Raman evidence for dimerization and Mott collapse in \alpha-RuCl{}_{3} under pressures

Raman evidence for dimerization and Mott collapse in -RuCl under pressures

Gaomin Li School of Advanced Materials, Shenzhen Graduate School Peking University, Shenzhen 518055, P. R. China Shenzhen Institute for Quantum Science and Engineering, and Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China    Xiaobin Chen School of Science, Harbin Institute of Technology, Shenzhen 518055, China    Yuan Gan    Fenglei Li    Mingqi Yan Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China    Shenghai Pei    Yujun Zhang Shenzhen Institute for Quantum Science and Engineering, and Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China    Le Wang Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China    Huimin Su    Junfeng Dai Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China    Yuanzhen Chen Shenzhen Institute for Quantum Science and Engineering, and Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China Shenzhen Key Laboratory of Quantum Science and Engineering, Shenzhen 518055, PR China.    Youguo Shi Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China    XinWei Wang School of Advanced Materials, Shenzhen Graduate School Peking University, Shenzhen 518055, P. R. China    Liyuan Zhang    Shanmin Wang Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China    Dapeng Yu Shenzhen Institute for Quantum Science and Engineering, and Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China Shenzhen Key Laboratory of Quantum Science and Engineering, Shenzhen 518055, PR China.    Fei Ye yef@sustc.edu.cn    Jia-Wei Mei meijw@sustc.edu.cn Shenzhen Institute for Quantum Science and Engineering, and Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China    Mingyuan Huang huangmy@sustc.edu.cn Shenzhen Institute for Quantum Science and Engineering, and Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China Shenzhen Key Laboratory of Quantum Science and Engineering, Shenzhen 518055, PR China.
July 15, 2019

We perform Raman spectroscopy studies on -RuCl at room temperature to explore its phase transitions of magnetism and chemical bonding under pressures. The Raman measurements resolve two critical pressures, about  GPa and  GPa, involving very different intertwining behaviors between the structural and magnetic excitations. With increasing pressures, a stacking order phase transition of -RuCl layers develops at  GPa, indicated by the new Raman phonon modes and the modest Raman magnetic susceptibility adjustment. The abnormal softening and splitting of the Ru in-plane Raman mode provide direct evidence of the in-plane dimerization of the Ru-Ru bonds at  GPa. The Raman susceptibility is greatly enhanced with pressure increasing and sharply suppressed after the dimerization. We propose that the system undergoes Mott collapse at  GPa and turns into a dimerized correlated band insulator. Our studies demonstrate competitions between Kitaev physics, magnetism, and chemical bondings in Kitaev compounds.

Introduction– The spin-orbit coupling always invigorates new vitality to the intertwines of magnetism and chemical bonds Goodenough (1963); Dzyaloshinsky (1958); Moriya (1960); Shekhtman et al. (1992); Pesin and Balents (2010), and generates the bond-dependent Dzyaloshinsky-Moriya-type Dzyaloshinsky (1958); Moriya (1960) and Ising-type interactions Shekhtman et al. (1992). While the former interactions yield non-trivial magnetic topology Nagaosa et al. (2012); Nagaosa and Tokura (2012), the latter terms on a honeycomb lattice provide a pathway to realize the Kitaev exactly solvable spin model Kitaev (2006); Jackeli and Khaliullin (2009); Chaloupka et al. (2010). The ground state of Kitaev spin model Kitaev (2006) represents a typical quantum paramagnetism dubbed quantum spin liquid, in which the spin degree of freedom does not freeze even at zero temperature Anderson (1987). Quantum spin liquid displays various patterns of long-range quantum entanglement Wen (2004); Kitaev (2006); Levin and Wen (2006) and supports the fractional excitations Laughlin (1983); Kivelson et al. (1987); Read and Chakraborty (1989); Read and Sachdev (1991); Wen (1991); Ye et al. (2015, 2017). Kitaev interactions have been identified in layered honeycomb magnetic materials, such as -LiIrOBiffin et al. (2014) and -RuClPlumb et al. (2014). However, due to further non-Kitaev interactions, these materials have long-range magnetic orders at low temperatures Johnson et al. (2015); Sears et al. (2015); Banerjee et al. (2016); Williams et al. (2016); Ran et al. (2017). To achieve the quantum spin liquid state, in-plane magnetic fields have been implemented to suppress the magnetic order in -RuCl, and the magnetic properties are consistent with theoretical expectations Zheng et al. (2017); Yu et al. (2018); JanÅ¡a et al. (2018); Baek et al. (2017); Banerjee et al. (2018); Wolter et al. (2017); Wang et al. (2017); Hentrich et al. (2018); Kasahara et al. (2018).

