Spin Liquid Ground State Research Articles

Rigorous Criterion for Reentrance in the Spin-1/2 Ising-Heisenberg Model on Diamond-Like Decorated Bethe Lattices

The ferromagnetic spin-1/2 Ising–Heisenberg model on planar lattices currently attracts a great deal of attention as it may exhibit a variety of interesting phenomena such as a quantum critical point [1, 2], peculiar spontaneous antiferromagnetic long-range order [1] or several unusual spin-liquid ground states [2]. In this work, the spin-1/2 Ising–Heisenberg model on diamond-like decorated Bethe lattices will be treated exactly with the aim to study its ground-state and finite-temperature phase diagrams.

Site Specific X-ray Anomalous Dispersion of the Geometrically Frustrated Kagomé Magnet, Herbertsmithite, ZnCu3(OH)6Cl2

Structural characterization, exploiting X-ray scattering differences at elemental absorption edges, is developed to quantitatively determine crystallographic site-specific metal disorder. We apply this technique to the problem of Zn-Cu chemical disorder in ZnCu(3)(OH)(6)Cl(2). This geometrically frustrated kagomé antiferromagnet is one of the best candidates for a spin-liquid ground state, but chemical disorder has been suggested as a mundane explanation for its magnetic properties. Using anomalous scattering at the Zn and Cu edges, we determine that there is no Zn occupation of the intralayer Cu sites within the kagomé layer; however there is Cu present on the Zn intersite, leading to a structural formula of (Zn(0.85)Cu(0.15))Cu(3)(OH)(6)Cl(2). The lack of Zn mixing onto the kagomé lattice sites lends support to the idea that the electronic ground state in ZnCu(3)(OH)(6)Cl(2) and its relatives is nontrivial.

Interplay of thermal and quantum spin fluctuations in the kagome lattice compound herbertsmithite

We present a Raman spectroscopic investigation of the herbertsmithite ${\text{ZnCu}}_{3}{(\text{OH})}_{6}{\text{Cl}}_{2}$, a realization of a Heisenberg $s=1/2$ antiferromagnet on a perfect kagome lattice. Focusing on its magnetic excitation spectrum we find two components, a high-temperature quasielastic signal and a low temperature, broad maximum. The latter has a linear low-energy slope and extends to high energy. We have investigated the temperature dependence and symmetry properties of both signals. Our data agree with previous calculations and point to a gapless spin liquid ground state.

Dynamic Scaling in the Susceptibility of the Spin-12Kagome Lattice Antiferromagnet Herbertsmithite

The spin-1/2 kagome lattice antiferromagnet herbertsmithite, ZnCu(3)(OH)(6)Cl(2), is a candidate material for a quantum spin liquid ground state. We show that the magnetic response of this material displays an unusual scaling relation in both the bulk ac susceptibility and the low energy dynamic susceptibility as measured by inelastic neutron scattering. The quantity chiT(alpha) with alpha approximately 0.66 can be expressed as a universal function of H/T or omega/T. This scaling is discussed in relation to similar behavior seen in systems influenced by disorder or by the proximity to a quantum critical point.

High-Field ESR Measurements of S=1/2 Kagome Lattice Antiferromagnet BaCu3V2O8(OH)2

High-field electron spin resonance (ESR) measurements have been performed on vesignieite BaCu 3 V 2 O 8 (OH) 2 , which is considered as a nearly ideal model substance of S =1/2 kagome antiferromagnet, in the temperature region from 1.9 to 265 K. The frequency region is from 60 to 360 GHz and the applied pulsed magnetic field is up to 16 T. Observed g -value and linewidth show the increase below 20 K, which suggest the development of the short range order. Moreover, a gapless spin liquid ground state is suggested from the frequency–field relation at 1.9 K.

Ground State of the Easy-Axis Rare-Earth Kagome LangasitePr3Ga5SiO14

We report muon spin relaxation and {69,71}Ga nuclear quadrupolar resonance local-probe investigations of the kagome compound Pr3Ga5SiO14. Small quasistatic random internal fields develop below 40 K and persist down to our base temperature of 21 mK. They originate from hyperfine-enhanced 141Pr nuclear magnetism which requires a nonmagnetic Pr3+ crystal-field (CF) ground state. In addition, we observe a broad maximum of the relaxation rate at approximately 10 K which we attribute to the population of the first excited magnetic CF level. Our results yield a Van Vleck paramagnet picture, at variance with the formerly proposed spin-liquid ground state.

