Modified spin-wave theory with ordering vector optimization II: Spatially anisotropic triangular lattice and $J_1J_2J_3$ model with Heisenberg interactions
Philipp Hauke, Tommaso Roscilde, Valentin Murg, J. Ignacio Cirac, Roman Schmied
We study the ground state phases of the $S=1/2$ Heisenberg quantum antiferromagnet on the spatially anisotropic triangular lattice and on the square lattice with up to next-next-nearest neighbor coupling (the $J_1J_2J_3$ model), making use of Takahashi's modified spin-wave (MSW) theory supplemented by ordering vector optimization. We compare the MSW results with exact diagonalization and projected-entangled-pair-states calculations, demonstrating their qualitative and quantitative reliability. We find that MSW theory correctly accounts for strong quantum effects on the ordering vector of the magnetic phases of the models under investigation: in particular collinear magnetic order is promoted at the expenses of non-collinear (spiral) order, and several spiral states which are stable at the classical level, disappear from the quantum phase diagram. Moreover, collinear states and non-collinear ones are never connected continuously, but they are separated by parameter regions in which MSW breaks down, signaling the possible appearance of a non-magnetic ground state. In the case of the spatially anisotropic triangular lattice, a large breakdown region appears also for weak couplings between the chains composing the lattice, suggesting the possible occurrence of a large non-magnetic region continuously connected with the spin-liquid state of the uncoupled chains.
A mixed Ising-Heisenberg spin system consisting of triangular XXZ-Heisenberg spin clusters assembled into a chain by alternating with Ising spins interacting to all three spins in the triangle is considered. The exact solution of the model is given in terms of the generalized decoration--iteration map and within the transfer-matrix technique. Exact expressions for thermodynamic functions are derived. Ground state phase diagrams, thermodynamic and magnetic properties of the system are examined.
The $S=1/2$ kagome- and triangular-lattice Heisenberg antiferromagnets are investigated using the numerical exact diagonalization and the finite-size scaling analysis. The behaviour of the field derivative at zero magnetization is examined for both systems. The present result indicates that the spin excitation is gapless for each system.
Low-temperature magnetization curves and thermodynamics of a frustrated spin-1/2 Heisenberg triangular bilayer with the antiferromagnetic intradimer interaction and either ferromagnetic or antiferromagnetic interdimer interaction are investigated in a highly frustrated parameter region, where localized many-magnon eigenstates provide the most dominant contribution to magnetothermodynamics. Low-energy states of the highly frustrated spin-1/2 Heisenberg triangular bilayer can be accordingly found from a mapping correspondence with an effective triangular-lattice spin-1/2 Ising model in a field. …
An $S=1/2$ triangular-lattice Heisenberg antiferromagnet with next-nearest-neighbor interactions is investigated under a magnetic field by the numerical-diagonalization method. It is known that, in both cases of weak and strong next-nearest-neighbor interactions, this system reveals a magnetization plateau at one-third of the saturated magnetization. We examine the stability of this magnetization plateau when the amplitude of next-nearest-neighbor interactions is varied. We find that a nonplateau region appears between the plateau phases in the cases of weak and strong next-nearest-neighbor in…
Effect of exchange anisotropy on the relaxation time of spin and vector chirality is studied for the antiferromagnetic classical Heisenberg model on the triangular lattice by using the nonequilibrium relaxation Monte Carlo method. We identify the Berezinskii-Kosterlitz-Thouless (BKT) transition and the chiral transition in a wide range of the anisotropy, even for very small anisotropy of $\sim$ 0.01%. As the anisotropy decreases, both the critical temperatures steeply decrease, while the BKT critical region becomes divergently wide. We elucidate a sharp "V shape" of the phase diagram around th…
The ground state of the spin-$1/2$ Heisenberg antiferromagnet on a distorted triangular lattice is studied using a numerical-diagonalization method. The network of interactions is the $\sqrt{3}\times\sqrt{3}$ type; the interactions are continuously controlled between the undistorted triangular lattice and the dice lattice. We find new states between the nonmagnetic 120-degree-structured state of the undistorted triangular case and the up-up-down state of the dice case. The intermediate states show spontaneous magnetizations that are smaller than one third of the saturated magntization correspo…
We theoretically investigate the Heisenberg antiferromagnet on a triangular lattice doped with nonmagnetic impurities. Two nontrivial effects resulting from collective impurity behavior are predicted. The first one is related to presence of uncompensated magnetic moments localized near vacancies as revealed by the low-temperature Curie tail in the magnetic susceptibility. These moments exhibit an anomalous growth with the impurity concentration, which we attribute to the clustering mechanism. In an external magnetic field, impurities lead to an even more peculiar phenomenon lifting the classic…
We apply the coupled cluster method and exact diagonalzation to study the uniform susceptibility and the ground-state magnetization curve of the triangular-lattice spin-1 Heisenberg antiferromagnet. Comparing our theoretical data for the magnetization curve with recent measurements on the s=1 triangular lattice antiferromagnet Ba3NiSb2O9 we find a very good agreement.
