Overview of electronic structure

Previous work focusing on how the electronic structure of NbS 2 is modified with Cr intercalation for temperatures below the helimagnetic transition temperature (Fig. 1b) is reported by Sirica et al.32. To summarize these results, Fig. 1c, d shows a schematic diagram of both the FS and band dispersion along the high-symmetry ΓK-axis, where crossing points α, β 1,2 , γ, and δ follow the same labeling convention as used in this previous study32. As expected, Cr intercalation injects electronic charge into the NbS 2 layers, resulting in a sinking of the bonding, bilayer split NbS 2 band (S) below E F , while the remaining NbS 2 -derived, anti-bonding band has crossing points α and γ consistent with a raise in chemical potential. However, the electronic charge introduced by the Cr intercalant not only changes the total number of carriers but also causes a significant modification to the electronic structure of NbS 2 through the addition of two additional bands at Γ (β 1 , β 2 ), and one additional band at Κ (δ). Since these bands cannot be rationalized on the basis of a rigid band picture, it is natural to inquire about their origin. Here, we focus on the temperature dependence of the α and β 1,2 bands in proximity to Γ, as the bands at Κ are found to exhibit no significant change with temperature across T C .

Temperature-dependent angle-resolved photoemission

Temperature-dependent ARPES is used to map the dispersion of the α and β 1,2 bands in proximity to E F as the temperature is tuned across T C (Fig. 2). For T < 131 K, three dispersive bands can be identified at Γ, while only two bands are present as temperature is raised above T C . From Fig. 2, it is evident that the outermost β 2 band shifts towards Γ with increasing temperature until the two β-bands can no longer be distinguished. Such behavior is more clearly demonstrated in Fig. 3, which gives the temperature dependence of the band crossing points (k F ) along the two high-symmetry directions ΓM (Fig. 3a) and ΓK (Fig. 3b). Here, momentum distribution curves (MDCs) illustrating the distributions of spectral weight at a fixed energy E = E F along these two high-symmetry directions reveals a monotonic shift in k F for the β 2 band to be accompanied by a progressive decrease in spectral weight for 50 K < T < 120 K. The fact that this behavior is observed along both the ΓM and ΓK directions suggests it to be isotropic about Γ. Moreover, given the close proximity to T C , the relative shift of β 2 towards β 1 implies the β 1,2 bands arise from magnetic exchange splitting. While dedicated spin-resolved ARPES measurements are required to establish unambiguously the spin polarization of these bands, such a finding is consistent with the notion that the β 1,2 bands result from intercalation of a magnetic element (Cr) into NbS 2 , and suggest the presence of Cr-derived states at E F . Indeed, this finding has been confirmed with ResPES, a methodology that allows photoemission spectra of the valence band (VB) to acquire elemental sensitivity33,34.

Fig. 2: Temperature-dependent angle-resolved photoemission. Temperature-dependent angle-resolved photoemission spectra obtained along the ΓΜ direction at a 10 K, b 50 K, c 90 K, d 120 K, e 131 K, f 140 K, g 170 K, and h 220 K using π-polarized photons having an energy, hν = 48 eV. Here, band crossing points are denoted by white arrows in a, while the dashed line in a, e denotes the presence and absence of a β 2 band crossing as temperature is raised above the helimagnetic transition temperature. Full size image

Fig. 3: Temperature dependence of band crossing points. Momentum distribution curves extracted at the Fermi level from spectra measured along a ΓM and b ΓK using photons of energy hν = 48eV. Note the emergence of a split β 1,2 band for temperatures below 120 K, and a loss of spectral weight along both high-symmetry axes for temperatures below the helimagnetic transition temperature. Full size image

Resonant photoemission

By tuning the incident photon energy across the Cr L 3 -edge, it is possible to identify Cr 3d states in the VB within 3 eV of E F (Fig. 4a, b). The increase in signal intensity at resonance, that is, with the photon energy tuned on the maximum of the Cr absorption edge, reveals that the structures at ≈2.5 eV and within ≈1 eV from E F are states possessing Cr 3d character.

