Spin-liquid Behavior Research Articles

Plaquette order in a dimerized frustrated spin ladder

We study the effect of spin-Peierls instability on the phase-diagram of a frustrated antiferromagnetic spin-1/2 ladder, with weak transverse and diagonal rung coupling. Our analysis focuses on a one-dimensional version of the model (i.e. a single two-leg ladder) where we consider two forms of spin-Peierls (SP) instabilities on the legs: columnar dimers (CD) and staggered dimers (SD). We particularly examine the regime of parameters (corresponding to an intermediate XXZ anisotropy) where the SP and rung coupling terms are equally relevant. In both the CD and SD cases we find that the effective field theory describing the system is a self-dual sine-Gordon model, which favors ordering and the opening of a gap to excitations. The order parameter, which reflects the interplay between the SP and rung interactions, represents a crystal of 4-spin plaquettes on which longitudinal and transverse dimers are in a superposition. Depending on the SP instability mode these plaquettes are closed or open, however both types spontaneously break reflection symmetry across the ladder. The closed plaquettes are stable, while the open plaquette-order is relatively fragile and the corresponding gap may be tuned to zero under extreme conditions. We further find that a first order transition occurs from the Plaquette order to a valence bond crystal (VBC) of dimers on the legs. It is suggestive that in a higher dimensional version of this system, this variety of distinct VBC states with comparable energies leads to the formation of domains. Effectively one-dimensional gapless spinon modes on domain boundaries can possibly account for the experimental observation of a spin-liquid behavior in a physical realization of the model.

Absence of quasiclassical coherence in mean-field dynamics of bosons in a kinetically frustrated regime

We study numerically the dynamics of bosons on a triangular lattice after quenching both the on-site interactions and the external trapping potential to negative values. In a similar situation on the square lattice, the dynamics can be understood in terms of an effectively reversed Hamiltonian. On the triangular lattice, however, the kinetic part of the reversed Hamiltonian is frustrated and whether coherence can develop is an open question. The strength of the frustration can be changed by tuning the ratio of the hopping rates along different directions. We calculate time-of-flight images at different times after the quench for different values of the hopping anisotropy. We observe peaks at the maxima of the original non-interacting dispersion relation both in the isotropic case and also in the rhombic limit of high hopping anisotropy. For an intermediate value, however, no coherence develops up to the longest simulation times. These results imply that experiments along similar lines could study unconventional superfluidity of bosons and aspects of the conjectured spin-liquid behavior in the hard-core limit.

Short-range magnetic correlations in the highly correlated electron compoundCeCu4Ga

We present experimental results for the heavy-electron compound CeCu$_{4}$Ga which show that it possesses short-range magnetic correlations down to a temperature of $T = 0.1$ K. Our neutron scattering data show no evidence of long-range magnetic order occurring despite a peak in the specific heat at $T^{*} =1.2$ K. Rather, magnetic diffuse scattering occurs which corresponds to short-range magnetic correlations occurring across two unit cells. The specific heat remains large as $T\sim0$ K resulting in a Sommerfeld coefficient of $\gamma_{0} = 1.44(2)$ J/mol-K$^{2}$, and, below $T^{*}$, the resistivity follows $T^{2}$ behavior and the ac magnetic susceptibility becomes temperature independent. A magnetic peak centered at an energy transfer of $E_{\rm{c}}=0.24(1)$ meV is seen in inelastic neutron scattering data which shifts to higher energies and broadens under a magnetic field. We discuss the coexistence of large specific heat, magnetic fluctuations, and short-range magnetic correlations at low temperatures and compare our results to those for materials possessing spin-liquid behavior.

Spin-liquid phase and order by disorder of classical Heisenberg spins on the swedenborgite lattice

Frustration refers to the inability to satisfy competing interactions simultaneously, often leading to a large number of degenerate ground states. This can suppress ordering tendencies, sometimes resulting in a spin-liquid phase. An intrinsic effect lifting this degeneracy is entropic order by disorder. We present strong evidence that a classical nearest-neighbor Heisenberg model on the swedenborgite lattice exhibits both an extended spin-liquid phase as well as entropic order-by-disorder choosing coplanar configurations after a first-order transition. We argue that this observation renders magnetic insulators such as ${R\mathrm{BaCo}}_{4}{\mathrm{O}}_{7}$, where $R$ denotes a rare-earth atom, prime candidates for displaying spin-liquid behavior and entropic order-by-disorder physics due to their large exchange constant.

