Spin-liquid phase in a spin-1/2 quantum magnet on the kagome lattice

We study a model of hard-core bosons with short-range repulsive interactions at half filling on the kagome lattice. Using quantum Monte Carlo numerics, we find that this model shows a continuous superfluid-insulator quantum phase transition, with exponents z=1 and nu approximately 0.67(5). The insulator, I*, exhibits short-ranged density and bond correlations, topological order, and exponentially decaying spatial vison correlations, all of which point to a Z2 fractionalized phase. We estimate the vison gap in I* from the temperature dependence of the energy. Our results, together with the equivalence between hard-core bosons and S=1/2 spins, provide compelling evidence for a spin-liquid phase in an easy-axis spin-1/2 model with no special conservation laws.     

Effective spin model for the spin-liquid phase of the Hubbard model on the triangular lattice

We show that the spin-liquid phase of the half-filled Hubbard model on the triangular lattice can be described by a pure spin model. This is based on a high-order strong coupling expansion (up to order 12) using perturbative continuous unitary transformations. The resulting spin model is consistent with a transition from three-sublattice long-range magnetic order to an insulating spin-liquid phase, and with a jump of the double occupancy at the transition. Exact diagonalizations of both models show that the effective spin model is quantitatively accurate well into the spin-liquid phase, and a comparison with the Gutzwiller projected Fermi sea suggests a gapless spectrum and a spinon Fermi surface.     

Non-Abelian spin liquid in a spin-one quantum magnet

We study a time-reversal invariant non-Abelian spin-liquid state in an SU(2) symmetric spin S=1 quantum magnet on a triangular lattice. The spin liquid is obtained by quantum disordering a noncollinear nematic state. We show that such a spin liquid cannot be obtained by the standard projective construction for spin liquids. We also study the phase transition between the spin liquid and the noncollinear nematic state and show that it cannot be described within the Landau-Ginzburg-Wilson paradigm.     

High-pressure effect on the crystal and magnetic structures of the frustrated antiferromagnet YMnO<Subscript>3</Subscript>

The high-pressure (to 5 GPa) effect on the crystal and magnetic structures of the hexagonal manganite YMnO₃ is studied by neutron diffraction in the temperature range 10–295 K. A spin-liquid state due to magnetic frustration on the triangular lattice formed by Mn ions is observed in this compound at normal pressure and T > T_N = 70 K, and an ordered triangular antiferromagnetic state with the symmetry of the irreducible representation Γ₁ arises at T < T_N. The high-pressure effect leads to a spin reorientation of Mn magnetic moments and a change in the symmetry of the antiferromagnetic structure, which can be described by a combination of the irreducible representations Γ₁ and Γ₂. In addition, it is observed that the ordered magnetic moment of Mn ions decreases from 3.27 μ_B (5 GPa) to 1.52 μ_B (5 GPa) at T = 10 K and diffuse scattering is enhanced at temperatures close to T_N. These effects can be explained within the model of the coexistence of the ordered antiferromagnetic phase and the spin-liquid state, whose volume fraction increases with pressure due to the enhancement of frustration effects.     

Phase diagram of a frustrated two-dimensional J1-J2-J3 quantum antiferromagnet: An approach based on spherically symmetric green’s functions

The phase diagram of the frustrated J ₁-J ₂-J ₃ S = 1/2 Heisenberg model on a square lattice is studied in the range of parameters corresponding to the spin-liquid state of the system. The study is performed using the self-consistent two-time retarded spin-spin Green’s functions, which do not break both translational and SU(2) symmetries. The inclusion of the damping of spin fluctuations allows us to obtain a good agreement with the cluster calculations. Using a consistent analytical approach, we have found continuous transitions via the spin-liquid state between the phases with three types of the long-range order: checkerboard, stripe, and (k, k) helical. In addition, there are indications confirming the existence of the (k, π) helical phase.     

On the scaling theory of antiferromagnetic ordering in frustrated Kondo lattices

A scaling theory of the Kondo lattices with frustrated exchange interactions is developed, criterium of antiferromagnetic ordering being investigated. Depending on the bare model parameters, one or two quantum phase transitions into non-magnetic spin-liquid and Kondo Fermi-liquid ground states can occur with increasing the bare coupling constant. Whereas the renormalization of the magnetic moment in the ordered phase can reach orders of magnitude, spin fluctuation frequency and coupling constant are moderately renormalized in the spin-liquid phase. This justifies application of the scaling approach.     

