At low temperatures, atomic magnetic moments usually exhibit some order, for example ferromagnetic order. An exception is frustrated magnets, in which the symmetry impedes the minimization of energy by pairwise magnetic interactions. In such frustrated magnets, new quantum phases, such as spin liquids, are expected. Theoretically, a quantum liquid based on the orbital degree of freedom has also been considered possible when spin and orbital degrees of freedom are entangled. However, to date, experimental observation of such a dynamic spin-orbital state has been a challenge. Here we report an X-ray scattering study of a dynamic spin-orbital state in the frustrated magnet Ba 3 CuSb 2 O 9 . Orbital dynamical motion and increasing short-range orbital correlation with cooling are observed. The most significant feature is that the temperature variation of the orbital correlation is clearly affected by the magnetic interaction. This finding strongly supports a new quantum state in which spins and orbitals are entangled.
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 ...
Structural fluctuation in Ba 3 CuSb 2 O 9 , which is proposed to exhibit a spin-orbital entangled state, has been studied by diffuse x-ray scattering, x-ray fluorescence holography, and inelastic x-ray scattering. Two kinds of spatial fluctuations are observed: temperature-independent and temperature-dependent ones. The former is related to Cu/Sb arrangement. The short-range chemical correlation in Ba 3 CuSb 2 O 9 is honeycomblike, whereas the correlation length is as short as the diameter of the honeycomb unit. The temperature variation of ferro-and antiferro-orbital correlations is extracted from Huang scattering intensity distributions. Both of these correlations increase with decreasing temperature down to 60 K, which corresponds to the energy of magnetic interaction of Ba 3 CuSb 2 O 9 . A wide distribution of the characteristic time scale of the orbital motion is proposed from the spatial fluctuation of the ionic arrangement in Ba 3 CuSb 2 O 9 .
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