Introduction

The interaction between localized and itinerant electrons has long been a central topic in condensed matter physics, as it gives rise to a variety of emergent phenomena, including unconventional magnetism, Mott insulating behavior, superconductivity, and Kondo physics1,2,3,4,5,6. A long-standing debate persists as to whether d electrons are better described by localized Heisenberg models or itinerant band models. These frameworks lead to contrasting interpretations in high-temperature superconductors: for instance, parent cuprates are Mott insulators with strong electron correlations and localized d electrons, which are believed to be essential for superconductivity7. In contrast, iron pnictides exhibit metallic behavior with coexisting localized and itinerant electrons, and their correlations are not as strong as cuprates8. Distinctions between itinerant magnetism and local-moment-driven magnetism are also well documented across a wide range of compounds1,2,9. It is now widely recognized that the complex exchange interactions between local moments and itinerant electrons play a crucial role in determining the magnetic and transport properties of recently studied 3d transition-metal (TM = V, Cr, Mn, Fe, Co, Ni) intercalated transition metal dichalcogenides (TMDs)10,11,12,13,14,15,16,17,18,19,20,21,22,23.

TMDs with layered two-dimensional (2D) structures formed by the van der Waals force are easily manipulated and are promising platforms for exploring abundant quantum phases. 2H-NbS2 is a well-studied superconductor in this system with a critical transition temperature of around 6 K and an absence of charge density wave order24,25. Intercalating 3d atoms into the van der Waals gaps suppresses the superconductivity and leads to form complicated magnetic orders and electronic structures10. 1/3 concentration of intercalated atoms, (TM)1/3NbS2 (P6322 space group), is optimal doping for achieving high-quality crystals, where TM atoms occupy different sites above and below each NbS2 layer making the crystal non-centrosymmetric and forming a superlattice rotated by 30° concerning the 1 × 1 unit cell of 2H-NbS2, as shown in Fig. 1a.

Fig. 1: Crystal structure and low-energy electronic states of Mn1/3NbS2 and 2H-NbS2.
Fig. 1: Crystal structure and low-energy electronic states of Mn1/3NbS2 and 2H-NbS2.
Full size image

a Crystal structure of 3d atoms intercalted NbS2. TM represents 3d transitional metal atoms. b, c The calculated DOS of Mn1/3NbS2 and 2H-NbS2, respectively. d Integrated intensity plots at EF ± 10 meV taken on the kz ~ 0 plane for Mn1/3NbS2. The solid lines is a BZ of Mn1/3NbS2 and the dashed lines is a primitive BZ of NbS2. e Intensity plots and the corresponding second derivative plots along the Γ − M − K0 for Mn1/3NbS2. The second derivative is made by the 2D curvature method37. The MDC at EF is appended and the solid red lines in the second derivative plots show the bands near EF. f Integrated intensity plots (±10 meV) and corresponding second derivative plots on the kx-kz plane at EF taken by various photon energies for Mn1/3NbS2. High-symmetry points and the band names are indicated.

In (TM)1/3NbS2, the electronic states near the Fermi energy (EF) are primarily derived from the NbS2 layer, particularly from Nb 4d orbitals. Although the 3d states of the intercalated TM atoms do contribute, they are mainly located away from EF, split on either side of the Nb-derived bands20. Except for V1/3NbS211, it has been proposed that hybridization of TM 3d and Nb 4d states near EF enhances interlayer coupling and introduces out-of-plane electronic dispersions, as experimentally demonstrated through resonant spectroscopy and photon-energy-dependent angle-resolved photoemission spectroscopy (ARPES)14,15,16,17. The saturated magnetic moments of the TM atoms in Cr- and Mn-intercalated NbS2 compounds are smaller than those inferred from Curie constants, but somewhat larger than those predicted by first-principles calculations, indicating an itinerant character of magnetism21,22,23. However, magneto-transport and temperature-dependent ARPES studies have demonstrated that Hund’s rule coupling at the TM sites plays a significant role14,15. These findings suggest that TM atoms actively mediate the interplay between local magnetic moments and itinerant carriers.

