Spin-orbit excitations and electronic structure of the putative Kitaev magnet $\alpha -{\mathrm{RuCl}}_3$

Mott insulators with strong spin-orbit coupling have been proposed to host unconventional magnetic states, including the Kitaev quantum spin liquid. The $4d$ system $\alpha -{\mathrm{RuCl}}_3$ has recently come into view as a candidate Kitaev system, with evidence for unusual spin excitations in magnetic scattering experiments. We apply a combination of optical spectroscopy and Raman scattering to study the electronic structure of this material. Our measurements reveal a series of orbital excitations involving localized total angular momentum states of the Ru ion, implying that strong spin-orbit coupling and electron-electron interactions coexist in this material. Analysis of these features allows us to estimate the spin-orbit coupling strength, as well as other parameters describing the local electronic structure, revealing a well-defined hierarchy of energy scales within the Ru $d$ states. By comparing our experimental results with density functional theory calculations, we also clarify the overall features of the optical response. Our results demonstrate that $\alpha -{\mathrm{RuCl}}_3$ is an ideal material system to study spin-orbit coupled magnetism on the honeycomb lattice.

Figure 1

Optical and Raman response of ${\mathrm{RuCl}}_3$. (a) Imaginary part of the dielectric function ${\epsilon }_2\left(\omega \right)$ at 295 K. (b) Raman susceptibility Im $\chi \left(\omega \right)$ for two polarization channels at 10 K. Below 1 eV, orbital excitations lead to narrow features, which we label $A_0–A_3$, in both ${\epsilon }_2\left(\omega \right)$ and Im $\chi \left(\omega \right)$.

Figure 2

Temperature dependence of the $A_0$–$A_3$ orbital excitations. (a) ${\epsilon }_2\left(\omega \right)$ at 10 and 295 K. (b) Spectral weight $SW={\int }_{0.1\text{eV}}^{0.87\text{eV}}\omega {\epsilon }_2\left(\omega \right)d\omega$. The smooth decrease in total $\mathit{SW}$ is consistent with phonon-assisted orbital excitations.

Figure 3

Orbital excitations in ${\mathrm{RuCl}}_3$. In the absence of spin-orbit coupling, the Ru $d^5$ ion is in a low-spin $t_{2g}^5$ (${}^2{T}_2$) configuration. The first excited state is then the intermediate-spin $t_{2g}^4{e}_g$ state. As shown, spin-orbit coupling splits these states, leading to the four transitions observed experimentally.

Figure 4

High-energy optical response and electronic structure of ${\mathrm{RuCl}}_3$. (a) ${\epsilon }_2\left(\omega \right)$ from 0.1 to 6 eV and (b) density functional theory band structure and orbitally projected density of states (PDOS).