Pressure also promotes the breakdown of magnetic order in -RuCl Wang et al. (2018); Cui et al. (2017); Bastien et al. (2018); Biesner et al. (2018). Above a critical pressure, the magnetic signal disappears Wang et al. (2018); Cui et al. (2017); Bastien et al. (2018); however, the charge gap does not change significantly, and the system remains an insulating state Wang et al. (2018). A present debate is whether the phase transition under pressures involves the structural deformation due to chemical bondings. X-ray diffraction (XRD) measurements in Ref. Wang et al. (2018) didn’t detect any crystal structural phase transition up to 150 GPa, and hence a new quantum magnetic disordered state was proposed. However, XRD measurements in Ref. Bastien et al. (2018) revealed a Ru-Ru bond dimerization of about 0.6 Å above a critical pressure, and supported a non-magnetic gapped dimerized state at high pressures. Ref. Biesner et al. (2018) reached a similar non-magnetic dimerized scenario in optical measurements. This is reminiscent of recent high-pressure investigations on the 2D Kitaev material -LiIrO Hermann et al. (2018) and its 3D polymorph -LiIrO Majumder et al. (2018). At high pressures, -LiIrO dimerizes Hermann et al. (2018), while -LiIrO manifests the coexistence of dynamically correlated and frozen spins without structural deformation Majumder et al. (2018). Raman spectrum simultaneously detects the lattice and magnetic excitations, and their mutual couplings Lemmens et al. (2003); Devereaux and Hackl (2007). It is an exemplary experimental tool to study competition between spin-orbit couplings Moriya (1968); Fleury and Loudon (1968); Nasu et al. (2016); Fu et al. (2017), magnetism Shastry and Shraiman (1990); Lemmens et al. (2003); Devereaux and Hackl (2007); Ko et al. (2010), and chemical bondings in Kitaev compoundsKnolle et al. (2014); Sandilands et al. (2015); Glamazda et al. (2016); Nasu et al. (2016); Glamazda et al. (2017).

In this Letter, we perform Raman scattering measurements on -RuCl to study the nature of the phase transitions under pressures. Measurements are carried out at room temperature if the temperature is not specified. From the evolution of the Raman spectra, we identify two characteristic pressures  GPa and  GPa for structural phase transitions. The inversion symmetry of the monoclinic breaks at  GPa and the system turns out to be trigonal owing to the stacking pattern changes of the -RuCl layers. At  GPa, the Ru in-plane Raman mode (161 cm at ambient pressure) softens and splits, indicating the dimerization of the Ru-Ru bonds. The Raman susceptibility is greatly enhanced with pressure increasing, mildly adjusts at  GPa, and sharply suppressed after the dimerization at  GPa. We conclude that the system undergoes the Mott collapse and turns out to be dimerized correlated band insulator with the pressure larger than  GPa.

Experimental setup– High-quality single crystals of -RuCl are grown from commercial RuCl powder by chemical vapor transport method. We use the diamond anvil cell to apply hydrostatic pressures on the samples, and calibrate the value of pressures by the shift of the photoluminescence of Ruby. Raman spectrum measurement is conducted in the backscattering configuration with the light polarized in the basal plane. Light from a 633 nm and 488 nm laser is focused down to 3 m with the power below 1 mW. Two ultra-narrow band notch filters are used to suppress the Rayleigh scattering light. The scattering light is dispersed by a Horiba iHR550 spectrometer and detected by a liquid nitrogen cooled CCD detector.

Figure 1: Evolution of the Raman spectra of the -RuCl under different pressure at room temperature.

Raman spectral evolution – Figure. 1 displays the evolution of the Raman spectra of -RuCl with the pressure from ambient pressure to 9.4 GPa. The highest measured pressure is up to 24 GPa and the pressure process is reversible 111See Supplemental Materials for more details.. Here, we can identify two characteristic pressures,  GPa and  GPa, at which the dramatic change of Raman spectra implies the structural phase transitions. At ambient pressure, five Raman modes are clearly resolved at 116, 161, 268, 294, and 310 cm. At  GPa, three new Raman modes at 201, 290 and 363 cm appear. The original five modes evolves as following. For the mode at 116 cm, a new mode splits out at the right side and the original mode disappears at  GPa. A similar splitting can be identified for the mode at 161 cm at the same pressure, but the original mode remains after that. A splitting can be seen at the left side of the mode at 268 cm at  GPa and the original peak disappears at  GPa. No splitting behavior can be resolved for the mode at 294 cm and the intensity of the mode at 310 cm experiences a dramatic increasing after 1.7 GPa. After  GPa, no sudden change is observed up to 24 GPa Note1 ().

Figure 2: (a) The atomic displacements of Raman mode eigenvectors for 5 Raman active modes () in -RuCl under ambient pressure. Only one represented mode is shown for the double degenerated modes. (b) Pressure dependence of the frequencies of the 5 dominate Raman peaks.  GPa and  GPa are two critical pressures.