Low temperature heat capacity measurements of the spin-liquid states of hydrogenated and deuterated κ-(BEDT-TTF) 2Cu 2(CN) 3

Heat capacity measurements of organic triangular lattice compound κ-(BEDT-TTF) 2Cu 2(CN) 3 were performed to discuss the low energy excitations from the spin-liquid ground states. Existence of the T-linear electronic coefficient with finite electronic heat capacity coefficient γ was confirmed in three different samples from different batches, although small sample dependence was observed in the absolute values of the heat capacities. Concerning the sample in which hydrogen atoms in ethylene group in BEDT-TTF molecule have been substituted by deuterons, we have observed almost similar thermodynamic behavior as the hydrogenated sample. The absence of drastic change of electronic properties of this compound is consistent with the electronic phase diagram given by Kurosaki et al. [11] (Phys. Rev. Lett. 95 (2005) 17001). The obtained data are well consistent with the previous heat capacity experiments. The existence of the γ term demonstrates that the excitations from the quantum spin-liquid states show a gapless behavior at least down to 0.7 K.

Mott Insulators of Ultracold Fermionic Alkaline Earth Atoms: Underconstrained Magnetism and Chiral Spin Liquid

We study Mott insulators of fermionic alkaline earth atoms, described by Heisenberg spin models with enhanced SU(N) symmetry. In dramatic contrast to SU(2) magnetism, more than two spins are required to form a singlet. On the square lattice, the classical ground state is highly degenerate and magnetic order is thus unlikely. In a large-N limit, we find a chiral spin liquid ground state with topological order and Abelian fractional statistics. We discuss its experimental detection. Chiral spin liquids with non-Abelian anyons may also be realizable with alkaline earth atoms.

Spin-Liquid State Study of Equilateral Triangle S=3/2 Spin Tubes Formed in CsCrF4

Topological effects on spin frustration in equilateral triangle S =3/2 spin tubes formed in CsCrF 4 were studied by magnetic susceptibility, heat capacity [ C ( T )], and electron spin resonance experiments. The experimental data show that there is no magnetic long-range order down to T =1.3 K, and that no spin gap due to a chiral spin structure appears. Furthermore, since the C ( T ) curve has a T -linear component, a gapless spin-liquid ground state in one-dimensional antiferromagnets, the so-called Tomonaga–Luttinger liquid, is realized. This is characteristic of equilateral triangle spin tubes with S = half-integer.

Collective Magnetic Excitations in the Spin LadderSr14Cu24O41Measured Using High-Resolution Resonant Inelastic X-Ray Scattering

We investigate magnetic excitations in the spin-ladder compound Sr_{14}Cu_{24}O_{41} using high-resolution Cu L_{3} edge resonant inelastic x-ray scattering (RIXS). Our findings demonstrate that RIXS couples to two-triplon collective excitations. In contrast to inelastic neutron scattering, the RIXS cross section changes only moderately over the entire Brillouin zone, revealing high sensitivity also at small momentum transfers, allowing determination of the two-triplon energy gap as 100 +/- 30 meV. Our results are backed by calculations within an effective Hubbard model for a finite-size cluster, and confirm that optical selection rules are obeyed for excitations from this spherically symmetric quantum spin-liquid ground state.

Dimensional crossover in a spin-liquid-to-helimagnet quantum phase transition

Neutron scattering is used to study magnetic-field-induced ordering in the quasi-one-dimensional quantum spin-tube compound ${\text{Sul-Cu}}_{2}{\text{Cl}}_{4}$ that in zero field has a nonmagnetic spin-liquid ground state. The experiments reveal an incommensurate chiral high-field phase stabilized by a geometric frustration of the magnetic interactions. The measured critical exponents $\ensuremath{\beta}\ensuremath{\approx}0.235$ and $\ensuremath{\nu}\ensuremath{\approx}0.34$ at ${H}_{c}\ensuremath{\approx}3.7\text{ }\text{T}$ point to an unusual subcritical scaling regime and may reflect the chiral nature of the quantum critical point.

