Ligand field luminescence in the honeycomb Mott insulator α-RuCl3

Novel electronic structure is central to Kitaev-like quantum spin liquid ground state in the van der Waals antiferromagnet α-RuCl3. In this octahedral low-spin 4d5 system, the rich bandstructure includes Mott–Hubbard insulating bandgap of ∼1.1 eV and ligand field induced gap of ∼2 eV. Though the bandgap is extensively reported in previous optical and photoemission studies, the latter gap is less understood. In this regard, we probed the ligand field-induced electronic structure of bulk α-RuCl3 single crystals via unpolarized photoluminescence (PL) spectroscopy under linearly polarized excitation in the visible region. We observed the broad principal PL peak at E PL ≈ 1.87 eV, close to the energy required for the optical transition across the ligand field splitting gap (∼2 eV). This gap (E PL) monotonically increases with temperature, described by the thermal expansion of lattice parameters dominating the electron–phonon interaction in this Honeycomb Mott insulator. Moreover, we observed the multiplet structure of the PL spectra, which can be explained by parity-forbidden d–d transitions in the light of single ion ligand-field theory. We attribute the broad PL linewidths to strong vibronic coupling modeled by the Huang–Rhys parameter. Further we observed the signature of structural transitions, indicated by thermal hysteresis in normalized integrated PL intensity.

The electronic structure of α-RuCl 3 have been investigated extensively in many ways like photoemission, x-ray absorption spectroscopy [30], Raman scattering [19,31], THz spectroscopy [32][33][34], and resonant inelastic x-ray scattering [28,35]. Mott insulating state with narrowly dispersive Ru 4d bands was observed near the Fermi level (E F ). Recently, Koitzsch et al has used the combination of photoemission and electron energy loss spectroscopy [12] to evaluate the optical or charge gap of ∼1.1 eV along with a gap of ∼2 eV attributed to cubic crystal ligand field splitting.
Photoluminescence (PL) spectroscopy probe novel electronic structure of various layered semiconductors, for example, MoS 2 [36], MoSe 2 [37], WS 2 , WSe 2 [38,39] and so on. This spectroscopy is conducted via photoexcitation, followed by capturing luminescent photons characteristics of details of the band structures including the bandgap. For instance, evolution of PL spectra in bulk MoS 2 down to monolayer limit shows the transition from indirect to direct bandgap [36]. In most vdW non-metallic materials, tightly bound Wannier-Mott excitons dominate the intrinsic optical response. Therefore, PL spectra become prolific in studying light-matter interactions, 2D excitonic interactions, dynamics, and spin/valley physics. However, in some transition metal compounds such as chromium (Cr) trihalides [40][41][42][43][44], Nickel halides [45], and Eu dichalcogenides [46], known as Mott insulators, the novel photo-physical phenomena involves physics incompatible with the Wannier-Mott excitonic picture. Rather, the optical response is governed by ligand-field and charge transfer excitations involving localized molecular orbitals. Moreover, the octahedral ligand field transitions follow Laporte and spin-selection rule involving newly split energy levels, each denoted as 'term' . Eventually, PL spectra are reminiscent of the electronic transitions between 'terms' in a lattice vibrational environment.
In this maiden work, we reveal ligand-field transitions in bulk SO assisted Mott insulator α-RuCl 3 single crystal by steady-state PL spectroscopy. After structural and magnetic characterization of our as-grown single crystals, we focus on the temperature evolution of steady-state PL spectra and analyze our data via widely acceptable ligand-field theory involving parity forbidden d-d transitions in the presence of strong vibronic coupling. In this regard, we introduced the modified Tanabe-Sugano (TS) formalism to map out the transitions between 'terms' , using Laporte and spin selection rules in combination with quantum chemistry calculations by Yadav et al [47]. We observed the effect of trigonal distortion and SO coupling on the emission spectra, forming a multiplet structure. We employed the Huang-Rhys model to elucidate the vibronic character of our PL spectra. Moreover, we analyzed the temperature dependence of PL in the light of thermal variation of lattice parameters and phonons interacting with photo-excited electrons.