Raman phonon mode assignment – At ambient pressure, we perform Raman and IR measurements on exfoliated -RuCl samples down to three atomic layers and no significant difference is observed Note1 (). Hence we can assign the Raman modes at ambient pressure according to the point group of the single -RuCl layer. From group theory, the irreducible representation of atomic displacement at the point is . Among them, Raman active modes are . From the polarization measurement Note1 () and previous Raman studies Sandilands et al. (2015), the first four modes are assigned as doubly degenerated mode and the last mode as mode. Other two small Raman modes at 219 and 339 cm, can also be resolved by using 488 nm laser as the excitation light Note1 ().

We assign the Raman mode eigenvectors with the help of first-principle calculations Note1 () and the atomic displacement of 5 Raman active modes are displayed in Fig. 2 (a). For the 4 modes, the mode at 116 cm is dominated by the twist of the Ru-Cl-Ru-Cl plane; the mode at 161 cm is associated with Ru in-plane relative movement; the mode at 268 cm is related to the Ru-Cl-Ru-Cl plane shearing, and the mode at 294 cm is the Ru-Cl-Ru-Cl ring breathing mode. The mode at 310 cm can be assigned as the symmetrical layer breathing mode. The other A mode is the triangular distortion mode and the calculated frequency is about 149 cm, which is close to the frequencies of the modes observed in CrCl Glamazda et al. (2017) and FeCl Caswell and Solin (1978), 142 and 165 cm, respectively. Since there is no A peak observed in this range, we believe that the triangular distortion mode is unresolvable due to the small scattering cross section, other than the small Raman mode observed at 339 cm.

Inversion symmetry breaking at  GPa – The main feature at  GPa is the appearance of three new Raman modes at 201, 290 and 363 cm. The original five Raman modes at ambient pressure change slightly at . According the group theory and the first-principle calculations of the single -RuCl layer, we assign the mode at 201 cm as an IR-active mode, 290 cm as an inactive mode, and 363 cm as an IR-active mode which has the highest frequency and is related to the asymmetrical layer breathing Note1 (). The appearance of IR-active modes in Raman spectrum indicates the inversion symmetry breaking. To confirm this, the second harmonic generation (SHG) measurement is performed on pressured samples Note1 (). No SHG signal was detected before  GPa, but SHG signal was detected at 1.4 GPa and higher pressure, which is consistent with inversion symmetry breaking at around  GPa. Because of no significant change in other Raman modes, we can conclude that the inversion symmetry breaking is due to stacking pattern change of the -RuCl layers.

Dimerization transition at  GPa – As shown in Fig. 2 (b), almost all of the Raman modes show blue-shift with the pressure increasing, however, the Ru in-plane mode at 161 cm displays anomalous red-shift and a large splitting at  GPa. As shown in Fig. 2 (b), a split peak appears at around 171 cm after 1.7 GPa and rapidly increases to 181 cm at around 2.4 GPa. The the split peak has the higher frequency indicating that two Ru atoms move close to each other and form the dimerization state. By simply assuming that the distance of the nearest Ru atoms is inversely proportional with the frequency of the Ru in-plane mode, we can estimate that the Ru-Ru bond dimerization is about 0.5 Å at 2.4 GPa and increases with pressure.

The Ru-Ru dimerization in the -RuCl layers splits all degenerated modes into modes. We do observe such a splitting for the twist mode at 116 cm, shearing mode at 268 cm (it splits at lower pressure probably due to the interlayer interaction). We don’t detect the splitting for the ring breathing mode at 294 cm probably due to its low intensity and the adjacent intensive layer breathing mode. By considering the normal modes of the split Ru in-pane mode, we can assign the high frequency one as and the low frequency one as . As shown in Fig. 1, the peak becomes much more intense than the peak with pressure increasing. By using 488 nm laser as excitation light, the peak even becomes unresolvable Note1 (). Similarly, the peak of the split twist mode is the low frequency one and cannot be observed after the dimerization. For the shearing mode, the peak is the high frequency one and disappears after the phase transition. In a summary, the softening and large splitting of the Ru in-plane mode provide a direct evidence of dimerization and the behaviors of other Raman modes are consistent with this picture.

Figure 3: Pressure dependence of the magnetic Raman conductivity (a) and the magnetic Raman susceptibility (b). (c) Data and fittings of the phonon Raman spectra (after subtracting the magnetic continuum) for the twisting mode (peak 1) and the Ru in-plane mode (peak 2) under various pressures. The spectra under 0.0 GPa and 0.8 GPa were fitted by Fano peaks. The spectrum under 2.4 GPa was fitted by Lorentz peaks. (d) Pressure dependence of the full width at half maximum (FWHM) and the Fano asymmetry parameter (the inset) for the peak 1 and peak 2.