We study the S=1 Heisenberg antiferromagnet on a spatially anisotropic triangular lattice by the numerical diagonalization method. We examine the stability of the long-range order of a three-sublattice structure observed in the isotropic system between the isotropic case and the case of isolated one-dimensional chains. It is found that the long-range-ordered ground state with this structure exists in the range of 0.7 \simle J_2/J_1 \le 1, where J_1 is the interaction amplitude along the chains and J_2 is the amplitude of other interactions.
We study thermodynamic properties as well as the dynamical spin and quadrupolar structure factors of the O(3)-symmetric spin-1 Heisenberg model with bilinear-biquadratic exchange interactions on the triangular lattice. Based on a sign-problem-free quantum Monte Carlo approach, we access both the ferromagnetic and the ferroquadrupolar ordered, spin nematic phase as well as the SU(3)-symmetric point which separates these phases. Signatures of Goldstone soft-modes in the dynamical spin and the quadrupolar structure factors are identified, and the properties of the low-energy excitations are compa…
Antiferromagnetically coupled moments on the frustrated triangular lattice typically order in a coplanar state at low temperature. Here, we demonstrate that the presence of not-very-large easy axis single ion anisotropy leads to an interesting orientationally ordered collinear state in triangular lattice antiferromagnets with moments $S \ge 3/2$. This ordered state breaks the symmetry of $π/3$ rotations about a lattice site, while leaving intact the translational symmetry of the lattice.
We study the phase transition behavior of a frustrated Heisenberg model on a stacked triangular lattice by Monte Carlo simulations. The model has three types of interactions: the ferromagnetic nearest-neighbor interaction $J_1$ and antiferromagnetic third nearest-neighbor interaction $J_3$ in each triangular layer and the ferromagnetic interlayer interaction $J_\perp$. Frustration comes from the intralayer interactions $J_1$ and $J_3$. We focus on the case that the order parameter space is SO(3)$\times C_3$. We find that the model exhibits a first-order phase transition with breaking of the SO…
We present a numerical study of the SU(3) Heisenberg model of three-flavor fermions on the triangular and square lattice by means of the density-matrix renormalization group (DMRG) and infinite projected entangled-pair states (iPEPS). For the triangular lattice we confirm that the ground state has a three-sublattice order with a finite ordered moment which is compatible with the result from linear flavor wave theory (LFWT). The same type of order has recently been predicted also for the square lattice [PRL 105, 265301 (2010)] from LFWT and exact diagonalization. However, for this case the orde…
We report magnetization, specific heat, muon spin rotation and Na NMR measurements on the S=3/2 rhombohedrally stacked Heisenberg antiferromagnet NaCrO2. This compound appears to be an ideal candidate for the study of triangular Heisenberg antiferromagnets with very weak interlayer coupling. While specific heat and magnetization measurements indicate the occurrence of a transition in the range 40-46 K, both muon spin rotation and NMR reveal a fluctuating regime extending well below T_c, with a peak of relaxation rate 1/T1 around 30 K. This novel finding is discussed within the context of excit…
We study phase transition behavior of the Heisenberg model on a distorted triangular lattice with competing interactions. The ground-state phase diagram indicates that underlying symmetry can be changed by tuning parameters. We focus on two cases in which a phase transition with discrete symmetry breaking occurs. The first is that the order parameter space is SO(3)$\times C_3$. In this case, a first-order phase transition, with threefold symmetry breaking, occurs. The second has the order parameter space SO(3)$\times Z_2$. In this case, a second-order phase transition occurs with twofold symme…
Dynamical properties of the classical Heisenberg antiferromagnet on the triangular lattice are investigated by means of a spin-dynamics simulation and an analytical calculation. While the model was suggested to exhibit a topological transition driven by the Z_2-vortex binding-unbinding, weakness of the associated thermodynamic singularity has made it difficult to observe the evidence of the Z_2 vortex experimentally so far, only some indirect support. Here, we show that the signature of the Z_2-vortex excitation and the vortex-induced topological transition can be captured from the dynamical s…
