$J_{\mathrm{eff}}$ Description of the Honeycomb Mott Insulator $\alpha \text{−}{\mathrm{RuCl}}_3$

Novel ground states might be realized in honeycomb lattices with strong spin-orbit coupling. Here we study the electronic structure of $\alpha \text{−}{\mathrm{RuCl}}_3$, in which the Ru ions are in a $d^5$ configuration and form a honeycomb lattice, by angle-resolved photoemission, x-ray photoemission, and electron energy loss spectroscopy supported by density functional theory and multiplet calculations. We find that $\alpha \text{−}{\mathrm{RuCl}}_3$ is a Mott insulator with significant spin-orbit coupling, whose low energy electronic structure is naturally mapped onto $J_{\mathrm{eff}}$ states. This makes $\alpha \text{−}{\mathrm{RuCl}}_3$ a promising candidate for the realization of Kitaev physics. Relevant electronic parameters such as the Hubbard energy $U$, the crystal field splitting 10 Dq, and the charge transfer energy $\mathrm{\Delta }$ are evaluated.

Figure 1

(a)–(c) $J_{\mathrm{eff}}$ description of the $d$-level electronic structure. (a) Schematic density of states without interactions. (b) Under the presence of strong spin-orbit coupling. (c) With spin-orbit coupling and on-site correlation $U$. (d) Calculated density of states of $\alpha \text{−}{\mathrm{RuCl}}_3$ with spin-orbit coupling and on-site correlation.

Figure 2

Valence band of $\alpha \text{−}{\mathrm{RuCl}}_3$ measured by photoemission spectroscopy with different photon energies at room temperature compared to an orbital projected density of states calculation.

Figure 3

(a) Color coded representation of the angle dependence of the full valence band. Energy regions of mainly Ru $4d$ and Cl $3p$ character are denoted on the right side. Red dotted lines are results of band structure calculations under the same renormalization as the DOS in Fig. 2. (b) Expansion of the Ru $4d$ region. (c) Band structure without bandwidth renormalization but with offset. The color corresponds to the degree of Ru $4d$ orbital character. (d) Comparison of experimental and theoretical $\mathrm{\Gamma }$-point spectra extracted from calculations with and without spin-orbit coupling (SOC). (e) Band structure without inclusion of the SOC.

Figure 4

Loss function measured by EELS at $\mathbf{q}=0.1\AA$. Lower inset: Low energy loss function as a function of momentum transfer. Upper inset: Orbital projected DOS with transitions labeled according to the peaks in the main panel.

Figure 5

Ru $3p$ EELS and XPS. Red lines show charge-transfer multiplet calculations (see text for details).