Kondo stripes in an Anderson-Heisenberg model of heavy fermion systems

We study the interplay between the spin-liquid and Kondo physics, as related to the nonmagnetic part of the phase diagram of heavy fermion materials. Within the unrestricted mean-field treatment of the infinite-U 2D Anderson-Heisenberg model, we find that there are two topologically distinct nondegenerate uniform heavy Fermi liquid states that may form as a consequence of the Kondo coupling between spinons and conduction electrons. For certain carrier concentrations, the uniform Fermi liquid becomes unstable with respect to the formation of a new kind of anharmonic "Kondo stripe" state with inhomogeneous Kondo screening strength and the charge density modulation. These features are experimentally measurable and thus may help to establish the relevance of the spin-liquid correlations to heavy fermion materials.     

Unconventional state with two coexisting long-range orders for frustrated Heisenberg model at quantum phase transition

For the frustrated two-dimensional S=1/2 antiferromagnetic Heisenberg model close to quantum phase transition we consider the singlet ground states retaining both translational and SU(2) symmetry. Besides usually discussed checkerboard, spin-liquid and stripe states an unconventional state with two coexisting long-range orders appears to be possible at sufficiently large damping of spin excitations. The problem is treated in the frames of self-consistent spherically symmetric approach.     

Frontiers in frustrated magnetism

This article discusses at a qualitative level a number of issues at the forefront of current understanding and developments in frustrated quantum magnetism. The focal point of the presentation is the spin liquid, which is introduced in terms of (un)broken spin and lattice symmetries. An overview of the full spectrum of research activity in the field is obtained by considering selected examples from experimental approaches to realising spin-liquid states, from theoretical efforts which seek both to classify spin liquids according to their physical properties and to broaden the search for spin-liquid behaviour, and from numerical techniques which offer the prospect of qualitatively new insight into frustrated spin systems.     

Mesoscopic spin clusters, phase separation, and induced order in spin-gap magnets: A review

In many low-dimensional systems with antiferromagnetic interactions, a magnetic order of the Néel type is absent. These systems remain in a quantum-disordered (spin-liquid) state down to zero temperature. The disordered state appears to be stable to weak perturbations when magnetic excitations are separated from the ground state by an energy gap. The stability of the spin-liquid ground state is destroyed upon introduction of impurities or in a sufficiently strong magnetic field. This paper presents a review of the main results of the experimental investigations performed in order to reveal and identify mesoscopic spin clusters formed in the vicinity of impurity ions, to determine the spatial structure of an impurity-induced magnetic order in spin-gap systems, and to examine the low-frequency excitation spectra of field-induced antiferromagnetic phases.     

Mott transition from a spin liquid to a Fermi liquid in the spin-frustrated organic conductor kappa-(ET)2Cu2(CN)3

The pressure-temperature phase diagram of the organic Mott insulator kappa-(ET)2Cu2(CN)3, a model system of the spin liquid on triangular lattice, has been investigated by 1H NMR and resistivity measurements. The spin-liquid phase is persistent before the Mott transition to the metal or superconducting phase under pressure. At the Mott transition, the spin fluctuations are rapidly suppressed and the Fermi-liquid features are observed in the temperature dependence of the spin-lattice relaxation rate and resistivity. The characteristic curvature of the Mott boundary in the phase diagram highlights a crucial effect of the spin frustration on the Mott transition.     

Thermal studies of the spin liquid state and analog to the He melting curve in a geometrically frustrated magnet

Gadolinium gallium garnet, Gd₃Ga₅O₁₂ (GGG) has an extraordinary low-temperature phase diagram. Although the Curie–Weiss temperature of GGG is −2 K, GGG shows no long-range order down to T0.4 K. At low temperatures GGG has a spin glass phase at low fields (0.1 T), a field-induced long-range ordered antiferromagnetic state at fields of between 0.7 and 1.3 T, and, at intermediate fields, an apparent spin-liquid state without long-range order. We have characterized the intermediate field (IF) state through heat capacity, thermal conductivity, and magnetocaloric measurements. Our results show a sharp high-field phase boundary of the thermal irreversibility of the spin glass phase of GGG implying that the intermediate field phase is distinct from the spin glass. The lower field boundary of the AFM phase is shown to have distinct minimum at T0.2 K, in analogy to the minimum in the melting curve of ⁴He. The existence of such a minimum is confirmed by measurements of the latent heat of the transition below that temperature.     

Projected-wave-function study of the spin-1/2 Heisenberg model on the Kagomé lattice

We perform a Gutzwiller projected-wave-function study for the spin-1/2 Heisenberg model on the Kagomé lattice to compare energies of several spin-liquid states. The result indicates that a U(1)-Dirac spin-liquid state has the lowest energy. Furthermore, even without variational parameters, the energy turns out to be very close to that found by exact diagonalization. We show that such a U(1)-Dirac state represents a quantum phase whose low-energy physics is governed by four flavors of two-component Dirac fermions coupled to a U(1) gauge field. These results are discussed in the context of recent experiments on ZnCu(3)(OH)(6)Cl(2).     