In this work, we present a combined study of ARPES using micro (μ)-focused synchrotron radiation light and first-principles calculations to investigate the temperature-dependent evolution of the low-energy electronic structure of Mn1/3NbS2, and to compare its band structure near EF with that of Cr1/3NbS2. Our results reveal that exchange splitting in Mn1/3NbS2 persists well above the Curie temperature (TC), deviating from the behavior expected for itinerant magnetism as described by the Stoner model. In contrast to Cr1/3NbS2, the additional electron contributed by Mn in Mn1/3NbS2 does not result in a simple rigid-band shift. Instead, it induces anomalous modifications in the electronic structure around EF, primarily associated with subtle interlayer hybridization between TM 3d and Nb 4d states, governed by Hund’s rule coupling.

Results

Low-energy electronic structure

Although the intercalated TM 3d atoms in NbS2 significantly modify its magnetic and electronic structure, the dispersions around -1 eV to EF still mainly originate from NbS2 layers, as shown in Fig. 1b, c. The introduction of a superlattice in (TM)1/3NbS2 reduces the size of the Brillouin zone (BZ) and rotates it by 30°, as indicated by the red lines overlaid on the Fermi surfaces (FSs) in Fig. 1d. Using μ-ARPES with a beam spot smaller than 20 × 20 μm2, we focused our measurements on regions terminated by NbS2 surfaces, following procedures established in prior work13. ARPES data reveal three hole-like bands (α, β, and γ) centered at the BZ center (Γ), and two additional hole-like bands (δ and κ) near the corner of the original NbS2 BZ (K0), as identified in the momentum distribution curve (MDC) at EF and the band dispersions shown in Fig. 1e. Figure 1f shows the intensity as a function of the photon energy and in-plane momentum kx along the Γ − M direction at EF taken by the photon energies from 40 to 128 eV. The β and γ bands do not show distinguishable three-dimensional (3D) kz dispersions, and the α band with weak intensity is not clearly resolved under the present experimental condition probably due to the matrix element effect also associated with complicated magnetism. In Cr1/3NbS2, prior studies report a strongly dispersive α band along kz and weakly dispersive β and γ bands15, which is consistent with our observations in Mn1/3NbS2. Since our analysis primarily focuses on the β and γ bands, data collected on the kz  ~ 0 (Γ − M − K) plane are sufficient to capture the essential band structure features relevant to this study.

Temperature evolution of the electronic structure

We carry out a circle of temperature-dependent measurements in detail, namely, conducting from 70 K to 10 K, and then back to 90 K to overcome the thermal broadening effect and the possibility of sample aging during measurements. The β band is highlighted among all dispersions at EF and its clear changes along with temperatures can be seen directly in the intensity plots (Fig. 2a). The broadening structure suggests existing band splittings. The corresponding MDCs at -18 meV below EF have been displayed for a precise analysis in Fig. 2b. It needs two Lorentzian functions and one linear background to fit these MDCs well, even at temperatures above TC ~ 45 K, a magnetic transition temperature. Although these splittings are not easy to figure out at high temperatures (70 and 90 K) as they are below 50 K, these MDCs cannot be eventually fitted well by a single Lorentzian function, suggesting the persistence of band splittings at these temperatures. It is consistent with previous observations of Cr1/3NbS215 that suggests a short-range exchange interaction, a drastic contrast to the Stoner model.

Fig. 2: Temperature-dependent ARPES measurements on the β band of Mn1/3NbS2.
Fig. 2: Temperature-dependent ARPES measurements on the β band of Mn1/3NbS2.
Full size image

a Intensity plots around β taken at different temperatures. The blue arrows indicate the measuring sequence. b The MDCs taken at −18 meV below EF as marked by the blue dashed lines in (a).

Comparing electronic structure between Cr- and Mn-intercalated NbS2

In 3d transition-metal substituted compounds, increasing atomic number not only introduces additional carriers and shifts the chemical potential, but also moves the 3d shell toward or away from half-filling, where strong correlations and Mott physics often emerge. Such orbital-dependent correlations can produce non-rigid band shifts, a hallmark of Hund metals. In some cases, however, the overall band framework remains largely comparable across doping levels, as in ferropnictides26. By contrast, 3d substitution may also drive pronounced changes in magnetism and band topology, exemplified by (Fe1−xCox)Sn27.

