Dynamical spin–orbital correlation in the frustrated magnet Ba3CuSb2O9

Ishiguro, Yuki; Kimura, Kazuhiro; Nakatsuji, Satoru; Tsutsui, Satoshi; Baron, Alfred Q. R.; Kimura, T.; Wakabayashi, Yusuke

doi:10.1038/ncomms3022

Cited by 47 publications

(72 citation statements)

References 26 publications

(34 reference statements)

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“…Noncooperative static JT distortion must break threefold symmetry in each Cu 2+ site and generate anisotropic g factors within the in-plane directions in ESR experiments, similarly to the low-temperature phase of the orthorhombic sample, thus clearly inconsistent with our observations for the hexagonal sample. Significantly, orbital degree of freedom exists at high temperatures in the present samples because the orthorhombic sample undergoes a cooperative JT transition at around 200 K, and, furthermore, a dynamic orbital state has been already confirmed at 290 K in a hexagonal sample using an inelastic X-ray scattering experiment (24). Thus, our study using the single crystals without any orthorhombic components has confirmed that the hexagonal sample shows no signs of symmetry lowering on cooling and further demonstrates the absence of the noncooperative static JT distortion in all temperature regions.…”

Section: Resultsmentioning

confidence: 99%

“…If the magnetic exchange interactions are enhanced to the point that they are comparable with the orbital energy, the interplay between spin and orbital would destabilize the conventional orbital-ordered state, leading to a novel spin-orbital entangled state. Indeed, such spin-orbital correlation has been already pointed out by using Huang scattering (24). According to the present structural study, the possible ground states have been already proposed theoretically, including a short-range resonating-valence bond state (25,26) and an emergent dimer state involving nearest-neighbor spin singlets with orbital order (27).…”

Section: Structural Differences Between the Hexagonal And Orthorhombicmentioning

confidence: 91%

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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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Section: Resultsmentioning

confidence: 99%

Section: Structural Differences Between the Hexagonal And Orthorhombicmentioning

confidence: 91%

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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“…Apart from the intrinsic anisotropy and the relative complexity of the orbital couplings, it has been shown that the interplay between the two frustrated degrees of freedom may lead to exotic states of matter. An x-ray scattering study of a dynamic spin-orbital state in the frustrated magnet Ba 3 CuSb 2 O 9 supports spin liquid state [28,29], while FeSc 2 S 4 [30][31][32] and the d 1 effective models on the triangular lattice [33] and on the honeycomb lattice [34,35] are found to be candidates for spin-orbital liquids in the theory. Recently remarkable progress was achieved due to rapidly developed resonant inelastic x-ray scattering (RIXS) techniques [36] which helped to explore the elementary excitations in Sr 2 CuO 3 [37,38] and Sr 2 IrO 4 [39], with antiferromagnetic (AF) and ferro-orbital (FO) order in ground states.…”

Section: Introductionmentioning

confidence: 96%

Quantum entanglement in the one-dimensional spin-orbitalSU(2)⊗XXZmodel

2015

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We investigate the phase diagram and the spin-orbital entanglement of a one-dimensional SU(2)⊗XXZ model with SU(2) spin exchange and anisotropic XXZ orbital exchange interactions and negative exchange coupling. As a unique feature, the spin-orbital entanglement entropy in the entangled ground states increases here linearly with system size. In the case of Ising orbital interactions we identify an emergent phase with long-range spin-singlet dimer correlations triggered by a quadrupling of correlations in the orbital sector. The peculiar translational invariant spin-singlet dimer phase has finite von Neumann entanglement entropy and survives when orbital quantum fluctuations are included. It even persists in the isotropic SU(2)⊗SU(2) limit. Surprisingly, for finite transverse orbital coupling the long-range spin singlet correlations also coexist in the antiferromagnetic spin and alternating orbital phase making this phase also unconventional. Moreover we also find a complementary orbital singlet phase that exists in the isotropic case but does not extend to the Ising limit. The nature of entanglement appears essentially different from that found in the frequently discussed model with positive coupling. Furthermore we investigate the collective spin and orbital wave excitations of the disentangled ferromagnetic-spin/ferro-orbital ground state and explore the continuum of spin-orbital excitations. Interestingly one finds among the latter excitations two modes of exciton bound states. Their spin-orbital correlations differ from the remaining continuum states and exhibit logarithmic scaling of the von Neumann entropy with increasing system size. We demonstrate that spin-orbital excitons can be experimentally explored using resonant inelastic x-ray scattering, where the strongly entangled exciton states can be easily distinguished from the spin-orbital continuum.