Magnetic breakdown from Raman susceptibility – Raman spectroscopy also measures the magnetic response in the strong spin-orbit coupling system Moriya (1968); Fleury and Loudon (1968); Lemmens et al. (2003); Nasu et al. (2016). The Raman intensity is proportional to the dynamical Raman tensor susceptibility, . Here is the imaginary part of the correlation functions of Raman tensor, . In general, we can expand the Raman tensor in powers of spin-1/2 operators, . The first term corresponds to Rayleigh scattering, the second and third term are linear and quadratic in the spin operators and correspond to the one magnon Moriya (1968); Fleury and Loudon (1968); Lemmens et al. (2003) and two-magnon process Moriya (1968); Fleury and Loudon (1968); Lemmens et al. (2003); Knolle et al. (2014); Nasu et al. (2016); Fu et al. (2017), respectively. The complex tensor determines the strength of the coupling of light to the spin system associated with spin-orbit coupling.

Figure 4: Schematic phase diagram of -RuCl under pressures. The crystal structure changes from to at , and further to at due to the Ru-Ru bond dimerization. Meanwhile, before the dimerization at , the system is a Mott insulator with magnetism; after dimerization, it is a correlated band insulator without magnetism.

To extract the Raman susceptibility, we first get Raman tensor conductivity for frequencies down to cm, as shown in Fig. 3 (a) and then integrated over the frequency rang of 15-220 cm to get the Raman susceptibility in Fig. 3 (b), by using the Kramers-Kronig relation. The pressure dependent of manifests a rapid increase with increasing the pressure and then a sharp drop to zero at  GPa. The Raman susceptibility contains the static spin susceptibility and multi-spin susceptibility (e.g., bond spin operators), corresponding to one-magnon and multi-magnon process, respectively. As we notice that the static magnetic susceptibility of -RuCl at room temperatures changes little reported in Refs. Cui et al. (2017); Biesner et al. (2018) before dimerization, we suspect that the increasing Raman susceptibility mainly comes from the multi-magnon processes. Above  GPa, both magnetic susceptibility and Raman susceptibility break down, implying the dimerized non-magnetic state.

The Raman spectra of the phonon modes at 116 cm and 161 cm display significant Fano asymmetry before  GPa as shown in Fig. 3 (c). It captures the mutual couplings between the lattice and magnetic excitations. The full width at half maximum (FWHM) and the Fano asymmetry parameter measure the strength of the coupling between the lattice and magnetic excitations, as shown in Fig. 3 (d). We can see that the coupling between lattice and magnetic excitations increases with pressure and is completely suppressed after dimerization, consistent with the evolution of Raman susceptibility in Fig. 3 (b).

Discussions and conclusions– -RuCl has a monoclinic structure at room temperature at ambient pressure. At  GPa, the inversion symmetry is breaking and the system probably turns into the trigonal structure where the inter-layer interaction distorts the inversion symmetry. The structural transition at  GPa is first-order type since the space group changes. The softening and big splitting of the Ru in-plane mode at  GPa provide a direct evidence of dimerization. However, the softening is not complete, but a little. According the “little phonon softening” theory Krumhansl and Gooding (1989), the structural dimerization at  GPa is a first-order transition. We suspect the system has the space group after the dimerization. Dimerization brings the magnetic breakdown due to Mott collapse and the system remains insulating after dimerization. The schematic phase diagram is summarized in Fig. 4.

More remarks on the Mott collapse are needed here. At ambient pressure, -RuCl is a spin-orbit Mott insulator with the Kitaev magnetism. Comparing to the iridates, -RuCl has a larger electron correlation, but the effective and bands near the Fermi surface are not well separated due to a smaller spin-orbit coupling. The mixing between the effective and bands brings -RuCl closer to a Mott transition. According to the first-principle calculations Kim et al. (2015), when the on-site Coulomb interaction is introduced while fixing a paramagnetic state, the bands near the Fermi level take on a predominantly character and a band gap develops, suggesting a correlation-induced insulating phase. The pressure increases the band width, and hence the mixing between the effective and bands. It would finally drive the system into a correlated band insulator via the Mott collapse. The Ru-Ru bond dimerization accelerates the Mott collapse process. Magnetism and chemical bondings is also studied the isostructural counterpart -MoCl by the Raman scattering McGuire et al. (2017). The spin-orbit coupling and quantum spin liquid physics brings more significant relativity and quantum effects in the studies of magnetism and chemical bonds Goodenough (1963).

In conclusions, we perform Raman studies on the relation between Kitaev magnetism and chemical bondings in -RuCl under pressures. At the critical pressure  GPa, -RuCl undergoes the structural transition with the inversion symmetry breaking from the monoclinic to the trigonal . due to different layer stacking. At the critical  GPa, Ru-Ru bonds in the -RuCl dimerizes, and the system turns out to a correlated band insulator due to the Mott collapse.

