Detuning the Honeycomb of $α$-RuCl$_{3}$: Pressure-Dependent Optical Studies Reveal Broken Symmetry
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 Martin Dressel






    
    1. Physikalisches Institut, Universität Stuttgart, Pfaffenwaldring 57, 70550 Stuttgart, Germany
    
    Institut für Theoretische Physik, Goethe-Universität Frankfurt, 60438 Frankfurt am Main, Germany
    
    1. Physikalisches Institut, Universität Stuttgart, Pfaffenwaldring 57, 70550 Stuttgart, Germany
    
    1. Physikalisches Institut, Universität Stuttgart, Pfaffenwaldring 57, 70550 Stuttgart, Germany
    
    1. Physikalisches Institut, Universität Stuttgart, Pfaffenwaldring 57, 70550 Stuttgart, Germany
    
    Institut für Theoretische Physik, Goethe-Universität Frankfurt, 60438 Frankfurt am Main, Germany
    
    Leibniz Institut für Festkörper- und Werkstoffforschung (IFW) Dresden, 01171 Dresden, Germany
    
    Leibniz Institut für Festkörper- und Werkstoffforschung (IFW) Dresden, 01171 Dresden, Germany
    Institut für Festkörperphysik, Technische Universität Dresden, 01062 Dresden, Germany
    
    Fachrichtung Chemie und Lebensmittelchemie, Technische Universität Dresden, 01062 Dresden, Germany
    
    Fachrichtung Chemie und Lebensmittelchemie, Technische Universität Dresden, 01062 Dresden, Germany
    
    Institut für Theoretische Physik, Goethe-Universität Frankfurt, 60438 Frankfurt am Main, Germany
    
    Institut für Theoretische Physik, Goethe-Universität Frankfurt, 60438 Frankfurt am Main, Germany
    
    1. Physikalisches Institut, Universität Stuttgart, Pfaffenwaldring 57, 70550 Stuttgart, Germany

    


The honeycomb Mott insulator α-RuCl_3 loses its low-temperature magnetic order by pressure. We report clear evidence for a dimerized structure at P>1 GPa and observe the breakdown of the relativistic j_ eff picture in this regime strongly affecting the electronic properties. A pressure-induced Kitaev quantum spin liquid cannot occur in this broken symmetry state. We shed light on the new phase by broad-band infrared spectroscopy of the low-temperature properties of α-RuCl_3 and  ab initio density functional theory calculations, both under hydrostatic pressure.



75.10.Jm,    
75.10.Kt,    
78.20.-e,    

61.50.Ks,    
78.30.-j    

Detuning the Honeycomb of α-RuCl_3:

Pressure-Dependent Optical Studies Reveal Broken Symmetry
    Martin Dressel
    December 30, 2023
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Interest in quantum spin liquids has grown steadily during the last decade, as more materials could be realized successfully. For instance, the organic charge transfer salts reach a high degree of frustration by forming an almost ideal triangular lattice <cit.> or the herbertsmithites crystallize in a perfect kagome lattice <cit.>. In all of these examples no signs of magnetic order could be detected down to temperatures several orders of magnitude below the dominant magnetic couplings – thus providing strong evidence for a quantum spin liquid state.

Over the last years a new class of frustrated magnets, the so-called honeycomb Kitaev systems <cit.>, has attracted the attention of the condensed matter community. Prominent examples are  <cit.> together with Li_2IrO_3 and Na_2IrO_3 <cit.>. Although  shows zigzag antiferromagnetic order below T_ N≈ 7 K, neutron and Raman scattering experiments identified a continuum of excitations <cit.> whose origin is intensively discussed in terms of magnon breakdown <cit.> and possible fractionalized Majorana excitations <cit.>. Furthermore,  undergoes a transition to a quantum disordered state in an external magnetic field <cit.> and suggestions of appearance of possible spin-liquid behavior are presently being discussed <cit.>. The application of pressure to further tune the magnetic couplings is an attractive approach only recently being explored <cit.>.