Spin-liquid versus dimer phases in an anisotropicJ1-J2frustrated square antiferromagnet

The spin-1/2 ${J}_{1}$-${J}_{2}$ antiferromagnet is a prototypical model for frustrated magnetism and one possible candidate for a realization of a spin-liquid phase. The generalization of this system on the anisotropic square lattice is given by the ${J}_{1}$-${J}_{2}$-${J}_{1}^{\ensuremath{'}}$-${J}_{2}^{\ensuremath{'}}$ Heisenberg model, which can be treated by a renormalization group analysis of coupled frustrated chains. The ${J}_{1}$-${J}_{2}$-${J}_{1}^{\ensuremath{'}}$-${J}_{2}^{\ensuremath{'}}$-model shows an interesting interplay of N\'eel order, dimerization, and spin-liquid behavior. Extrapolating the analytical findings supported by numerical results indicates that for the isotropic model the phase at intermediate coupling strength $0.4{J}_{1}\ensuremath{\lesssim}{J}_{2}\ensuremath{\lesssim}0.6{J}_{1}$ is not a spin liquid, but has instead a staggered dimer order.

Quantum Spin-Liquid Behavior in the Spin-1/2 Random Heisenberg Antiferromagnet on the Triangular Lattice

Experimental quest for the hypothetical "quantum spin liquid" state has recently met a few promising candidate materials including organic salts \kappa-(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 observation, we propose as a minimal model of the observed quantum spin-liquid behavior the S=1/2 antiferromagnetic Heisenberg on the triangular lattice with a quenched randomness in the exchange interaction. We study both zero- and finite-temperature properties of the model by an exact diagonalization method, to find that when the randomness exceeds a critical value the model exhibits a quantum spin-liquid ground state. This randomness-induced quantum spin-liquid state exhibits gapless behaviors including the temperature-linear specific heat. The results provide a consistent explanation of the recent experimental observations on organic salts.

Electronic structure ofBa3CuSb2O9: A candidate quantum spin liquid compound

Using density-functional methods, we study the electronic structure of ${\mathrm{Ba}}_{3}\mathrm{Cu}{\mathrm{Sb}}_{2}{\mathrm{O}}_{9}$, a candidate material for the quantum spin liquid behavior. We study both the triangular lattice as well as the recently proposed hexagonal lattice structures with flipped Cu-Sb dumbbells. The band structure near the Fermi energy is described very well by a tight-binding Hamiltonian involving the Cu (${e}_{g}$) orbitals, confirming their central role in the physics of the problem. A minimal tight-binding Hamiltonian for the triangular structure is presented. The Cu (${d}^{9}$) ions (a single ${e}_{g}$ hole in the band structure) present in the compound are expected to be Jahn-Teller centers, while the nature of the Jahn-Teller distortions in this material is still under debate. Solving a simple model by exact diagonalization, we show that electronic correlation effects in general enhance the tendency towards a Jahn-Teller distortion by reducing the kinetic energy due to correlation effects. Our density-functional calculations do indeed show a significant Jahn-Teller distortion of the $\mathrm{Cu}{\mathrm{O}}_{6}$ octahedra when we include the correlation effects within the Coulomb-corrected GGA+U method, so that the Jahn-Teller effect is correlation driven. We argue for the presence of a random static Jahn-Teller distortion in the hexagonal structure rather than a dynamical one because of the broken octahedral symmetry around the $\mathrm{Cu}{\mathrm{O}}_{6}$ octahedra and the potential fluctuations inherently present in the system caused by a significant disorder, which is believed to be present, in particular, due to the flipped Cu-Sb dumbbells.

