Experimental realization of a quantum spin liquid (QSL) state is among the central topics of condensed matter physics. In a QSL state, spins do not form long-range order even down to absolute zero, characterized by strong long-range entanglement[1]. Geometric frustrations and competing interactions are central ingredients to realizing QSL states. However, almost all candidate materials discovered possess chemical or structural disorders. Thus, it is crucial to understand the role of structural disorders. Can structural disorder be a factor that stabilizes a QSL state, as proposed in some theoretical studies [2]? How to experimentally distinguish the effects of structural disorders from that induced by the intrinsic lattice dynamics?

To answer these questions, we performed Raman scattering spectroscopy to separate dynamic lattice effects from the structural disorders on the Pr-based pyrochlore oxides Pr₂Zr₂O₇ and Pr₂Ir₂O₇[3,4]. Both materials host exotic ground states without long-range orders. Their CEF ground state is an Eg non-Kramers doublet, which is unprotected by the time-reversal symmetry and thus can be split by a slight deviation from the D3d local symmetry. As a result, structural disorders may play an essential role in shaping the ground-state properties of both systems. 

Our Raman studies reveal that splitting of the ground state E_g doublet and the E_g doublet at 55 meV results from different physical origins [3]. Figures 1(a) and (b) show the Raman spectra of CEF excitation and the CEF level scheme of Pr₂Zr₂O₇ at 14 K, respectively. The E_g level at 55 meV is split by the T_2g phonons instead of structural disorder. The observed splitting characterized by a well-defined symmetry can only occur in the presence of mixing with another excitation of E symmetry, leading to a vibronic state (Fig. 1(c)). Based on DFT calculations, the vibronic state in Pr₂Zr₂O₇ is most likely driven by T_2g phonon lying at 64.6 meV at the Γ point (Fig. 1(d)). The associated eigenvectors involve motion of O1 oxygens that modulates the Pr³⁺ oxygen environment (Fig. 1(e)).

Fig. 1. (a) Raman spectra of Pr₂Zr₂O₇ at 14 K. (b) A schematic diagram of the Pr³⁺ CEF levels in Pr₂Zr₂O₇. (c) A schematic diagram of the vibronic coupling between the phonons and CEF states. (d) The Pr₂Zr₂O₇ phonon dispersion obtained by DFT calculations. The energy range close to the vibronic features is shown. Dashed blue lines represent the experimentally observed CEF vibronic excitations. The vibronic coupling is expected to occur at the intersection point of the nonsplit CEF doublet (solid blue line) and the T_2g phonon branch (red curve). (e) Atomic displacements of the T_2g phonon mode. Upper panel: View of the unit cell. Lower panel: PrO₈ octahedron site viewed from the [111] direction.

Our second study [4] reveals that Pr₂Zr₂O₇ exhibits phonon softening, which modulates the Pr-O-Pr angle and changes the magnetic super-exchange interaction. Compared to Pr₂Zr₂O₇, Pr₂Ir₂O₇ shows a similar but much broader phonon spectrum (Fig. 2). Given that the metallic Pr₂Ir₂O₇ features phonon-electron scattering mechanisms, which are absent in the insulating Pr₂Zr2O₇, the difference in their phonon spectrum is likely a result of phonon-electron scattering rather than disorders.

Fig. 2. Raman scattering spectra of (a) Pr₂Ir₂O₇ and (b) Pr₂Zr₂O₇ at 14 K in parallel polarization configuration.

References

• [1] P.W. Anderson, Mat. Res. Bull. 8, 153 (1973).
• [2] L. Savary and L. Balents, Phys. Rev. Lett. 118, 087203 (2017).
• [3] Y. Xu, H. Man, N. Tang, T. Ohtsuki, S. Baidya, S. Nakatsuji, D. Vanderbilt, and N. Drichko, Phys. Rev. B 89, 075137 (2022).
• [4] Y. Xu, H. Man, N. Tang, S. Baidya, H. Zhang, S. Nakatsuji, D. Vanderbilt, and N. Drichko, Phys. Rev. B 104, 075125 (2021).

Authors

• Y. Xu^a, H. Man^a, N. Tang, T. Ohtsuki, S. Baidya^b, S. Nakatsuji, D. Vanderbilt^b, and N. Drichko^a, and H. Zhang^b
• ^aJohn Hopkins University
• ^bRutgers University