Low-temperature crystal and magnetic structure of $α$-RuCl3 (1602.08112v2)

Abstract: Single crystals of the Kitaev spin-liquid candidate $\alpha$-RuCl$3$ have been studied to determine low-temperature bulk properties, structure and the magnetic ground state. Refinements of x-ray diffraction data show that the low temperature crystal structure is described by space group $C2/m$ with a nearly-perfect honeycomb lattice exhibiting less than 0.2 \% in-plane distortion. The as-grown single crystals exhibit only one sharp magnetic transition at $T{N}$ = 7~K. The magnetic order below this temperature exhibits a propagation vector of $k$ = (0, 1, 1/3), which coincides with a 3-layer stacking of the $C2/m$ unit cells. Magnetic transitions at higher temperatures up to 14~K can be introduced by deformations of the crystal that result in regions in the crystal with a 2-layer stacking sequence. The best fit symmetry allowed magnetic structure of the as-grown crystals shows that the spins lie in the $ac$-plane, with a zigzag configuration in each honeycomb layer. The three layer repeat out-of-plane structure can be refined as a 120$^o$ spiral order or a collinear structure with spin direction 35$^o$ away from the $a$-axis. The collinear spin configuration yields a slightly better fit and also is physically preferred. The average ordered moment in either structure is less than 0.45(5) $\mu_B$ per Ru$^{3+}$ ion.

Low-Temperature Crystal and Magnetic Structure of $\alpha$-RuCl$_3$

The paper of $\alpha$-RuCl$_3$, a candidate for the Kitaev quantum spin liquid (QSL), reveals significant insights into its low-temperature crystal and magnetic structures. The paper explores single crystals of $\alpha$-RuCl$_3$, focusing on their structure and magnetic order at low temperatures. This compound is an excellent system for investigating QSL behaviors due to the presence of Ru$^{3+}$ ions, which are essential for realizing the Kitaev interactions.

Crystal Structure and Stacking Faults

The low-temperature crystal structure of $\alpha$-RuCl$_3$ is determined by x-ray diffraction, identifying a monoclinic $C2/m$ symmetry. Within this space group, a nearly perfect honeycomb lattice with minimal in-plane distortion is prevalent. These findings contrast with earlier reports that suggested different symmetries and reveal less than 0.2% distortion in the Ru-Ru distances within the honeycomb layers. The stacking sequence of the layers is crucial, as variations can induce different magnetic behaviors.

Stacking faults, common in layered materials like $\alpha$-RuCl$_3$, significantly influence the observed magnetic order. The paper identifies that mechanical deformations can induce stacking faults leading to different magnetic transition temperatures — a transition at $T_{N}=7$ K for faultless crystals and an additional transition at $14$ K for faulted crystals. Such findings emphasize the sensitivity of this material's magnetic properties to its stacking sequence, with faults potentially favoring energetically different stacking sequences like ABAB and ABC that correspond to distinct magnetic orders.

Magnetic Structure and Order

Neutron diffraction on pristine $\alpha$-RuCl$_3$ crystals reveals a consistent zigzag in-plane magnetic order below $T_{N}=7$ K, characterized by a propagation vector $k$ = (0, 1, 1/3). This zigzag configuration aligns with previous proposals for systems dominated by Kitaev physics and highlights the smallness of the ordered moment (~0.45(5) $\mu_B$ per Ru$^{3+}$ ion), implying significant quantum fluctuations.

Two potential magnetic structures are presented: a spiral or modulated collinear configuration. The collinear model offers a slightly better refinement, indicating spins are tilted away from the $a$-axis by 35 degrees, reinforcing theoretical predictions from a dominant Kitaev-Heisenberg model. The zigzag ordering points to the critical role of sub-leading interactions in establishing long-range order in $\alpha$-RuCl$_3$, while the small ordered moments suggest proximity to a QSL state.

Implications and Future Directions

These insights have considerable implications for understanding frustrated magnets and their potential for QSL states. They emphasize the subtle interplay between lattice structural details and magnetic properties, especially in systems with competing interactions and low-dimensional characteristics. The paper reinforces the susceptibility of $\alpha$-RuCl$_3$ to stacking faults that alter its magnetic behavior. Such findings are essential for future research and applications in quantum computing, where exploiting QSL properties could lead to robust qubits.

Continued investigations should aim to refine the understanding of the interlayer interactions and their contribution to the magnetic ground state. Additionally, exploration of the precise form of the spin Hamiltonian through theoretical and experimental approaches, such as inelastic neutron scattering or polarized neutron studies, would be valuable for solidifying the physical models underlying $\alpha$-RuCl$_3$.

In summary, this paper advances the understanding of $\alpha$-RuCl$_3$, presenting a comprehensive view of its low-temperature crystal and magnetic structures while highlighting areas for future research within the framework of QSLs and frustrated magnetism.