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Register a new userSpin-orbit excitations and electronic structure of the putative Kitaev magnet $alpha$-RuCl$_3$
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Mott insulators with strong spin-orbit coupling have been proposed to host unconventional magnetic states, including the Kitaev quantum spin liquid. The 4$d$ system $alpha$-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 $alpha$-RuCl$_3$ is an ideal material system to study spin-orbit coupled magnetism on the honeycomb lattice.
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We report on THz, infrared reflectivity and transmission experiments for wave numbers from 10 to 8000 cm$^{-1}$ ($sim$ 1 meV - 1 eV) and for temperatures from 5 to 295 K on the Kitaev candidate material {alpha}-RuCl$_3$. As reported earlier, the compound under investigation passes through a first-order structural phase transition, from a monoclinic high-temperature to a rhombohedral low-temperature phase. The phase transition shows an extreme and unusual hysteretic behavior, which extends from 60 to 166 K. In passing this phase transition, in the complete frequency range investigated we found a significant reflectance change, which amounts almost a factor of two. We provide a broadband spectrum of dielectric constant, dielectric loss and optical conductivity from the THz to the mid infrared regime and study in detail the phonon response and the low-lying electronic density of states. We provide evidence for the onset of an optical energy gap, which is of order 200 meV, in good agreement with the gap derived from measurements of the DC electrical resistivity. Remarkably, the onset of the gap exhibits a strong blue shift on increasing temperatures.
The pure Kitaev honeycomb model harbors a quantum spin liquid in zero magnetic fields, while applying finite magnetic fields induces a topological spin liquid with non-Abelian anyonic excitations. This latter phase has been much sought after in Kitaev candidate materials, such as $alpha$-RuCl$_3$. Currently, two competing scenarios exist for the intermediate field phase of this compound ($B=7-10$ T), based on experimental as well as theoretical results: (i) conventional multiparticle magnetic excitations of integer quantum number vs. (ii) Majorana fermionic excitations of possibly non-Abelian nature with a fractional quantum number. To discriminate between these scenarios a detailed investigation of excitations over a wide field-temperature phase diagram is essential. Here we present Raman spectroscopic data revealing low-energy quasiparticles emerging out of a continuum of fractionalized excitations at intermediate fields, which are contrasted by conventional spin-wave excitations. The temperature evolution of these quasiparticles suggests the formation of bound states out of fractionalized excitations.
Kitaev interactions underlying a quantum spin liquid have been long sought, but experimental data from which their strengths can be determined directly is still lacking. Here, by carrying out inelastic neutron scattering measurements on high-quality single crystals of $alpha$-RuCl$_3$, we observe spin-wave spectra with a gap of $sim$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-principle calculations, and find that the anisotropic Kitaev interaction $K$ term and the isotropic antiferromagentic off-diagonal exchange interaction $Gamma$ 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 $Gamma=9.5$ meV. These results demonstrate explicitly that Kitaev physics is realized in real materials.
Raman scattering has been employed to investigate lattice and magnetic excitations of the honeycomb Kitaev material $alpha$-RuCl$_3$ and its Heisenberg counterpart CrCl$_3$. Our phonon Raman spectra give evidence for a first-order structural transition from a monoclinic to a rhombohedral structure for both compounds. Significantly, only $alpha$-RuCl$_3$ features a large thermal hysteresis, consistent with the formation of a wide phase of coexistence. In the related temperature interval of $70-170$ K, we observe a hysteretic behavior of magnetic excitations as well. The stronger magnetic response in the rhombohedral compared to the monoclinic phase evidences a coupling between the crystallographic structure and low-energy magnetic response. Our results demonstrate that the Kitaev magnetism concomitant with fractionalized excitations is susceptible to small variations of bonding geometry.
Recently, $alpha$-$textrm{RuCl}_3$ has attracted much attention as a possible material realization of the honeycomb Kitaev model, which may stabilize a quantum-spin-liquid state. Compared to extensive studies on its magnetic properties, there is still a lack of understanding on its electronic structure, which is strongly related with its Kitaev physics. Here, the electronic structure of $alpha$-$textrm{RuCl}_3$ is investigated by photoemission (PE) and inverse photoemission (IPE) spectroscopies. The band gap, directly measured from PE/IPE spectra, is found to be 1.9 eV, much larger than previous estimations. The LDA calculations show that the on-site Coulomb interaction $textit{U}$ can open the band gap without spin-orbit coupling (SOC). However, the SOC should also be incorporated to reproduce the proper gap size, indicating that the interplay between $textit{U}$ and SOC plays an essential role in the physics of $alpha$-$textrm{RuCl}_3$. There exist some spectral features in PE/IPE spectra which cannot be explained by the LDA calculations. To explain such discrepancies, we perform the configuration-interaction calculations for a ${textrm{RuCl}}_6^{3-}$ cluster. The experimental data and calculations demonstrate that the 4$textit{d}$ compound $alpha$-$textrm{RuCl}_3$ is a $J_{textrm{eff}}$ = 1/2 Mott insulator rather than a quasimolecular-orbital insulator. Our study also provides important physical parameters, required in verifying the proposed Kitaev physics in $alpha$-$textrm{RuCl}_3$.
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