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Zichen Yang, Lichen Wang, Dong Zhao, Mingdi Luo, Sourav Laha, Achim Güth, [Takashi Taniguchi](https://orcid.org/0000-0002-1467-3105), [Kenji Watanabe](https://orcid.org/0000-0003-3701-8119), Bettina V. Lotsch, Jurgen H. Smet, Matteo Minola, Hlynur Gretarsson, Bernhard Keimer

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[Resonant inelastic x-ray scattering from electronic excitations in <math>  <mrow>    <mi>α</mi>    <mtext>−</mtext>    <msub>      <mi>RuCl</mi>      <mn>3</mn>    </msub>  </mrow></math> nanolayers](https://mdr.nims.go.jp/datasets/c1161ce3-d4bc-4959-9fa6-0c3543a4715c)

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Resonant inelastic x-ray scattering from electronic excitations in $\alpha\text{-}{\rm RuCl}_3$ nanolayersPHYSICAL REVIEW B 108, L041406 (2023)LetterResonant inelastic x-ray scattering from electronic excitations in α-RuCl3 nanolayersZichen Yang,1 Lichen Wang ,1 Dong Zhao ,1 Mingdi Luo ,1 Sourav Laha ,1,* Achim Güth,1 Takashi Taniguchi,2Kenji Watanabe ,2 Bettina V. Lotsch ,1 Jurgen H. Smet,1 Matteo Minola ,1 Hlynur Gretarsson ,3 and Bernhard Keimer 1,†1Max Planck Institute for Solid State Research, Heisenbergstrasse 1, D-70569 Stuttgart, Germany2National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan3Deutsches Elektronen-Synchrotron DESY, Notkestraße 85, D-22607 Hamburg, Germany(Received 7 March 2023; accepted 29 June 2023; published 27 July 2023)We present Ru L3-edge resonant inelastic x-ray scattering (RIXS) measurements of spin-orbit and d-dexcitations in exfoliated nanolayers of the Kitaev spin-liquid candidate RuCl3. Whereas the spin-orbit excitationsare independent of thickness, we observe a pronounced redshift and broadening of the d-d excitations in layerswith thicknesses below ∼7 nm. Aided by model calculations, we attribute these effects to distortions of theRuCl6 octahedra near the surface. Our study paves the way towards RIXS investigations of electronic excitationsin various other two-dimensional materials and heterostructures.DOI: 10.1103/PhysRevB.108.L041406Since the discovery of the Scotch-tape exfoliationmethod [1,2], two-dimensional (2D) materials and het-erostructures have grown into a unique laboratory for quantumphysics. By reconfiguring the crystal symmetry and reduc-ing the dimensionality of the electron system, exfoliation ofatomically thin sheets can generate electronic ground stateswith physical properties radically different from those of bulkanalogs. Superstructures generated by vertical stacking [3–5]and lateral twisting [6] of these sheets add numerous optionsfor the control and design of collective quantum phenom-ena. To realize these perspectives, experimental informationon the electron-electron and electron-lattice interactions thatdetermine the stability of different quantum states is indis-pensable. Research on bulk quantum materials has shownthat data from energy- and momentum-resolved spectro-scopic probes provide particularly insightful information forrealistic model calculations. Prominent examples includeangle-resolved photoemission spectroscopy (ARPES) and in-elastic neutron scattering (INS), which yield the dispersionrelations of electronic bands and collective excitations, re-spectively. Whereas ARPES has been widely applied to 2Dmaterials, however, INS experiments are not feasible becausethey require sample volumes in the cm3 range.Resonant inelastic x-ray scattering (RIXS) has recentlygained prominence as a momentum-resolved spectroscopic*Present address: Department of Chemistry, National Institute ofTechnology Durgapur, Mahatma Gandhi Avenue, Durgapur-713209,India.