The selection of the ground state among nearly degenerate states due to quantum fluctuations is studied for the S=1/2 XY-like Heisenberg antiferromagnets on the triangular lattice in the magnetic field applied along the hard axis, which was first pointed out by Nikuni and Shiba. We find that the selected ground state sensitively depends on the degree of the anisotropy and the magnitude of the magnetic field. This dependence is similar to that in the corresponding classical model at finite temperatures where various types of field induced phases appear due to the entropy effect. It is also foun…
Frustrated quantum spin systems such as the Heisenberg and Kitaev models on various lattices, have been known to exhibit various exotic properties not only at zero temperature but also for finite temperatures. Inspired by the remarkable development of the quantum frustrated spin systems in recent years, we investigate the finite-temperature properties of the $S=1/2$ Kitaev-Heisenberg models on kagome and triangular lattices by means of finite-temperature Lanczos methods with improved accuracy. In both lattices, multiple peaks are confirmed in the specific heat. To find the origin of the multip…
Ordering of the frustrated classical Heisenberg model on the triangular-lattice with an incommensurate spiral spin structure is studied under magnetic fields by means of a mean-field analysis and a Monte Carlo simulation. Several types of multiple-q states including the "skyrmion-lattice" state is observed in addition to the standard single-q state. In contrast to the Dzyaloshinskii-Moriya interaction driven system, the present model allows both skyrmions and anti-skyrmions, together with a new thermodynamic phase where skyrmion and anti-skyrmion lattices form a domain state.
We report the results of magnetization and specific heat measurements on Ba$_3$CoSb$_2$O$_9$, in which the magnetic Co$^{2+}$ ion has a fictitious spin-1/2, and show evidence that a spin-1/2 Heisenberg antiferromagnet on a regular triangular lattice is actually realized in Ba$_3$CoSb$_2$O$_9$. We found that the entire magnetization curve including the one-third quantum magnetization plateau is in excellent agreement with theoretical calculations at a quantitative level.
We study the anisotropic spin-half antiferromagnetic triangular Heisenberg lattice in two dimensions, seen as a set of chains with couplings J (J') along (in between) chains, respectively. Our focus is on the incommensurate correlation that emerges in this system in a wide parameter range due to the intrinsic frustration of the spins. We study this system with traditional DMRG using cylindrical boundary conditions to least constrain possible incommensurate order. Despite that the limit of essentially decoupled chains J'/J < 0.5 is not very accessible numerically, it appears that the spin-spin …
We study the $J_1$-$J_2$-$J_3$ classical Heisenberg model with ferromagnetic $J_1$ on the triangular lattice using the nematic bond theory. For parameters where the momentum space coupling function $J_{\vec{q}}$ shows a discrete set of minima, we find that the system in general exhibits a single first-order phase transition between the high-temperature ring liquid and the low-temperature single-$\vec{q}$ planar spiral state. Close to where $J_{\vec{q}}$ shows a continuous minimum, we on the other hand find several phase transitions upon lowering the temperature. Most interestingly, we find an …
We investigate the two-magnon Raman scattering from an anisotropic S=1/2 triangular Heisenberg antiferromagnet Cs2CuCl4. We find that the Raman response is very sensitive to magnon-magnon interactions and to scattering geometries, a feature that is in remarkable contrast with the polarization-independent Raman signal from the isotropic triangular Heisenberg antiferromagnet. Since a spin-liquid ground state gives rise to a similar rotationally invariant Raman response, our results on the polarization dependence of the scattering spectrum suggest that Raman spectroscopy provides a useful probe, …
Magnetic excitations in the triangular-lattice Heisenberg antiferromagnet (TLHA) CuCrO2 were studied using single-crystal inelastic neutron scattering. A diffusive quasielastic component that persisted without developing a correlation length over a wide temperature range both below and above the ordering temperature was observed. Furthermore, characteristic momentum dependence was observed that was reproduced using minimum spin clusters. The robust spin clusters contrast with conventional magnetic ordering and may be universal in TLHAs.