Note added – During the preparation of our manuscript, similar results about the structural phase transition studied by XRD and infrared spectroscopy were reported by other researchersBastien et al. (2018); Biesner et al. (2018).

Acknowledgments – We would like to thank Prof. Hugen Yan for the IR measurement on the exfoliated -RuCl layers. J.W. Mei thanks Dr. Shunhong Zhang for useful discussions at the early stage of this work. This work was supported by the Science,Technology and Innovation Commission of Shenzhen Municipality (Grant No.ZDSYS20170303165926217). M.H. was partially supported by the Science,Technology and Innovation Commission of Shenzhen Municipality (Grant No.JCYJ20170412152334605 and JCYJ20160531190446212). F.Y. was partially supported by National Nature Science Foundation of China 11774143 and JCYJ20160531190535310.


  • Goodenough (1963) J.B. Goodenough, Magnetism and Chemical Bond, Interscience monographs on chemistry: inorganic chemistry section, v. 1 (Interscience Publ., 1963).
  • Dzyaloshinsky (1958) I. Dzyaloshinsky, “A thermodynamic theory of weak ferromagnetism of antiferromagnetics,” J. Phys. Chem. Solids 4, 241 – 255 (1958).
  • Moriya (1960) Tôru Moriya, “Anisotropic superexchange interaction and weak ferromagnetism,” Phys. Rev. 120, 91–98 (1960).
  • Shekhtman et al. (1992) L. Shekhtman, O. Entin-Wohlman,  and Amnon Aharony, “Moriya’s anisotropic superexchange interaction, frustration, and dzyaloshinsky’s weak ferromagnetism,” Phys. Rev. Lett. 69, 836–839 (1992).
  • Pesin and Balents (2010) Dmytro Pesin and Leon Balents, “Mott physics and band topology in materials with strong spin-orbit interaction,” Nature Physics 6, 376 (2010).
  • Nagaosa et al. (2012) N. Nagaosa, X. Z. Yu,  and Y. Tokura, “Gauge fields in real and momentum spaces in magnets: monopoles and skyrmions,” Philos. Trans. Royal Soc. A 370, 5806–5819 (2012).
  • Nagaosa and Tokura (2012) Naoto Nagaosa and Yoshinori Tokura, “Emergent electromagnetism in solids,” Phys. Scr. 2012, 014020 (2012).
  • Kitaev (2006) Alexei  Kitaev, ‘‘Anyons in an exactly solved model and beyond,” Annals of Physics 321, 2 – 111 (2006).
  • Jackeli and Khaliullin (2009) G. Jackeli and G. Khaliullin, “Mott insulators in the strong spin-orbit coupling limit: From heisenberg to a quantum compass and Kitaev models,” Phys. Rev. Lett. 102, 017205 (2009).
  • Chaloupka et al. (2010) Ji ří Chaloupka, George Jackeli,  and Giniyat Khaliullin, ‘‘Kitaev-heisenberg model on a honeycomb lattice: Possible exotic phases in iridium oxides ,” Phys. Rev. Lett. 105, 027204 (2010).
  • Anderson (1987) Philip W Anderson, “The Resonating Valence Bond State in LaCuO and Superconductivity.” Science 235, 1196–8 (1987).
  • Wen (2004) X.G. Wen, Quantum Field Theory of Many-Body Systems:From the Origin of Sound to an Origin of Light and Electrons, Oxford Graduate Texts (OUP Oxford, 2004).
  • Levin and Wen (2006) Michael Levin and Xiao-Gang Wen, ‘‘Detecting Topological Order in a Ground State Wave Function,” Phys. Rev. Lett. 96, 110405 (2006).
  • Laughlin (1983) R. B. Laughlin, “Anomalous Quantum Hall Effect: An Incompressible Quantum Fluid with Fractionally Charged Excitations,” Phys. Rev. Lett. 50, 1395–1398 (1983).
  • Kivelson et al. (1987) Steven A. Kivelson, Daniel S. Rokhsar,  and James P. Sethna, “Topology of the resonating valence-bond state: Solitons and high- superconductivity,” Phys. Rev. B 35, 8865–8868 (1987).
  • Read and Chakraborty (1989) N. Read and B. Chakraborty, “Statistics of the excitations of the resonating-valence-bond state,” Phys. Rev. B 40, 7133–7140 (1989).
