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Register a new userSpin-wave excitations evidencing the Kitaev interaction in single crystalline $alpha$-RuCl$_3$
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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.
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We study on transport and magnetic properties of hydrated and lithium-intercalated $alpha$-RuCl$_3$, Li$_x$RuCl$_3 cdot y$H$_2$O, for investigating the effect on mobile-carrier doping into candidate materials for a realization of a Kitaev model. From thermogravitometoric and one-dimensional electron map analyses, we find two crystal structures of this system, that is, mono-layer hydrated Li$_x$RuCl$_3 cdot y$H$_2$O~$(xapprox0.56, yapprox1.3)$ and bi-layer hydrated Li$_x$RuCl$_3 cdot y$H$_2$O~$(xapprox0.56, yapprox3.9)$. The temperature dependence of the electrical resistivity shows a temperature hysteresis at 200-270 K, which is considered to relate with a formation of a charge order. The antiferromagnetic order at 7-13 K in pristine $alpha$-RuCl$_3$~ is successfully suppressed down to 2 K in bi-layer hydrated Li$_x$RuCl$_3 cdot y$H$_2$O, which is sensitive to not only an electronic state of Ru but also an interlayer distance between Ru-Cl planes.
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.
$alpha$-RuCl$_3$ is drawing much attention as a promising candidate Kitaev quantum spin liquid. However, despite intensive research efforts, controversy remains about the form of the basic interactions governing the physics of this material. Even the sign of the Kitaev interaction (the bond-dependent anisotropic interaction responsible for Kitaev physics) is still under debate, with conflicting results from theoretical and experimental studies. The significance of the symmetric off-diagonal exchange interaction (referred to as the $Gamma$ term) is another contentious question. Here, we present resonant elastic x-ray scattering data that provides unambiguous experimental constraints to the two leading terms in the magnetic interaction Hamiltonian. We show that the Kitaev interaction ($K$) is ferromagnetic, and that the $Gamma$ term is antiferromagnetic and comparable in size to the Kitaev interaction. Our findings also provide a natural explanation for the large anisotropy of the magnetic susceptibility in $alpha$-RuCl$_3$ as arising from the large $Gamma$ term. We therefore provide a crucial foundation for understanding the interactions underpinning the exotic magnetic behaviours observed in $alpha$-RuCl$_3$.
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.
The Kitaev quantum spin liquid epitomizes an entangled topological state, for which two flavors of fractionalized low-energy excitations are predicted: the itinerant Majorana fermion and the Z2 gauge flux. Detection of these excitations remains challenging, because of their fractional quantum numbers and non-locality. It was proposed recently that fingerprints of fractional excitations are encoded in the phonon spectra of Kitaev quantum spin liquids through a novel fractional-excitation-phonon coupling. Here, we uncover this effect in $alpha$-RuCl3 using inelastic X-ray scattering with meV resolution. At high temperature, we discover interlaced optical phonons intercepting a transverse acoustic phonon between 3 and 7 meV. Upon decreasing temperature, the optical phonons display a large intensity enhancement near the Kitaev energy, JK~8 meV, that coincides with a giant acoustic phonon softening near the Z2 gauge flux energy scale. This fractional excitation induced phonon anomalies uncover the key ingredient of the quantum thermal Hall effect in $alpha$-RuCl3 and demonstrates a proof-of-principle method to detect fractional excitations in topological quantum materials.
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