The spin liquid state of the antiferromagnetic Heisenberg model on a triangular lattice is studied within the self-consistent Green's function method. It is shown that the spin excitation spectra is gapless, and ground-state energy per site is $E_{g}/NJ=-0.966$, which is in very good agreement with the results obtained within the variational Monte Carlo method based on the resonating-valence-bond state. Some thermodynamic properties are also discussed.
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…
We investigate the phase diagram of the anisotropic spin-1/2 triangular lattice antiferromagnet, with interchain diagonal exchange J' much weaker than the intrachain exchange J. We find that fluctuations lead to a competition between (commensurate) collinear antiferromagnetic and (zig-zag) dimer orders. Both states differ in symmetry from the spiral order known to occur for larger J', and are therefore separated by quantum phase transitions from it. The zero-field collinear antiferromagnet is succeeded in a magnetic field by magnetically-ordered spin-density-wave and cone phases, before reachi…
Motivated by experiments on non-magnetic triangular-lattice Mott insulators, we study one candidate paramagnetic phase, the columnar dimer (or valence-bond) phase. We apply variants of the bond-operator theory to a dimerized and spatially anisotropic spin-1/2 Heisenberg model and determine its zero-temperature phase diagram and the spectrum of elementary triplet excitations (triplons). Depending on model parameters, we find that the minimum of the triplon energy is located at either a commensurate or an incommensurate wavevector. Condensation of triplons at this commensurate-incommensurate tra…
The spin Green's function of the antiferromagnetic Heisenberg model on a triangular lattice is calculated using Mori's projection operator technique. At T=0 the spin excitation spectrum is shown to have gaps at the wave vectors of the classical Neel ordering. This points to the absence of the antiferromagnetic long-range order in the ground state. The calculated spin correlation on the neighboring sites of the same sublattice is in good agreement with the value derived from exact diagonalization. The temperature dependencies of the spin correlations and the gaps are calculated.
Experimental quest for the hypothetical "quantum spin liquid" state has recently met a few promising candidate materials including organic salts κ-(ET)2Cu2(CN)3 and EtMe3Sb[Pd(dmit)2]2, S=1/2 triangular-lattice Heisenberg antiferromagnets consisting of molecular dimers. These compounds exhibit no magnetic ordering nor the spin freezing down to very low temperature, while various physical quantities exhibit gapless behaviors. Recent dielectric measurements revealed the glassy dielectric response suggesting the random freezing of the electric polarization degrees of freedom. Inspired by this obs…
The S=1 bilinear-biquadratic Heisenberg model on anisotropic triangular lattices is investigated by several complementary methods. Our focus is on the stability of the three-sublattice spin nematic state against spatial anisotropy. We find that, deviated from the case of isotropic triangular lattice, quantum fluctuations enhance and the three-sublattice spin nematic order is reduced. In the limit of weakly coupling chains, by mapping the systems to an effective one-dimensional model, we show that the three-sublattice spin nematic order develops at infinitesimal interchain coupling. Our results…
We use Schwinger boson mean field theory to study the antiferromagnetic spin-1/2 Heisenberg model on an anisotropic triangular lattice in the presence of a uniform external magnetic field. We calculate the field dependence of the spin incommensurability in the ordered spin spiral phase, and compare the results to the recent experiments in Cs$_{2}$CuCl$_{4}$ by Coldea et al. (Phys. Rev. Lett. 86, 1335 (2001)).