Quantum spin liquids in the absence of spin-rotation symmetry: Application to herbertsmithite

It has been suggested that the nearest-neighbour (NN) antiferromagnetic Heisenberg (HAF) model on the Kagome lattice may be a good starting point to understand the quantum spin-liquid (QSL) behaviour discovered in Herbertsmithite. We investigate possible QSL phases in the presence of experimentally relevant spin-rotation symmetry-breaking perturbations such as Dzyaloshinskii-Moriya and Ising interactions, as well as second-neighbour antiferromagnetic Heisenberg interactions. We use the projective symmetry group analysis within the slave-fermion framework of QSL phases and systematically classify possible QSLs in the presence of these perturbations. The dynamical spin-structure factor for relevant QSLs is computed and their effects are studied. Our calculations reveal dispersive features in the spin structure factor embedded in a generally diffuse background due to the existence of fractionalized S=1/2 excitations called spinons. For two of the previously proposed $Z_2$ states, the dispersive features are almost absent, and diffuse scattering dominates over a large energy window throughout the Brillouin zone. This resembles the structure factor observed in recent inelastic neutron scattering experiments on singlet crystals of Herbertsmithite. Furthermore, one of the $Z_2$ states with the spin structure factor with mostly diffuse scattering is gapped, and it may be adiabatically connected to the gapped QSL state observed in recent DMRG calculations for the NN HAF. The above perturbations are found to enhance the diffuse nature of the spin structure factor and reduce the momentum dependencies of the spin gap. We also calculate the electron spin resonance absorption spectra that further characterize the role of spin-rotation symmetry breaking perturbations, and can shed more light into the nature of the ground state in Herbertsmithite.

Majorana spin liquid and dimensional reduction in Cs2CuCl4

The low-temperature behavior of the magnetic insulator Cs${}_{2}$CuCl${}_{4}$ can be modeled by an anisotropic triangular lattice spin-$1/2$ Heisenberg antiferromagnet with two different exchange couplings $J$ and ${J}^{\ensuremath{'}}\ensuremath{\approx}J/3$. We show that in a wide range of magnetic fields the experimentally observed field dependence of the crossover temperature ${T}_{c}$ for spin-liquid behavior can be explained within a mean-field theory based on the representation of spin operators in terms of Majorana fermions. We also show that for small magnetic fields the specific heat and the spin susceptibility both exhibit a maximum as a function of temperature at ${T}_{c}=J/2$. In the spin-liquid regime, the Majorana fermions can only propagate along the direction of the strongest bond, in agreement with the dimensional reduction scenario advanced by Balents [Nature (London) 464, 199 (2010)].

Dynamical Jahn-Teller effect in a spin-orbital coupled system

Dynamical Jahn-Teller (DJT) effect in a spin-orbital coupled system on a honeycomb lattice is examined, motivated from recently observed spin-liquid behavior in Ba${}_{3}$CuSb${}_{2}$O${}_{9}$. An effective vibronic Hamiltonian, where the superexchange interaction and the DJT effect are taken into account, is derived. We find that the DJT effect induces a spin-orbital resonant state where local spin-singlet states and parallel orbital configurations are entangled with each other. This spin-orbital resonant state is realized in between an orbital-ordered state, where spin-singlet pairs are localized, and an antiferromagnetic ordered state. Based on the theoretical results, a possible scenario for Ba${}_{3}$CuSb${}_{2}$O${}_{9}$ is proposed.

Quantum Monte Carlo study of the half-filled Hubbard model on the honeycomb lattice

The half-filled Hubbard model on the honeycomb lattice is investigated by numerically exact large-scale quantum Monte Carlo simulations for lattice sizes up to 2592 sites. By performing careful finite-size scaling for the spin-spin correlation functions, calculated with a high degree of accuracy, we find that the ground state is antiferromagnetically long-range ordered at U/t = 4, where U is the on-site Hubbard interaction and t is the nearest neighbor hopping. Our result is in sharp contrast to a recent report [Meng et al., Nature 464, 847 (2010)], where instead strong evidence of spin liquid behavior is found.