Experimental methods
Single crystals were prepared by vacuum sublimation method from commercial RuCl 3 powder (Alfa aesar, anhydrous, Ru content 47.7% min) described previously [48]. We obtained black lustrous plate like crystals, having wider surfaces parallel to the ab plane. At first, one of the crystals was characterized by the powder x ray diffraction (XRD) method using a Rigaku Smart Lab 4-circle x-ray diffractometer with a Cu target. The phase purity and the stoichiometric composition were confirmed by EPMA (electron probe micro analyzer). Magnetization was measured as a function of temperature using SQUID magnetometer (Quantum Design MPMS).
Micro-Raman and micro-PL spectroscopy was carried out on the bulk crystals in the quasibackscattering geometry, with light linearly polarized in the basal (cleavage) plane of our crystal. Light from a 532 nm laser (Nd:YAG solid-state laser) was focused down to a spot of size ∼2 µm) by a confocal microscope attached, and the power at the sample is estimated to be (∼500 µW). A holographic notch filter was used to reject light from the fundamental, leading to a lower cutoff of about 50 cm −1 , following the detection of unpolarized scattered light. The samples were installed into a vacuum sealed He-closed cycle cryostat (Montana Instruments) to perform low-temperature Raman experiments with a temperature range of T = 3.5-300 K. Laser-induced heating effects do not exceed 1 K, confirmed by acquiring repetitive spectra. The PL and Raman spectra were recorded using 300 lines per mm and 1800 lines per mm gratings, respectively.
Electrical characterization of a bulk crystal was conducted in a close-cycle refrigerator system with a vacuum of 10 −5 mbar via 6517B electrometer (Keithley Instruments).

Structural and magnetic characterization
We performed room-temperature XRD measurements on the millimeter-sized as-grown bulk α-RuCl 3 flake, as depicted in figure 1(a). As evident in figure 1(b), the XRD pattern supported the c-axis (00l) growth with a flat ab-plane, indicative of the layered structure of this material, where cleaving is favorable in the c-direction owing to weak vdW bonding. This observation is consistent with monoclinic (C2/m) structure [15,16]. Rhombohedral (R3m) structure of α-RuCl 3 is also reported at low temperature. This structural transition is discussed elsewhere. We further determined the stoichiometric ratio of as-grown multiple α-RuCl 3 flakes to be Ru:Cl ≈ 1:3 via EPMA, indicating fewer crystal defects. Figure 1(c) displays the susceptibility (χ || ) of a bulk RuCl 3 flake as a function of temperature (T) in both heating and cooling cycles when the system is field-cooled by a small in-plane field (H = 10 Oe). We did not observe any shift in cooling and heating curves, a possible characteristic of the spin liquid system. However, the zigzag AFM ordering in our crystals sets in at T N1 ≈ 8 K with sharp kink due to the natural ABC type stacking (three-layer periodicity) and T N2 ≈ 15 K with broad feature, indicative of small amount of ABAB type orientation, regarded as stacking faults [11,[13][14][15][16][17]49]. So, the sharpness of AFM transition indicates a small amount of stacking faults in our crystals introduced in the growth process or possible mishandling.
Several reports on RuCl 3 mentioned the structural transitions at T S1 ≈ 50 K and T S2 ≈ 170 K from high-temperature monoclinic (C2/m) to low-temperature rhombohedral (R3m) structure [16,17,31,50]. Here, we could not magnetically probe T S1 and T S2 possibly due to the small change in magnetic moment compared to the sensitivity of the instrument used. However, we captured the evidence of structural transitions in PL spectroscopy (discussed later), Raman spectroscopy and electrical transport measurements (figures S7 and S11, respectively, in the supplementary).
Curie-Weiss analysis on paramagnetic contribution to high-temperature susceptibility yields the effective magnetic moment (µ eff ) of ∼2.3 µ B while the magnetic moment for a single S = 1/2 spin is 1.73 µ B , implying substantial orbital contribution (see the supplementary). The large difference in the µ eff indicates the prominent SOC and the presence of non-cubic (trigonal) distortion in RuCl 3 [49], leading to the admixture of J eff = 1/2 and J eff = 3/2 states.

