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arXiv:1908.11617 · Physical review. B./Physical review. B

High-field quantum disordered state in α−RuCl3 : Spin flips, bound states, and multiparticle continuum

Anuja Sahasrabudhe, David A. S. Kaib, S. Reschke, Raphael German, T. C. Koethe, Jonathan Buhot, D. Kamenskyi, Ciarán Hickey, P. Becker, V. Tsurkan, Alois Loidl, Seung-Hwan Do, Kwang‐Yong Choi, M. Grüninger, Stephen M. Winter, Zhe Wang, Roser Valentí, Paul H. M. van Loosdrecht

Published Apr 24, 2020• 74 citations
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Abstract

Raman and terahertz spectroscopy, combined with exact diagonalization studies, reveal the nature of the high-field phase of the proximate Kitaev material $\ensuremath{\alpha}$-RuCl${}_{3}$ as a partially polarized quantum disordered state. The state is characterized by a gapped multiparticle continuum, out of which a two-particle bound state emerges, together with a well-defined single-particle excitation at low energy. The results underline the unusual nature of the high-field phase, and the important role of Kitaev and off-diagonal interactions in $\ensuremath{\alpha}$-RuCl${}_{3}$.

DOI
10.1103/physrevb.101.140410

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Raman and terahertz spectroscopy, combined with exact diagonalization studies, reveal the nature of the high-field phase of the proximate Kitaev material \ensuremathα\ensuremath{\alpha}\ensuremathα-RuCl3{}_{3}3​ as a partially polarized quantum disordered state. The state is characterized by a gapped multiparticle continuum, out of which a two-particle bound state emerges, together with a well-defined single-particle excitation at low energy. The results underline the unusual nature of the high-field phase, and the important role of Kitaev and off-diagonal interactions in \ensuremathα\ensuremath{\alpha}\ensuremathα-RuCl3{}_{3}3​.
Abstract We present comprehensive inelastic neutron spectroscopic maps of the magnetic field-induced disordered phase of the Kitaev quantum spin liquid candidate material α-RuCl 3 . For fields along both in-plane high symmetry directions we observe that the spin excitation spectrum at and above a magnetic field of 8 T is gapped. Excitation modes then sharpen for increasing field but are consistently broader than experimental resolution even at 13.5 T. The out-of-plane dispersion diminishes in the 7-10 T regime, signifying enhanced two-dimensional behavior as the in-plane liquid correlations are established. In this regime, excitations are very broad and largely flat for all accessible energy-momenta, which is kinematically at odds with a magnon-decay picture. By contrast, a continuum of fractionalized excitations naturally yields a broad continuum response, which crucially may be accompanied by sharper modes of bound states of fractionalized excitations. Their damping by the continuum accounts for the observed spectral broadening and field dependence. Our results provide strong evidence for the existence of fractionalized excitations in α-RuCl 3 in a magnetic field.
Intermediate Field Spin(on) Dynamics in ααα-RuCl3_33​
We present comprehensive inelastic neutron spectroscopic maps of the magnetic field-induced disordered phase of the Kitaev quantum spin liquid candidate material ααα-RuCl3_33​. For fields along both in-plane high-symmetry directions we observe that the spin excitation spectrum at and above a magnetic field of 8~T is gapped. Excitation modes then sharpen for increasing field but are consistently broader than experimental resolution even at 13.5~T. The out-of-plane dispersion diminishes in the 7-10~T regime, signifying enhanced two-dimensional behavior as the in-plane liquid correlations are established. In this regime, excitations are very broad and largely flat for all accessible energy-momenta, which is kinematically at odds with a magnon-decay picture. By contrast, a continuum of fractionalized excitations naturally yields a broad continuum response, which crucially may be accompanied by sharper modes of bound states of fractionalized excitations. Their damping by the continuum accounts for the observed spectral broadening and field dependence. Our results provide strong evidence for the existence of fractionalized excitations in ααα-RuCl3_33​ in a magnetic field.
