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arXiv:1408.1963

Spin susceptibility anomaly in cluster Mott insulators on a partially-filled anisotropic Kagome lattice: applications to LiZn2Mo3O8

Gang Chen, Hae‐Young Kee, Yong Baek Kim

Published Aug 8, 2014• 1 citation
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Abstract

Motivated by recent experiments on the quantum-spin-liquid candidate material LiZn2Mo3O8, we study a single-band extended Hubbard model on an anisotropic Kagome lattice with the 1/6 electron filling. Due to the partial filling of the lattice, the inter-site repulsive interaction is necessary to generate Mott insulators, where electrons are localized in clusters, rather than at lattice sites. We provide examples of such cluster Mott insulators and study the phase transitions between metallic states and cluster Mott insulators on an anisotropic Kagome lattice. It is shown that these cluster Mott insulators are generally U(1) quantum spin liquids with spinon Fermi surfaces. However, the nature of charge excitations in different cluster Mott insulators could be quite different and we show that there exists a novel cluster Mott insulator where charge fluctuations around the hexagonal cluster induce a plaquette charge order (PCO). The spinon excitation spectrum in this spin-liquid cluster Mott insulator is reconstructed due to the PCO so that only 1/3 of the total spinon excitations are magnetically active. The strong coupling limit of the same model is also analyzed via a Kugel-Khomskii-like model. Based on these results, we propose that the anomalous behavior of the finite-temperature spin-susceptibility in LiZn2Mo3O8 may be explained by finite-temperature properties of the cluster Mott insulator with the PCO as well as fractionalized spinon excitations. Existing and possible future experiments on LiZn2Mo3O8, and other Mo-based cluster magnets are discussed in light of these theoretical predictions.