Exact and rigorous solutions of the ground-state problem for the classical Heisenberg model with nearest-neighbor interactions on two- and three-dimensional lattices composed of zigzag (triangular) ladders are obtained in a very simple way, with the use of a cluster method. It is shown how the geometrical frustration due to the presence of triangles as structural units leads to the emergence of incommensurate spiral orderings and their collinear limits. Interestingly, these orderings are determined by a single angle (along with the signs of the interactions between neighboring spins); therefor…
A linear spin-wave approach, a variational method and exact diagonlization are used to investigate the magnetic long-range order (LRO) of the spin-1/2 Heisenberg antiferromagnet on a two-dimensional 1/7-depleted triangular (maple leaf) lattice consisting of triangles and hexagons only. This lattice has z=5 nearest neighbors and its coordination number z is therefore between those of the triangular (z=6) and the kagome (z=4) lattices. Calculating spin-spin correlations, sublattice magnetization, spin stiffness, spin-wave velocity and spin gap we find that the classical 6-sublattice LRO is stron…
We study a spin-1/2 model with triangular XXZ-clusters on the orthogonal-dimer chain in the presence of an external magnetic field. First, we discuss the case where the triangular clusters are coupled via intermediate "classical" Ising spins. Diagonalization of the triangular XXZ-clusters yields the exact ground states; finite-temperature properties are computed exactly by an additional transfer-matrix step. A detailed analysis reveals a large variety of ground states at magnetization M equal to fractions 0, 1/4, and 1/2 of the saturation magnetization M=1. Some of these ground states break tr…
A brief review is provided of earlier work on the low temperature phases of $S=1$ kagome and triangular lattice antiferromagnets in which there is sufficiently strongly single-ion anisotropy $D$ that dominates over the antiferromagnetic exchange $J$.
Motivated by recent experimental progress on triangular lattice heavy-fermion compounds, we investigate possible Lifshitz transitions and the scanning tunnel microscope (STM) spectra of the Kondo-Heisenberg model on the triangular lattice. In the heavy Fermi liquid state, the introduced Heisenberg antiferromagnetic interaction ($J_H$) results in the twice Lifshitz transition at the case of the nearest-neighbour electron hopping but with next-nearest-neighbour hole hopping and the case of the nearest-neighbour hole hopping but with next-nearest-neighbour electron hopping, respectively. Driven b…
We study the phase diagram of the frustrated Heisenberg model on the triangular lattice with nearest and next-nearest neighbor spin exchange coupling, on 3-leg ladders. Using the density-matrix renormalization-group method, we obtain the complete phase diagram of the model, which includes quasi-long-range $120^\circ$ and columnar order, and a Majumdar-Ghosh phase with short-ranged correlations. All these phases are non-chiral and planar. We also identify the nature of phase transitions.
We have theoretically investigated transport properties of the classical Heisenberg antiferromagnet on the triangular lattice in which a binding-unbinding topological transition of $\mathbb{Z}_2$ vortices is predicted to occur at a finite temperature $T_v$. It is shown by means of the hybrid Monte-Carlo and spin-dynamics simulations that the longitudinal spin-current conductivity exhibits a divergence at $T_v$, while the thermal conductivity only shows a monotonic temperature dependence with no clear anomaly at $T_v$. The significant enhancement of the spin-current conductivity is found to be …
We study the quantum and thermal phase transition phenomena of the SU(3) Heisenberg model on triangular lattice in the presence of magnetic fields. Performing a scaling analysis on large-size cluster mean-field calculations endowed with a density-matrix-renormalization-group solver, we reveal the quantum phases selected by quantum fluctuations from the massively degenerate classical ground-state manifold. The magnetization process up to saturation reflects three different magnetic phases. The low- and high-field phases have strong nematic nature, and especially the latter is found only via a n…
The spin-$\frac12$ triangular lattice antiferromagnetic Heisenberg model has been for a long time the prototypical model of magnetic frustration. However, only very recently this model has been proposed to be realized in the Ba$_8$CoNb$_6$O$_{24}$ compound. The ground-state and thermodynamic properties are evaluated from a high-temperature series expansions interpolation method, called "entropy method", and compared to experiments. We find a ground-state energy $e_0 = -0.5445(2)$ in perfect agreement with exact diagonalization results. We also calculate the specific heat and entropy at all tem…
Using mean-field theory, exact diagonalizations and SU(3) flavour theory, we have precisely mapped out the phase diagram of the S=1 bilinear-biquadratic Heisenberg model on the triangular lattice in a magnetic field, with emphasis on the quadrupolar phases and their excitations. In particular, we show that ferroquadrupolar order can coexist with short-range helical magnetic order, and that the antiferroquadrupolar phase is characterized by a remarkable 2/3 magnetization plateau, in which one site per triangle retains quadrupolar order while the other two are polarized along the field. Implicat…
We present a high-temperature series expansion code for spin-1/2 Heisenberg models on arbitrary lattices. As an example we demonstrate how to use the application for an anisotropic triangular lattice with two independent couplings J1 and J2 and calculate the high-temperature series of the magnetic susceptibility and the static structure factor up to 12th and 10th order, respectively. We show how to extract effective coupling constants for the triangular Heisenberg model from experimental data on Cs2CuBr4.