We calculate polarized terahertz (THz) spectra of two effective models for a honeycomb-lattice magnet α-RuCl3 by using a numerical exact-diagonalization method. One of the two models is the ab initio model proposed in H.-S. Kim and H.-Y. Kee [Phys. Rev. B 93, 155143 (2016)] and the other is the large-|K| model that we have proposed by an empirical way in order to explain experimental results for α-RuCl3. We discuss the magnetic-field dependence of the lowest-excitation mode in the polarized THz spectra for the two models. We find that the energy gap of the lowest-excitation mode in both models does not close and increases almost linearly above the critical field, where the zigzag order is suppressed. From the obtained results, we point out that the low-energy excitation is mainly governed not by the Kitaev interaction but by the Heisenberg interaction and the off-diagonal interactions.
We report on terahertz spectroscopy of quantum spin dynamics in $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{RuCl}}_{3}$, a system proximate to the Kitaev honeycomb model, as a function of temperature and magnetic field. We follow the evolution of an extended magnetic continuum below the structural phase transition at Ts2=62  K{T}_{s2}=62\text{ }\text{ }\mathrm{K}Ts2​=62  K. With the onset of a long-range magnetic order at TN=6.5  K{T}_{N}=6.5\text{ }\text{ }\mathrm{K}TN​=6.5  K, spectral weight is transferred to a well-defined magnetic excitation at $\ensuremath{\hbar}{\ensuremath{\omega}}_{1}=2.48\text{ }\text{ }\mathrm{meV}$, which is accompanied by a higher-energy band at $\ensuremath{\hbar}{\ensuremath{\omega}}_{2}=6.48\text{ }\text{ }\mathrm{meV}$. Both excitations soften in a magnetic field, signaling a quantum phase transition close to Bc=7  T{B}_{c}=7\text{ }\text{ }\mathrm{T}Bc​=7  T, where a broad continuum dominates the dynamical response. Above Bc{B}_{c}Bc​, the long-range order is suppressed, and on top of the continuum, emergent magnetic excitations evolve. These excitations follow clear selection rules and exhibit distinct field dependencies, characterizing the dynamical properties of a possibly field-induced quantum spin liquid.
Recent studies have brought α-RuCl_{3} to the forefront of experimental searches for materials realizing Kitaev spin-liquid physics. This material exhibits strongly anisotropic exchange interactions afforded by the spin-orbit coupling of the 4d Ru centers. We investigate the dynamical response at finite temperature and magnetic field for a realistic model of the magnetic interactions in α-RuCl_{3}. These regimes are thought to host unconventional paramagnetic states that emerge from the suppression of magnetic order. Using exact diagonalization calculations of the quantum model complemented by semiclassical analysis, we find a very rich evolution of the spin dynamics as the applied field suppresses the zigzag order and stabilizes a quantum paramagnetic state that is adiabatically connected to the fully polarized state at high fields. At finite temperature, we observe large redistributions of spectral weight that can be attributed to the anisotropic frustration of the model. These results are compared to recent experiments and provide a road map for further studies of these regimes.
Abstract Significant efforts have focused on the magnetic excitations of relativistic Mott insulators, predicted to realize the Kitaev quantum spin liquid (QSL). This exactly solvable model involves a highly entangled state resulting from bond-dependent Ising interactions that produce excitations which are non-local in terms of spin flips. A key challenge in real materials is identifying the relative size of the non-Kitaev terms and their role in the emergence or suppression of fractional excitations. Here, we identify the energy and temperature boundaries of non-Kitaev interactions by direct comparison of the Raman susceptibility of α -RuCl 3 with quantum Monte Carlo (QMC) results for the Kitaev QSL. Moreover, we further confirm the fractional nature of the magnetic excitations, which is given by creating a pair of fermionic quasiparticles. Interestingly, this fermionic response remains valid in the non-Kitaev range. Our results and focus on the use of the Raman susceptibility provide a stringent new test for future theoretical and experimental studies of QSLs.