Ligand field PL
To elucidate the electronic structure of RuCl 3 near ligand field splitting gap (∼2 eV [12,18,29]), we conducted PL spectroscopy in the visible region (∼1.6-2.3 eV). The effect of cubic ligand field is discussed and the corresponding gap assigned as 'B' peak in [12]. The octahedral ligand field (10Dq) split 4d 5 orbitals into triply degenerate t 2g orbitals of lower energy and doubly degenerate e g orbitals of higher energy (figure 2). A large 10Dq in α-RuCl 3 push all five d-electrons in t 2g orbitals circumventing Hund's rule, thus giving rise to low-spin ground state. Further, SOC split the partially filled t 2g orbitals into J eff = 1 2 and J eff = 3 2 subsets. Ultimately, the optical or charge gap of α-RuCl 3 is ∼1.1 eV, originating from Mott gap between the t 2g lower Hubbard band and upper Hubbard band (UHB) (see figure 2). We reproduced the optical gap using Fourier transform infrared spectroscopy (see the supplementary, figure S12).
Our optical spectra consists of PL signal on the Raman background contributed by multiple SO or Mott-Hubbard excitons (A 0 , A 1 and A 2 ) [29,51,52]. So, after selecting the PL spectra and subtracting the suitable Raman background, we fitted the resultant curve (from ∼1.55 to ∼2.0 eV) with three Lorentzian line shape functions (see the supplementary for details, figure S8). After deconvolution at T = 3.5 K, we found the PL peaks at ≈1.87 eV, ≈1.83 eV, and ≈1.80 eV, indicating three interband transitions (see figure 7). These transitions can be explained in terms of the band structures of the Mott insulating phase in RuCl 3 , including appreciable SO coupling in a trigonally distorted octahedral field environment.   As evident in figure 3 the most intense PL peak ('Peak 1') at E PL ≈ 1.87 eV is lesser than but close to the ligand field splitting gap for RuCl 3 . [12,18,29,35]. This blueshift of E PL can be explained by nonradiative decay from higher vibrational level to zeroth vibrational level in an electronic state, as represented in the figure 4.
To address the origin of luminescence in RuCl 3 , we introduced the ligand field theory, widely used to describe the parity-forbidden d − d transition in transition metal complexes, displaying broad linewidth due to strong vibronic coupling with localized molecular orbital states [53]. For instance, the bulk Cr trihalides  [47], considering the highest (H) and lowest (L) levels of 4 T2g. The notation for split levels of 2 T2g have been adapted from [53]. have long been known as Mott insulators with an optical response governed by ligand-field and charge transfer excitations. While characterizing ligand-field transitions in the luminescence of RuCl 3 , we took the help of the TS diagram. Tanabe and Sugano indigenously proposed a formalism to describe energy splitting of vibronically coupled electronic states in the presence of octahedral ligand field [54] (see the supplementary, figure S4). According to the diagram, the ground state of a 4d 5 system transforms from a high-spin to a low-spin state while increasing 10Dq/B, where B is the Racah's parameter.
Ru 3+ ion with J eff = 1/2 pseudospin in a [RuCl 6 ] 3− octahedron has low-spin ground state denoted as 2 T 2g (t 5 2g ). The excited states in the ligand field multiplets of Ru 3+ 4d-shell electronic structure are 4 T 1g (t 4 2g e 1 g ), 4 T 2g (t 4 2g e 1 g ), 6 A 1g (t 3 2g e 2 g ) and so on. In the single ion case, the ratio 10Dq/B lies close to 48 (see the table 1) [27]. So, the possible allowed ligand-field transitions would be 2 T 2 ← 2 E (2.08 eV), 2 T 2 ← 2 A 2 , 2 T 1 (1.96 eV), extracted from the TS diagram without SOC and non-cubic distortion (see the supplementary, figure S4). This kind of single-ion physics has been predicted to display in transition metal complexes with [RuCl 6 ] 3− octahedron [55]. However, since α-RuCl 3 is formed by the network of [RuCl 6 ] 3− octahedra where two neighboring octahedra share two Cl ligands, the single-ion physics becomes invalid. Moreover, the appreciable SOC present in the system complicates the single ion physics.