Spin-liquid state in the S=1/2 hyperkagome antiferromagnet Na4Ir3O8

A spinel related oxide, Na(4)Ir(3)O(8), was found to have a three dimensional network of corner shared Ir(4+) (t(2g)(5)) triangles. This gives rise to an antiferromagnetically coupled S = 1/2 spin system formed on a geometrically frustrated hyperkagome lattice. Magnetization M and magnetic specific heat C(m) data showed the absence of long range magnetic ordering at least down to 2 K. The large C(m) at low temperatures is independent of applied magnetic field up to 12 T, in striking parallel to the behavior seen in triangular and kagome antiferromagnets reported to have a spin-liquid ground state. These results strongly suggest that the ground state of Na(4)Ir(3)O(8) is a three dimensional manifestation of a spin liquid.     

Quantum spin fluctuations in the spin-liquid state of Tb?Ti?O?

Neutron scattering experiments on a polycrystalline sample of the frustrated pyrochlore magnet Tb(2)Ti(2)O(7), which does not show any magnetic order down to 50 mK, have revealed that it shows condensation behavior below 0.4 K from a thermally fluctuating paramagnetic state to a spin-liquid ground state with quantum spin fluctuations. Energy spectra change from quasielastic scattering to a continuum with a double-peak structure at energies of 0 and 0.8 K in the spin-liquid state. Specific heat shows an anomaly at the crossover temperature.     

Fractional spin textures in the frustrated magnet SrCr(9p)Ga(12-9p)O₁₉

We consider the archetypal frustrated antiferromagnet SrCr(9p)Ga(12-9p)O?? in its well-known spin-liquid state, and demonstrate that a Cr(3+) spin S=3/2 ion in direct proximity to a pair of vacancies (in disordered p<1 samples) is cloaked by a spatially extended spin texture that encodes the correlations of the parent spin liquid. In this spin-liquid regime, our analytic theory predicts that the combined object has a magnetic response identical to a classical spin of length S/2=3/4, which dominates over the small intrinsic susceptibility of the pure system. This fractional-spin texture leaves an unmistakable imprint on the measured ?1Ga nuclear magnetic resonance line shapes, which we compute using Monte Carlo simulations and compare with experimental data.     

Phase diagram of frustrated mixed-spin ladders in the strong-coupling limit

We study the ground-state properties of frustrated Heisenberg ferrimagnetic ladders with antiferromagnetic exchange interactions and two types of alternating sublattice spins. In the limit of strong rung couplings, we show that the mixed spin-1/2 and spin-1 ladders can be systematically mapped onto a spin-1/2 Heisenberg model with additional next-nearest-neighbor exchanges. The system is either in a ferrimagnetic state or in a critical spin-liquid state depending on the competition between the spin exchanges along the legs and the diagonal exchanges.     

Spinons in a crossed-chains model of a 2D spin liquid

Using the random phase approximation, we show that a crossed-chains model of spin-1/2 Heisenberg chains with frustrated interchain couplings has a nondimerized spin-liquid ground state in 2D, with deconfined spinons as the elementary excitations. The results are confirmed by a bosonization study, which shows that the system is an example of a "sliding Luttinger liquid." In an external field, the system develops an incommensurate field-induced long-range order with a finite transition temperature.     

From quantum disorder to magnetic order in an s=1/2 kagome lattice: a structural and magnetic study of herbertsmithite at high pressure

The structural and magnetic properties of deuterated herbertsmithite have been studied by means of neutron powder diffraction and magnetic susceptibility measurements in a wide range of temperatures and pressures. The experimental data demonstrate that a phase transition from the quantum-disordered spin-liquid phase to the long-range ordered antiferromagnetic phase with the Néel temperature T(N)=6 K is induced at P=2.5 GPa. The observed decrease of T(N) upon compression correlates with the anomalies in pressure behavior of Cu-O bond length and Cu-O-Cu bond angles. The reasons for the observed spin-freezing transition are discussed within the framework of the available theoretical models and the recent observation of the field-induced spin freezing.     

Spin glass behavior upon diluting frustrated magnets and spin liquids: a Bethe-Peierls treatment

A Bethe-Peierls treatment to dilution in frustrated magnets and spin liquids is given. A spin glass phase is present at low temperatures and close to the percolation point as soon as frustration takes a finite value in the dilute magnet model; the spin glass phase is reentrant inside the ferromagnetic phase. An extension of the model is given, in which the spin glass/ferromagnet phase boundary is shown not to reenter inside the ferromagnetic phase asymptotically close to the tricritical point whereas it has a turning point at lower temperatures. We conjecture similar phase diagrams to exist in finite dimensional models not constraint by a Nishimori's line. We increase frustration to study the effect of dilution in a spin liquid state. This provides a “minimal” ordering by disorder from an Ising paramagnet to an Ising spin glass. Received 9 April 1999 and Received in final form 27 September 1999