Gapless Spin Liquids on the Three-Dimensional Hyperkagome Lattice ofNa4Ir3O8

Recent experiments indicate that Na4Ir3O8, a material in which s=1/2 Ir local moments live on a three-dimensional "hyperkagome" lattice of corner-sharing triangles, may have a quantum spin liquid ground state with gapless spin excitations. Using a combination of exact diagonalization, symmetry analysis of fermionic mean field ground states and Gutzwiller projected variational wave functions studies, we propose a quantum spin liquid with spinon Fermi surfaces as a favorable candidate for the ground state of the Heisenberg model on this lattice. We point out implications of this proposal for thermodynamic properties and discuss possible weak instabilities of the spinon Fermi surfaces.

XXZand Ising spins on the triangular kagome lattice

The recently fabricated two-dimensional magnetic materials ${\text{Cu}}_{9}{X}_{2}{(\text{cpa})}_{6}\ensuremath{\cdot}x{\text{H}}_{2}\text{O}$ ($\text{cpa}=2$-carboxypentonic acid and $X=\text{F},\text{Cl},\text{Br}$) have copper sites which form a triangular kagome lattice (TKL), formed by introducing small triangles (``$a$-trimers'') inside of each kagome triangle (``$b$-trimer''). We show that in the limit where spins residing on $b$-trimers have Ising character, quantum fluctuations of $XXZ$ spins residing on the $a$-trimers can be exactly accounted for in the absence of applied field. This is accomplished through a mapping to the kagome Ising model, for which exact analytic solutions exist. We derive the complete finite-temperature phase diagram for this $XXZ$-Ising model, including the residual zero-temperature entropies of the seven ground-state phases. Whereas the disordered (spin liquid) ground state of the pure Ising TKL model has macroscopic residual entropy $\text{ln}\text{ }72=4.2767\dots{}$ per unit cell, the introduction of transverse (quantum) couplings between neighboring $a$-spins reduces this entropy to $2.5258\dots{}$ per unit cell. In the presence of applied magnetic field, we map the TKL $XXZ$-Ising model to the kagome Ising model with three-spin interactions and derive the ground-state phase diagram. A small (or even infinitesimal) field leads to a new phase that corresponds to a nonintersecting loop gas on the kagome lattice, with entropy $1.4053\dots{}$ per unit cell and a mean magnetization for the $b$-spins of 0.12(1) per site. In addition, we find that for moderate applied field, there is a critical spin liquid phase that maps to close-packed dimers on the honeycomb lattice, which survives even when the $a$-spins are in the Heisenberg limit.

Thermodynamic properties of a spin-1/2 spin-liquid state in a κ-type organic salt

In two-dimensional triangular lattices, geometric frustration prohibits the formation of ordering even at the lowest temperatures, and therefore a liquid-like ground state is expected. The spin-liquid problem has been one of the central topics of condensed-matter science for more than 30 yr in relation to the resonating-valence-bond model1. One of the characteristic features proposed is the existence of a linear temperature-dependent contribution to the heat capacity, as the degeneracy of the energy states should give rise to gapless excitations. Here, we show thermodynamic evidence for the realization of a spin-liquid ground state through a single-crystal calorimetric study of the dimer-based organic charge-transfer salt κ-(BEDT-TTF)2Cu2(CN)3, with a triangular lattice structure down to 75 mK. In addition, we report an unexpected hump structure in the heat capacity around 6 K, which may indicate a crossover into the quantum spin liquid.

Square-Lattice Algebraic Spin Liquid with SO(5) Symmetry

We propose a critical spin liquid ground state for S=1/2 antiferromagnets on the square lattice. In a renormalization group analysis of the "staggered flux" algebraic spin liquid, we examine perturbations, present in the antiferromagnet, which break its global SU(4) symmetry to SO(5). At physical parameter values, we find an instability towards a fixed point with SO(5) symmetry. We discuss the possibility that this fixed point describes a transition between the Néel and valence bond solid states, and the relationship to the SO(5) nonlinear sigma model of Tanaka and Hu.

