Stacking orders and magnetic ground state in the Kitaev antiferromagnet α-RuCl3*

Quantum spin liquids (QSLs) are of great interest in condensed matter physics due to the strong quantum fluctuations rising from the infinite manifolds of the magnetic ground state. Among various mechanisms that stabilize QSLs, the Kitaev model has garnered significant attention because it is exactly solvable by expressing the Hamiltonian using Majorana fermion operators.  α-RuCl₃ is a recognized Kitaev quantum spin liquid candidate with unique properties such as quantized thermal-Hall effects, a fingerprint of the Majorana fermion modes. However, the sample-dependent thermal transport properties in α-RuCl₃ and the debated spin Hamiltonian calls for a conclusive understanding of its crystal structure and magnetic ground state, which has been elusive due to the complex stacking faults. Here, we investigated the stacking orders of several different α-RuCl₃ crystals, including one untwinned crystal, in their magnetic ordered state using neutron diffraction. While all crystals follow the rhombohedral ABC-stacking extinction rule, the intensities of equivalent rhombohedral-lattice Bragg peaks show systematic deviation from the C₃ symmetry, indicating a lower symmetry than R-3 in the long-ranged average structure. By introducing a degree of stacking disorder, we found that the low-temperature crystal structure of α-RuCl₃ follows the rhombohedral stacking but with stacking faults related to the monoclinic stacking history. The stacking faults present during the structural transition from the high-temperature monoclinic phase in a chiral manner. It also ensures the low-temperature structure phase can be returned to the high-temperature phase with the domain fraction as that before cooling, an interesting “memory effect”. The stacking defects explain the two-fold symmetry in torque, susceptibility, and other anisotropic measurements. Understanding the crystal structure allows precise determination of the ordered magnetic moment size and orientations in the zigzag magnetic ground state. Our result serves as the basis for constructing the spin Hamiltonians and understanding the different thermal-Hall effect observations.