1. Spin-Orbital Short-Range Order in the Honeycomb Based Lattice of Ba3CuSb2O9 [1.1]
Quantum liquid robust against disorder
Nature favors the lowest energy so called ground state of a system, but at high temperatures disorder, called entropy, is dominant and provides the driving force for fascinating behavior such as phase transition from solid to liquid and from liquid to gas. Conversely, when temperature is lowered, the system solidifies because atoms or molecules, which move relatively freely in gas or liquid phase, spontaneously break the symmetry of the system to reduce its energy, leading to variety of intriguing phenomena. However, in some cases the liquid state can survive down to lowest temperature by lowering its quantum mechanical energy, which is known as quantum liquid. Examples are the superfluidity of Helium and the superconductivity of electrons. These quantum states have attracted much attention not only as a scientific subject of importance, but also as a subject in an applied research because of its robustness against disorder and the absence of dissipation at the quantum level.
Figure 1.1 Crystal structure with short-ranged honeycomb-based lattice of Ba3CuSb2O9
Figure 1.2 Quantum state formed by cooperative phenomenon of spins and orbitals. Upper panel: Resonant state of spins arising from orbital order with ring pattern. Neighboring orbitals (green) forms a ferro-order. Arrows (blue and green) and blue shaded regions indicate spin-singlet dimers having a spin gap. Bottom panel: Resonant state of spins and orbitals. This corresponds to resonance state of pi electrons in benzene.
Recent studies on magnets revealed that, under particular circumstances, the spins and orbitals which carry magnetism can remain liquid down to the lowest temperature with unbroken symmetry. This unusual behavior has attracted much attention because of its possibility as a new quantum liquid. It has been recognized, however, that such a liquid state of spin or orbital character is fragile and is easily frozen by, for example, structural disorder in magnets. In the present study on a copper oxide, we have discovered a new quantum liquid state that is robust against disorder by controlling cooperative phenomenon of spins and orbitals in electrons of copper atoms [1.1].
Figure 1.3 Energy gap of spin liquid state revealed by inelastic neutron scattering experiments at 25 K.
The material is Ba3CuSb2O9, consisting of electric dipoles formed by a pair of divalent copper ions (Cu) and pentavalent antimony ions (Sb). This material was previously considered to be a ferroelectric in which the electric dipoles form a triangular lattice [1.2,1.3]. However, our recent diffraction measurements using synchrotron x-ray at SPring-8 revealed that the intrinsic aspect of this material is frustration on triangular lattice, and, as a result, the electric dipoles spontaneously form a short range ordering, which intrisically stabilizes the disordered honeycomb lattice of CuO6 octahedra against the Jahn-Teller distortion (Fig. 1.1).
Generally, cations with orbital degrees of freedom exhibit orbital order by lowering the symmetry of the spatial distribution of surrounding anions (ligands) so that the electrostatic energy of each orbital is reduced. This phenomenon is called “Jahn-Teller phase transition”. The typical example of this phenomena are copper oxide based materials famous for high-temperature superconductivity, and it is known that all copper oxide based materials have a Jahn-Teller phase transition. In this work we have performed a comprehensive study of structural and magnetic properties of Ba3CuSb2O9 using high-quality single crystal samples, and discovered that this material shows neither magnetic ordering nor a macroscopic Jahn-Teller phase transition down to low temperature. In addition, neutron scattering measurements (US-Japan Cooperative Program) revealed that copper ions form a dimer, a local resonant state of S=1/2 of a copper ion and a neighboring copper ion (Figs. 1.2 and 1.3). On the other hand, X-ray absorption fine structure measurements found that all copper ion sites undergo Jahn-Teller distortion for short time scale as well as for local length scale. These observations indicate two possibilities: firstly, the orbitals order with a ring pattern along the honeycomb hexagon so that the spins can form the pair of the local spin dimer and secondly, both spins and orbitals cooperatively form a dynamic state which is a quantum mechanical resonant state (Fig. 1.2).
The realization of state without macroscopic Jahn-Teller phase transition in copper oxides is quite remarkable, and this state may stabilize a spin liquid, a novel quantum mechanical state. Furthermore, this state originates from a self-assembly of copper ions due to the electrostatic interaction between electric dipoles made by copper and antimony. This indicates that the quantum properties in condensed matter can be controlled using the pattern of electric dipoles, and provides an importance guide for future materials development. The present discovery of a material that shows quantum liquid state robust against disorder can open a new route to exploring materials required for the practical development of quantum information processing and quantum computing.[1.1] S. Nakatsuji, K. Kuga, K. Kimura, R. Satake, N. Katayama, E. Nishibori, H. Sawa, R. Ishii, M. Hagiwara, F. Bridges, T. U. Ito, W. Higemoto, Y. Karaki, M. Halim, A. A. Nugroho, J. A. Rodriguez-Rivera, M. A. Green, C. Broholm, Science 336, 559 (2012).
2. Observation of the orbital quantum dynamics in the spin-1/2 hexagonal antiferromagnet Ba3CuSb2O9
In condensed matter physics, exploration of a novel quantum liquid state, such as Bose-Einstein condensation of cold atoms, superconductivity and quantum Hall state of electron systems, has been a subject of intense research both experimentally and theoretically. While many candidates of “quantum spin liquid” in which spin degrees of freedom does not freeze even at very low temperatures have been reported, almost no example has been found for an orbital liquid state, where the orbital degree of freedom remain fluctuating without lattice deformation down to a very low temperature. In our previous studies on the copper oxide 6H- Ba3CuSb2O9 with a perovskite structure, we reported the first observation of striking absence of the static Jahn-Teller distortion down to the lowest temperature in this oxide based on copper (II), which is known as a strong Jahn-Teller active ion [2.1,2.2]. However, to date, the orbital dynamics have never been investigated.
