The emergence of resonating valence bond physics in spin–orbital models

Mila, Frédéric; Vernay, F.; Ralko, Arnaud; Becca, Federico; Fazekas, P.; Penc, Karlo

doi:10.1088/0953-8984/19/14/145201

Cited by 16 publications

(20 citation statements)

References 40 publications

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“…In particular, compass models appear in effective low energy description of quantum magnets that have a chiral degree of freedom (Budnik and Auerbach, 2004;Capponi et al, 2004;Ferrero et al, 2003;Mila et al, 2007). In these systems, the degree of freedom plays the role of the pseudo-spin with non-trivial directional dependence of the coupling.…”

Section: Chiral Degrees Of Freedom In Frustrated Magnetsmentioning

confidence: 99%

Compass models: Theory and physical motivations

2015

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Compass models are theories of matter in which the couplings between the internal spin (or other relevant field) components are inherently spatially (typically, direction) dependent. A simple illustrative example is furnished by the 90 • compass model on a square lattice in which only couplings of the form τ x i τ x j (where {τ a i }a denote Pauli operators at site i) are associated with nearest neighbor sites i and j separated along the x axis of the lattice while τ y i τ y j couplings appear for sites separated by a lattice constant along the y axis. Such compass-type interactions can appear in diverse physical systems. This includes Mott insulators with orbital degrees of freedom where interactions sensitively depend on the spatial orientation of the orbitals involved, the low energy effective theories of frustrated quantum magnets, vacancy centers and cold atomic gases. The fundamental inter-dependence between internal (spin, orbital, or other) and external (i.e., spatial) degrees of freedom which underlies compass models generally leads to very rich behaviors including the frustration of (semi-)classical ordered states on non-frustrated lattices and to enhanced quantum effects prompting, in certain cases, the appearance of zero temperature quantum spin liquids. As a consequence of these frustrations, new types of symmetries and their associated degeneracies may appear. These intermediate symmetries lie midway between the extremes of global symmetries and local gauge symmetries and lead to effective dimensional reductions. We review compass models in a unified manner, paying close attention to exact consequences of these symmetries, and to thermal and quantum fluctuations that stabilize orders via order out of disorder effects. This is complemented by a survey of numerical results.

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Section: Chiral Degrees Of Freedom In Frustrated Magnetsmentioning

confidence: 99%

Compass models: Theory and physical motivations

2015

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“…Perovskite-type 6H-Ba 3 CuSb 2 O 9 is a good candidate material for the spin-orbital liquid state that has been theoretically proposed (9)(10)(11). Recently, we reported that spin-orbital short-range ordering occurs in the short-range honeycomb lattice of Cu 2+ with e g orbital degrees of freedom, as depicted in Fig.…”

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confidence: 96%

Absence of Jahn−Teller transition in the hexagonal Ba ₃ CuSb ₂ O ₉ single crystal

Katayama

Kimura

Han

et al. 2015

Proc. Natl. Acad. Sci. U.S.A.