  • Read and Sachdev (1991) N. Read and Subir Sachdev, “Large-n expansion for frustrated quantum antiferromagnets,” Phys. Rev. Lett. 66, 1773–1776 (1991).
  • Wen (1991) X. G. Wen, ‘‘Mean-field theory of spin-liquid states with finite energy gap and topological orders,” Phys. Rev. B 44, 2664–2672 (1991).
  • Ye et al. (2015) F. Ye, P. A. Marchetti, Z. B. Su,  and L. Yu, “Hall effect, edge states, and haldane exclusion statistics in two-dimensional space,” Phys. Rev. B 92, 235151 (2015).
  • Ye et al. (2017) Fei Ye, P A Marchetti, Z B Su,  and L Yu, ‘‘Fractional exclusion and braid statistics in one dimension: a study via dimensional reduction of chern–simons theory,” Journal of Physics A: Mathematical and Theoretical 50, 395401 (2017).
  • Biffin et al. (2014) A. Biffin, R. D. Johnson, Sungkyun Choi, F. Freund, S. Manni, A. Bombardi, P. Manuel, P. Gegenwart,  and R. Coldea, “Unconventional magnetic order on the hyperhoneycomb Kitaev lattice in : Full solution via magnetic resonant x-ray diffraction,” Phys. Rev. B 90, 205116 (2014).
  • Plumb et al. (2014) K. W. Plumb, J. P. Clancy, L. J. Sandilands, V. Vijay Shankar, Y. F. Hu, K. S. Burch, Hae-Young Kee,  and Young-June Kim, “: A spin-orbit assisted mott insulator on a honeycomb lattice,” Phys. Rev. B 90, 041112 (2014).
  • Johnson et al. (2015) R. D. Johnson, S. C. Williams, A. A. Haghighirad, J. Singleton, V. Zapf, P. Manuel, I. I. Mazin, Y. Li, H. O. Jeschke, R. Valentí,  and R. Coldea, “Monoclinic crystal structure of and the zigzag antiferromagnetic ground state,” Phys. Rev. B 92, 235119 (2015).
  • Sears et al. (2015) J. A. Sears, M. Songvilay, K. W. Plumb, J. P. Clancy, Y. Qiu, Y. Zhao, D. Parshall,  and Young-June Kim, “Magnetic order in : A honeycomb-lattice quantum magnet with strong spin-orbit coupling,” Phys. Rev. B 91, 144420 (2015).
  • Banerjee et al. (2016) A. Banerjee, C. A. Bridges, J.-Q. Yan, A. A. Aczel, L. Li, M. B. Stone, G. E. Granroth, M. D. Lumsden, Y. Yiu, J. Knolle, S. Bhattacharjee, D. L. Kovrizhin, R. Moessner, D. A. Tennant, D. G. Mandrus,  and S. E. Nagler, “Proximate Kitaev quantum spin liquid behaviour in a honeycomb magnet,” Nature Materials 15, 733 (2016).
  • Williams et al. (2016) S. C. Williams, R. D. Johnson, F. Freund, Sungkyun Choi, A. Jesche, I. Kimchi, S. Manni, A. Bombardi, P. Manuel, P. Gegenwart,  and R. Coldea, “Incommensurate counterrotating magnetic order stabilized by Kitaev interactions in the layered honeycomb ,” Phys. Rev. B 93, 195158 (2016).
  • Ran et al. (2017) Kejing Ran, Jinghui Wang, Wei Wang, Zhao-Yang Dong, Xiao Ren, Song Bao, Shichao Li, Zhen Ma, Yuan Gan, Youtian Zhang, J. T. Park, Guochu Deng, S. Danilkin, Shun-Li Yu, Jian-Xin Li,  and Jinsheng Wen, “Spin-wave excitations evidencing the Kitaev interaction in single crystalline ,” Phys. Rev. Lett. 118, 107203 (2017).
  • Zheng et al. (2017) Jiacheng Zheng, Kejing Ran, Tianrun Li, Jinghui Wang, Pengshuai Wang, Bin Liu, Zheng-Xin Liu, B. Normand, Jinsheng Wen,  and Weiqiang Yu, “Gapless spin excitations in the field-induced quantum spin liquid phase of ,” Phys. Rev. Lett. 119, 227208 (2017).
  • Yu et al. (2018) Y. J. Yu, Y. Xu, K. J. Ran, J. M. Ni, Y. Y. Huang, J. H. Wang, J. S. Wen,  and S. Y. Li, ‘‘Ultralow-temperature thermal conductivity of the Kitaev honeycomb magnet across the field-induced phase transition,” Phys. Rev. Lett. 120, 067202 (2018).
  • JanÅ¡a et al. (2018) Nejc JanÅ¡a, Andrej Zorko, Matjaž GomilÅ¡ek, Matej Pregelj, Karl W. Krämer, Daniel Biner, Alun Biffin, Christian Rüegg,  and Martin KlanjÅ¡ek, “Observation of two types of fractional excitation in the Kitaev honeycomb magnet,” Nature Physics  (2018).