†B.Keimer@fkf.mpg.dePublished by the American Physical Society under the terms of theCreative Commons Attribution 4.0 International license. Furtherdistribution of this work must maintain attribution to the author(s)and the published article’s title, journal citation, and DOI. Openaccess publication funded by the Max Planck Society.probe of electronic and vibrational excitations [7,8]. Whereasthe energy resolution of RIXS for collective magnetic andvibrational excitations remains lower than the one of INS,the latest generation of RIXS instruments has enabled thedetection of such excitations in many materials, and RIXSadditionally probes charge and orbital excitations over a widespectral range (meV–eV). This includes ligand-field exci-tations which are hard to access with other spectroscopictechniques and whose knowledge is often crucial to under-stand the physics of 2D materials and van der Waals (vdW)heterostructures. Crucially, the large resonant enhancementof the scattering cross section at x-ray absorption edges,combined with the high photon flux at modern synchrotronsources, endow RIXS with a sensitivity that greatly exceedsthe one of INS and has allowed the detection of excitationsfrom microcrystals and thin films [9–12]. In exfoliated layersand vdW heterostructures, RIXS has the potential to reveal awealth of information about atomic-scale interactions includ-ing crystalline electric fields, spin-orbit coupling, magneticexchange, and electron-phonon interactions. The element-selective nature of RIXS allows one to focus exclusively onthe properties of a specific layer of a vdW heterostructure,without interference from substrates and protective cappinglayers. However, as the lateral dimensions of typical exfo-liated nanoflakes are below the x-ray beam diameter, suchexperiments present formidable challenges, and the poten-tial of RIXS for research on 2D materials remains largelyuntapped.Here, we report RIXS experiments on exfoliated nanolay-ers of α-RuCl3 (RuCl3 hereafter), a possible solid-staterealization of the intensely investigated Kitaev spin liq-uid [13–15]. The crystal structure of RuCl3 [Fig. 1(a)] iscomposed of edge-sharing RuCl6 octahedra with magneticRu atoms arranged on a honeycomb lattice. As a conse-quence of the strong spin-orbit coupling (SOC) of Ru, thelow-energy magnetic dynamics can be described in termsof pseudospins S̃ = 1/2 that interact via bond-directional,2469-9950/2023/108(4)/L041406(6) L041406-1 Published by the American Physical Societyhttps://orcid.org/0000-0002-2392-6063https://orcid.org/0000-0002-7753-7637https://orcid.org/0000-0002-0100-499Xhttps://orcid.org/0000-0002-4554-5042https://orcid.org/0000-0003-3701-8119https://orcid.org/0000-0002-3094-303Xhttps://orcid.org/0000-0003-4084-0664https://orcid.org/0009-0008-3209-6736https://orcid.org/0000-0001-5220-9023http://crossmark.crossref.org/dialog/?doi=10.1103/PhysRevB.108.L041406&domain=pdf&date_stamp=2023-07-27https://doi.org/10.1103/PhysRevB.108.L041406https://creativecommons.org/licenses/by/4.0/ZICHEN YANG et al. PHYSICAL REVIEW B 108, L041406 (2023)FIG. 1. (a) In-plane crystal structure of RuCl3. Red, green, andblue lines illustrate the bond-directional Kitaev interactions betweenmagnetic Ru ions on the honeycomb lattice. (b) Schematic of thescattering geometry. The incident x-ray photons are π polarized, andthe polarization of the scattered x-ray photons is not analyzed. Thescattering angle is fixed at 90◦ throughout the experiment to suppresscharge scattering. (c) Schematic of the elementary excitations ofRuCl3. The S̃ = 1/2 → 3/2 spin-orbit exciton (green) is locatedat the excitation energy ∼3/2λ. The higher-energy d-d excitations(blue) are superposed by the electron-hole continuum (gray).frustrated Kitaev interactions as well as conventional Heisen-berg and off-diagonal exchange interactions. The confluenceof these interactions drives the system into a state withzigzag antiferromagnetic (AFM) order at low temperatures.Nevertheless, a continuum of (possibly fractionalized) mag-netic excitations [16,17] and a magnetic-field-induced phasewith highly unusual thermal transport properties [18–21] havebeen ascribed to Kitaev interactions. Since adjacent honey-comb layers are chemically bonded predominantly throughvan der Waals forces, RuCl3 has also been investigated inthe form of exfoliated nanosheets [22–26] and vdW het-erostructures [27–30]. These developments raise the prospectof