Specific heat measurements  <cit.> reveal that the Néel temperature T_ N of  is initially enhanced by pressure, but magnetic order is sharply suppressed at a pressure of P ≈ 0.7 GPa. NMR and magnetization studies consistently indicated a magnetically disordered high-pressure phase with strongly reduced susceptibility <cit.>; hence, Cui et al. posited the existence of a structural instability. This reminds of a recent investigation on α-Li_2IrO_3 <cit.>, which indicated dimerization above a critical pressure. Such instabilities could be rather general to the family of honeycomb Kitaev materials <cit.>. In order to shed light on these issues, we have conducted comprehensive spectroscopic investigations of the optical properties of  under pressure, which are combined with ab initio density functional theory calculations of the phonon spectrum and electronic properties. Our observations show that  undergoes a structural transition at moderate pressures where Ru-Ru dimers are formed.



High-quality single crystals of  were grown by chemical vapour transport as described in Ref. <cit.>. The crystals were characterized by magnetic susceptibility measurements with the field along the ab–plane where magnetic order at T_ N≈ 11 K and 8 K is observed; the high temperature Curie-Weiss fit yields θ_ CW=38 K and μ_ eff=2.3 μ_B. Optical reflectivity experiments employed several Fourier-transform spectrometers covering the range from 100 up to 20 000 . For measurements from the near-infrared up to the ultraviolet spectral range spectroscopic ellipsometry was utilized. Ambient pressure experiments were performed in helium-bath and flow cryostats, with the help of an infrared microscope if required. While the magnetic transitions at T_ N do show up as minor changes in the optical spectra, applying an external magnetic field up to 7.4 T (both in-plane and out-of-plane) does not affect the infrared transmission noticeably. In addition, we conducted reflectivity measurements in a piston pressure cell operating up to 2 GPa and down to temperatures as low as 10 K  by using Daphne oil as the pressure transmitting medium <cit.>. For those measurements we prepared a powder and pressed pellets. The optical conductivity was obtained from a Kramers-Kronig analysis of the combined data using common high- and low-frequency extrapolations.








In order to identify a possible structural transition under pressure, we begin with the phononic contributions to the optical spectra of
, observed below 400 .
In Fig. <ref>(a) the optical conductivity at T=10 K is displayed for the whole pressure range. Two phonon modes are clearly visible at 290  and 320  (peak 1) at low pressures. In previous ambient-pressure infrared <cit.> and Raman experiments <cit.>, these two features were identified as out-of-plane A_2u and in-plane E_u vibrations, respectively, with reference to an idealized P3̅1m symmetry of the individual RuCl_3 layers.
For the presently studied powder samples, the presence of stacking faults likely reduces the symmetry even at low pressure, effectively mixing the ambient pressure ABC (rhombohedral R3̅) and AB (monoclinic C2/m) stacking motifs. In order to assign the vibrations, we therefore performed phonon calculations using the linear response method <cit.> in the lower C2/m symmetry (see Fig. <ref>). The displacements are sketched in Fig. <ref>(c–g). At ambient pressure, we find a weak infrared-active out-of-plane mode with frequency 287 , which can be identified with the observed peak at 290  (see Supplemental Material <cit.>). At higher frequencies, the calculations suggest a trio of nearly degenerate modes with mostly in-plane polarization vectors; the frequencies of these modes are computed to be ω_0 ≈ 321, 322, and 326 . The near-degeneracy of the modes (Δω/ω_0 ≈ 1.5%) stems from the quasi-threefold symmetry of the individual RuCl_3 layers, which is preserved regardless of the stacking pattern.  The pronounced deflection of Ru and Cl sites for the modes near 320  provides a large dipole moment, resulting in a larger intensity compared to the 290  vibration. Complementary optical transmission measurements on single crystals at ambient pressure support these assignments; they are presented in Fig.  <cit.>.


Under applied pressure, both modes shift to high energy as expected for reduced lattice spacing. For P > 0.7 GPa, the 320  peak (1) develops a pronounced shoulder (peak 2 in Fig. <ref>(a)), which eventually splits off with increasing P, producing two features with an intensity ratio of approximately 1:2. In Fig. <ref>(b) and (c) the frequency shift and linewidth Γ are quantified as a function of pressure, on the basis of Lorentzian fits. Between 0.96 and 1.08 GPa (P_c) the linewidth of the main mode around ω_0 = 320  suddenly decreases to Γ≈ 10  while the phonon mode splits. This large splitting can be taken as direct evidence that the quasi-threefold lattice symmetry of the layers is broken at high pressure, suggesting the possibility of dimerization.