Compared to Cr1/3NbS2, Mn atoms in Mn1/3NbS2 contribute one additional electron, effectively half-filling the 3d shell. In principle, this should lead to an upward shift of the chemical potential and enhanced electronic correlation effects. To investigate these effects, we compare the low-energy electronic structures of Cr- and Mn-intercalated NbS2 in Fig. 3. To ensure a meaningful comparison, we maintained consistent measurement conditions wherever possible, using horizontally polarized photons corresponding to the kz ~ 0 (Γ − M − K) plane and identical experimental setups. The band structures of the two compounds along the two high-symmetry directions (Γ − M − K0 and Γ − K − M0) are shown in Fig. 3a and b, respectively. The spectra in these figures were normalized using the background above EF. The energy distribution curves (EDCs) at the high-symmetry points for both materials, shown in Fig. 3c, were extracted directly without further normalization and are color-coded (black for Cr1/3NbS2, red for Mn1/3NbS2). Here, we would like to note that the primary purpose here is to compare the peak positions in the EDCs, as the peak intensities themselves are not of significant physical relevance. Overall, from approximately −2.4 eV to EF, the electronic structures of the two materials exhibit comparable features. In the EDCs at Cut1 and Cut3, the spectral intensity is peaked at a higher binding energy of about 1.7 eV in both compounds.

Fig. 3: Comparing the low-energy dispersions between Cr- and Mn-intercalated NbS2.
Fig. 3: Comparing the low-energy dispersions between Cr- and Mn-intercalated NbS2.
Full size image

a Intensity plots along the Γ − M and Γ − K directions of Cr1/3NbS2. b The same as (a) but for Mn1/3NbS2. c EDCs along Cut1 and Cut2 in (a) and (b). Different colors represent cuts in different materials: black for Cr1/3NbS2 and red for Mn1/3NbS2. The horizontal blue dashed lines that run through (a–c) are guides for comparing energy positions. d kz dispersion of the ω band at the M0 point. e The crossing bands along Γ − K in (a, b) are fitted by parabolic curves and the Fermi velocities are fitted by lines, respectively [see details in Supplementary Fig. 1] (Supplementary Information for the first-principles electronic structure calculations). The size of each marker reflects the measurement uncertainty (~15 meV and  ±0.01 Å−1), while the black (±20 meV and 0.01 Å−1) and red (±40 meV and 0.01 Å−1) bars at the bottom represent the maximum fitting errors in the energy and momentum directions, respectively. f Electron configurations of TM in D3d and Nb in D3h crystal fields. In the upper panel, the black solid arrows represent the electron filling of Cr d3 in the t2g orbitals, while the additional electron in Mn d4 occupies one of the eg orbitals. In the lower panel, the black dashed arrow represents an electron transferring from the TM to the NbS2 layer.

In contrast, when comparing the bands near EF, such as the EDCs at Cut2 and Cut4, we observe clear relative energy shifts of ~0.2 eV at the M point and the M0 point (corresponding to the ω band). These shifts cannot be attributed to kz dispersion effects, as both materials were measured in the kz ~ 0 plane. Moreover, the β and γ bands exhibit only weak kz dispersion, while the ω band does show a kz-dependent dispersion (Fig. 3d), with its band minimum occurring near kz ~ 0. This suggests that the energy shifts may be even more pronounced at other kz values. Together, although Mn atoms contribute one more electron than Cr atoms, the EF of Mn1/3NbS2 is lowered by ~0.2 eV compared to Cr1/3NbS2, which contradicts conventional expectations. According to Luttinger’s theorem, we evaluated the net FS area enclosed within the first BZ to estimate the carrier density per unit cell and the degree of charge transfer between the intercalant and the NbS2 layer. In pristine 2H-NbS2 (see Fig. 2 in ref. 25), two predominantly hole-like FS pockets surround the Γ and K points, together enclosing about 1.33 holes per unit cell. For Cr1/3NbS2 and Mn1/3NbS2, the net hole-enclosed FS areas correspond to approximately 32.6  ± 4.2% and 41.9  ± 4.2%, respectively. These results indicate that Cr adopts the expected valence of  ~ 3+, corresponding to a transfer of one electron, as shown in Fig. 3f. While Mn1/3NbS2 exhibits larger hole-like FS pockets owing to a downward chemical-potential shift, implying a smaller net charge transfer than in Cr1/3NbS2. Furthermore, by fitting the β band with a parabolic dispersion (Fig. 3e), we find that the β band top of Mn1/3NbS2 is indeed about 0.2 eV higher than that of Cr1/3NbS2, consistent with the observed band shift. The Fermi velocity of the β band in Mn1/3NbS2 is higher than in Cr1/3NbS2, suggesting weaker electronic correlations near EF in the Mn-intercalated compound—another counterintuitive finding.