Crystal structure and band parameters of mixed crystals derived from quantum spin liquid β′‐EtMe3Sb[Pd(dmit)2]2 (dmit = 1,3‐dithiol‐2‐thione‐4,5‐dithiolate)

AbstractA molecular Mott insulator β′‐EtMe3Sb[Pd(dmit)2]2 with a quasi‐triangular lattice of a dimer unit [Pd(dmit)2] exhibits quantum spin liquid (QSL) behavior. We introduced Me4Sb+ or Et2Me2Sb+ to the cation site of this anion radical salt without altering its crystal symmetry. The mixing ratio and lattice parameters of these mixed crystals can be continuously tuned. We calculated intermolecular transfer integrals between highest occupied molecular orbitals (HOMOs) based on structural data. Increasing the number of ethyl groups at the cation site reduces the anisotropy of the triangular lattice, and the dimer units form an almost regular triangular lattice in pure Et2Me2Sb salt. In this process, the Pd(dmit)2 molecule is slightly curved to exhibit a crescent shape. This distortion plays an important role in tuning the interdimer transfer integrals.

Exact quantum critical points and phase separation instabilities in Betts Hubbard nanoclusters

Spontaneous phase separation instabilities with the formation of various types of charge and spin pairing (pseudo)gaps in U>0 Hubbard model including the next nearest neighbor coupling are calculated with the emphasis on the two-dimensional (square) lattices generated by 8- and 10-site Betts unit cells. The exact theory yields insights into the nature of quantum critical points, continuous transitions, dramatic phase separation instabilities and electron condensation in spatially inhomogeneous systems. The picture of coupled antiparallel (singlet) spins and paired charged holes suggests full Bose condensation and coherent pairing in real space at zero temperature of electrons complied with the Bose-Einstein statistics. Separate pairing of charge and spin degrees at distinct condensation temperatures offers a new route to superconductivity different from the BCS scenario. The conditions for spin liquid behavior coexisting with unsaturated and saturated Nagaoka ferromagnetism due to spin-charge separation are established. The phase separation critical points and classical criticalities found at zero and finite temperatures resemble a number of inhomogeneous, coherent and incoherent nanoscale phases seen near optimally doped high-Tc cuprates, pnictides and CMR nanomaterials.

Short-range correlations and persistent spin fluctuations in the undistorted kagome lattice Ising antiferromagnet Co3Mg(OH)6Cl2

Spin fluctuations and spin-liquid behaviors of frustrated kagome antiferromagnets have received intense recent attention. Although most severe frustration was predicted for an Ising kagome antiferromagnet, a real material system of undistorted kagome lattice has not been found so far. Here we report the frustrated magnetism of a new Ising kagome antiferromagnet, MgCo${}_{3}$(OH)${}_{6}$Cl${}_{2}$, which can be viewed as a Co version of the intensively researched quantum kagome antiferromagnet of Herbertsmithite ZnCu${}_{3}$(OH)${}_{6}$Cl${}_{2}$. Experiments of magnetization, heat capacity, \ensuremath{\mu}SR, and neutron scattering demonstrated a partially frozen state with persistent spin fluctuations below around $T$ = 2.7 K. The present study has provided a real material system to study the Ising spin behaviors on undistorted kagome lattice.

Field-Induced Freezing of a Quantum Spin Liquid on the Kagome Lattice

We report (17)O NMR measurements in the S=1/2 (Cu(2+)) kagome antiferromagnet Herbertsmithite ZnCu(3)(OH)(6)Cl(2) down to 45 mK in magnetic fields ranging from 2 to 12 T. While Herbertsmithite displays a gapless spin-liquid behavior in zero field, we uncover an instability toward a spin-solid phase at sub-Kelvin temperature induced by an applied magnetic field. The latter phase shows largely suppressed moments ≲0.1 μ(B) and gapped excitations. The H-T phase diagram suggests the existence of a quantum critical point at the small but finite magnetic field μ(0)H(c)=1.55(25) T. We discuss this finding in light of the perturbative Dzyaloshinskii-Moriya interaction which was theoretically proposed to sustain a quantum critical regime for the quantum kagome Heisenberg antiferromagnet model.