DOI
10.48550/arxiv.1408.1963

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Motivated by recent experiments on the quantum-spin-liquid candidate material LiZn2Mo3O8, we study a single-band extended Hubbard model on an anisotropic Kagome lattice with the 1/6 electron filling. Due to the partial filling of the lattice, the inter-site repulsive interaction is necessary to generate Mott insulators, where electrons are localized in clusters, rather than at lattice sites. We provide examples of such cluster Mott insulators and study the phase transitions between metallic states and cluster Mott insulators on an anisotropic Kagome lattice. It is shown that these cluster Mott insulators are generally U(1) quantum spin liquids with spinon Fermi surfaces. However, the nature of charge excitations in different cluster Mott insulators could be quite different and we show that there exists a novel cluster Mott insulator where charge fluctuations around the hexagonal cluster induce a plaquette charge order (PCO). The spinon excitation spectrum in this spin-liquid cluster Mott insulator is reconstructed due to the PCO so that only 1/3 of the total spinon excitations are magnetically active. The strong coupling limit of the same model is also analyzed via a Kugel-Khomskii-like model. Based on these results, we propose that the anomalous behavior of the finite-temperature spin-susceptibility in LiZn2Mo3O8 may be explained by finite-temperature properties of the cluster Mott insulator with the PCO as well as fractionalized spinon excitations. Existing and possible future experiments on LiZn2Mo3O8, and other Mo-based cluster magnets are discussed in light of these theoretical predictions.
Motivated by recent experiments on the quantum-spin-liquid candidate material LiZn2Mo3O8{\mathrm{LiZn}}_{2}{\mathrm{Mo}}_{3}{\mathrm{O}}_{8}LiZn2​Mo3​O8​, we study a single-band extended Hubbard model on an anisotropic kagome lattice with the 16\frac{1}{6}61​ electron filling. Due to the partial filling of the lattice, the intersite repulsive interaction is necessary to generate Mott insulators, where electrons are localized in clusters rather than at lattice sites. It is shown that these cluster Mott insulators are generally U(1) quantum spin liquids with spinon Fermi surfaces. The nature of charge excitations in cluster Mott insulators can be quite different from conventional Mott insulator and we show that there exists a cluster Mott insulator where charge fluctuations around the hexagonal cluster induce a plaquette charge order (PCO). The spinon excitation spectrum in this spin-liquid cluster Mott insulator is reconstructed due to the PCO so that only 13\frac{1}{3}31​ of the total spinon excitations are magnetically active. Based on these results, we propose that the two Curie-Weiss regimes of the spin susceptibility in LiZn2Mo3O8{\mathrm{LiZn}}_{2}{\mathrm{Mo}}_{3}{\mathrm{O}}_{8}LiZn2​Mo3​O8​ may be explained by finite-temperature properties of the cluster Mott insulator with the PCO as well as fractionalized spinon excitations. Existing and possible future experiments on LiZn2Mo3O8{\mathrm{LiZn}}_{2}{\mathrm{Mo}}_{3}{\mathrm{O}}_{8}LiZn2​Mo3​O8​, and other Mo-based cluster magnets are discussed in light of these theoretical predictions.
Motivated by the recent developments on cluster Mott insulating materials such as the cluster magnet LiZn2Mo3O8{\mathrm{LiZn}}_{2}{\mathrm{Mo}}_{3}{\mathrm{O}}_{8}LiZn2​Mo3​O8​, we consider the strong plaquette charge ordered regime of the extended Hubbard model on a breathing kagome lattice and reveal the properties of the cluster Mottness. The plaquette charge order arises from the intersite charge interaction and the collective motion of three localized electrons on the hexagon plaquettes. This model leads naturally to a reduction of the local moments by 2/3, as observed in LiZn2Mo3O8{\mathrm{LiZn}}_{2}{\mathrm{Mo}}_{3}{\mathrm{O}}_{8}LiZn2​Mo3​O8​. Furthermore, at low temperatures, each hexagon plaquette contains an extra orbital-like degree of freedom in addition to the remaining spin 1/2. We explore the consequence of this emergent orbital degree of freedom. We point out the interaction between the local moments is naturally described by a Kugel-Khomskii spin-orbital model. We develop a parton approach and suggest a spin-liquid ground state with spinon Fermi surfaces for this model. We further predict an emergent orbital order when the system is under a strong magnetic field. Various experimental consequences for LiZn2Mo3O8{\mathrm{LiZn}}_{2}{\mathrm{Mo}}_{3}{\mathrm{O}}_{8}LiZn2​Mo3​O8​ are discussed, including an argument that the charge ordering must be short ranged if the charge per Mo is slightly off stoichiometric.
We study the Mott transition from a metal to cluster Mott insulators in the 1/4- and 1/8-filled pyrochlore lattice systems [corrected]. It is shown that such Mott transitions can arise due to charge localization in clusters or in tetrahedron units, driven by the nearest-neighbor repulsive interaction. The resulting cluster Mott insulator is a quantum spin liquid with a spinon Fermi surface, but at the same time a novel fractionalized charge liquid with charge excitations carrying half the electron charge. There exist two emergent U(1) gauge fields or "photons" that mediate interactions between spinons and charge excitations, and between fractionalized charge excitations themselves, respectively. In particular, it is suggested that the emergent photons associated with the fractionalized charge excitations can be measured in x-ray scattering experiments. Various other experimental signatures of the exotic cluster Mott insulator are discussed in light of candidate materials with partially filled bands on the pyrochlore lattice.
Mott insulators with localized magnetic moments will exhibit a quantum spin liquid state when the quantum fluctuations are strong enough to suppress the ordering of the spins. Such an entangled state will give rise to collective excitations, in which spin and charge information are carried separately. Our angle-resolved photoemission spectroscopy measurements on single-layer 1T-TaS_{2} show a flat band around the zone center and a gap opening of about 200 meV in the low temperature, indicating 2D Mott insulating nature in the system. This flat band is dispersionless in momentum space but shows anomalously broad width around the zone center and the spectral weight decays rapidly as momentum increases. The observation is described as a spectral continuum from electron fractionalization, corroborated by a low energy effective model. The intensity of the flat band is reduced by surface doping with magnetic adatoms and the gap is closing, a result from the interaction between spin impurities coupled with spinons and the chargons, which gives rise to a charge redistribution. Doping with nonmagnetic impurities behaves differently as the chemical potential shift dominates. These findings provide insight into the quantum spin liquid states of strongly correlated electrons on 2D triangular lattices.
The Kagome lattice Fermi-Hubbard model is one of the most physically rich, and at the same time most challenging, models to study in strongly-correlated physics. Among its special features are geometric frustration and a flat energy band that create conditions favorable to ferromagnetism near the band insulating limit. Here, we utilize two exact finite-temperature methods, the numerical linked-cluster expansion and the determinant quantum Monte Carlo, to study the extent as well as doping and interaction dependence of ferromagnetic correlations and other thermodynamic properties of the model. We find that repulsive interactions enhance ferromagnetic correlations at high electron densities and that increasing the interaction strength, extends the region with strong ferromagnetic correlations towards half filling, smoothly connecting it to Nagaoka ferromagnetism near the Mott insulating region. We also use the charge compressibility to obtain an accurate estimate for the critical interaction strength for the metal-insulator transition at half filling. These results improve our understanding of the magnetic tendencies of the model away from half filling and pave the way for further studies, including with ultracold atoms in optical lattices.
We study the metal-insulator transition in the half-filled Hubbard model on a Kagome lattice using the variational cluster approximation. The strong coupling limit of the model corresponds to the S=1/2S=1/2S=1/2 Kagome Heisenberg antiferromagnet, which is known to have a singlet ground state, although its detail is still debated. As the results of the cluster methods generally depend much on the choice of the unit cluster, we have chosen the clusters that are compatible with these singlet ground states in the strong coupling case found so far, which basically consist of even number of sites. It is found that the correlated electrons on the Kagome lattice have a strong tendency to form valence-bond structures, which are the resonation of electrons on a single bond or several bonds forming loops. The zero-temperature metal-insulator transition at some interaction strength is possibly driven by the formation of such short range valence bonds and shows a second order character, which is distinctive from the Brinkman-Rice scenario. The electrons on these valence bonds further localizes onto each site as the interaction increases, and the valence bonds of electrons finally turn into magnetic singlet bonds between localized S=1/2S=1/2S=1/2 spins, which are consistent with the ground states of the Kagome antiferromagnet.