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“…In this Letter, we report the THE in Ba 3 CuSb 2 O 9 (BCSO) [23][24][25][26][27][28][29], which according to us is an ideal compound to study a phonon THE owing to its strong spinlattice coupling and the presence of a spin gap. The hexagonal (6H) perovskite-type BCSO [ Fig.…”

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Thermal Hall Effect in a Phonon-Glass Ba3CuSb2O9

et al. 2017

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A distinct thermal Hall signal is observed in a quantum spin liquid candidate Ba3CuSb2O9. The transverse thermal conductivity shows a power-law temperature dependence below 50 K, where a spin gap opens. We suggest that because of the very low longitudinal thermal conductivity and the thermal Hall signals, a phonon Hall effect is induced by strong phonon scattering of orphan Cu 2+ spins formed in the random domains of the Cu 2+ -Sb 5+ dumbbells in Ba3CuSb2O9.Hall measurements of metals are fundamental tools to investigate their physical properties and play important roles in the study of quantum phenomena, such as the quantum Hall effect or the anomalous Hall effect [1]. On the other hand, no Hall effect is expected in insulators because the Hall effect originates from conduction electrons. However, a Hall effect of charge-neutral excitations, which is observed as a thermal Hall effect (THE), has been predicted to occur in magnetic and non-magnetic insulators [2][3][4][5][6][7][8][9][10][11], thereby providing new insights into the research on quantum spin liquids and other frustrated materials. So far, three kinds of THEs have been reported in insulators: THEs of magnons in ordered magnets [12][13][14], spin excitations in disordered magnets [14][15][16], and phonon THEs [17,18]. Among them, the most studied case is the magnon THE which has been observed in ferromagnetic insulators [12][13][14] and is understood in terms of the Berry phase associated with the magnon bands [2,3]. The THEs of spin excitations in paramagnetic states have also been studied theoretically [2,4,5]; these THEs were reported recently in a spin ice compound Tb 2 Ti 2 O 7 [15], a ferromagnetic kagomé lattice system [14], and a frustrated kagomé lattice system [16].In contrast, reports on the THE of phonons have been limited to studies on a dielectric garnet Tb 3 Ga 5 O 12 (TbGG) [17,18]. The theoretical origin of the phonon THE has been discussed as a Raman-type interaction between phonons and large spins [6,7], a Berry curvature of phonon bands [8,9], and a resonant skew scattering of phonons by superstoichiometric Tb 3+ ions [10]. Experimentally, it has been determined that there is a large magneto-elastic coupling in TbGG [19,20]. Moreover, the smaller thermal conductivity of TbGG than that of other rare-earth gallium garnets indicates that there is strong scattering of phonons by the Tb 3+ ions [21,22]. These observations imply that the strong phonon scattering is important for the THE. However, the mechanism for the THE in TbGG is poorly understood because the measurement of the THE in TbGG has been limited only to ∼5 K [17,18]. Furthermore, because TbGG is paramagnetic at 5 K, it is impossible to separate the THE of phonons from that of spins. Thus, to investigate the phonon THE, it is crucial to observe the THE over a wide temperature range in a single crystal that has strong phonon scattering and no spin THE.In this Letter, we report the THE in Ba 3 CuSb 2 O 9 (BCSO) [23][24][25][26][27][28][29], which according to us is an ideal c...

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Dynamical spin–orbital correlation in the frustrated magnet Ba3CuSb2O9

Cited by 47 publications

References 26 publications

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

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

Quantum entanglement in the one-dimensional spin-orbitalSU(2)⊗XXZmodel

Thermal Hall Effect in a Phonon-Glass Ba3CuSb2O9

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Dynamical spin–orbital correlation in the frustrated magnet Ba3CuSb2O9

Cited by 47 publications

References 26 publications

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

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

Quantum entanglement in the one-dimensional spin-orbitalSU(2)⊗XXZmodel

Thermal Hall Effect in a Phonon-Glass Ba3CuSb2O9

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

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