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Odd-Parity Multipole Order in the Spin-Orbit Coupled Metallic Pyrochlore Pb2Re2O7−δ

PI of Joint-use project: D. Hirai
Host lab: Hiroi and Okamoto Groups

Transition metal compounds containing 4d and 5d electrons have attracted attention for their novel physical properties resulting from their strong spin–orbit interaction (SOI) [1,2]. L. Fu pointed out that SOI induces Fermi-liquid instability in metals, leading to the formation of various electronic phases, and proposed the concept of spin-orbit-coupled metals (SOCM) [3]. In SOCM, the strong SOI induces a structural phase transition with spontaneous spatial-inversion-symmetry breaking (ISB), which is associated with an unconventional odd-parity multipole ordering [4]. To date, the candidate compounds of SOCM are limited and only few of them have been experimentally verified. Progress in material development is key to reveal the diversity of electronic orders formed in SOCM and further scrutinize the physics of SOCM.

So far, many studies have focused on α-pyrochlore oxide Cd2Re2O7 (CRO), the most investigated candidate for SOCM [4]. Three successive structural phase transitions occur in CRO; an ISB transition from the regular pyrochlore structure (phase I) to the tetragonal phase II occurs at Ts1; on further cooling, transitions to an orthorhombic phase XI at Ts2 and to the tetragonal phase III at Ts3 occur. A theoretical work suggests that, in the phases II and III, the electronic order associated with ISB can be described by an odd-parity multipole order [3]. As depicted in Fig. 1, the displacements of Re atoms in phase II and III can be viewed as electric dipoles, certain pairs of which generate electric toroidal moments. These virtual electric toroidal moments are organized as x2y2 and 3z2r2 configurations, respectively. Thus, the emerged electronic orders are regarded as electric toroidal quadrupole (ETQ) orders [2]. This unconventional odd-parity multipole ordering will induce ETQ-driven phenomena, such as the spin-split Fermi surface, the magneto-current effect, and nonreciprocal transport in an applied magnetic field.

The relevant rhenium-containing pyrochlore oxide, Pb2Re2O7-δ (PRO), has also been reported to exhibit an ISB phase transition from the α-pyrochlore structure (phase I) to a noncentrosymmetric structure (phase II) at Ts = 300 K [5,6]. Based on the ISB transition and similarity in the physical properties with CRO, PRO likely to be a SOCM. Therefore, an odd-parity multipole order may be realized. However, the crystal structure of phase II, which is crucial to identify the multipole order, is contradicting; two different structures, a cubic F4-3m and a tetragonal I-4m2 structures are proposed [5,6]. Both crystal structures differ from that of CRO in the lowest temperature phase, which suggest a different multipole order is formed in PRO.

In this study, we investigated the low temperature phase of a SOCM candidate PRO by temperature-dependent synchrotron x-ray diffraction (XRD) measurements using single crystals [7]. As shown in Fig. 2, the appearance of superlattice peaks in the diffraction data of phase II indicates the violation of the d-glide plane derived extinction rule. To obtain more evidence for a lower crystal symmetry, we probed the temperature dependence of the two Bragg reflections (18 0 0) and (20 0 0) in phase I, as shown in Fig. 2 (c). Below Ts, the (18 0 0) reflection emerges upon cooling, indicating structural transition at Ts. In addition, the (20 0 0) reflection splits into two peaks (a low-angle and a high-angle peaks at an intensity ratio of approximately 2:1) demonstrating a cubic to tetragonal transition. It is noted that the (18 0 0) reflection is a single peak, not a double peak like the (20 0 0) reflection, demonstrating the presence of an additional extinction rule in phase II.

Since the phase transition at Ts is of second order, the group-subgroup relation of the space group is applied to deduce the space group of phase II. Based on the observed reflection conditions, we propose the I4122 space group for the phase II. This space group is identical to that of CRO in phase III.

The electronic order emerging in phase III of CRO is considered to be ETQ order with 3z2r2 component. Since the lowest temperature structure of CRO and PRO is revealed to be identical, 3z2r2-type ETQ is likely formed in the phase II of PRO. Here, 3z2r2-type order is selected as the ground state from the doubly degenerate x2y2 and 3z2r2-type ETQ orders. Electronic details about the origin of this symmetry breaking are of interest for future studies. Further comparison of the ISBs with respect to their origin and final manifestation in CRO and PRO would be useful for fundamental understanding of SOCM.


References
  • [1] T. Takayama, J. Chaloupka, A. Smerald, G. Khaliullin, and H. Takagi, J. Phys. Soc. Japan 90, 062001 (2021).
  • [2] L. Fu, Phys. Rev. Lett. 115, 026401 (2015).
  • [3] S. Hayami, Y. Yanagi, H. Kusunose, and Y. Motome, Phys. Rev. Lett. 122, 147602 (2019).
  • [4] Z. Hiroi, J.-I. Yamaura, T. C. Kobayashi, Y. Matsubayashi, and D. Hirai, J. Phys. Soc. Japan 87, 024702 (2018).
  • [5] K. Ohgushi, J. I. Yamaura, M. Ichihara, Y. Kiuchi, T. Tayama, T. Sakakibara, H. Gotou, T. Yagi, and Y. Ueda, Phys. Rev. B 83, 125103 (2011).
  • [6] C. Michioka, Y. Kataoka, H. Ohta, and K. Yoshimura, J. Phys. Condens. Matter 23, 445602 (2011).
  • [7] Y. Nakayama, D. Hirai, H. Sagayama, K. Kojima, N. Katayama, J. Lehmann, Z. Wang, N. Ogawa, and K. Takenaka, Phys. Rev. Mater. 8, 055001 (2024).
Authors
  • Y. Nakayamaa, D. Hiraia, H. Sagayamab, K. Kojimaa, N. Katayamaa, J. Lehmannc, Z. Wangc, N. Ogawac, and K. Takenakaa
  • aNagoya University
  • bKEK
  • cRIKEN