In this study, we investigate the magnetic susceptibility, entropy, and isothermal magnetization curve of the spin-1/2 Heisenberg model on an anisotropic triangular lattice using the orthogonalized finite-temperature Lanczos method. In addition, we investigate the adiabatic magnetization curve and magnetocaloric effect. We estimate these physical quantities with sufficient accuracy in the thermodynamic limit, except at low temperatures. We observe a 1/3 magnetization plateau in the isothermal magnetization process, whereas the plateau is observed to have a slope in the adiabatic process. We sh…
We study the spin-$1$ model in a triangular lattice in presence of a uniaxial anisotropy field using a Cluster Mean-Field approach (CMF). The interplay between antiferromagnetic exchange, lattice geometry and anisotropy forces Gutzwiller mean-field approaches to fail in a certain region of the phase diagram. There, the CMF yields two supersolid (SS) phases compatible with those present in the spin-$1/2$ XXZ model onto which the spin-$1$ system maps. Between these two SS phases, the three-sublattice order is broken and the results of the CMF depend heavily on the geometry and size of the cluste…
We study the quantum phase transition of an $S=1/2$ anisotropic $α$ $(\equiv J_z/J_{xy})$ Heisenberg antiferromagnet on a triangular lattice. We calculate the sublattice magnetization and the long-range helical order-parameter and their Binder ratios on finite systems with $N \leq 36$ sites. The $N$ dependence of the Binder ratios reveals that the classical 120$^{\circ}$ Néel state occurs for $α\lesssim 0.55$, whereas a critical collinear state occurs for $1/α\lesssim 0.6$. This result is at odds with a widely-held belief that the ground state of a Heisenberg antiferromagnet is the 120$^{\circ…
We present the results of muon-spin relaxation measurements on the triangular lattice Heisenberg antiferromagnet $α$-KCrO$_{2}$. We observe sharp changes in behaviour at an ordering temperature of $T_{\mathrm{c}}=23$ K, with an additional broad feature in the muon-spin relaxation rate evident at T=13 K, both of which correspond to features in the magnetic contribution to the heat capacity. This behaviour is distinct from both the Li- and Na- containing members of the series. These data may be qualitatively described with the established theoretical predictions for the underlying spin system.
The anomalous thermodynamic properties of the paradigmatic frustrated spin-1/2 triangular lattice Heisenberg antiferromagnet (TLH) has remained an open topic of research over decades, both experimentally and theoretically. Here we further the theoretical understanding based on the recently developed, powerful exponential tensor renormalization group (XTRG) method on cylinders and stripes in a quasi one-dimensional (1D) setup, as well as a tensor product operator approach directly in 2D. The observed thermal properties of the TLH are in excellent agreement with two recent experimental measureme…
Spin liquids occuring in 2D frustrated spin systems were initially assumed to appear at strongest frustration, but evidence grows that they more likely intervene at transitions between two different types of order. To identify if this is more general, we here analyze a generalization of the spatially anisotropic triangular lattice (SATL) with antiferromagnetic Heisenberg interactions, the spatially \emph{completely} anisotropic triangular lattice (SCATL). Using Takahashi's modified spin-wave theory, complemented by exact diagonalizations, we find indications that indeed different kinds of orde…
The perovskite Ba8CoNb6O24 comprises equilateral effective spin-1/2 Co2+ triangular layers separated by six non-magnetic layers. Susceptibility, specific heat and neutron scattering measurements combined with high-temperature series expansions and spin-wave calculations confirm that Ba8CoNb6O24 is basically a twodimensional (2D) magnet with no detectable spin anisotropy and no long-range magnetic ordering down to 0.06 K. In other words, Ba8CoNb6O24 is very close to be a realization of the paradigmatic spin-1/2 triangular Heisenberg model, which is not expected to exhibit symmetry breaking at f…
We report 7Li NMR studies of single crystals of triangular-lattice Heisenberg antiferromagnet Li7RuO6. Slow critical divergence with a wide critical region of |T/TN - 1|< 7 was observed in 7Li nuclear spin-lattice relaxation rate. The slowing down of staggered spin fluctuations was analyzed in a renormalized classical region of a two-dimensional triangular-lattice non-linear sigma model. A spin stiffness constant was found to reduce to about 20 % from the value in a spin-wave approximation. The effect of spin frustration, e.g., Z2 vortex excitations on the critical phenomena is suggested.
