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arXiv:1108.3070 · Physical Review B

Exotic S=1 spin-liquid state with fermionic excitations on the triangular lattice

Maksym Serbyn, T. Senthil, Patrick A. Lee

Published Nov 3, 2011• 49 citations
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Abstract

Motivated by recent experiments on the material Ba${}_{3}$NiSb${}_{2}$O${}_{9}$, we consider a spin-one quantum antiferromagnet on a triangular lattice with the Heisenberg bilinear and biquadratic exchange interactions and a single-ion anisotropy. Using a fermionic ``triplon'' representation for spins, we study the phase diagram within mean-field theory. In addition to a fully gapped spin-liquid ground state, we find a state where one gapless triplon mode with a Fermi surface coexists with $d+id$ topological pairing of the other triplons. Despite the existence of a Fermi surface, this ground state has fully gapped bulk spin excitations. Such a state has linear in-temperature specific heat and constant in-plane spin susceptibility, with an unusually high Wilson ratio.

DOI
10.1103/physrevb.84.180403

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Motivated by recent experiments on the material Ba3{}_{3}3​NiSb2{}_{2}2​O9{}_{9}9​, we consider a spin-one quantum antiferromagnet on a triangular lattice with the Heisenberg bilinear and biquadratic exchange interactions and a single-ion anisotropy. Using a fermionic ``triplon'' representation for spins, we study the phase diagram within mean-field theory. In addition to a fully gapped spin-liquid ground state, we find a state where one gapless triplon mode with a Fermi surface coexists with d+idd+idd+id topological pairing of the other triplons. Despite the existence of a Fermi surface, this ground state has fully gapped bulk spin excitations. Such a state has linear in-temperature specific heat and constant in-plane spin susceptibility, with an unusually high Wilson ratio.
Motivated by recent experiments on Ba3{}_{3}3​NiSb2{}_{2}2​O9{}_{9}9​, we investigate possible quantum spin liquid ground states for spin S=1S=1S=1 Heisenberg models on the triangular lattice. We use variational Monte Carlo techniques to calculate the energies of microscopic spin liquid wave functions where spin is represented by three flavors of fermionic spinon operators. These energies are compared with the energies of various competing three-sublattice ordered states. Our approach shows that the antiferromagnetic Heisenberg model with biquadratic term and single-ion anisotropy does not have a low-temperature spin liquid phase. However, for an SU(3)-invariant model with sufficiently strong ring-exchange terms, we find a paired chiral quantum spin liquid with a Fermi surface of deconfined spinons that is stable against all types of ordering patterns we considered. We discuss the physics of this exotic spin liquid state in relation to the recent experiment and suggest new ways to test this scenario.
Abstract Quantum spin liquids (QSL) are prototypical examples of ground states with massive many-body entanglement. While an unambiguous realization of this long-sought-after state remains elusive, a growing number of materials candidates keep emerging with varieties of novel and exotic properties. Here, we report a combined experimental and theoretical study of a new antiferromagnet Ba 3 CuNb 2 O 9 which has an in-plane anisotropic exchange interaction arising from distorted triangular arrangements of magnetic Cu 2 + (spin-1/2) ions. We show an unconventional gapless QSL like ground state in this material which does not exhibit any signature of magnetic ordering down to 0.3 K, while a finite Curie–Weiss temperature ∼ − 41 K is evident. The gapless QSL state is supported by a high spin fluctuation, a power-law dependence of magnetic specific heat ( C m ∝ T γ ) and a unique scaling of magnetic susceptibility and specific heat with temperature and magnetic field respectively. Our ab-initio simulation also confirms the anisotropic exchange interaction which can only be explained via superexchange mechanism. While the combined results strongly suggest a random singlet state driven QSL behavior in present material, we strongly believe that the anisotropic exchange interaction has a possible role for this exotic ground state behavior.
We describe a new class of spin liquids with global SU(2) spin-rotation symmetry in spin-1/2 systems on the triangular lattice, which have real Majorana fermion excitations carrying spin S=1S=1S=1. The simplest translationally invariant mean-field state on the triangular lattice breaks time-reversal symmetry and is stable to fluctuations. It generically possesses gapless excitations along three Fermi lines in the Brillouin zone. These intersect at a single point where the excitations scale with a dynamic exponent z=3z=3z=3. An external magnetic field has no orbital coupling to the SU(2) spin-rotation-invariant fermion bilinears that can give rise to a transverse thermal conductivity, thus leading to the absence of a thermal Hall effect. The Zeeman coupling is found to gap out two-thirds of the z=3z=3z=3 excitations near the intersection point and this leads to a suppression of the low-temperature specific heat, the spin susceptibility, and the Wilson ratio. We also compute physical properties in the presence of weak disorder and discuss possible connections to recent experiments on organic insulators.
In this paper, we generalize the fermionic representation for S=1/2S=1/2S=1/2 spins to arbitrary spins. Within a mean field theory we obtain several spin liquid states for spin S=1S=1S=1 antiferromagnets on triangular lattices, including gapless fff-wave spin liquid and topologically nontrivial px+ipy{p}_{x}+i{p}_{y}px​+ipy​ spin liquid. After considering different competing orders, we construct a phase diagram for the ${J}_{1}\ensuremath{-}{J}_{3}\ensuremath{-}K$ model. The application to recently discovered material NiGa2S4{\text{NiGa}}_{2}{\text{S}}_{4}NiGa2​S4​ is discussed.
Abstract Motivated by the fact that the study of disordered phases at zero temperature is of great interest, I study the spin-one quantum antiferromagnet with a next-nearest neighbor interaction on a triangular lattice with bilinear and biquadratic exchange interactions and a single ion anisotropy, using a SU(3) Schwinger boson mean-field theory. I calculate the critical properties, at zero temperature, for values of the single ion anisotropy parameter D above a critical value D C , where a quantum phase transition takes place from a higher D disordered phase to a lower D ordered phase.
Phase diagrams and excitations of anisotropic S=1S=1S=1 quantum magnets on the triangular lattice
The S=1S=1S=1 bilinear-biquadratic Heisenberg exchange model on the triangular lattice with a single-ion anisotropy has previously been shown to host a number of exotic magnetic and nematic orders [Moreno-Cardoner et al.\textit{et al.}et al., Phys. Rev. B 90\textbf{90}90, 144409 (2014)], including an extensive region of "supersolid" order. In this work, we amend the model by an XXZ anisotropy in the exchange interactions. Tuning to the limit of an exactly solvable S=1S=1S=1 generalized Ising-/Blume-Capel-type model provides a controlled limit to access phases at finite transverse exchange. Notably, we find an additional macroscopically degenerate region in the phase diagram and study its fate under perturbation theory. We further map out phase diagrams as a function of the XXZ anisotropy parameter, ratio of bilinear and biquadratic interactions and single-ion anisotropy, and compute corrections to the total ordered moment in various phases using systematically constructed linear flavor-wave theory. We also present linear flavor-wave spectra of various states, finding that the lowest-energy band in three-sublattice generalized (i.e. with Sz=±1,0S^z=\pm1,0Sz=±1,0) Ising/Blume-Capel states, stabilized by strong exchange anisotropies, is remarkably flat, opening up the way to flat-band engineering of magnetic excitation via stabilizing non-trivial Ising-ordered ground states.