  • Baek et al. (2017) S.-H. Baek, S.-H. Do, K.-Y. Choi, Y. S. Kwon, A. U. B. Wolter, S. Nishimoto, Jeroen van den Brink,  and B. Büchner, “Evidence for a field-induced quantum spin liquid in -,” Phys. Rev. Lett. 119, 037201 (2017).
  • Banerjee et al. (2018) Arnab Banerjee, Paula Lampen-Kelley, Johannes Knolle, Christian Balz, Adam Anthony Aczel, Barry Winn, Yaohua Liu, Daniel Pajerowski, Jiaqiang Yan, Craig A. Bridges, Andrei T. Savici, Bryan C. Chakoumakos, Mark D. Lumsden, David Alan Tennant, Roderich Moessner, David G. Mandrus,  and Stephen E. Nagler, “Excitations in the field-induced quantum spin liquid state of -rucl-3,” npj Quantum Materials 3, 8 (2018).
  • Wolter et al. (2017) A. U. B. Wolter, L. T. Corredor, L. Janssen, K. Nenkov, S. Schönecker, S.-H. Do, K.-Y. Choi, R. Albrecht, J. Hunger, T. Doert, M. Vojta,  and B. Büchner, “Field-induced quantum criticality in the Kitaev system ,” Phys. Rev. B 96, 041405 (2017).
  • Wang et al. (2017) Zhe Wang, S. Reschke, D. Hüvonen, S.-H. Do, K.-Y. Choi, M. Gensch, U. Nagel, T. Rõ om,  and A. Loidl, “Magnetic excitations and continuum of a possibly field-induced quantum spin liquid in ,” Phys. Rev. Lett. 119, 227202 (2017).
  • Hentrich et al. (2018) Richard Hentrich, Anja U. B. Wolter, Xenophon Zotos, Wolfram Brenig, Domenic Nowak, Anna Isaeva, Thomas Doert, Arnab Banerjee, Paula Lampen-Kelley, David G. Mandrus, Stephen E. Nagler, Jennifer Sears, Young-June Kim, Bernd Büchner,  and Christian Hess, “Unusual phonon heat transport in : Strong spin-phonon scattering and field-induced spin gap,” Phys. Rev. Lett. 120, 117204 (2018).
  • Kasahara et al. (2018) Y. Kasahara, T. Ohnishi, Y. Mizukami, O. Tanaka, S. Ma, K. Sugii, N. Kurita, H. Tanaka, J. Nasu, Y. Motome, T. Shibauchi,  and Y. Matsuda, “Majorana quantization and half-integer thermal quantum Hall effect in a Kitaev spin liquid,” ArXiv e-prints  (2018), arXiv:1805.05022 [cond-mat.str-el] .
  • Wang et al. (2018) Zhe Wang, Jing Guo, F. F. Tafti, Anthony Hegg, Sudeshna Sen, Vladimir A. Sidorov, Le Wang, Shu Cai, Wei Yi, Yazhou Zhou, Honghong Wang, Shan Zhang, Ke Yang, Aiguo Li, Xiaodong Li, Yanchun Li, Jing Liu, Youguo Shi, Wei Ku, Qi Wu, Robert J. Cava,  and Liling Sun, “Pressure-induced melting of magnetic order and emergence of a new quantum state in ,” Phys. Rev. B 97, 245149 (2018).
  • Cui et al. (2017) Y. Cui, J. Zheng, K. Ran, Jinsheng Wen, Zheng-Xin Liu, B. Liu, Wenan Guo,  and Weiqiang Yu, “High-pressure magnetization and nmr studies of ,” Phys. Rev. B 96, 205147 (2017).
  • Bastien et al. (2018) G. Bastien, G. Garbarino, R. Yadav, F. J. Martinez-Casado, R. Beltrán Rodríguez, Q. Stahl, M. Kusch, S. P. Limandri, R. Ray, P. Lampen-Kelley, D. G. Mandrus, S. E. Nagler, M. Roslova, A. Isaeva, T. Doert, L. Hozoi, A. U. B. Wolter, B. Büchner, J. Geck,  and J. van den Brink, “Pressure-induced dimerization and valence bond crystal formation in the Kitaev-heisenberg magnet ,” Phys. Rev. B 97, 241108 (2018).
  • Biesner et al. (2018) Tobias Biesner, Sananda Biswas, Weiwu Li, Yohei Saito, Andrej Pustogow, Michaela Altmeyer, Anja U. B. Wolter, Bernd Büchner, Maria Roslova, Thomas Doert, Stephen M. Winter, Roser Valentí,  and Martin Dressel, ‘‘Detuning the honeycomb of : Pressure-dependent optical studies reveal broken symmetry,” Phys. Rev. B 97, 220401 (2018).
  • Hermann et al. (2018) V. Hermann, M. Altmeyer, J. Ebad-Allah, F. Freund, A. Jesche, A. A. Tsirlin, M. Hanfland, P. Gegenwart, I. I. Mazin, D. I. Khomskii, R. Valentí,  and C. A. Kuntscher, ‘‘Competition between spin-orbit coupling, magnetism, and dimerization in the honeycomb iridates: under pressure,” Phys. Rev. B 97, 020104 (2018).