We study the effects of bond randomness in the spin-$1/2$ $J_1-J_2$ triangular Heisenberg model using exact diagonalization and density matrix renormalization group. With increasing bond randomness, we identify a randomness induced spin-liquid-like phase without any magnetic order, dimer order, spin glass order, or valence-bond glass order. The finite-size scaling of gaps suggests the gapless nature of both spin triplet and singlet excitations, which is further supported by the broad continuum of dynamical spin structure factor. By studying the bipartite entanglement spectrum of the system on …
The spin-1 Heisenberg model on a triangular lattice with the ferromagnetic nearest- and antiferromagnetic third-nearest-neighbor exchange interactions, $J_1=-(1-p)J$ and $J_2=pJ$, $J>0$ $ (0 \leq p \leq 1)$, is studied with the use of the SPINPACK code. This model is applicable for the description of the magnetic properties of NiGa$_2$S$_4$. The ground, low-lying excited state energies and spin-spin correlation functions have been found for lattices with N=16 and N=20 sites with the periodic boundary conditions. These results are in qualitative agreement with earlier authors' results obtained …
Breakdown of the conventional spin-wave dynamics and its double-constraint modification in the spin-$\mathbf{\frac{1}{2}}$ triangular-prism Heisenberg antiferromagnet
We study the spin-half Heisenberg models on an anisotropic two-dimensional lattice which interpolates between the square-lattice at one end, a set of decoupled spin-chains on the other end, and the triangular-lattice Heisenberg model in between. By series expansions around two different dimer ground states and around various commensurate and incommensurate magnetically ordered states, we establish the phase diagram for this model of a frustrated antiferromagnet. We find a particularly rich phase diagram due to the interplay of magnetic frustration, quantum fluctuations and varying dimensionali…
We extend the nonlinear spin wave theory (NLSWT) for the spin 1/2 antiferromagnetic Heisenberg model on a triangular lattice (TAFHM). This novel NLSWT considers the corrections one order higher in 1/S than the linear spin wave theory (LSWT). It also distinguishes in which circumstance the negative energy excitation, the sign of the breakdown of LSWT, shall be renormalized to be positive both by a boson normal ordering and a self-consistent iteration. We draw a phase diagram by testing the stability of various magnetic orders for different parameters. In particular, the incommensurate configura…
We solve the Sp(N) Heisenberg and SU(N) Hubbard-Heisenberg models on the anisotropic triangular lattice in the large-N limit. These two models may describe respectively the magnetic and electronic properties of the family of layered organic materials $κ$-(BEDT-TTF)$_2$X. The Heisenberg model is also relevant to the frustrated antiferromagnet, Cs$_2$CuCl$_4$. We find rich phase diagrams for each model. The Sp(N) antiferromagnet is shown to have five different phases as a function of the size of the spin and the degree of anisotropy of the triangular lattice. The effects of fluctuations at finit…
We investigate non-equilibrium properties of the frustrated Heisenberg antiferromagnets on the triangular lattice. Nonequilibrium critical relaxation of frustrated Heisenberg antiferromagnets shows a dynamic transition (or, at least, sharp crossover) at the same temperature $T_{\rm u}=0.282 J$ as for static properties due to unbinding of $\mathbb{Z}_2$-vortices. We show that starting from the high-temperature initial state, due to presence of $\mathbb{Z}_2$-vortices in the considering system, in a broad temperature range $T<T_{\rm u}$ the dynamic properties in the intermediate time range are s…
We investigate the $J_1$-$J_2$ Heisenberg model on the triangular lattice with an additional scalar chirality term and show that a chiral spin liquid is stabilized in a sizeable region of the phase diagram. This topological phase is situated in between a coplanar $120^\circ$ Néel ordered and a non-coplanar tetrahedrally ordered phase. Furthermore we discuss the nature of the spin-disordered intermediate phase in the $J_1$-$J_2$ model. We compare the groundstates from Exact Diagonalization with a Dirac spin liquid wavefunction and propose a scenario where this wavefunction describes the quantum…
