ doublet, which comprises a spin-orbital entangled Kramers pair with the effective moment $J_{\rm eff}=1/2$. By using the Wannier orbitals from the {\it ab initio} calculations, we find that the effective interactions between the $J_{\r…
The coupled cluster method (CCM) is employed to very high orders of approximation to study the ground-state (GS) properties of the spin-$s$ Heisenberg antiferromagnet (with isotropic interactions, all of equal strength, between nearest-neighbour pairs only) on the honeycomb lattice. We calculate with high accuracy the complete set of GS parameters that fully describes the low-energy behaviour of the system, in terms of an effective magnon field theory, viz., the energy per spin, the magnetic order parameter (i.e., the sublattie magnetization), the spin stiffness and the zero-field (uniform, tr…
The crystal structure and magnetic property of the single crystalline hexagonal rare-earth indium oxides GdInO$_3$ have been studied by combing experiments and model calculations. The two inequivalent Gd$^{3+}$ ions form the centered honeycomb lattice, which consists of honeycomb and triangular sublattices. The dc magnetic susceptibility and specific heat measurements suggest two antiferromagnetic phase transitions at $T_\textrm{N1}$ = 2.3 K and $T_\textrm{N2}$ = 1.02 K. An inflection point is observed in the isothermal magnetization curve, which implies an up-up-down phase with a 1/3 magnetiz…
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…
The spin-1/2 Heisenberg antiferromagnet on the distorted honeycomb (DHC) lattice is studied by means of the tensor renormalization group method. It is unveiled that the system has a quantum phase transition of second-order between the gapped quantum dimer phase and a collinear Neel phase at the critical point of coupling ratio α_{c} = 0.54, where the quantum critical exponents ν= 0.69(2) and γ= 1.363(8) are obtained. The quantum criticality is found to fall into the O(3) universality class. A ground-state phase diagram in the field-coupling ratio plane is proposed, where the phases such as the…
We examine the thermal properties of the spin-1 Heisenberg antiferromagnet on the honeycomb lattice in the presence of an easy-plane single-ion anisotropy as well as the effects of an additional weak in-plane easy-axis anisotropy. In particular, using large-scale quantum Monte Carlo simulations, we analyze the scaling of the correlation length near the thermal phase transition into the ordered phase. This allows us to quantify the temperature regime above the critical point in which -- in spite of the additional in-plane easy-axis anisotropy -- characteristic easy-plane physics, such as near a…
We study the magnetic phase diagram of the $J_1$--$J_2$ Heisenberg antiferromagnet on a honeycomb lattice at the strongly frustrated point $J_2/J_1=1/2$ using large-scale Monte Carlo simulations. At low temperatures we find three different field regimes, each characterized by different broken discrete symmetries. In low magnetic fields up to $h_{c1}/J_1\approx 2.9$ the $Z_3$ rotational lattice symmetry is spontaneously broken while a 1/2-magnetization plateau is stabilized around $h_{c2}/J_1=4$. The collinear plateau state and the coplanar state in higher fields break the $Z_4$ translational s…
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…
Co4Ta2O9 exhibits a three-dimensional magnetic lattice based on the buckled honeycomb motif. It shows unusual magnetoelectric effects, including the sign change and non-linearity. These effects cannot be understood without the detailed knowledge of the magnetic structure. Herein, we report neutron diffraction and direction-dependent magnetic susceptibility measurements on Co4Ta2O9 single crystals. Below 20.3 K, we find a long-range antiferromagnetic order in the alternating buckled and flat honeycomb layers of Co2+ ions stacked along the c axis. Within experimental accuracy, the magnetic momen…
Li2MnO3 with a S=3/2 two-dimensional Mn honeycomb lattice has a Neel-type antiferromagnetic transition at TN=36 K with a broad maximum in the magnetic susceptibility at TM=48 K. We have investigated site percolation effects by replacing Mn with nonmagnetic Ti, and completed a full phase diagram of Li2Mn1-xTixO3 solid solution systems to find that the antiferromagnetic transition is suppressed continuously without a clear sign of changes in the Neel-type antiferromagnetic structure. The magnetic ordering eventually disappears at a critical concentration of xc=0.7. This experimental observation …
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…
We report on the experimental results of magnetic susceptibility, specific heat, electron spin resonance (ESR), and high-field magnetization measurements on a polycrystalline sample of the spin-$1/2$ distorted honeycomb-lattice antiferromagnet Cu$_2$(pymca)$_3$(ClO$_4$). Magnetic susceptibility shows a broad peak at about 25~K, which is typical of a low dimensional antiferromagnet, and no long range magnetic order is observed down to 0.6~K in the specific heat measurements. Magnetization curve up to 70~T at 1.4~K shows triple stepwise jumps. Assuming three different exchange bonds $J_{\rm A}$,…