studying magnetism in the 2D limit, without the influ-ence of the interlayer interactions that are found to have anon-negligible influence on the magnetic structure of bulkRuCl3 [31,32]. They also open up perspectives for targetedmodification of the electronic properties, for instance by dop-ing charge carriers into the correlated pseudospin system viadoping across heterointerfaces, or by interfacial proximitycoupling to other quantum states such as superconductiv-ity [33–36].Motivated by these prospects and by the detailed informa-tion on crystal-field, spin-orbit, and exchange interactions ob-tained from previous RIXS experiments on bulk RuCl3 [37],we prepared a series of RuCl3 nanoflakes of varying thicknessdown to 3.5 nm and lateral dimensions comparable to thoseof the x-ray beams required for RIXS. We obtained high-quality Ru L3-edge RIXS spectra on all samples, without anysign of x-ray beam damage. With decreasing thickness, weobserved a redshift and broadening of electronic transitionsfrom the Ru t2g orbitals in the crystal-field ground state intoexcited states in the eg manifold, whereas intra-atomic spin-orbit excitations are thickness independent. Based on ionicmodel calculations and a comparison to prior surface-sensitivestudies, we attribute this trend to an altered ligand field nearthe surface, which controls the ratio of Kitaev and Heisenberginteractions and hence the magnetic ground state. Our resultsindicate that RIXS experiments on a variety of 2D materialsand vdW heterostructures—and the resulting wellspring ofinformation on electronic interactions—are within reach ofcurrent instrumentation.The experiments were performed at the intermediate x-rayenergy RIXS spectrometer (IRIXS) at the Dynamics Beam-line P01 of the synchrotron PETRA III, DESY [10,37–40],which operates at the Ru-L3 absorption edge (photon en-ergy 2837 eV). We used IRIXS in two configurations, i.e.,with inline high-resolution monochromator (HRM) (beam-spot size 150 × 20 µm2) and nested HRM (beam-spot size20 × 20 µm2), yielding a combined resolution of 77 and96 meV, respectively [41]. Figure 1(b) shows the experimentalgeometry. The incoming beam is π polarized and the polariza-tion of the outgoing beam collected at a scattering angle of 90◦was not analyzed. Thin layers of RuCl3 were mechanicallyexfoliated from bulk crystals onto Si/SiO2 substrates andthe selected nanolayers were protected by a thick hexagonalboron nitride (hBN) flake. The substrate was then flushed byoxygen plasma to get rid of unwanted RuCl3 pieces. Severalsilver lines pointing at the target flakes were drawn on thesubstrate surface to facilitate sample alignment in the RIXSchamber [41].Before presenting the experimental results, we brieflysummarize the outcome of previous RIXS experiments onbulk RuCl3 [Fig. 1(c)]. The excitation spectrum of interestcomprises two segments at low and high energy, respec-tively: spin-orbit excitations from the S̃ = 1/2 ground stateof the Ru3+ ions (electron configuration d5) into the S̃ = 3/2excited-state manifold (∼240 meV); and d-d excitations fromthe t2g crystal-field ground state into the eg excited states ofthe Ru ions (1.5–4 eV), which are superposed by a contin-uum of charge-transfer excitations (emerging from ∼1 eV).Excitations within the S̃ = 1/2 manifold, which are heavilyoverdamped in the paramagnetic state, were not studied.Figure 2(a) shows the measured low-energy RIXS spectraof nanoflakes with various thicknesses, as well as referencespectra of a RuCl3 bulk crystal and a Si/SiO2 substrate.For all measured nanoflakes, we observe an elastic peakdue to residual defects in the substrates and samples, anda pronounced inelastic feature around 240 meV. As shownL041406-2RESONANT INELASTIC X-RAY SCATTERING FROM … PHYSICAL REVIEW B 108, L041406 (2023)-200 0 200 400 600Energy (meV)00.511.52Intensity (arb. units)bulk20.7 nm15.6 nm10.7 nm5.9 nm3.5 nmsubstrate(a)0 5 10 15 20 bulkThickness (nm)200220240260280Energy (meV)(b)10 20 30 40°234567Intensity (arb. units)103-200 0 200 400Energy (meV)00.511.52Intensity (arb. units) =40°=10°(c)(d)FIG. 2. (a) Low-energy RIXS spectra of RuCl3 nanoflakes, andreference spectrum of a bulk crystal. The incoming x-ray energy was2837 eV and the sample angle θ = 40◦, with in-plane momentumtransfer close to the � point. Details of counting time and HRMconfiguration are in the Supplemental Material [41]. The spectralintensity of bulk crystal is scaled by a factor of 0.01. Vertical off-sets were applied for clarity. The gray dashed line is a guide tothe eye to indicate the center of the excitation peak. (b) Spin-orbitexciton energies for RuCl3 bulk crystal and thin flakes. Within thefitting error, the spin-orbit exciton exhibits no thickness-dependentenergy shift. (c) Ru-L3 scattering intensity of the 5.9-nm-thin flakeincreases monotonically when approaching grazing-incidence geom-etry. (d) Low-energy spectra of the 5.9-nm flake at θ = 10◦ and40◦. The spin-orbit exciton peak intensity is enhanced for θ = 10◦,despite the large lateral waste of photon flux.in Fig. 2(d), the peak energy is almost independent of theincident angle θ [which modulates the momentum transfer inthe honeycomb layers; Fig. 1(b)]. The lack of a significantmomentum-space dispersion implies that this feature arisesfrom a local, intra-atomic excitation. Following prior RIXSstudies on bulk RuCl3 [37], we assign it to S̃ = 1/2 → 3/2transitions with energy ∼3/2λ, where λ is the SOC constantof Ru. Figure 2(b) shows that the spin-orbit exciton energyis independent of thickness and identical to the one in bulkcrystals. This is expected because the SOC is an intra-atomicinteraction that is not significantly influenced by the crys-talline environment [42]. Remarkably, despite the increasinglateral photon flux waste at grazing-incidence angles due tothe small size of the nanoflakes, the RIXS signal increases[Figs. 2(c) and 2(d)], due to the longer travel path within thesample which enhances the scattering probability [41].The high-energy range of the RIXS spectra comprisesa broad intersite charge-transfer continuum emerging abovethe charge gap at 1 eV, and sharp d-d excitation peaks1 2 3 4Energy (eV)00.40.800.40.800.40.800.40.800.40.800.40.8Normalized Intensity (arb. units)bulk3.5 nm5.9 nm7.0 nm13.0 nm16.4 nm0.5 1 1.5 2 2.5 3 3.5 4Energy (eV)00.20.40.60.81Normalized Intensity (arb. units)bulk3.5 nm5.9 nmbulk00.40.8 3.5 nm5.9 nm00.40.8Normalized Intenisty (arb. units)7.0 nm13.0 nm1 2 3 4Energy (eV)00.40.8 16.4 nm1 2 3 4Energy (eV)(a) (b)(c)FIG. 3. (a) Thickness-dependent multiplet excitation spectra ofRuCl3 for θ = 40◦. The incident x-ray energy was 2839 eV. Thespectral difference Iflake − Ibulk (smoothed for clarity) is shown as agray area. As the flake thickness decreases below 7 nm, a redshiftis observed. (b) Comparison of the spectra of a bulk crystal andtwo thin flakes. The charge-transfer continuum exhibits no thickness-dependent behavior, as seen within the spectral ranges below 1.5 eVand above 3.5 eV. (c) d-d excitation decomposition for all measuredflakes and bulk sample. The blue shaded component represents thecharge continuum, independent of flake thickness. The green shadedcomponent is the Lorentzian profile of the main d-d excitation. Opencircles and black solid lines represent the experimental data andthe results of fits to a model function including both components,respectively.corresponding to intra-ionic crystal-field transitions from thet52g ground state to t42ge1g excited-state multiplets [Fig. 1(c)]. Inagreement with a previous report on bulk RuCl3 [37], we findthat a single peak at 2.3 eV dominates the spectrum, whereasother d-d excitations are much weaker and cannot be clearlyseparated from the continuum. Figure 3(a) displays the thick-ness evolution of the high-energy spectra (normalized to theintegrated spectral weight between 1 and 4 eV) in comparisonto the bulk. The spectral difference Iflake − Ibulk [gray shadedarea in Fig. 3(a)] calculated from flakes of thickness 7 nmand larger exhibits only minor differences to the bulk. Asthe thickness decreases further, however, the spectral weightbroadens