Band calculations

We have also performed band calculations to compare the electronic structures of the two compounds, as shown in Fig. 4. First-principles modeling of magnetic metals remains challenging due to the interplay of magnetism and correlations, which often prevents a quantitative match with experimental results. On the experimental side, ARPES studies of magnetic systems are further complicated by domain formation, multiple cleavage planes, and strong matrix-element effects, all of which reduce band visibility and spectral resolution. In this work, we employed μ-ARPES to mitigate issues related to multi-domain structures and irregular surfaces while maintaining sufficient photon flux. As illustrated in Fig. 4a, b, the calculated bands reproduce the overall framework and main features of the experimental spectra, highlighting a qualitative consistency between theory and measurement.

Fig. 4: Bands calculations on Cr- and Mn-intercalated NbS2.
Fig. 4: Bands calculations on Cr- and Mn-intercalated NbS2.
Full size image

a, b Calculated band structures of the two compounds in the ferromagnetic ground state without spin-orbit coupling. Red and blue lines represent opposite spin orientations. c Spin-resolved and orbital-projected DOS for both compounds. d Comparison of spin-integrated and orbital-projected DOS for Cr/Mn 3d, Nb 4d, and S 3p states in the two compounds.

The ferromagnetic ground state, corresponding to the lowest-energy configuration, was selected for the calculations [see details in Supplementary Fig. 2 and Supplementary Table 1] (Supplementary Information for the first-principles electronic structure calculations). The calculated magnetic moments in this state are 2.79 μB for Cr1/3NbS2 and 3.95 μB for Mn1/3NbS2, in good agreement with the saturated magnetic moments determined from neutron scattering experiments21,23. As shown in Fig. 4c, d, the dominant peaks in DOS for the occupied and unoccupied Cr 3d orbitals are located at approximately −1.7 eV and 0.6 eV, respectively. For Mn, these peaks appear at about −2.5 eV and 1.0 eV. Notably, there is significant hybridization between the spin-up Cr 3d and Nb 4d orbitals near EF, resulting in a characteristic V-shape spin-up DOS at EF. The unoccupied spin-down 3d orbitals of both Cr and Mn hybridize with the Nb 4d orbitals above EF, causing a downward shift in the spin-down Nb 4d orbitals and pronounced spin polarization at EF. A direct comparison of the atom-resolved DOS in the two compounds [Fig. 4d] shows relatively minor differences in the Cr/Mn 3d states, but a substantial enhancement of the Nb 4d DOS from -1 eV to EF in Mn1/3NbS2. This increase may be attributed to the interlayer covalent bonding and hybridization—a phenomenon referred to as a pseudodoping effect28,29.

Discussion

In 3d-atom intercalated NbS2, the electrons introduced by the 3d atoms not only change the total carrier concentration but also significantly modify the electronic structure of NbS2 through the emergence of new bands around EF (see Supplementary Fig. 3) (Supplementary Information for the first-principles electronic structure calculations). These modifications cannot be rationalized based on a rigid band picture. The bands near EF are still largely dominated by NbS2-derived orbitals, and the 3d states are divided into lower and upper Hubbard bands, producing an observable gap-like feature commonly observed in various TM atoms intercalated TMDs14,15,16,17,20.

