Spin-orbit excitation energies, anisotropic exchange, and magnetic phases of honeycomb RuCl3 (1604.04755v1)

Abstract: Using quantum chemistry calculations we shed fresh light on the electronic structure and magnetic properties of RuCl3, a proposed realization of the honeycomb Kitaev spin model. It is found that the nearest-neighbor Kitaev exchange K is weaker than in 5d5 Ir oxides but still larger than other effective spin couplings. The electronic-structure computations also indicate a ferromagnetic K in the halide, which is supported by a detailed analysis of the field-dependent magnetization. From exact-diagonalization calculations for extended Kitaev-Heisenberg Hamiltonians we additionally find that a transition from zigzag order to a spin-liquid ground state can be induced in RuCl3 with external magnetic field.

• The paper details how quantum chemistry calculations reveal a distinct anisotropic electronic structure in α‑RuCl₃ due to significant trigonal splitting.
• The paper demonstrates that ferromagnetic Kitaev exchange in α‑RuCl₃ is decisively stronger than competing interactions, influencing its magnetic behavior.
• The paper predicts that external magnetic fields can trigger a transition from zigzag order to a quantum spin-liquid state, highlighting a delicate interaction balance.

Spin-Orbit Excitation Energies, Anisotropic Exchange, and Magnetic Phases of Honeycomb $\alpha$-RuCl$_3$

The presented paper explores the electronic structure and magnetic properties of $\alpha$-RuCl$_3$, a candidate material for realizing the Kitaev spin model on a honeycomb lattice. Utilizing quantum chemistry calculations, the research aims to elicit key insights into the nearest-neighbor Kitaev exchange interactions, analogous to those found in iridium oxides, and their implications for potential spin-liquid states.

Key Findings

1. Electronic Structure: The paper provides a detailed quantum chemistry analysis of the Ru$^{3+}$ $4d$-shell electronic structure, indicating a significant deviation from the $j_{\text{eff}} = 1/2$ scenario due to substantial trigonal splitting. This results in two distinct primary impacts:
   • A departure from the idealized cubic $t_{2g}$ crystal-field environment.
   • The formation of low-symmetry Coulombic environments which produce substantial anisotropy in the $g$ factors.
2. Magnetic Couplings: It is determined that the nearest-neighbor Kitaev exchange interaction, $K$, in $\alpha$-RuCl$_3$ is ferromagnetic, contrary to the antiferromagnetic $K$ in iridate counterparts. This ferromagnetic nature of $K$ is critical, as it underpins the material's behavior under magnetic fields and its propensity to host unique quantum states. Importantly, $K$ is found to be decisively stronger than other magnetic interactions, with the exception of Heisenberg-type $J$ couplings.
3. Phase Transition Under Magnetic Fields: Via exact-diagonalization calculations, the paper predicts that an external magnetic field can induce a transition from zigzag magnetic order to a quantum spin-liquid state. This transition illustrates the delicate balance of interactions, further impacted by longer-range couplings.
4. Phase Diagram and Magnetic Order: The comprehensive phase diagram emphasizes the emergence of various commensurate phases, notably a spin-liquid phase that emerges as part of the interplay between Kitaev interactions and geometric frustration. The experimental zigzag order at low temperatures serves as a reference for this theoretical model.

Implications and Future Directions

The findings have dual implications: practical, in their potential to guide the development of materials that support quantum spin-liquid states, and theoretical, by challenging existing paradigms of Kitaev interactions on honeycomb lattices, particularly in materials like $\alpha$-RuCl$_3$. The results may stimulate further exploration into the anisotropic interactions and exotic phases that occur due to pressure or chemical substitution, which could reveal more about the underlying quantum behaviors.

Furthermore, the paper raises questions about the current understandings of neutron scattering results, which must reconcile the claimed ferromagnetic nature of $K$ with observed data, previously interpreted under an antiferromagnetic framework.

Conclusion

The paper provides valuable insights into the complex physics of $\alpha$-RuCl$_3$, highlighting the importance of ferromagnetic Kitaev interactions and offering a reconceptualization of its magnetic phases under field perturbations. This underscores the need for experimental verification of the theoretical predictions, possibly through advanced spectroscopy or scattering techniques. As a prospective quantum spin-liquid candidate, $\alpha$-RuCl$_3$ stands as a significant focus for future condensed matter research.