Electronically highly cubic conditions for Ru in $\alpha -{\mathbf{RuCl}}_3$

We studied the local Ru $4d$ electronic structure of $\alpha -{\mathrm{RuCl}}_3$ by means of polarization-dependent x-ray absorption spectroscopy at the $\mathrm{Ru} L_{2,3}$ edges. We observed a vanishingly small linear dichroism indicating that electronically the Ru $4d$ local symmetry is highly cubic. Using full multiplet cluster calculations we were able to reproduce the spectra excellently and to extract that the trigonal splitting of the $t_{2g}$ orbitals is $-12\pm 10$ meV, i.e., negligible as compared to the Ru $4d$ spin-orbit coupling constant. Consistent with our magnetic circular dichroism measurements, we found that the ratio of the orbital and spin moments is 2.0, the value expected for a $J_{\text{eff}}=\frac{1}{2}$ ground state. We have thus shown that as far as the Ru $4d$ local properties are concerned, $\alpha -{\mathrm{RuCl}}_3$ is an ideal candidate for the realization of Kitaev physics.

Figure 1

Ru $L_{2,3}$ XAS spectra of a ${\mathrm{RuCl}}_3$ single crystal for incoming linear polarized light with the electric field vector $\mathbf{E}$ normal (black line) and parallel (red line) to the $ab$ plane. Inset: Sketch of the trigonal distortion.

Figure 2

Partial density of states of the Cl $3p$ orbitals for different polarization (top) and of the Ru $4d$ orbitals (bottom). The inset compares the broadened unoccupied DOS of Cl $3p$ to the Cl $K$ edge of the measured XAS spectra.

Figure 3

(a) Closeup of the Ru $L_{2,3}$ XAS spectra of a ${\mathrm{RuCl}}_3$ single crystal for incoming linear polarized light with the electric field vector $\mathbf{E}$ normal (black lines) and parallel (red lines) to the $ab$ plane. (b) Experimental difference spectrum (red circles) compared with calculations for different values of $D_{\text{trig}}$.

Figure 4

Setup of the XMCD experiment: The magnetic field $B$ is applied parallel to the Poynting vector of the circularly polarized photons and forms an angle of ${20}^{\circ }$ with the $ab$ plane.

Figure 5

Experimental Ru $L_{2,3}$ XAS (blue circles) and XMCD (green circles) spectra of a ${\mathrm{RuCl}}_3$ single crystal together with calculated XAS (blue line) and XMCD (green line). The spectra were measured at $T=2\mathrm{K}$ and $B=6\mathrm{T}$.