Hybridization leads to significant variations in the occupancy of specific bands, governed by the orbital configuration within the crystal field [Fig. 3f] and dictated by Hund’s rule coupling. This hybridization further modifies the effective interactions within the hybridized bands, resembling the pseudodoping effect observed in some layered 2D materials28,29. Notably, this mechanism differs from the conventional non-rigid band shifts seen in ferropnictides26 and (Fe1−xCox)Sn27 as mentioned above. The hybridization effect significantly influences the (spin-polarized) DOS and correlation strength. In Mn1/3NbS2, the additional electron in the Mn 3d shell unexpectedly causes a downward shift in the chemical potential and weakens the electronic correlations near EF. Enhanced correlations are instead observed in Mn 3d-dominated bands around −2.5 eV and 1 eV, as shown in Fig. 4, and a net charge transfer is even less than that in Cr1/3NbS2. A key distinction lies in the half-filled spin-up eg orbitals of Cr [Fig. 3f], which maintains a DOS at EF comparable to that of Nb 4d states, promoting strong hybridization between Cr 3d and Nb 4d orbitals.

To further clarify the origin of the anomalous Fermi-level shift, we analyzed the core-level spectra of Cr1/3NbS2 and Mn1/3NbS2 (Supplementary Fig. 4) (Supplementary Information for the first-principles electronic structure calculations). The S 3p peaks near  −14 eV remain unchanged, excluding significant charge transfer, while the Nb 4p states near  −32 eV exhibit a modified line shape, consistent with hybridization-induced redistribution at Nb sites. These results support our interpretation that the shift originates from hybridization-driven pseudodoping. We acknowledge that possible contributions from local structural distortions or variations in Nb–S bonding cannot be fully excluded, providing a more open perspective for future investigations.

Previous studies on V1/3NbS2 suggest minimal hybridization between V- and Nb-derived states at EF, with band splitting attributed to exchange interactions between the itinerant Nb 4d states and localized V magnetic moments11. As the number of 3d electrons increases, more pronounced hybridization near EF is observed in Cr1/3NbS2 and Mn1/3NbS2 compared to V1/3NbS2 (see Supplementary Fig. 5) (Supplementary Information for the first-principles electronic structure calculations), leading to enhanced interlayer coupling and noticeable kz dispersion14,15,16,17. Temperature-dependent ARPES measurements reveal that exchange splitting persists far above TC, indicating the presence of local-moment magnetism and short-range magnetic correlations—findings supported by neutron diffraction results15,23. However, the reduced correlation in Mn1/3NbS2 near EF compared to Cr1/3NbS2 supports a more itinerant character for Mn1/3NbS2. This itinerancy is also reflected in the discrepancy between the magnetic moments obtained from Curie-Weiss fits to χ(T) and those determined by neutron scattering23. While a fully quantitative description of the coexistence of localized and itinerant electrons in these systems remains challenging, our study provides important insights into how intercalated 3d atoms influence electronic structure near EF through hybridization. These findings offer a potential strategy to tune the low-energy band structure of layered materials by selecting appropriate intercalants.

Methods

ARPES experiments

High-quality single crystals were synthesized by the vapor-transport technique as described elsewhere21,23. ARPES measurements within a wide range of photon energies were performed at the 03U and 09U endstations at the Shanghai Synchrotron Radiation Facility (SSRF). The μ-ARPES with the beam size is less than 20 × 20 μm2. The energy and momentum resolutions were set to be better than about 15 meV and 0.02 Å−1, respectively. Samples smaller than 1 × 1 mm2 were cleaved in situ, yielding flat mirror-like (001) surfaces. The pressure was maintained at less than 2 × 10−10 Torr in temperature-dependent measurements.

Band calculations

The first-principles calculations were performed in the framework of density functional theory (DFT)30,31 using the Vienna Abinitio Simulation Package (VASP)32,33,34. The generalized gradient approximation (GGA) of the Perdew–Burke–Ernzerhof (PBE) type35 was adopted for the exchange-correlation function. The projector-augmented wave (PAW) method36 was adopted to describe the interactions between valence electrons and nuclei.