Influence of Orbital Character on the Ground State Electronic Properties in the van Der Waals Transition Metal Iodides VI3 and CrI3

Two-dimensional van der Waals magnetic semiconductors display emergent chemical and physical properties and hold promise for novel optical, electronic and magnetic “few-layers” functionalities. Transition-metal iodides such as CrI3 and VI3 are relevant for future electronic and spintronic applications; however, detailed experimental information on their ground state electronic properties is lacking often due to their challenging chemical environment. By combining X-ray electron spectroscopies and first-principles calculations, we report a complete determination of CrI3 and VI3 electronic ground states. We show that the transition metal-induced orbital filling drives the stabilization of distinct electronic phases: a wide bandgap in CrI3 and a Mott insulating state in VI3. Comparison of surface-sensitive (angular-resolved photoemission spectroscopy) and bulk-sensitive (X-ray absorption spectroscopy) measurements in VI3 reveals a surface-only V2+ oxidation state, suggesting that ground state electronic properties are strongly influenced by dimensionality effects. Our results have direct implications in band engineering and layer-dependent properties of two-dimensional systems.

R esearch on two-dimensional (2D) van der Waals (vdW) materials has been recently boosted by the discovery of layer-dependent long-range magnetic order, 1−4 Dirac physics 5,6 as well as Mott transitions. 7 Among 3d transition-metal vdW semiconductors, CrI 3 and VI 3 have attracted significant attention, as they undergo structural and electronic transitions as a function of temperature, net long-range magnetization within layers, and in the case of CrI 3 layered antiferromagnetism. 8−14 The importance of dimensionality effects has been recognized and for this reason the majority of experimental and theoretical work has focused on monolayers and few-layers films. However, both the interplay of dimensionality with relevant interactions, such as spin−orbit coupling (SOC), and the possible crossover of 3D vs 2D electronic properties are not well understood. In this respect, open questions include: (i) the role of Coulomb interaction and SOC in determining the 3d electronic states and their long-and short-range ordered collective excitations, 15 (ii) if and how the orbital filling in the electronic ground state is modified at the surface, (iii) what are the changes in the bandwidth and of the hybridization of halogen and transition metal states when dimensionality is reduced. These issues need to be addressed, since they have a significant impact in the potential electronic and spintronic applications, and their control may drive the realization of tailored heterostructures. 16,17 The crystal structure of MI 3 (M = Cr, V) is characterized by one M cation surrounded by six I anions, arranged in edgesharing octahedra. Within the planes, the M atoms are arranged in a honeycomb geometry (Figure 1a). CrI 3 undergoes a structural transition at T S,CrI3 = 220 K from the high-temperature monoclinic structure to the low-temperature rhombohedral structure R3̅ , while VI 3 changes from the rhombohedral structure R3̅ above T S,VI3 = 79 K to a monoclinic phase below the transition temperature. 18 Concerning the electronic structure, for VI 3 two different descriptions were proposed in literature: (i) a metallic ground state, in which the a 1g orbital state is fully occupied, and the doubly degenerate e g ′ orbital state is half occupied; 9,19,20 (ii) a Mott-insulating ground state, in which the e g ′ state is fully occupied, while the a 1g state is unoccupied. 17,21 This last picture appears to be consistent with a previous experimental measure of the optical band gap in VI 3 22 and a recent spectroscopic investigation; 23 indeed, no density of states at the Fermi level has been detected. The authors suggest that despite the trigonal distortion in this system being small and thus alone not being able to significantly split the t 2g orbital state into e g ′ and a 1g states, the energy gap is opened by the additional on-site Coulomb interaction contribution. However, a firm characterization of the ground state of VI 3 has not been reached yet.
As for CrI 3 , it has been proposed that a surface structural relaxation may explain the onset of bulk ferromagnetism vs few-layers antiferromagnetism; 24 it has also been argued that parallel spin states are energetically favored in both stacking configurations, and the result strongly depends on the on-site Coulomb energy employed in the calculations. 17 Hence, a better understanding of the surface electronic configuration and orbital occupation/arrangement would be helpful to better understand how interlayer interaction affects electronic states.
