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Kitaev interactions underlying a quantum spin liquid have long been sought, but experimental data from which their strengths can be determined directly, are still lacking. Here, by carrying out inelastic neutron scattering measurements on high-quality single crystals of α-RuCl_{3}, we observe spin-wave spectra with a gap of ∼2  meV around the M point of the two-dimensional Brillouin zone. We derive an effective-spin model in the strong-coupling limit based on energy bands obtained from first-principles calculations, and find that the anisotropic Kitaev interaction K term and the isotropic antiferromagnetic off-diagonal exchange interaction Γ term are significantly larger than the Heisenberg exchange coupling J term. Our experimental data can be well fit using an effective-spin model with K=-6.8  meV and Γ=9.5  meV. These results demonstrate explicitly that Kitaev physics is realized in real materials.

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Summary Microstructural evolution is a key aspect of understanding and exploiting the processing-structure-property relationship of materials. Modeling microstructure evolution usually relies on coarse-grained simulations with evolution principles described by partial differential equations (PDEs). Here we demonstrate that convolutional recurrent neural networks can learn the underlying physical rules and replace PDE-based simulations in the prediction of microstructure phenomena. Neural nets are trained by self-supervised learning with image sequences from simulations of several common processes, including plane-wave propagation, grain growth, spinodal decomposition, and dendritic crystal growth. The trained networks can accurately predict both short-term local dynamics and long-term statistical properties of microstructures assessed herein and are capable of extrapolating beyond the training datasets in spatiotemporal domains and configurational and parametric spaces. Such a data-driven approach offers significant advantages over PDE-based simulations in time-stepping efficiency and offers a useful alternative, especially when the material parameters or governing PDEs are not well determined.

is a robust model anode for Li-insertion in batteries. The influence of nanocrystal size on the equilibrium potential and kinetics of Li-insertion is investigated with in operando spectroelectrochemistry of thin film electrodes. Distinct visible and infrared responses correlate with Li-insertion and electron accumulation, respectively, and these optical signals are used to deconvolute Li-insertion from other electrochemical responses, such as double-layer capacitance and electrolyte leakage.Electrochemical titration and phase-field simulations reveal that a difference in surface energies between anatase and lithiated phases of TiO 2 systematically tunes Li-insertion potentials with particle size. However, particle size does not affect the kinetics of Li-insertion in ensemble electrodes. Rather, Li-insertion rates depend on applied overpotential, electrolyte concentration, and initial state-of-charge. We conclude that Li diffusivity and phase propagation are not rate-limiting during Li-insertion in TiO 2 nanocrystals. Both of these processes occur rapidly once the transformation between the low-Li anatase and high-Li orthorhombic phases begins in a particle. Instead, discontinuous kinetics of Li accumulation in TiO 2 particles prior to the phase transformations limits (dis)charging rates. We demonstrate a practical means to deconvolute non-equilibrium charging behavior in nanocrystalline electrodes through a combination of colloidal synthesis, phase field simulations and spectroelectrochemistry. File list (2)download file view on ChemRxiv Manuscript_DynamicsofLithiumInsertion.pdf (2.46 MiB) download file view on ChemRxiv SupportingInfo_DynamicsofLithiumInsertion.pdf (3.34 MiB)