Role of intercalated cobalt in the electronic structure of ${\mathrm{Co}}_{1/3}{\mathrm{NbS}}_2$

${\mathrm{Co}}_{1/3}{\mathrm{NbS}}_2$ is the magnetic intercalate of 2H-${\mathrm{NbS}}_2$ where electronic itinerant and magnetic properties strongly influence each other throughout the phase diagram. Here we report the angle-resolved photoelectron spectroscopy (ARPES) study in ${\mathrm{Co}}_{1/3}{\mathrm{NbS}}_2$. In agreement with previous reports, the observed electronic structure seemingly resembles the one of the parent material 2H-${\mathrm{NbS}}_2$, with the shift in Fermi energy of 0.5 eV accounting for the charge transfer of approximately two electrons from each Co ion into the ${\mathrm{NbS}}_2$ layers. However, in addition, and in contrast to previous reports, we observe significant departures that cannot be explained by the rigid band shift accompanied by minor deformation of bands: First, entirely unrelated to the 2H-${\mathrm{NbS}}_2$ electronic structure, a shallow electronic band is found crossing the Fermi level near the boundary of the first Brillouin zone of ${\mathrm{Co}}_{1/3}{\mathrm{NbS}}_2$. The evolution of the experimental spectra upon varying the incident photon energy suggests the Co origin of this band. Second, the Nb bonding band, found deeply submerged below the Fermi level at the $\mathrm{\Gamma }$ point, indicates that the interlayer hybridization is significantly amplified by intercalation, with Co magnetic ions probably acting as strong covalent bridges between ${\mathrm{NbS}}_2$ layers. The strong hybridization between orbitals that support the itinerant states and the orbitals hosting the local magnetic moments indicates the importance of strong electronic correlations, with the interlayer coupling playing an exquisite role.

Figure 1

(a) Crystal structure of ${\mathrm{Co}}_{1/3}{\mathrm{NbS}}_2$, with two ${\mathrm{NbS}}_2$ layers and two Co-layers entering the crystal unit cell, drawn by VESTA [38]. (b) The orientations of the photoelectron analyzer and the incident photon beam at the UARPES beamline of the SOLARIS synchrotron. The horizontal and vertical light polarizations are defined by blue and red arrows. The horizontal and vertical polarizations correspond to the $p$ and $s$ polarizations of Ref. [39], respectively. (c) Atomic subshell photoionization cross sections for S $3p$, Co $3d$, and Nb $4d$, from Ref. [40].

Figure 2

(a) Bulk Brillouin zone of 2H-${\mathrm{NbS}}_2$ (top) and the surface Brillouin zones of 2H-${\mathrm{NbS}}_2$ and ${\mathrm{Co}}_{1/3}{\mathrm{NbS}}_2$ (bottom), shown in black and blue lines, respectively. (b) The low-energy electron diffraction (LEED) pattern of ${\mathrm{Co}}_{1/3}{\mathrm{NbS}}_2$ obtained by using the 250 eV electrons. The stronger red dots correspond to the crystal structure of 2H-${\mathrm{NbS}}_2$. The weaker intensity white peaks correspond to the $(\sqrt{3}\times \sqrt{3})R{30}^{\circ }$ superlattice of 2H-${\mathrm{NbS}}_2$. The unit cells in the reciprocal space for two lattices are shown as blue and red rhombuses, respectively.

Figure 3

Energy distribution curves (EDCs) along (a) $\mathrm{\Gamma }{\mathrm{M}}_0$ and (b) $\mathrm{\Gamma }{\mathrm{K}}_0$ lines in the $k$ space. The ARPES intensity plots for ${\mathrm{Co}}_{1/3}{\mathrm{NbS}}_2$ measured along (c) $\mathrm{\Gamma }{\mathrm{M}}_0$ and (d) $\mathrm{\Gamma }{\mathrm{K}}_0$ directions using the $h\nu =40\mathrm{eV}$ photons, and horizontal polarization. In order to cover an extended momentum range, three ARPES images collected $\pm {15}^{\circ }$ frame are stitched. The vertical-dashed lines represent the boundaries of the ${\mathrm{Co}}_{1/3}{\mathrm{NbS}}_2$ first Brillouin zone. The lines composed of blue and yellow dots represent the energy bands calculated for 2H-${\mathrm{NbS}}_2$, with the unit cell adjusted to ${\mathrm{Co}}_{1/3}{\mathrm{NbS}}_2$, and additional $4/3$ electrons per unit cell (see text). The blue and yellow dots stand for states predominantly composed of Nb- and S-derived orbitals, respectively. The calculated bands are subsequently shifted by 0.1 eV with respect to the Fermi level in the direction that increases the conduction band filling.

Figure 4

The ARPES intensity plots along $\mathrm{\Gamma }{\mathrm{K}}_0$ direction measured with different energy of the photons used in the experiment. All ARPES images are measured using horizontal polarization and plotted in the same intensity scale. Blue-dashed lines correspond to the boundaries of the first Brillouin zone of ${\mathrm{Co}}_{1/3}{\mathrm{NbS}}_2$. The green-vertical lines in the first panel denote the cuts taken in the spectrum leading to 40 eV curves in Figs. 8 and 8.

