We examine the role of spin-orbit coupling in the electronic structure of $\alpha -{\mathrm{RuCl}}_3$, in which Ru ions in $4d^5$ configuration form a honeycomb lattice. Our x-ray absorption spectroscopy measurements at the Ru $L$ edges exhibit distinct spectral features associated with the presence of substantial spin-orbit coupling, as well as an anomalously large branching ratio. Furthermore the measured optical spectra can be described very well with first-principles electronic structure calculations obtained by taking into account both spin-orbit coupling and electron correlations. We propose that $\alpha -{\mathrm{RuCl}}_3$ is a spin-orbit assisted Mott insulator, and that the bond-dependent Kitaev interaction may be important for understanding magnetism of this compound.

Systematic low-energy neutron-scattering studies have been performed on float-zone-grown single crystals of ${\mathrm{La}}_{2-x}{\mathrm{Sr}}_x{\mathrm{CuO}}_4$ with $x$ extending from zero doping, $x=0\mathrm{}$, to the overdoped, weakly superconducting regime, $x=0.25\mathrm{}$. For $x$ beyond a critical doping value of $x_c\approx 0.05$ the low-energy spin-fluctuation peak position shifts from ($\frac{1}{2}$, $\frac{1}{2}$) to ($\frac{1}{2}$±δ, $\frac{1}{2}$), and ($\frac{1}{2}$, $\frac{1}{2}$±δ); $x_c$ also represents the onset concentration for superconductivity. For $0.06<~x<~0.12$ the incommensurability $\delta$ follows approximately the quantitative relation $\delta =x$. However, beyond $x\approx 0.12$ the incommensurability tends to saturate around $\delta \approx 1/8$. The superconducting-transition temperature $T_c\mathrm{}\left(x\right)\mathrm{}$ for stoichiometric samples at a given doping scales linearly with $\delta$ up to the optimal doping value of $x$. The peak momentum width of the spin fluctuations at low energies is small throughout the superconducting concentration region except in the strongly overdoped region. An anomalously small width is observed for $x=\frac{1}{8}$. The incommensurate spatial modulation is found to be robust with respect to pair-breaking effects that lower $T_c,$ such as deoxygenation of the sample or replacement of Cu by Zn.

We report magnetic and thermodynamic properties of single crystal $\alpha -{\text{RuCl}}_3$, in which the ${\text{Ru}}^{3+}\left(4d^5\right)$ ion is in its low spin state and forms a honeycomb lattice. Two features are observed in both magnetic susceptibility and specific heat data; a sharp peak at 7 K and a broad hump near 10–15 K. In addition, we observe a metamagnetic transition between 5 and 10 T. Our neutron diffraction study of single crystal samples confirms that the low temperature peak in the specific heat is associated with a magnetic order with unit cell doubling along the honeycomb (100) direction, which is consistent with zigzag order, one of the types of magnetic order predicted within the framework of the Kitaev-Heisenberg model.

The combination of electronic correlation and spin-orbit coupling is thought to precipitate a variety of highly unusual electronic phases in solids, including topological and quantum spin liquid states. We report a Raman scattering study that provides evidence for unconventional excitations in $\alpha \text{−}{\mathrm{RuCl}}_3$, a spin-orbit coupled Mott insulator on the honeycomb lattice. In particular, our measurements reveal unusual magnetic scattering, typified by a broad continuum. The temperature dependence of this continuum is evident over a large scale compared to the magnetic ordering temperature, suggestive of frustrated magnetic interactions. This is confirmed through an analysis of the phonon linewidths, which show a related anomaly due to spin-phonon coupling. These observations are in line with theoretical expectations for the Heisenberg-Kitaev model and suggest that $\alpha \text{−}{\mathrm{RuCl}}_3$ may be close to a quantum spin liquid ground state.

We used resonant inelastic x-ray scattering to reveal the nature of magnetic interactions in ${\mathrm{Sr}}_2{\mathrm{IrO}}_4$, a $5d$ transition-metal oxide with a spin-orbit entangled ground state and $J_{\mathrm{eff}}=1/2$ magnetic moments. The magnon dispersion in ${\mathrm{Sr}}_2{\mathrm{IrO}}_4$ is well-described by an antiferromagnetic Heisenberg model with an effective spin one-half on a square lattice, which renders the low-energy effective physics of ${\mathrm{Sr}}_2{\mathrm{IrO}}_4$ much akin to that in superconducting cuprates. This point is further supported by the observation of exciton modes in ${\mathrm{Sr}}_2{\mathrm{IrO}}_4$, whose dispersion is strongly renormalized by magnons, which can be understood by analogy to hole propagation in the background of antiferromagnetically ordered spins in the cuprates.

We report a combined experimental and theoretical investigation of the magnetic structure of the honeycomb-lattice magnet Na${}_2$IrO${}_3$, a candidate for a realization of a gapless spin liquid. Using resonant x-ray magnetic scattering at the Ir ${\mathrm{L}}_3$ edge, we find three-dimensional long-range antiferromagnetic order below $T_N=13.3$ K. From the azimuthal dependence of the magnetic Bragg peak, the ordered moment is determined to be predominantly along the $a$ axis. Combining the experimental data with first-principles calculations, we propose that the most likely spin structure is a zig-zag structure.