In the present study, we have determined the frequency of the orbital quantum fluctuation in this compound by multi-frequency electron spin resonance (ESR) measurements in high magnetic fields [2.3]. We report the first determination of the orbital fluctuating frequencies, namely dynamic Jahn-Teller frequencies, at wide temperature range between 1.5 K and 100 K. The aforementioned results pave the way to investigate the dynamics of a new quantum liquid state named “quantum spin-orbital liquid” by multi-frequency ESR in high magnetic fields. The results demonstrate how high magnetic fields are useful for the studies on a quantum spin-orbital-liquid state.
Figure 2.1 The possible dynamic orbital states in the hexagonal sample, which form resonating singlet dimers in the honeycomb-based lattice. The light blue ovals show the temporally averaged special distribution of the copper orbitals.
[2.1] S. Nakatsuji et al., Science 336, 559-563 (2012).Figure 2.2 Temperature dependence of the dynamic Jahn-Teller fluctuating frequency (νJT) determined from the observed electromagnetic frequency (νEM) where the ESR signal line shape changes from symmetric to asymmetric. The solid circles show the fluctuating frequencies at measurement temperatures, and the frequencies become constant (about 10 GHz, 100 picosecond) below 20 K, indicating the formation of the quantum liquid state.
[2.2] N. Katayama et al., Proc. Natl. Acad. Sci. USA, 112, 9305-9309 (2015).
[2.3] Han et al., Phys. Rev. B 92, 180410(R) (2015).
3.Copper oxide with no static Jahn-Teller distortion
The quantum spin liquid (QSL) state has been intensively pursued since Anderson proposed the resonating valence bond model. For realizing a novel QSL state, orbital degree of freedom has been considered as a nuisance because orbital ordering usually appears at high temperature accompanying with a cooperative Jahn-Teller (JT) distortion and spin ordering. Therefore, the QSL candidates found so far have been mostly in spin only systems without orbital degree of freedom.
Perovskite-type 6H-Ba3CuSb2O9 is a novel candidate material for the spin-orbital liquid state, which we have reported recently [3.1]. In the material, spin-orbital short-range ordering occurs in the short-range honeycomb lattice of Cu2+ with e g orbital degrees of freedom, as shown in Fig. 3.1(a). Powder x-ray diﬀraction experiment shows that even at low temperatures, the hexagonal components remain along with some orthorhombically distorted components. In the hexagonal phase, three-fold symmetry exists for the Cu2+ sites which are surrounded by octahedrally coordinated oxygen, indicating the absence of a cooperative JT distortion. To explain this unusual feature, we proposed two possible scenarios. (i) Orbital glass state with a non-cooperative static JT distortion. In this scenario, the local symmetry is lowered by a static JT distortion, as schematically shown in Fig. 3.1(b), but the overall hexagonal symmetry remains. (ii) Spin-orbital liquid state. The static JT distortion is absent and instead, a dynamic JT distortion appears, leading to a novel spin-orbital liquid state, as depicted in Fig. 3.1(c). These two possible scenarios cannot be distinguished by experimental results using powder specimens alone. A thorough structural study using a single crystal without orthorhombic components is required.
Our progress in preparing single crystalline samples enabled us to obtain single crystalline samples without any orthorhombic components down to the lowest temperature. Figures 3.2(a) and 3.2(b) show single crystal x-ray diffraction experimental data. The peaks show no signs of splitting or broadening down to 20 K, the lowest temperature of our measurements (“hexagonal sample”). The hexagonal sample can be well reﬁned by using the centro-symmetric space groupP63/mmc for all temperatures. For P63/mmc, the three-fold symmetry is retained for Cu 2+ sites, indicating the absence of the cooperative JT distortion. These observations are in sharp contrast with our previous single crystal x-ray diﬀraction study of 6H-Ba3CuSb2O9. There, we reported that the Bragg peak splits into several separate reﬂections upon decreasing temperature, as shown in Figs. 3.2(c) and 3.2(d). This result indicates that the hexagonal P63/mmc symmetry is lowered to the orthorhombic Cmcm symmetry (“orthorhombic sample”). We attribute this eﬀect to a cooperative JT distortion induced by uniform ferro-orbital ordering of Cu2+ ions (Fig.3.1(d)).
While x-ray diffraction experiment gives us the averaged structural information, the electron spin resonance (ESR) enables us to study the local orbital conﬁguration. Using the single crystals, we confirmed the isotropic g factors are realized within the in-plane directions in the hexagonal samples down to 3.5 K, clearly indicating that the non-cooperative JT scenario is not realized and instead, a dynamic JT distortion appears [3.2]. Further studies using the crystals will address the open questions on the quantum spin-orbital liquid state, such as the orbital dynamics and the mechanism to stabilize such an exotic liquid state.
Fig. 3.1. (a) Schematic view of the local structure for hexagonal and orthorhombic samples. (b) Schematic picture of a non-cooperative static JT distortion. (c) and (d) Schematic pictures of spin-singlet formation in short-range honeycomb lattices of Cu2+ for (c) hexagonal and (d) orthorhombic samples.
Fig. 3.2. Single crystal x-ray diﬀraction proﬁles for (a-b) hexagonal and (c-d) orthorhombic samples. The insets in (a) and (c) are photographs of the transparent brown single crystals for the hexagonal and orthorhombic samples, respectively. The hexagonal samples are darker than the orthorhombic samples.
[3.1] S. Nakatsuji et al., Science 336, 559-563 (2012).
[3.2] N. Katayama et al., Proc. Natl. Acad. Sci. USA, 112, 9305-9309 (2015).