In order to verify whether  is susceptible to dimerization under pressure, we performed ab initio calculations for structural optimization under pressure (see Supplemental Materials <cit.> for all computational details).
Similar to previous calculations on α-Li_2IrO_3 <cit.>, we find that parallel dimerization becomes energetically favored at high pressure over the homogeneous ambient pressure structure. The high-pressure phase is triclinic P1̅, and is shown in Fig. <ref>(b); the computation of phonons for the dimerized structure shows a splitting of the almost degenerate modes in the homogeneous structure [Fig. <ref>(c–e)] into two dominant in-plane modes [Fig. <ref>(f,g)] with frequencies reaching 330 and 345  in the limit P = 10 GPa. Consistent with the experiment, we also find that the calculated infrared intensity of the latter mode is higher than the former. The large computed splitting of Δω≈ 15  compares well with the results from the conductivity measurements in Fig. <ref>(b), providing further support for a pressure-driven structural phase transition of  to a dimerized phase.




This observed reduction of lattice symmetry is expected to severely affect the electronic structure.
In order to determine the electronic properties under pressure, we performed temperature-dependent infrared reflectivity experiments on  pellets while applying hydrostatic pressures step-by-step up to 1.7 GPa. A general overview of the electrodynamic properties is given in Fig. <ref>(a). The sharp absorption edge at 1.1 eV (α-peak) is assigned to intersite d^5-d^5 → d^6-d^4 excitations <cit.> yielding a final d^4 triplet ^3T_1 state. Transitions to higher-energy multiplets appear above 1.5 eV. In addition to the main α-peak, on the high-frequency wing a weak shoulder appears around 10 500 , which we call α^'. On the lower-frequency side, a narrow peak
labeled Λ develops at 8800  below T=120 K, which is likely a bound excitonic state <cit.>. Intrasite t_2g^5-e_g^0 → t_2g^4-e_g^1 excitations (see Fig.  <cit.>) are also identified at 0.28 eV <cit.>, while higher energy bands around 5.2 eV originate from transitions between Cl 3p and Ru 4d states [Fig.  <cit.>].

Fig. <ref>(b–d) displays the temperature evolution of the conductivity spectra for selected pressure values. The effect of P on the low-temperature conductivity can be followed in Fig. <ref>(e,f). From Lorentz fits of the conductivity we obtain the pressure-dependent peak position, spectral weight and width for each contribution, as plotted in Fig. <ref>(g–k). The α- and Λ-features generally broaden and slightly redshift with increasing P. In accord with transport data <cit.>, our optical measurements therefore do not reveal a closure of the Mott gap under pressure. Near P_c, the spectral weight of the α-feature instead diminishes dramatically by almost one order of magnitude, cf. Fig. <ref>(k). The drop is most pronounced between P=0.85 and 1.08 GPa. When pressurized further, the α-peak cannot be well identified anymore.
The excitonic Λ-feature behaves likewise before it vanishes above 1.22 GPa. The similar pressure dependence observed for both peaks α and Λ [Fig. <ref>(h)] not only supports the assignment of Λ as an excitonic resonance <cit.> but sheds light on their common physical origin. From the α^'-shoulder a broad maximum emerges around 11 000  above P_c, which becomes more pronounced with cooling and eventually dominates the entire infrared spectrum.  This mode rapidly shifts up by about 800  in the range from 0.44 to 1.73 GPa, as shown in Fig. <ref>(i). This distinct pressure dependence suggests a different physical origin compared to the α and Λ modes.