and redistributes towards lower energies. Figure 3(b)shows a direct comparison between the spectra of bulk RuCl3and the two thinnest flakes. The good match in the spectralranges below 1.5 eV and above 3.5 eV indicates an essentiallyunchanged charge continuum, and that the observed broad-ening and redshift can be mostly ascribed to the main d-dexcitation peak at 2.3 eV. Next, the spectra are fitted to a modelcomposed of two components: a Lorentzian profile with vari-able energy and width describing the main d-d excitation, anda broad background describing the charge continuum (withsubmerged minor d-d excitations) that was kept fixed for allL041406-3ZICHEN YANG et al. PHYSICAL REVIEW B 108, L041406 (2023)0 5 10 15 20 bulkThickness (nm)2.152.22.252.32.352.4Energy (eV)0 5 10 15 20 bulkThickness (nm)0.30.40.50.60.70.8FWHM (eV)2.3 2.35 2.4 2.45 2.5 2.5510Dq (eV)00.511.522.533.5Energy (eV)(a)(b)(c)FIG. 4. (a) Peak energy and (b) full width at half maximum(FWHM) of the main d-d excitation resulting from fits. The hori-zontal dashed lines indicate the values of bulk RuCl3. The red curveis a guide to the eye. (c) d-d excitation energies as a function ofthe octahedral crystal-field energy 10Dq resulting from model cal-culations. The red line corresponds to the t42ge1g state that yields themost intense ligand-field excitation in the RIXS spectra. The grayvertical lines indicate the bulk value and the average value for the3.5-nm flake.samples [41]. The excellent agreement of the resulting pro-files with the experimental data [Fig. 3(c)] indicates that thethickness dependence of the d-d excitations can be reliablydetermined by this procedure. Figures 4(a) and 4(b) show thethickness evolution of the energy and width of the main d-dexcitation profile resulting from these fits. In the two thinnestflakes, the profile is redshifted by 50–100 meV, and its widthincreases by about 50%.To clarify the origin of this observation, we implemented asingle-ion model calculation based on a Hamiltonian compris-ing the intraionic Hund’s coupling and spin-orbit coupling,as well as octahedral and tetragonal crystal fields [41]. Thismethod has been widely implemented in RIXS studies tounderstand and assign the various spectral features and toextract the interaction parameters [37,38,43]. We varied eachof these parameters while keeping the others fixed at the valueof bulk RuCl3, and monitored the resulting energy shift ofthe d-d feature. The results show that only a shift of theaverage octahedral crystal-field splitting 10Dq from 2.44 to2.39 eV can explain the observed redshift. Varying any of theother parameters within a physically reasonable range doesnot reproduce the experimental findings [41]. However, wecannot rule off lattice distortions of lower symmetry.In a point-charge crystal-field model, 10Dq is proportionalto 1/a5, where a is the Ru-Cl bond length, so that the observedredshift corresponds to an average expansion of the RuCl6octahedra by 0.4%. The concomitant broadening and thethickness evolution of both line-shape parameters [Figs. 4(a)and 4(b)] imply that any lattice distortion associated with thealtered ligand field is inhomogeneously distributed in the out-of-plane direction. We can hence rule out defects or impuritiesin the RuCl3 crystals from which the flakes were exfoliated(which would give rise to thickness-independent broaden-ing), and bending distortions generated by the exfoliationprocedure (which would broaden—but not shift—the spectralfeatures from both spin-orbit and crystal-field excitations).Rather, the data point to a mixture of bulklike inner layersand near-surface layers with different ligand field and, likely,octahedral distortions, which comprise a progressively largerfraction of the nanoflake volume with decreasing thickness(e.g., four inner and two surface monolayers in the 3.5-nmsample). We note that an analogous broadening and redshiftof a peak arising from Cu dx2−y2 − d3z2−r2 excitations was ob-served in a Cu-L3 edge RIXS study of (CaCuO2)3/(SrTiO3)2superlattices, and attributed to the