To validate the ligand field theory in RuCl 3 , Yadav et al computed the exact energies of ligand field multiplets of on-site Ru 3+ 4d-shell electronic structure [47]. They used complete-active-space self-consistent-field and multireference configuration-interaction levels of theory for embedded atomic clusters having one [RuCl 6 ] 3− octahedron reference unit including SO treatment. The result of this theoretical study validates the low-energy spectrum in Raman scattering and other optical experiments [19,29,52] which also claimed the feature at 2 eV is due to intersite d-d transitions (d 5 d 5 → d 4 d 6 ). Still, we successfully explain the peak at ∼2 eV with intrasite ligand field transitions.
Based on calculations in [47], we find that our luminescence feature can be assigned to 2 T 2 (t 5 2g ) ← 4 T 2 (t 4 2g e 1 g ) transition. However, any vibronic transition obeys the Laporte symmetry-selection rule and spin-multiplicity conservation [53]. Still, symmetry breaking happens via local vibrations, supporting phonon-mediated electronic transition. Therefore, Laporte or parity forbidden d-d transition ( 2 T 2g ← 4 T 2g ) becomes partially allowed even having dissimilar spin multiplicities (2 for 2 T 2 and 4 for 4 T 2 ). In addition, Figure 5. Low-temperature photoluminescence spectroscopy: (a) and (b) represent the full spectra consisting of photoluminescence (PL) spectra and Raman spectra for a bulk RuCl3 crystal acquired using the excitation wavelength of 532 nm in the cooling cycle (blue arrow). Each spectrum is deconvoluted by three Lorentzian peaks. (c) and (d) depicts the fitted PL spectra acquired using the same laser in the heating cycle (red arrow). In each figure, 'peak 1' , 'peak 2' , and 'peak 3' are indicated for PL peaks and A0 and A1 indicate spin-orbit (SO) or Mott-Hubbard excitons [52].  (1)). Fitting parameters are noted in the inset. small but influential trigonal distortion (≈70 meV [28]) and SOC (≈150 meV [18,35]) facilitates those parity-and spin-forbidden transition via lifting orbital degeneracy. As per [47], the energy difference between 2 T 2g and 4 T 2g levels are as follows using the lowest and highest energy values of split levels of 4 T 2g configuration and neglecting the further intermediate splitting due to SOC. The term ∆E signifies the difference between zero-phonon PL (ZPL) energies of different configurations. ZPL originates from the transition between the zeroth vibrational levels of the excited and the ground state. We can assign the PL peak with broad linewidth to the phonon-sideband, which generally appears at the lower energy side of the ZPL peak.
As evident in figure 5, the appearance of three PL peaks can be explained in terms of the splitting of the 4 T 2 level in the presence of SO interaction and trigonal distortion. We assigned those PL peaks to the ZPL energy values, ∆E = 1.936 eV, 1.895 eV, and 1.856 eV, selected from the six possible ligand field transitions mentioned earlier. The other three allowed transitions are probably masked by the Raman spectra that appeared in the same energy range. The blue shift of observed PL peaks relative to the proposed peaks indicates the phonon sidebands corresponding to each split ligand-field level.

Huang-Rhys model: vibronic coupling
We analyzed the vibronic character of our optical spectra via the Franck-Condon principle and considering strong electron-lattice coupling [53]. We can assume the low-temperature PL response to be the phonon sideband corresponding to single zero-phonon line originating from 4 T 2 ← 2 T 2 transition, expressed in the single-site configurational-coordinate system ( figure 4). The phonon sideband is the convolution of multiple vibronic subbands. Under these assumptions, the Huang-Rhys model has the approximate form for the emission at energy E and temperature T as follows: Here, I(E) denotes the transition probability, S is the Huang-Rhys parameter, ℏω is the effective phonon energy involved in the luminescence process, k B is the Boltzmann constant, and E 0 is the energy of ZPL. A more detailed derivation of the model can be found in the supplementary. To calculate the transition probability for the vibronic transition, we divided the measured PL intensity by a factor of E 3 [53] and normalized it to set the maximum probability close to unity. The Huang-Rhys model captures the asymmetry and the linewidth of the PL spectrum.