Lack of evidence for a singlet crystal-field ground state in the magnetic pyrochlore Tb2Ti2O7

We present high-resolution inelastic neutron scattering data on the candidate spin liquid Tb${}_{2}$Ti${}_{2}$O${}_{7}$. We find that there is no evidence for a zero-field splitting of the ground-state doublet within the $0.2$ K resolution of the instrument. This result contrasts with a pair of recent works claiming that the spin-liquid behavior of Tb${}_{2}$Ti${}_{2}$O${}_{7}$ can be attributed to a 2 K split singlet-singlet single-ion spectrum at low energies. We also reconsider the entropy argument presented by Chapuis et al. [Phys. Rev. B 82, 100420 (2010)] as further evidence of a singlet-singlet crystal-field spectrum. We argue that estimates of the low-temperature residual entropy drawn from specific heat measurements are a poor guide to the single-ion spectrum without a proper understanding of the nature of the correlations in the spin-liquid regime.

Numerical Diagonalization Study on the S = 1/2 Frustrated Three-Leg Quantum Spin Ladder Systems

The spin ladder systems have attracted a lot of interest in the field of low-dimensional physics. It is well known that the S = 1/2 two-leg spin ladder has a spin gap, while the three-leg one has a gapless spin liquid ground state. Some spin liquid behaviors were observed in the recent experiments of some frustrated systems; the distorted triangular lattice and kagome lattice antiferromagnets etc. Thus we consider the S = 1/2 three-leg spin ladder system with the next-nearest-neighbor interaction to investigate the effect of frustration on the spin liquids. Using the exact numerical diagonalization of finite-cluster systems, we study the ground state of this system. The phase diagram with respect to some exchange interaction constants is presented. It is revealed that sufficiently large next-nearest-neighbor coupling leads to a ferrimagnetic phase, which has a frustration-induced spontaneous magnetization. In addition we find two spin liquid phases, one of which corresponds to a Néel-like spin configuration and the other a collinear spin configuration. As a result of the numerical study, we find a new phase which is different from three phases.

Quantum kagome antiferromagnet : ZnCu3(OH)6Cl2

Herbertsmithite, ZnCu3(OH)6Cl2, is the prototype candidate for a spin liquid behavior on a geometrically perfect kagome lattice. Its discovery and the absence of any evidence for spin-freezing down to the lowest probed temperature to-date enable one to explore the properties of kagome-related physics in an unprecedented temperature range. We review its properties and discuss some open issues. A tentative comparison to models is also performed.

Critical correlations for short-range valence-bond wave functions on the square lattice

We investigate the arguably simplest $SU(2)$-invariant wave functions capable of accounting for spin-liquid behavior, expressed in terms of nearest-neighbor valence-bond states on the square lattice and characterized by different topological invariants. While such wave functions are known to exhibit short-range spin correlations, we perform Monte Carlo simulations and show that four-point correlations decay algebraically with an exponent 1.16(4). This is reminiscent of the classical dimer problem, albeit with a slower decay. Furthermore, these correlators are found to be spatially modulated according to a wave vector related to the topological invariants. We conclude that a recently proposed spin Hamiltonian that stabilizes the here considered wave function(s) as its (degenerate) ground state(s) should exhibit gapped spin and gapless nonmagnetic excitations.

Magnetic properties ofBa2HoSbO6with a frustrated lattice geometry

The study of geometrically frustrated magnets with unusual crystal field ground states offers the possibility of discovering new aspects of the physics of cooperative paramagnetic states. In the rare-earth double perovskite ${\text{Ba}}_{2}{\text{HoSbO}}_{6}$ the ${\text{Ho}}^{3+}$ ions occupy a face-centered cubic lattice, which frustrates near-neighbor antiferromagnetic coupling. We present a systematic experimental study of the system using dc magnetization, heat capacity, muon-spin relaxation, inelastic neutron scattering, neutron powder diffraction, and neutron polarization analysis. The bulk measurements at first point to spin liquid behavior, but the microscopic measurements indicate that this system is an example of a ``nonmagnetic doublet'' crystal field ground state, with low-lying excited states. Our measurements are interpreted using crystal field theory of ${\text{Ho}}^{3+}$, including hyperfine coupling. We find that exchange and dipolar coupling are weak in this particular system and that the ``mock spin liquid'' behavior in fact reflects the unusual properties of the nonmagnetic doublet.