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Possible Intermediate Quantum Spin Liquid Phase in α-RuCl3 under High Magnetic Fields up to 100 T

Y. Matsuda and Kindo Group

Quantum spin liquid (QSL) constitutes a topological state of matter in frustrated magnets, where the constituent spins remain disordered even down to absolute zero temperature and share long-range quantum entanglement. Due to the lack of rigorous QSL ground states, such ultra quantum spin states are less well-understood in systems in more than one spatial dimension before Alexei Kitaev introduced the renowned honeycomb model with bond-dependent exchange.

The 4d spin-orbit magnet α-RuCl3 has been widely accepted as a prime candidate for Kitaev material. This compound is now believed to be described by the K-J-Γ-Γ’ effective model that includes the Heisenberg J(1, 3), Kitaev exchange K, and the symmetric off-diagonal exchange terms. The Kitaev interaction originates from chlorine-mediated exchange through edge-shared octahedra arranged on a honeycomb lattice. Similar to most of Kitaev candidate, additional non-Kitaev terms, unfortunately, stabilize a zigzag antiferromagnetic order below TN ≈ 7 K in the compound. Given that, a natural approach to realizing the Kitaev QSL is to suppress the zigzag order by applying magnetic fields to the compound.

Recently, the theoretical studies point out an interesting two-transition scenario with a field-induced intermediate QSL phase under the out-of-plane magnetic field [1], which is later confirmed by a large Kitaev-term spin Hamiltonian also based on the K-J-Γ-Γ’ model [2]. With the precise model parameters determined from fitting the experimental thermodynamics data, they theoretically reproduced the suppression of zigzag order under the 7-T in-plane field, and find a gapless QSL phase located between two out-of-plane transition fields that are about 35 T and of 100-T class, respectively. However, because theoretical studies predict very high critical fields—where HlC ≈ 32.5 T and HlC is in 100-T range—they are challenging to observe experimentally.

In this work, we report the magnetization (M) process of α-RuCl3 by applying magnetic fields (H) in various directions within the honeycomb plane and along the c* axis (out-of-plane) up to 100 T, and find clear experimental evidence supporting the two-transition scenario. Here, the c* axis is the axis perpendicular to the honeycomb plane. Under fields applied along and close to the c* axis, an intermediate phase is found bounded by two transition fields HlC and HhC. In particular, besides the previously reported HlC ≈ 32.5 T [3], remarkably we find a second phase transition at a higher field HhC (higher than 83 T) [4]. Below HhC and above HlCthere exists an intermediate phase, i.e. the predicted field-induced QSL phase. When the field tilts an angle from the c* axis by 9°, only the transition field HC, is observed, indicating the intermediate QSL phase disappears. Accordingly, we also perform the density-matrix renormalization group (DMRG) calculations based on the previously proposed K-J-Γ-Γ’ model of α-RuCl3, and find the simulated phase transitions and extended QSL phase are in agreement with experiments. Therefore, we propose a complete field-angle phase diagram (as shown in Fig. 1) and provide the experimental evidence for the field-induced QSL phase in the prominent Kitaev compound α-RuCl3 [4].


References
  • [1] J. S. Gordon, A. Catuneanu, E. S. Sørensen, and H.-Y. Kee, Nat. Commun. 10, 2470 (2019).
  • [2] H Li, HK Zhang, J Wang, HQ Wu, Y Gao, DW Qu, ZX Liu, SS Gong, and W Li, Nat. Commun. 12, 4007 (2021).
  • [3] K. A. Modic, Ross D. McDonald, J. P. C. Ruff, M. D. Bachmann, Y. Lai, J. C. Palmstrom, D. Graf, M. K. Chan, F. F. Balakirev, J. B. Betts, G. S. Boebinger, M. Schmidt, M. J. Lawler, D. A. Sokolov, P. J. W. Moll, B. J. Ramshaw, and A. Shekhter, Nature Physics, 17, 240 (2021)
  • [4] Peer Review File of Nature Communications, 14(1), 5613 (2023).
  • [5] X.-G. Zhou, H. Li, Y. H. Matsuda, A Matsuo, W. Li, N. Kurita, G. Su, K. Kindo, H. Tanaka, Nature Communications, 14, 5613 (2023).
Authors
  • X.-G. Zhou, H. Lia, Y. H. Matsuda, A. Matsuo, W. Lia, N. Kuritab, G. Sua, K. Kindo , H. Tanakab
  • aChinese Academy of Sciences
  • bTokyo Institute of Technology