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.

Research 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, CrI3 and VI3 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 CrI3 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 MI3 (M = Cr, V) is characterized by one M cation surrounded by six I anions, arranged in edge-sharing octahedra. Within the planes, the M atoms are arranged in a honeycomb geometry (Figure a). CrI3 undergoes a structural transition at TS,CrI3 = 220 K from the high-temperature monoclinic structure to the low-temperature rhombohedral structure R3̅, while VI3 changes from the rhombohedral structure R3̅ above TS,VI3 = 79 K to a monoclinic phase below the transition temperature.[18] Concerning the electronic structure, for VI3 two different descriptions were proposed in literature: (i) a metallic ground state, in which the a1g orbital state is fully occupied, and the doubly degenerate eg′ orbital state is half occupied;[9,19,20] (ii) a Mott-insulating ground state, in which the eg′ state is fully occupied, while the a1g state is unoccupied.[17,21] This last picture appears to be consistent with a previous experimental measure of the optical band gap in VI3[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 t2g orbital state into eg′ and a1g states, the energy gap is opened by the additional on-site Coulomb interaction contribution. However, a firm characterization of the ground state of VI3 has not been reached yet.

Figure 1

(a) Crystal structure of CrI3 and VI3 monolayers. (b) Two-dimensional Brillouin zone. Crystal-field splitting and related electron filling for (c) Cr and (d) V.

As for CrI3, 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 3D-crystalline CrI3 and VI3, by combining different depth-sensitive electron spectroscopies with density functional theory (DFT) calculations for single layers. We observe that in CrI3 a wide band gap is opened between majority spin eg and t2g states, whereas in VI3 the t2g orbital state is split into (filled) eg′ and (empty) a1g 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 VI3 at the surface, characterized by a V2+ valence and an occupied a1g band, where the bandgap lies between the octahedral-split a1g and the higher-lying empty eg states. In contrast, the 3+ oxidation state measured both for bulk CrI3 and VI3 by X-ray absorption spectroscopy (XAS). Resonant photoemission spectroscopy (ResPES) data, compared to atom- and orbital-resolved 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 CrI3 and VI3.

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 single-layer electronic structure of MI3, referring to the surface-projected BZ reported in Figure b. We also report, for reference, in Figure c,d the expected crystal field splitting and related electronic filling for Cr3+ and V3+, respectively.

XAS measurements across the V and Cr L2,3 edges (Figure a,b) confirm the 3+ oxidation state of bulk CrI3 and VI3. As a matter of fact, the line shape and photon energy of L3 and L2 edges of the former are fully consistent with previous measurements on CrI3,[26,27] while V L2,3 edges of the latter closely resemble those of other vanadium compounds with a V3+ valence state such as V2O3, including the characteristic V 2p to V 3d empty t2g 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.

Figure 2

XAS spectrum of CrI3 (a) over the Cr L2,3 edge (T = 300 K), and VI3 (b) over the V L2,3 edge (T = 150 K). ARPES isoenergetic k–k maps of VI3 (T = 150 K, hv = 32 eV) at (c) 1.15 eV and (e) 2 eV, and CrI3 (T = 300 K, hv = 41 eV) at (d) 2.3 eV and (f) 1.8 eV, highlight the 3-fold symmetry of V/Cr-d states and the 6-fold symmetry of I-p states. The energy in red in the top-right corner of each map pinpoints the binding energy of the isoenergetic cut. DFT calculation of the total energy map with contours shown as black lines for specific energies of VI3, (g) 1.15 eV, (i) 2 eV and CrI3, (h) 2.3 eV, (j) 1.8 eV. Dashed lines in each image represent the 2D hexagonal first Brillouin zone. The energy in red in the top right corner of each map is the binding energy of the isoenergetic cut. ARPES spectra of (k) VI3 (T = 150 K, hv = 32 eV) and (l) CrI3 (T = 300 K, hv = 32 eV) along the Γ–K direction. Theoretical band structures with FM configuration and SOC for VI3 (GGA+U, U = 2 eV) and CrI3 (bare GGA) monolayers are superimposed on experimental data. The colors highlighting the bands represent the following components for V/Cr d-orbital, red denotes d3, green denotes d and d, yellow denotes d and d. For I p-orbital, gray denotes p, magenta denotes p, blue denotes p.