modified crystal structureat the interfaces [9]. We thus conclude that distortions ofthe RuCl6 octahedra at or near the surface are responsiblefor the thickness evolution of the crystal-field excitationsin our RuCl3 nanoflakes. A survey of the relevant litera-ture has revealed two possible origins of near-surface latticedisorder. First, a theoretical study of RuCl3-based vdW het-erostructures [27] suggests significant strain effects due tolattice mismatch, despite the weak vdW interlayer coupling.By analogy, epitaxial strain at the interface between ourRuCl3 flakes and the protective hBN capping layer mightincrease the Ru-Ru and Ru-Cl bond lengths, and thus weakenthe ligand-field interactions. Another possible cause of near-surface lattice distortions are defects such as Cl vacancies,surface adsorbates, or combinations thereof, which are hardto avoid during sample preparation. Evidence of Cl positionsdifferent from those in the bulk has indeed been reportedin several surface-sensitive experimental studies [44,45], butno agreement has been reached on the nature and strengthof these distortions. Our RIXS data can serve as a guidefor realistic model calculations of intrinsic and extrinsic lat-tice distortions and their possible impact on the electronicproperties.In conclusion, we have collected Ru-L3 RIXS spectra ofexfoliated RuCl3 layers with thicknesses down to 3.5 nm. Al-though the samples are protected by thick hBN capping layers,and their volumes are orders of magnitude smaller than thoseof bulk crystals, the signal-to-noise ratio of the RIXS data issufficient to capture the main spectral features observed in thebulk. We note that all RIXS spectra presented in this Lettershow no sign of x-ray beam damage [38]. The results reveala distinct thickness evolution of the low-energy spin-orbitexciton and high-energy crystal-field excitations. Whereas thespin-orbit exciton arises from intra-atomic SOC interactionsand is thus independent of thickness, the main crystal-fieldexcitation exhibits a clear broadening and redshift comparedto the bulk, which we are able to attribute to near-surfacealternations of the Ru ligand field. Modifications of the Ru-Clbond lengths and bond angles of the RuCl6 octahedra areimportant specifically for RuCl3, as they determine the ratioof Kitaev and Heisenberg interactions and hence the propen-sity for spin-liquid physics. More generally, direct detectionof d-d excitations by RIXS yields insights into the localcoordination of transition metal ions and associated ligandfields, which are often hard to access by other spectroscopicmethods and can be crucial to the physics of 2D materialsand vdW heterostructures, as exemplified by the influence ofL041406-4RESONANT INELASTIC X-RAY SCATTERING FROM … PHYSICAL REVIEW B 108, L041406 (2023)ligand-field interactions and charge-transfer transitions on theoptoelectronic response of atomically thin CrI3 [46]. Unlikesurface-sensitive methods, RIXS is able to detect manifes-tations of such distortions in samples protected by cappinglayers, which are routinely used for chemically sensitive 2Dmaterials, and at buried interfaces in vdW heterostructures.Our results point out various perspectives for furtherdevelopment of the methodology and scope of RIXS ex-periments on 2D materials. In particular, optimizing thelateral sample dimensions and the experimental geometry(including focusing conditions, incidence and exit angles,background suppression, and acquisition times) should en-able measurements on thinner samples, including monolayersand monolayer-based heterostructures. As the energy of thespin-orbit exciton in RuCl3 is comparable to the magnon andparamagnon energies in various transition metal compounds(including cuprates, iridates, and ruthenates), RIXS exper-iments on collective spin excitations in 2D materials willalso be feasible. Recent advances in high-resolution RIXSinstrumentation in the soft, intermediate, and hard x-rayregimes will greatly expand its range of applicability. 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