  • Majumder et al. (2018) M. Majumder, R. S. Manna, G. Simutis, J. C. Orain, T. Dey, F. Freund, A. Jesche, R. Khasanov, P. K. Biswas, E. Bykova, N. Dubrovinskaia, L. S. Dubrovinsky, R. Yadav, L. Hozoi, S. Nishimoto, A. A. Tsirlin,  and P. Gegenwart, “Breakdown of magnetic order in the pressurized Kitaev iridate ,” Phys. Rev. Lett. 120, 237202 (2018).
  • Lemmens et al. (2003) P. Lemmens, G. Güntherodt,  and C. Gros, “Magnetic light scattering in low-dimensional quantum spin systems,” Physics Reports 375, 1 – 103 (2003).
  • Devereaux and Hackl (2007) Thomas P. Devereaux and Rudi Hackl, “Inelastic light scattering from correlated electrons,” Rev. Mod. Phys. 79, 175–233 (2007).
  • Moriya (1968) Tôru Moriya, “Theory of absorption and scattering of light by magnetic crystals,” Journal of Applied Physics 39, 1042–1049 (1968).
  • Fleury and Loudon (1968) P. A. Fleury and R. Loudon, “Scattering of light by one- and two-magnon excitations,” Phys. Rev. 166, 514–530 (1968).
  • Nasu et al. (2016) J. Nasu, J. Knolle, D. L. Kovrizhin, Y. Motome,  and R. Moessner, “Fermionic response from fractionalization in an insulating two-dimensional magnet,” Nature Physics 12, 912 (2016).
  • Fu et al. (2017) Jianlong Fu, Jeffrey G. Rau, Michel J. P. Gingras,  and Natalia B. Perkins, “Fingerprints of quantum spin ice in raman scattering,” Phys. Rev. B 96, 035136 (2017).
  • Shastry and Shraiman (1990) B. Sriram Shastry and Boris I. Shraiman, “Theory of raman scattering in mott-hubbard systems,” Phys. Rev. Lett. 65, 1068–1071 (1990).
  • Ko et al. (2010) Wing-Ho Ko, Zheng-Xin Liu, Tai-Kai Ng,  and Patrick A. Lee, “Raman signature of the u(1) dirac spin-liquid state in the spin- kagome system,” Phys. Rev. B 81, 024414 (2010).
  • Knolle et al. (2014) J. Knolle, Gia-Wei Chern, D. L. Kovrizhin, R. Moessner,  and N. B. Perkins, “Raman scattering signatures of Kitaev spin liquids in iridates with or li,” Phys. Rev. Lett. 113, 187201 (2014).
  • Sandilands et al. (2015) Luke J. Sandilands, Yao Tian, Kemp W. Plumb, Young-June Kim,  and Kenneth S. Burch, ‘‘Scattering continuum and possible fractionalized excitations in ,” Phys. Rev. Lett. 114, 147201 (2015).
  • Glamazda et al. (2016) A. Glamazda, P. Lemmens, S. H. Do, Y. S. Choi,  and K. Y. Choi, “Raman spectroscopic signature of fractionalized excitations in the harmonic-honeycomb iridates - and -li2iro3,” Nature Communications 7, 12286 (2016).
  • Glamazda et al. (2017) A. Glamazda, P. Lemmens, S.-H. Do, Y. S. Kwon,  and K.-Y. Choi, “Relation between Kitaev magnetism and structure in ,” Phys. Rev. B 95, 174429 (2017).
  • (55) See Supplemental Materials for more details.
  • Caswell and Solin (1978) N. Caswell and S.A. Solin, “Vibrational excitations of pure fecl3 and graphite intercalated with ferric chloride,” Solid State Communications 27, 961 – 967 (1978).
  • Krumhansl and Gooding (1989) J. A. Krumhansl and R. J. Gooding, “Structural phase transitions with little phonon softening and first-order character,” Phys. Rev. B 39, 3047–3053 (1989).
  • McGuire et al. (2017) Michael A. McGuire, Jiaqiang Yan, Paula Lampen-Kelley, Andrew F. May, Valentino R. Cooper, Lucas Lindsay, Alexander Puretzky, Liangbo Liang, Santosh KC, Ercan Cakmak, Stuart Calder,  and Brian C. Sales, “High-temperature magnetostructural transition in van der waals-layered ,” Phys. Rev. Materials 1, 064001 (2017).
  • Kim et al. (2015) Heung-Sik Kim, Vijay Shankar V., Andrei Catuneanu,  and Hae-Young Kee, “Kitaev magnetism in honeycomb with intermediate spin-orbit coupling,” Phys. Rev. B 91, 241110 (2015).
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