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 CrI3 and VI3. The direct surface analysis and investigation of the energy and the overall symmetry of the electronic states of VI3 and CrI3 was addressed by collecting k–ky photoemission intensity maps at constant energy (see Figure c–f) and energy-momentum spectra, (see Figure k–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 VI3 and CrI3, 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 spin-polarized 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 VI3 and 1.35 eV for CrI3. 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 electron-density 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 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 CrI3[34] and also both from optical[12,22] and spectroscopic[23] measurements for VI3.

From Figure , we note that the overall electronic structures of VI3 and CrI3 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 k,l). On the other hand, the I-derived 5p orbitals are very dispersive and the orbital-mixing is strong for both VI3 and CrI3. 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 and I p–p orbitals at binding energies of ∼1 eV in VI3 and around 2.5 eV in CrI3. Moreover, the inclusion of SOC is relevant in closing the gap between V a1g and I p bands at Γ (see SI Figure S1).

Despite I p bands being fairly similar, our results show that VI3 and CrI3 behave in a different way from the electronic point of view. To emphasize this point, we carried out polarization-dependent measurements on both compounds. p-polarized 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 ). For VI3, we clearly see in Figure a that the orbitals contributing to the spectroscopic signal at ∼1 eV are mostly out of plane, that is, those with a1g character. A value of U = 2 eV is thus found to best simulate our data. Higher values of U would shift the V a1g 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 and d orbitals at an energy of ∼1 eV (Figure S1e-f) which is inconsistent with the data.

Figure 3

(a) VI3 (left) and CrI3 (right) spectra as a function of light polarization (p-polarization, s-polarization, difference p–s). p-polarized light has an out-of-plane component, while s-polarized light is completely in-plane. The “theory” panel displays the DFT band structure; a blue color indicates bands with out-of-plane component, while a red color emphasizes in-plane bands. (b) Angle-integrated spectra of VI3 (left) and CrI3 (right) evidencing polarization-dependent intensity of specific band features.

ARPES results for CrI3 are in striking difference with those shown above for VI3. First, from Figure a we deduce that bands at 2.5 eV BE are ascribed to the out-of-plane d3z2-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. CrI3 exhibits t2g–eg crystal-field splitting of d states; the different orbital filling of Cr3+ ions compared to V3+ results in a t2g level completely filled by majority electrons. The orbital splitting between eg and t2g 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 a1g orbital filling of VI3. The a1g are clearly revealed as filled states by ARPES, while are predicted to be empty by DFT consistently with a V3+ ionic charge. On top of this, XAS results also indicate a V3+ valency of the bulk. This peculiar behavior is nevertheless clearly revealed by ARPES, which probes just the topmost layer of the material, therefore including intrinsic and extrinsic surface effects like relaxation and defect-doping effects that can be responsible of the local electron filling of the a1g band. We thus suggest that a different ground state, characterized by a V2+ 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 a1g and eg′ levels. On the other hand, CrI3 does not show any evidence of a different surface electronic environment.

In Figure c–f, we note that the constant energy ARPES maps for VI3 and CrI3 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 g–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 VI3 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 VI3, 300 K for CrI3) were collected at sample temperatures well above the Curie point (CrI3, TC,CrI3 = 61 K; VI3, TC,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 VI3 and CrI3 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 VI3, 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 TS,CrI3 = 220 K and TS,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 a,c) is a direct signature of their V/Cr orbital nature, and can be mapped onto the DFT orbital projection of the DOS (Figure b,d).

Figure 4

(a) ResPES in the first BZ for VI3: the color map (left panels) displays the momentum-integrated photoemission intensity; the resonant EDCs (right panels) emphasize the band dispersion (or lack of) along the measured photon energy. (b) d-orbital projection DOS of VI3; the color scale represents d orbital characters as follows: filled red, m = 0; filled green, m = 1; orange, m = 2. (c,d) Same as (a,b), but for CrI3.

Photon energy dependent ARPES, such as ResPES, intrinsically also probes the k dispersion. The absence of dispersion of both V and Cr projected bands, highlighted by the EDC spectra (Figure a–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 CrI3 and VI3: 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. CrI3 shows a 3-fold t2g orbital degeneracy and a wide bandgap, while VI3 shows a Mott-insulator-like ground state with a1g-eg′ 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 a1g state at the surface of VI3 indicates that its surface is stabilized by an unconventional V2+ state, at variance with the V3+ bulk valency. Therefore, future research in ultrathin films or nanoparticles of MI3 van der Waals materials with variable surface to bulk ratios should carefully explore the effective ionic configurations that determine their electronic properties and related potential functionalities.