Fig. 4: Identifying Nb- and Cr-derived states in the valence band. Resonant photoemission spectra measured across the a, b Cr L 3 and c, d Nb M 5 absorption edges using linear horizontal photon polarization. Intensity maps (a, c) and selected photoemission spectra generated across the b Cr and d Nb x-ray absorption edge (XAS) shown in the inset. Spectra denoted 1–4 in a, c are taken through the Cr and Nb resonance, respectively. Hatched area in b, d denotes the difference between spectra taken on resonance (1–4) and off resonance (0). Full size image

The states at Γ have been shown by polarization-dependent ARPES to exhibit predominantly out-of-plane orbital character32. Therefore, in contrast to our previous ResPES measurements32, whose purpose was to identify non-dispersive Cr states remaining on the surface following sample cleave, the photon polarization used in this report was chosen to emphasize those bulk states having an out-of-plane character through ensuring a component of the photon polarization to lie perpendicular to the sample plane. In doing so, a direct comparison of ResPES spectra taken with photon energies tuned across the Cr L-edge (Fig. 4a, b) and Nb M-edge (Fig. 4c, d) reveals a clear resonance over the Nb “d z 2 sub-band”21 (E B ≈0.6 eV < E < E F ), indicating the presence of hybridization between Cr- and Nb-derived states in the VB. This is made possible by noting spectra taken across the Cr L 3 -edge to be sensitive, in these experimental conditions, to the projection of Cr 3d orbitals, whose splitting is dictated by a trigonally distorted octahedral environment22,23. Hence, our ResPES data clarify that the VB states at Γ originate from a linear combination of Nb d z 2 and mixed Cr 3d orbitals (\(\sqrt 2\)d xz − d x 2 − y 2 and \(\sqrt 2\)d yz + d xy ), having an overall out-of-plane orbital character.

In addition to taking ResPES measurements across the Cr L 3 ionization edge for T > T C (Fig. 4a, b), ARPES spectra were collected at T < T C along the ΓΚ-axis using photon energies that have likewise been tuned across the Cr resonance (Fig. 5a–c). In doing so, the α band, belonging to the host NbS 2 compound, and two β 1,2 bands, arising from Cr intercalation, are well separated, allowing for the elemental sensitivity of ResPES to benefit from an added momentum resolution. Here, a comparison of the integrated energy distribution curves (EDCs) shown in Figs. 4b and 5d reveal a resonant enhancement of Cr 3d states occurring near E F that is independent of temperature. However, MDCs extracted from Fig. 5a–c at E F as a function of photon energy show an initial resonance of the β 1,2 bands (k ~0.5 Å−1) occurring at the onset of absorption (Fig. 5e). This finding not only provides evidence for a Cr-derived elemental character of these bands but also reveals a lack of hybridization with the Nb-derived α band that is consistent with its anti-bonding orbital character32. Given the large separation distance between Cr neighbors, the formation of dispersive β 1,2 bands following Cr intercalation can only occur through hybridization with Nb. This is made clear from our ResPES results, but is also indicated by the higher degree of k z dispersion exhibited by the β 1,2 bands as compared to α32. Thus, by measuring ARPES across the Cr absorption edge, a band resolved picture of Cr-derived d states in the VB is obtained.

Fig. 5: Angle-resolved photoemission across the Cr resonance. Angle-resolved photoemission spectra measured below the helimagnetic transition temperature (110 K) using a photon energy tuned a off the Cr L 3 resonance (hν = 570 eV), b at the onset of Cr absorption (hν = 574eV) and c at the maximum of Cr absorption (hν = 576 eV), where the contribution due to photon momentum is taken into account. An angle of 60° is made between the polarization vector of the incoming light and the crystal surface plane, resulting in a dominant component perpendicular to the sample surface. d Integrated energy-dispersive curves taken over a momentum range, Δk = ±0.5 Å−1 with respect to Γ, encompassing the α and two β 1,2 , bands. e Resonant momentum distribution curves obtained by integrating ±50 meV about the Fermi level. For the resonance tuned on the maximum of Cr absorption, a featureless MDC is observed, indicating various scattering channels have opened across the Fermi surface. Full size image

Change in spectral weight in proximity to T C

By revealing the presence of Cr-derived d states at E F , our data show that a clear separation of magnetic and itinerant DOF does not occur in Cr 1/3 NbS 2 , as the same states forming LSMs are also participating in the formation of the FS. The consequences of this finding are illustrated in the temperature dependence of the EDCs integrated over a broad momentum range (k ΓΜ = 0.24–0.8 Å−1) encompassing both crossing points of the β 1,2 bands (Fig. 6a). Here, as T >50 K, the spectral weight in proximity to E F begins to drop and is transferred towards higher binding energies until T >120 K, whereupon there is no longer any change. Similarly, the temperature dependence of the α band appears to be less pronounced as compared to that of the β band, but still reveals a monotonic drop of spectral weight at E F , as well as a slight reduction in the separation between peaks at 100 and 400 meV as T > T C (Fig. 6b). In both cases, the spectral weight at E F changes in close proximity to T C (T = 130–90 K), allowing for thermal broadening effects to be excluded, suggesting instead a microscopic mechanism that links electron itinerancy to the onset of ferromagnetism.