At T = 3.5 K, the extracted E 0 ≈ 1.92 eV is well matched with the ZPL energy predicted for 2 T 2 ← 4 T 2 by Yadav et al [47] (figure 6). Moreover, the value of E 0 is close to the ligand-field splitting gap (≈2 eV). The estimated energy of phonons involved in the parity forbidden d-d transition is ℏω ≈ 29 meV, consistent with earlier reports on transition metal complexes, especially in CrCl 3 [56]. The S≈3 indicates the substantial electron-lattice coupling responsible for the d-d transition allowed by mixing of the odd parity states via phonon modes. Moreover, the value of S for α-RuCl 3 is consistent with the Huang-Rhys parameters of 3.6 reported for CrCl 3 [56]. Generally, S increases with the increase in metal-ligand distance [57]. Since Cr 3+ and Ru 3+ both have the same valency and identical ligands (Cl − ), we can expect a similar strength of electron-lattice coupling, indicated by S. We also obtain the Stokes shift to be 2Sℏω of ≈0.18 eV, which indicates that the absorption peak is supposed to appear at ≈2.05 eV [57]. This approximate position of absorption band edge is close to the value of 10Dq, also confirmed by optical absorption experiments [29]. Figure 5 showcases the deconvoluted luminescence spectra along with Raman background while cooling and heating the sample. The fitting parameters of all PL peaks are captured in figure 3. Peak energy for 'peak 1' increases with temperature, while the changes in other peaks' positions are not observable possibly due to less resolution in our experiments. The temperature-dependent redshift of 'peak 1' is discussed in the next section.

Temperature evolution of PL
We could not observe any hysteretic behavior in the temperature-dependent peak energies and full width half maxima curves, possibly due to less resolution (∼3 meV) in our experiments (see figure 3). However, we found the thermal hysteresis in normalized integrated PL intensities of all three peaks between T S1 ≈ 50 K and T S2 ≈ 170 K. We attribute such a large hysteresis most likely to structural rearrangement from low-temperature trigonal (P3 1 12) or rhombohedral (R3m) to high-temperature monoclinic (C2/m) structure and vice versa [11,15,17,31,48,50,58]. Such a structural transition involves the change in lattice constants as well as crystal symmetry which reflects in the electronic bandstructure of RuCl 3 , in turn, the ligand-field multiplet structure. So, we can expect the change in integrated peak intensities in our PL experiments. Figure 7 displays temperature dependence of peak energy of the most intense peak, 'peak 1'(E PL ≈ 1.87 eV). We identified the 'peak 1' as one of the ligand-field transitions (t 5 2g ← t 4 2g e 1 g ) closely indicating the ligand-field splitting gap as observed by Koitzsch et al [12]. Below 20 K, E PL is almost constant and does not show any observable change near T N = 8 K and 15 K. E PL starts rising monotonically from 20 K till room-temperature. In contrast, the band gap (∼1.1 eV) of RuCl 3 obtained from optical conductivity measurement is observed to shrink with the increase in temperature [60]. The opposite behavior of temperature evolution of the bandgap supports the formation of the conduction band mostly from Ru t 2g UHBs, whose bandwidth increases with temperature due to increase in electron-phonon (EP) interaction (figure 2). On the other hand, we explain the anomalous temperature dependence of E PL in terms of the competition between thermal expansion (TE) of bulk RuCl 3 and EP interaction.