Motivated by the above issues, in this Letter we report on the determination of the electronic ground state of 3Dcrystalline CrI 3 and VI 3 , by combining different depth-sensitive electron spectroscopies with density functional theory (DFT) calculations for single layers. We observe that in CrI 3 a wide band gap is opened between majority spin e g and t 2g states, whereas in VI 3 the t 2g orbital state is split into (filled) e g ′ and (empty) a 1g orbital states with a narrower band gap between them, consistently with DFT predictions. Surface-sensitive angular-resolved photoemission spectroscopy (ARPES) data reveal the stabilization of a different ground state in VI 3 at the surface, characterized by a V 2+ valence and an occupied a 1g band, where the bandgap lies between the octahedral-split a 1g and the higher-lying empty e g states. In contrast, the 3 + oxidation state measured both for bulk CrI 3 and VI 3 by Xray absorption spectroscopy (XAS). Resonant photoemission spectroscopy (ResPES) data, compared to atom-and orbitalresolved density of states obtained from DFT, provide consistent evidence of the orbital character of the different valence band contributions, revealing that the orbital character itself has a profound influence on the ground state electronic properties. The good consistency between experimental data and DFT single-layer calculations suggest that interlayer interactions are less important in determining the stable electronic configuration for both CrI 3 and VI 3 .
vdW crystals are quasi-two-dimensional systems with little interaction along the c-axis layer stacking direction. The extreme surface-sensitivity of ARPES when performed with photon energies in the 20−55 eV range (from 5 to 10 Å, 25 corresponding to a single layer unit) allows to study the singlelayer electronic structure of MI 3 , referring to the surfaceprojected BZ reported in Figure 1b. We also report, for reference, in Figure 1c,d the expected crystal field splitting and related electronic filling for Cr 3+ and V 3+ , respectively.
XAS measurements across the V and Cr L 2,3 edges ( Figure  2a,b) confirm the 3 + oxidation state of bulk CrI 3 and VI 3 . As a matter of fact, the line shape and photon energy of L 3 and L 2 edges of the former are fully consistent with previous measurements on CrI 3 , 26,27 while V L 2,3 edges of the latter closely resemble those of other vanadium compounds with a V 3+ valence state such as V 2 O 3 , including the characteristic V 2p to V 3d empty t 2g transitions in the near-edge regions at 514 and 522 eV. 27,28 The spectra of both compounds are unaffected by contamination as they were cleaved in-vacuo.
XAS spectra are intrinsically integrated over a thickness of 4−6 nm of material, 29 and as such it does not retain information coming from the very first layer of CrI 3 and VI 3 . The direct surface analysis and investigation of the energy and the overall symmetry of the electronic states of VI 3 and CrI 3 was addressed by collecting k x −k y photoemission intensity maps at constant energy (see Figure 2c−f) and energymomentum spectra, (see Figure 2k−l). Experimental results were compared to DFT calculated electronic structures, where the U value was changed in the range between 0 and 3 eV (see SI, Methods and Figure S1) for both materials, seeking the best agreement with ARPES data. The calculations were performed for a single-layer with FM configuration, i.e. the magnetic ground state in monolayer form for VI 3 and CrI 3 , both with and without SOC. The magnetization direction, when SOC was included, was out-of-plane, consistently with the orientation of the magnetic moments. We note that our ARPES data were measured above the Curie temperature; nevertheless, a much better agreement is found with spinpolarized DFT, rather than with nonmagnetic DFT calculations. The latter would in fact result in a metallic ground state, inconsistent with experimental results on these materials. Local magnetic correlations may actually occur even above the Curie temperature and this is implied by the good agreement of experimental data and spin-polarized DFT, even in the absence of long-range magnetic ordering.
Our experimental data show the existence of a sizable bandgap (the distance between the valence band maximum and the conduction band minimum) for both systems and allow us to evaluate the bandgap energies to be larger than 0.9 eV for VI 3 and 1.35 eV for CrI 3 . These values have been obtained by comparing ARPES data to the experimentally determined Fermi level (see Methods). It is important to underline that the experimental bandgap values are lower limits for the full bandgap, as ARPES detects occupied electrondensity of states (DOS) only; in addition, the presence of small charging effects of cleaved surfaces 30−32 cannot be excluded. The latter are common and well-understood in ARPES Nano Letters pubs.acs.org/NanoLett Letter measurements of insulating compounds and can determine an artifactual rigid shift of the Fermi level of a few hundreds of millielectronvolts, without further changes in the band structure, as we verified in our measurements (see SI Figure  S2). We note that we cannot use DFT calculations (as reported in SI Figure S3) for quantitative comparison, as the underestimate of band gaps is a well-known DFT problem in treating excited states. 33 Nevertheless, a good agreement with previous experimental results is found, yielding a similar value obtained from optical measurements for CrI 3 34 and also both from optical 12,22 and spectroscopic 23 measurements for VI 3 .