Focusing on the α peak, Fig. <ref>(g) displays the T dependence of the spectral weight (SW) obtained from Lorentz fits. Up to P=0.7 GPa, the α-peak notably intensifies upon cooling. Following <cit.>, the intensity of such excitations to the ^3T_1 triplet state is expected to scale like I∝  1+ 4 ⟨ S_i^γ S_j^γ⟩ (γ =x,y,z), providing a local probe of the magnetic correlations. An analogous enhancement of the α-peak intensity on cooling in recent EELS measurements was thus ascribed to the development of short-ranged ferromagnetic correlations (i.e. ⟨ S_i^γ S_j^γ⟩ > 0) below T= 100 K <cit.>. At higher pressures, we find that the spectral weight behaves fundamentally differently. For P ≥ 0.85 GPa it decreases upon cooling down to T=50 K and saturates at lower temperatures. For P > 1.22 GPa the spectral weight is almost completely suppressed, and nearly independent on T. The suppression of the α-peak therefore strongly suggests a collapse of the ferromagnetic Kitaev interactions above ∼ 0.7 GPa, which may be related to (i) a breakdown of the j_ eff picture, and/or (ii) the development of strong intradimer antiferromagnetic correlations. The latter effect is consistent with the greatly suppressed magnetic susceptibility observed above 0.7 GPa <cit.>.




In order to gain insight into the high-pressure electronic structure, in Fig. <ref>(a–d) we show the calculated orbital-dependent density of states (DOS) within the GGA+SOC+U method and the FPLO basis with U=1.5 eV for the undimerized (P=0) and dimerized P>P_c structures. For P=0 GPa, the narrow peak in the DOS at ∼ 1 eV represents the single t_2g hole at each Ru site, which resides in a relativistic j_ eff = 1/2 state composed of nearly equal contributions from each of the d_xy, d_xz, and d_yz orbitals [Fig. <ref>(a)]. The assignment is further verified by projecting onto the atomic J-states, for which the j_ eff = 1/2 orbital has purely J = 5/2 contributions, as shown in  Fig. <ref>(c). In this case, the hopping of holes between Ru sites occurs largely through Cl p_z orbitals, as described by the hopping integral t_2, shown in Fig. <ref>(e). This leads to a dominant ferromagnetic Kitaev interaction K S_i^γ S_j^γ at low P that scales as K ∝ -J_H(t_2)^2/U^2 <cit.>, although other magnetic interactions of similar scale are also present due to finite t_1 and t_3 <cit.>.

In contrast, for P > P_c, the dimerization is manifested by a strong splitting of the d_xy orbitals into bonding and antibonding states as shown in Fig. <ref>(b), which destroys the relativistic j_ eff states [compare to Fig. <ref>(d)]. These effects arise from a strong enhancement of the direct Ru-Ru t_3 hopping path along the dimerized bonds. Within the dimers, the magnetic couplings are thus dominated by large anti­ferromagnetic Heisenberg J  𝐒_i ·𝐒_j interactions, with J∝ +(t_3)^2/U  <cit.>.
Consistently, dimerization leads to complete suppression of the computed magnetic moments for the high pressure P1̅ structure at the level of GGA+SOC+U.
This observation explains the suppression of zig-zag order at pressures around 1 GPa <cit.>, in favour of a gapped state. These findings are all in analogy with the honeycomb iridate α-Li_2IrO_3 <cit.>.



We conclude from our pressure-dependent optical investigation of the electronic and phononic properties of  that the structural symmetry is broken around 1 GPa. The dimerization of Ru-Ru bonds at high pressure is seen by the splitting of the 320  phonon modes, which is consistently observed in the DFT calculations. This dimerization has dramatic effects on the electronic structure, as evidenced by the disappearance of the excitonic Λ feature above 1 GPa and the development of the second α^' excitation on the high energy side of the optical gap. The temperature and pressure dependence of the optical response suggest a collapse of the Kitaev couplings in the dimerized phase, which is further motivated by theoretical analysis of the electronic structure. These observations rule out the possibility that  can be tuned towards a Kitaev spin liquid state under pressure. Instead it appears as a gapped dimerized phase.





We thank Ying Li and Kira Riedl for fruitful discussions; Micha Schilling for assistance in the magneto-optical measurements
and Gabriele Untereiner for continuous experimental support. The project was supported by the Deutsche Forschungsgemeinschaft (DFG) through grant SFB/TR 49, SFB 1143, DR228/39-1 and DR228/51-1.







