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arXiv:2108.08878 · Physical review. B./Physical review. B

Footprints of Kitaev spin liquid in the Fano lineshape of Raman-active optical phonons

Kexin Feng, Swetlana Swarup, Natalia Borisovna Perkins

Published Mar 14, 2022• 19 citations
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Abstract

We develop a theoretical description of the Raman spectroscopy in the spin-phonon-coupled Kitaev system and show that it can provide observable signatures of fractionalized excitations characteristic of the underlying spin-liquid phase. In particular, we obtain the explicit form of the phonon modes and construct the coupling Hamiltonian based on the ${D}_{3d}$ symmetry. We then systematically compute the Raman intensity and show that the spin-phonon coupling renormalizes phonon propagators and generates the salient Fano lineshape. We find that the temperature evolution of the Fano lineshape displays two crossovers, and the low-temperature crossover shows pronounced magnetic-field dependence. We thus identify the observable effect of the Majorana fermions and the ${Z}_{2}$ gauge fluxes encoded in the Fano lineshape. Our results are consistent with the phonon Raman scattering experiments in the candidate material $\ensuremath{\alpha}\ensuremath{-}{\mathrm{RuCl}}_{3}$.

DOI
10.1103/physrevb.105.l121108

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We develop a theoretical description of the Raman spectroscopy in the spin-phonon-coupled Kitaev system and show that it can provide observable signatures of fractionalized excitations characteristic of the underlying spin-liquid phase. In particular, we obtain the explicit form of the phonon modes and construct the coupling Hamiltonian based on the D3d{D}_{3d}D3d​ symmetry. We then systematically compute the Raman intensity and show that the spin-phonon coupling renormalizes phonon propagators and generates the salient Fano lineshape. We find that the temperature evolution of the Fano lineshape displays two crossovers, and the low-temperature crossover shows pronounced magnetic-field dependence. We thus identify the observable effect of the Majorana fermions and the Z2{Z}_{2}Z2​ gauge fluxes encoded in the Fano lineshape. Our results are consistent with the phonon Raman scattering experiments in the candidate material \ensuremathα\ensuremath−RuCl3\ensuremath{\alpha}\ensuremath{-}{\mathrm{RuCl}}_{3}\ensuremathα\ensuremath−RuCl3​.
Candidate materials for the Kitaev spin liquid generically have residual interactions beyond the Kitaev coupling. It therefore becomes necessary to understand how signatures of the quantum spin liquid, e.g., fractionalization of the spin excitations, are affected by the presence of these interactions. Recently it was shown that phonon dynamics is an indirect but effective probe to study fractionalized excitations in the Kitaev spin liquid. Ultrasound experiments can measure sound attenuation, which should show characteristic temperature and angular dependence of the sound-attenuation coefficient if the scattering of phonons happens predominantly on Majorana fermions. So far the computation of the sound attenuation was only done in the pure spin-phonon coupled Kitaev model, without taking into account residual interactions. In order to understand experimental signatures, here we present a mean-field study of the sound attenuation in the generalized $J\text{\ensuremath{-}}K\text{\ensuremath{-}}\mathrm{\ensuremath{\Gamma}}$ model, which is relevant to candidate materials. Our findings show that as long as the system is in the spin liquid phase, characteristic features of the sound attenuation remain observable even in the presence of residual interactions.
Abstract We demonstrate a Kitaev spin liquid in a polyhedral cluster and propose detecting its fractional excitations—Majorana spinons—by magnetic Raman scattering. While little polarization dependence of the Raman spectra at sufficiently low temperatures is usual with quantum spin liquids, the present observations are primarily of geometric origin. The Raman scattering intensity peaks melt with increasing temperature, to be more precise, with increasing number of background gauge-flux excitations.
Long-range entanglement in quantum spin liquids (QSLs) leads to novel low-energy excitations with fractionalized quantum numbers and (in two dimensions) statistics. Experimental detection and manipulation of these excitations present a challenge particularly in view of diverse candidate magnets. A promising probe of fractionalization is their coupling to phonons. Here, we present Raman scattering results for the S=1/2S=1/2S=1/2 honeycomb iridate Cu2IrO3{\mathrm{Cu}}_{2}{\mathrm{IrO}}_{3}Cu2​IrO3​, a candidate Kitaev QSL with fractionalized Majorana fermions and Ising flux excitations. We observe anomalous low-temperature frequency shift and linewidth broadening of the Raman intensities in addition to a broad magnetic continuum, both of which, as we derive, are naturally attributed to the phonon decaying into itinerant Majoranas. The dynamic Raman susceptibility marks a crossover from the QSL to a thermal paramagnet at $\ensuremath{\sim}120$ K. The phonon anomalies below this temperature demonstrate a strong phonon-Majorana coupling. These results provide evidence of spin fractionalization in Cu2IrO3{\mathrm{Cu}}_{2}{\mathrm{IrO}}_{3}Cu2​IrO3​.
Abstract We study magnetic Raman, i.e. inelastic light, scattering of Kitaev’s quantum spin liquids realizable in honeycomb nanoribbons. Elementary excitations in the Kitaev spin liquids consist of itinerant Majorana (matter) fermions and localized gauge fluxes (visons). Matter fermions are characterized by the projective point (gauged rotation) group inherent in the lattice. Inelastic light scattering is mediated by a pair of matter fermions without any vison excitation. We can selectively “observe” matter fermions of the same symmetry and those of different symmetries depending on the polarization of incoming and/or outgoing lights. A pair of matter fermions with particular translational quantum numbers ±k cannot be Raman active.
We show how Raman spectroscopy can serve as a valuable tool for diagnosing quantum spin liquids (QSL). We find that the Raman response of the gapless QSL of the Kitaev-Heisenberg model exhibits signatures of spin fractionalization into Majorana fermions, which give rise to a broad signal reflecting their density of states, and Z(2) gauge fluxes, which also contribute a sharp feature. We discuss the current experimental situation and explore more generally the effect of breaking the integrability on response functions of Kitaev spin liquids.
Motivated by the ongoing effort to search for high-resolution signatures of quantum spin liquids, we investigate the temperature dependence of the indirect resonant inelastic x-ray scattering (RIXS) response for the Kitaev honeycomb model. We find that, as a result of spin fractionalization, the RIXS response changes qualitatively at two well-separated temperature scales, TL{T}_{L}TL​ and TH{T}_{H}TH​, which correspond to the characteristic energies of the two kinds of fractionalized excitations, Z2{\mathbb{Z}}_{2}Z2​ gauge fluxes and Majorana fermions, respectively. While thermally excited Z2{\mathbb{Z}}_{2}Z2​ gauge fluxes at temperature TL{T}_{L}TL​ lead to a general broadening and softening of the response, the thermal proliferation of Majorana fermions at temperature ${T}_{H}\ensuremath{\sim}10\phantom{\rule{0.16em}{0ex}}{T}_{L}$ results in a significant shift of the spectral weight, both in terms of energy and momentum. Due to its exclusively indirect nature, the RIXS process we consider gives rise to a universal magnetic response and, from an experimental perspective, it directly corresponds to the KKK-edge of Ru3+{\mathrm{Ru}}^{3+}Ru3+ in the Kitaev candidate material $\ensuremath{\alpha}\ensuremath{-}{\mathrm{RuCl}}_{3}$.