From Figure 2, we note that the overall electronic structures of VI 3 and CrI 3 show several similarities. In fact, the 3d electronic states originating from V or Cr give rise to similar nearly dispersionless features in the VB, whose intensity is prominent in the collected spectra (Figure 2k,l). On the other The energy in red in the top right corner of each map is the binding energy of the isoenergetic cut. ARPES spectra of (k) VI 3 (T = 150 K, hv = 32 eV) and (l) CrI 3 (T = 300 K, hv = 32 eV) along the Γ−K direction. Theoretical band structures with FM configuration and SOC for VI 3 (GGA+U, U = 2 eV) and CrI 3 (bare GGA) monolayers are superimposed on experimental data. The colors highlighting the bands represent the following components for V/Cr dorbital, red denotes d 3z2−r2 , green denotes d xz and d yz , yellow denotes d xy and d xd 2 −yd 2 . For I p-orbital, gray denotes p z , magenta denotes p y , blue denotes p z .

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Letter hand, the I-derived 5p orbitals are very dispersive and the orbital-mixing is strong for both VI 3 and CrI 3 . The orbital character of these bands, as inferred from DFT, shows that the SOC is crucial for explaining the observed energy-momentum spectra. The effect of SOC modulates the band structure involving the V/Cr d z2−3r2 and I p x −p y orbitals at binding energies of ∼1 eV in VI 3 and around 2.5 eV in CrI 3 . Moreover, the inclusion of SOC is relevant in closing the gap between V a 1g and I p bands at Γ (see SI Figure S1). Despite I p bands being fairly similar, our results show that VI 3 and CrI 3 behave in a different way from the electronic point of view. To emphasize this point, we carried out polarization-dependent measurements on both compounds. ppolarized light has both in-plane and out-of-plane components of the wavevector with respect to the sample surface, whereas s-polarized light has only the in-plane component. By exploiting the light polarization dependence we are thus selectively sensitive to in-and out-of-plane orbitals (Figure 3). For VI 3 , we clearly see in Figure 3a that the orbitals contributing to the spectroscopic signal at ∼1 eV are mostly out of plane, that is, those with a 1g character. A value of U = 2 eV is thus found to best simulate our data. Higher values of U would shift the V a 1g states up toward the Fermi level, opening a gap between them and the I bands which is not observed in the experiment ( Figure S1h). Lower values of U, instead, would place V d xz and d yz orbitals at an energy of ∼1 eV (Figure S1e-f) which is inconsistent with the data.
ARPES results for CrI 3 are in striking difference with those shown above for VI 3 . First, from Figure 3a we deduce that bands at 2.5 eV BE are ascribed to the out-of-plane d 3z2-r2 orbitals. Second, we observe that, as soon as U values different from zero are introduced in the DFT calculations, those orbitals move to higher BEs ( Figure S1n−p), a feature that is not observed by ARPES. This can be interpreted as follows. CrI 3 exhibits t 2g −e g crystal-field splitting of d states; the different orbital filling of Cr 3+ ions compared to V 3+ results in a t 2g level completely filled by majority electrons. The orbital splitting between e g and t 2g orbital states is sufficiently large in this case to stabilize a fully insulating state, even in the absence of a finite U-value within the DFT+U approach.
Another relevant difference between the two compounds is that DFT calculations compare well with ARPES spectra with the exception of the a 1g orbital filling of VI 3 . The a 1g are clearly revealed as filled states by ARPES, while are predicted to be empty by DFT consistently with a V 3+ ionic charge. On top of this, XAS results also indicate a V 3+ valency of the bulk. This peculiar behavior is nevertheless clearly revealed by ARPES, which probes just the topmost layer of the material, therefore

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Letter including intrinsic and extrinsic surface effects like relaxation and defect-doping effects that can be responsible of the local electron filling of the a 1g band. We thus suggest that a different ground state, characterized by a V 2+ orbital filling, stabilizes at the surface: it turns out that the gap between filled and empty states observed in ARPES measurements is opened by the octahedral crystal field, rather than that by the bulk trigonal crystal field splitting of a 1g and e g ′ levels. On the other hand, CrI 3 does not show any evidence of a different surface electronic environment.