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With decreasing temperature, liquids generally freeze into a solid state, losing entropy in the process. However, exceptions to this trend exist, such as quantum liquids, which may remain unfrozen down to absolute zero owing to strong quantum entanglement effects that stabilize a disordered state with zero entropy. Examples of such liquids include Bose−Einstein condensation of cold atoms, superconductivity, quantum Hall state of electron systems, and quantum spin liquid state in the frustrated magnets. Moreover, recent studies have clarified the possibility of another exotic quantum liquid state based on the spin-orbital entanglement in FeSc 2 S 4 . To confirm this exotic ground state, experiments based on single-crystalline samples are essential. However, no such single-crystal study has been reported to date. Here, we report, to our knowledge, the first single-crystal study on the spin-orbital liquid candidate, 6H-Ba 3 CuSb 2 O 9 , and we have confirmed the absence of an orbital frozen state. In strongly correlated electron systems, orbital ordering usually appears at high temperatures in a process accompanied by a lattice deformation, called a static Jahn−Teller distortion. By combining synchrotron X-ray diffraction, electron spin resonance, Raman spectroscopy, and ultrasound measurements, we find that the static Jahn−Teller distortion is absent in the present material, which indicates that orbital ordering is suppressed down to the lowest temperatures measured. We discuss how such an unusual feature is realized with the help of spin degree of freedom, leading to a spin-orbital entangled quantum liquid state.Q uantum spin liquids have been widely recognized as a new state of matter, as an increasing number of candidates with quantum spin S = 1/2 have been found recently (1-4), a long time after the first proposal was made for the resonating valence-bond state (5). On the other hand, quantum liquids based on another electronic degree of freedom, orbital, have been theoretically proposed (6). However, this type of liquid state has never been experimentally confirmed because the energy of orbital correlation is normally one order of magnitude stronger than spin exchange coupling, leading to an orbital ordering at a significantly high temperature accompanied by a cooperative Jahn-Teller (JT) distortion. Nevertheless, if we can bring down the orbital energy to the same scale as for the spin coupling, it may lead to a novel spin-orbital entangled state, a "quantum spin-orbital liquid." A possible spin-orbital entangled liquid state with dimer correlations has been theoretically discussed on a triangular lattice with singly occupied but triply degenerate t 2g orbitals (7). In comparison with the t 2g orbitals' case, the experimental realization of such a quantum spin-orbital liquid state in the e g orbital system has been even more challenging (8), because e g orbitals more strongly couple to the JT modes.Perovskite-type 6H-Ba 3 CuSb 2 O 9 is a good candidate material for the spin-orbital liquid state that has been ...

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“…The orbital degree of freedom also has an intrinsic frustration effect even without geometrical frustration; all bond energies in a certain orbitally ordered state cannot be minimized simultaneously. From these points of view, the QSL states in magnets with the orbital degeneracy, as well as the spin-orbital quantum liquid states, have been proposed theoretically [8][9][10][11][12], and candidate materials, such as LiNiO 2 and FeSc 2 S 4 , have been examined experimentally [13,14].…”

Section: Introductionmentioning

confidence: 99%

“…The QDM is also applicable to the quantum magnets with orbitally degeneracy. A description of the resonant spin-orbital dimers was attempted in a triangular lattice system motivated from the experiments in LiNiO 2 [11]. A spin-orbital system in a honeycomb lattice is another candidate, in which the spin-dimer picture gives an appropriate description for the ground state.…”

Section: Introductionmentioning

confidence: 99%

Resonating valence-bond state in an orbitally degenerate quantum magnet with dynamical Jahn-Teller effect

Nasu

Ishihara

2015

Phys. Rev. B

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Short-range resonating-valence bond states in an orbitally degenerate magnet on a honeycomb lattice is studied. A quantum-dimer model is derived from the Hamiltonian which represents the superexchange interaction and the dynamical Jahn-Teller (JT) effect. We introduce two local units termed "spin-orbital singlet dimer", where two spins in a nearest-neighbor bond form a singlet state associated with an orbital polarization along the bond, and "local JT singlet", where an orbital polarization is quenched due to the dynamical JT effect. A derived quantum-dimer model consists of the hopping of the spin-orbital singlet dimers and the JT singlets, and the chemical potential of the JT singlets. We analyze the model by the mean-field approximation, and find that a characteristic phase, termed "JT liquid phase", where both the spin-orbital singlet dimers and the JT singlets move quantum mechanically, is realized. Possible scenarios for the recently observed non magnetic-ordered state in Ba3CuSb2O9 are discussed.

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The emergence of resonating valence bond physics in spin–orbital models

Cited by 16 publications

References 40 publications

Compass models: Theory and physical motivations

Compass models: Theory and physical motivations

Absence of Jahn−Teller transition in the hexagonal Ba ₃ CuSb ₂ O ₉ single crystal

Resonating valence-bond state in an orbitally degenerate quantum magnet with dynamical Jahn-Teller effect

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The emergence of resonating valence bond physics in spin–orbital models

Cited by 16 publications

References 40 publications

Compass models: Theory and physical motivations

Compass models: Theory and physical motivations

Absence of Jahn−Teller transition in the hexagonal Ba 3 CuSb 2 O 9 single crystal

Resonating valence-bond state in an orbitally degenerate quantum magnet with dynamical Jahn-Teller effect

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Absence of Jahn−Teller transition in the hexagonal Ba ₃ CuSb ₂ O ₉ single crystal