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 [1,2]. However, to date, the orbital dynamics have never been investigated.

Fig. 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.

Fig. 2. Temperature dependence of the dynamic Jahn-Teller fluctuating frequency (ν_JT) determined from the observed electromagnetic frequency (ν_EM) 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.

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 [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.

References

• [1] S. Nakatsuji et al., Science 336, 559 (2012).
• [2] N. Katayama et al., Proc. Natl. Acad. Sci. USA, 112, 9305 (2015).
• [3] Y. Han et al., Phys. Rev. B 92, 180410R (2015).

Authors

• M. Hagiwara^a and S. Nakatsuji
• ^aOsaka University