In Figure 2c−f, we note that the constant energy ARPES maps for VI 3 and CrI 3 display a different symmetry in connection with the orbital character of the electronic states. I 5p states display an apparent 6-fold symmetry, while V and Cr 3d states show a 3-fold symmetric pattern, differently from DFT results (reported in Figure 2g−j). The 3-fold symmetry of V 3d states is highlighted also in SI Figure S4. Indeed, the expected trigonal symmetry is not necessarily reproduced in our single-layer calculations, since the primitive cell encompasses two layers. In previous works, it has been suggested that such a pattern could be connected with the onset of the ferromagnetic ground state, 23 that breaks time-reversal symmetry when VI 3 undergoes the magnetic transition. At the surface, this combines with the loss of inversion symmetry, giving rise to a P−T symmetry-breaking system. Our ARPES data (150 K for VI 3 , 300 K for CrI 3 ) were collected at sample temperatures well above the Curie point (CrI 3 , T C,CrI3 = 61 K; VI 3 , T C,VI3 = 50 K), and suggest a different interpretation with respect to the one given in ref 23. The reduction of symmetry of ARPES constant energy maps with respect to DFT results may be ascribed to surface effects, that are not accounted for in the DFT simulations of VI 3 and CrI 3 single-layers (i.e., not for semi-infinite crystals). However, we cannot rule out the existence of magnetic fluctuations and their role in breaking time-reversal symmetry.
The relevance of short-range magnetic interactions in vdW magnetic materials, including VI 3 , has been pointed out by numerous studies. 13,35−38 Well above the Curie temperature, thermal fluctuations randomly orient the electron spins in the valence band, but the nonmagnetic ground state can be locally described in terms of orbital filling of the TM states by majority electrons. The occurrence of magnetic fluctuations well above the Curie point in the absence of long-range order is well-documented for correlated materials; 39−42 the observed narrow bandwidth of V-and Cr-derived 3d bands hints at the importance of electron−electron interactions as well. Furthermore, V-and Cr-projected states would be more affected by short-range correlation effects, while the I contribution to the magnetic moment is negligible, 9 leaving the symmetry of I 5p states as dictated by the structure. The intralayer atomic arrangement does not change even at the structural transition that both crystals undergo at T S,CrI3 = 220 K and T S,VI3 = 78 K, involving only layer stacking. The comparison of calculations and surface-sensitive experimental data allows us to conclude that the band structure is largely unaffected across the structural transitions.
We also measured ResPES, exploiting the selective abrupt changes of photoionization cross sections, to identify the orbital contributions to the spectra. V 3d orbitals contributing to the bands at 1 eV BE, and similarly Cr 3d orbitals contributing to the bands at 2.5 eV BE, are resonantly enhanced when the photon energy reaches the photoionization threshold of the V and Cr 3p core levels, respectively. In this way, we experimentally probe the atomic character of the wave functions contributing to ARPES intensities. The large signal enhancement of the nondispersing bands when the photon energy coincides with the 3p edges (Figure 4a,c) is a direct signature of their V/Cr orbital nature, and can be mapped onto the DFT orbital projection of the DOS (Figure 4b,d).
Photon energy dependent ARPES, such as ResPES, intrinsically also probes the k z dispersion. The absence of dispersion of both V and Cr projected bands, highlighted by the EDC spectra (Figure 4a−c, right panel), indicates that those states are "2D-like" with negligible interlayer interaction (assuming no artifacts are introduced by rescaling the spectra to compensate charging effects). The consistency of ARPES results with single-layer calculations appears therefore strengthened.
In summary, we characterized the ground-state electronic structure of CrI 3 and VI 3 : based on the excellent agreement between photoemission data (angle-resolved, light polarization-dependent and resonant) and DFT-calculated band dispersion and orbital-resolved density of states, we give evidence of how substantially different can be the orbital configuration of magnetic trihalides for different TM ions. CrI 3 shows a 3-fold t 2g orbital degeneracy and a wide bandgap, while VI 3 shows a Mott-insulator-like ground state with a 1g -e g ′ orbital splitting and a narrower bandgap. Single-layer band structure calculations compare well with ARPES spectra suggesting weak electronic interaction between layers, including between the surface layer and the bulk. Moreover, the occupancy of the a 1g state at the surface of VI 3 indicates that its surface is stabilized by an unconventional V 2+ state, at variance with the V 3+ bulk valency. Therefore, future research in ultrathin films or