To understand the anomalous temperature dependence of ligand field splitting gap (E PL ), the molecular orbital energy diagram of α-RuCl 3 can give qualitative picture (see the supplementary, figure S3), which suggests that the valence band (VB) maximum is formed by the hybridization of d orbitals (t 2g (π * )) of Ru and p orbitals of Cl and their interaction determines the bandwidth of VB. On the increasing temperature, the TE of the crystal lattice weakens the interaction between those atomic orbitals forming molecular  (2). The Blue horizontal line denotes the temperature-independent behavior of EPL below 20 K. The change near TS2 ≈ 170 K is visible, however, neglected during fitting. orbitals. Moreover, the increase of unit cell volume in the crystal enhances the metal-ligand distances by moving the transition metal ions (Ru 3+ ) and ligands (Cl − ) further apart. Thus, the TE increases the gap between the band edges of t 2g (π * ) and e g (π * ) of α-RuCl 3 , which is equal to E PL .
There is an extensive study on how temperature affects the band gap via TE and EP interaction [61,62]. TE and EP interaction alter the electronic band structure via a change in lattice constant and the introduction of lattice vibrations, respectively. In the most conventional semiconductors with a single structural phase, the EP interaction term dominates over TE term, leading to temperature-induced bandgap reduction. However, in some semiconductors, for example, halide perovskites (like CsPbB 3 , and CsSnI 3 ,), the contribution of TE to the band gap exceeds that of the EP interaction due to the larger effective mass of the electrons, leading to an anomalous increase in the bandgap with temperature [63]. This fact supports the temperature evolution of the gap close to E PL and is explained well with the model in the following approximate form (see the supplementary for details).
Here we assume a linear temperature (T)-dependent lattice constant [58] and one-oscillator model for EP interaction, A TE and A EP are the weights of the TE and EP interaction, respectively, k B is Boltzmann's constant, and ℏΩ is the mean optical phonon energy related to EP coupling. E 0 is the unrenormalized constant and can be calculated using the relation: E 0 = E PL (T = 0)-A EP after taking into the quantum factor in the Bose-Einstein distribution. The second term in equation (2) indicates the contribution from the TE of the lattice that originated from the anharmonicity of inter-atomic potentials.
In figure 7, we found an excellent agreement between the experimental data and the proposed theoretical model (equation (2)). We extracted the corresponding contributions of the TE and the EP interaction to the temperature-dependent E PL , denoted as ∆ TE and ∆ EP , respectively, using the following relations: ∆ TE = E TE (T = 250 K)-E TE (T = 20 K), and ∆ TE = E TE (T = 250 K)-E TE (T = 20 K). The positive value of ∆ TE + ∆ EP (see table 2) indicates the dominance of the TE contribution to the temperature evolution of E PL . Crudely speaking, the E PL vs T curve resembles the temperature-dependent change in lattice constants of bulk RuCl 3 [58]. Pressure dependent study with a change in lattice constant is expected to support our observation.

Conclusion
In conclusion, we studied the PL spectra of bulk single crystalline α-RuCl 3 using the excitation wavelength (532 nm) close to the ligand splitting gap. Magnetic measurement of the high-quality crystal flakes reveals AFM transition at 8 K indicated by the most pronounced kink along with broad feature at 15 K. In the core of the paper, we presented the PL study featuring detailed information about the electronic structure probed by the ligand-field transitions (t 5 2g ←t 4 2g e 1 g ) of RuCl 3 with energy of ≈1.9 eV, close to the ligand splitting gap of ∼2 eV. The modified TS diagram based on quantum chemistry calculations [47] analyzes all optical transitions in the complex PL spectra, including SO interaction and trigonal distortion in the cubic ligand field. We observed the temperature evolution of the ligand field splitting gap follows positive monotonic behavior, unlike the bandgap of several semiconductors, and asserted the dominance of TE factor over the EP interaction due to a large enough effective mass of electrons in RuCl 3 , a Mott-Hubbard insulator. Our study paves a new avenue in the optical signature of a proximate quantum liquid candidate with ligand field induced electronic structure. In this regard, further magneto-PL study on the thickness and polarization dependence of the ligand field transitions will help to elucidate intriguing physics, for instance, coupling magnetism with optical signatures. The vdW nature of α-RuCl 3 also offer the possibility to study electronic structure via PL in atomically thin limit.

Data availability statement
The data cannot be made publicly available upon publication because they are not available in a format that is sufficiently accessible or reusable by other researchers. The data that support the findings of this study are available upon reasonable request from the authors.