Local Moment, Itinerancy, and Deviation from Fermi-Liquid Behavior inNaxCoO2for0.71≤x≤0.84

Here we report the observation of Fermi surface (FS) pockets via the Shubnikov-de Haas effect in NaxCoO2 for x=0.71 and 0.84, respectively. Our observations indicate that the FS expected for each compound intersects their corresponding Brillouin zones, as defined by the previously reported superlattice structures, leading to small reconstructed FS pockets, but only if a precise number of holes per unit cell is localized. For 0.71< or = x < 0.75 the coexistence of itinerant carriers and localized S=1/2 spins on a paramagnetic triangular superlattice leads at low temperatures to the observation of a deviation from standard Fermi-liquid behavior in the electrical transport and heat capacity properties, suggesting the formation of some kind of quantum spin-liquid ground state.

Impurity effects in the quantum kagome systemZnCu3(OH)6Cl2

Motivated by the recent experiments on the spin half kagome compound $\mathrm{Zn}{\mathrm{Cu}}_{3}{(\mathrm{O}\mathrm{H})}_{6}{\mathrm{Cl}}_{2}$, we study a phenomenological model of a frustrated quantum magnet. The model has a spin liquid ground state and is constructed so as to mimic the macroscopically large quasidegeneracies expected in the low-lying energy structure of a kagome system. We use numerical studies of finite size systems to investigate the static as well as the dynamical responses at finite temperatures. The results obtained using our simple model are compatible with a large number of recent experiments including neutron scattering data. Our study suggests that many of the anomalous features observed in experiments have a natural interpretation in terms of spin-$\frac{1}{2}$ defects (impurities) coupled to an underlying kagome-type spin liquid.

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 Neel 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.

Spin-Liquid State in theS=1/2Hyperkagome AntiferromagnetNa4Ir3O8

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.

SU(2) gauge theory of the Hubbard model and application to the honeycomb lattice

Motivated by recent experiments on the triangular lattice Mott-Hubbard system $\ensuremath{\kappa}\text{\ensuremath{-}}{(\mathrm{BEDT}\text{\ensuremath{-}}\mathrm{TTF})}_{2}{\mathrm{Cu}}_{2}{(\mathrm{C}\mathrm{N})}_{3}$, we develop a general formalism to investigate quantum spin liquid insulators adjacent to the Mott transition in Hubbard models. This formalism, dubbed the SU(2) slave-rotor formulation, is an extension of the SU(2) gauge theory of the Heisenberg model to the case of the Hubbard model. Furthermore, we propose the honeycomb lattice Hubbard model (at half filling) as a candidate for a spin liquid ground state near the Mott transition; this is an appealing possibility, as this model can be studied via quantum Monte Carlo simulation without a sign problem. The pseudospin symmetry of Hubbard models on bipartite lattices turns out to play a crucial role in our analysis, and we develop our formalism primarily for the case of a bipartite lattice. We also sketch its development for a general Hubbard model. We develop a mean-field theory to describe spin liquids and some competing states, and apply it to the honeycomb lattice. On the insulating side of the Mott transition, we find an SU(2) algebraic spin liquid (ASL), described by gapless $S=1∕2$ Dirac fermions (spinons) coupled to a fluctuating SU(2) gauge field. This result contrasts with that obtained via a U(1) slave-rotor approach, which instead found a U(1) ASL. That formulation does not respect the pseudospin symmetry, and is therefore not correct on the honeycomb lattice. We construct a low-energy effective theory describing the ASL phase, the conducting semimetal phase and the Mott transition between them. This physics can be detected in numerical simulations via the simultaneous presence of substantial antiferromagnetic and valence-bond solid correlations. In the SU(2) ASL, these observables have slowly decaying fluctuations in space and time, described by power laws with the same critical exponent. We recover the results of the U(1) slave-rotor formulation in the presence of a strong breaking of pseudospin symmetry. Our analysis suggests that both a third-neighbor electron hopping, and/or pseudospin-breaking terms such as a nearest-neighbor density interaction, may help to stabilize a spin liquid phase.