Figure 5

ARPES intensity plots of ${\mathrm{Co}}_{1/3}{\mathrm{NbS}}_2$ along the $\mathrm{\Gamma }{\mathrm{K}}_0$ direction for (a) horizontal and (b) vertical photon polarization. The spectra are measured with $h\nu =62\mathrm{eV}$ at 10 K. The dashed lines in light-blue mark the M high-symmetry point at the boundary of the first Brillouin zone of ${\mathrm{Co}}_{1/3}{\mathrm{NbS}}_2$.

Figure 6

Constant energy cuts at the Fermi level, measured at 10 K using $h\nu =40\mathrm{eV}$ photons, in (a) horizontal and (b) vertical polarization setups. The panels (c) and (d) show the data obtained using $h\nu =62\mathrm{eV}$ photons, respectively in horizontal and vertical polarization. The large black hexagon and the small hexagons shown in light-blue-dashed line represent the first Brillouin zones of ${\mathrm{NbS}}_2$ and ${\mathrm{Co}}_{1/3}{\mathrm{NbS}}_2$, respectively.

Figure 7

Constant energy cuts at (a) $E_{\mathrm{F}}$, (b) 20 meV below $E_{\mathrm{F}}$, and (c) 40 meV below the Fermi energy of ${\mathrm{Co}}_{1/3}{\mathrm{NbS}}_2$, measured at 10 K with $h\nu =62\mathrm{eV}$ in horizontal polarization. The large black hexagons and the small hexagon shown in light-blue-dashed line represent the first Brillouin zones of ${\mathrm{NbS}}_2$ and ${\mathrm{Co}}_{1/3}{\mathrm{NbS}}_2$, respectively. (d) Left half of the Fermi surface shown on panel (a) is presented with ARPES spectra along $\mathrm{\Gamma }$ - ${\mathrm{M}}_0$ direction down to 0.3 eV binding energy.

Figure 8

The energy distribution curves (EDCs) at two position in $k$ space are shown in panels (a) and (b). These positions are marked by green full vertical lines in the first panel of Fig. 4, labeled by $a$ and $b$, respectively. (a) The EDCs at $(k_x,k_y)=(0,0)\equiv \overline{\mathrm{\Gamma }}$ point, measured for various energies of incident photons. The main spectral features are indicated by vertical bars and labels below the bottommost curve. (b) The EDCs at $k=0.295 {\AA }^{-1}$ along the $\mathrm{\Gamma }{K}_0$ direction. (c) The data at the same $k$ point, $k_{\mathrm{\Gamma }{K}_0}=0.295 {\AA }^{-1}$ shown as the function the binding energy and $k_z$, given by Eq. (1). The labels (${\mathrm{\Gamma }}_n$) next to black dashed lines mark the $k_z$ levels of ${\mathrm{\Gamma }}_n\equiv (0,0,2\pi /c\times n)$, whereas the label $A_n$ stands for the midpoint between ${\mathrm{\Gamma }}_n$ and ${\mathrm{\Gamma }}_{n+1}$, as usual.

Figure 9

(a) The electronic spectra calculated for ${\mathrm{Co}}_{1/3}{\mathrm{NbS}}_2$ (see Ref. [35]) in the particular antiferromagnetically ordered state, termed the hexagonal order of the first kind (HOFK). The electronic bands are shown unfolded along ${\mathrm{M}}_0\mathrm{\Gamma }{\mathrm{K}}_0$ line of Brillouin zone of 2H-${\mathrm{NbS}}_2$, averaged over three equivalent directions by the hexagonal symmetry. (b) The comparison between measured and calculated spectra along the $\mathrm{\Gamma }-K_0$ line. (c) The comparison between the calculated and the experimental spectra at the Fermi level. The most obvious qualitative difference is the lack of the $\beta$-band signal in the DFT-calculated spectra along the boundary of the first Brillouin zone of the of ${\mathrm{Co}}_{1/3}{\mathrm{NbS}}_2$, shown in a dotted line. The color bar indicates the intensity scale.

Figure 10

(a) The unfolded spectra of the system modeled through the tight-binding reparameterization, with the parameters initially taken from our DFT/Wannier90 calculation. Very few modifications, detailed in the text, are inspired by studies of the effects of strong electron correlations in other systems. The image shows the spectral density along the ${\mathrm{M}}_0\mathrm{\Gamma }{\mathrm{K}}_0$ line in the $k$ space. (b) The comparison between measured and calculated spectra along the $\mathrm{\Gamma }-K_0$ line. The faint $\beta$-band signal appears on both sides, near the top of the M vertical line. The bonding band signals approach the $\mathrm{\Gamma }$ point at approximately the same energy from both sides. (c) The comparison between the calculated and the experimental at the Fermi level. The dotted lines mark the boundary of the first Brillouin zone of the of ${\mathrm{Co}}_{1/3}{\mathrm{NbS}}_2$. Both subpanels show the $\beta$-band signal that spreads along this boundary, particularly enhanced around the K point.

Figure 11

(a) The photon energy dependence of the momentum distribution curves (MDCs) along the $\mathrm{\Gamma }{\mathrm{K}}_0$ direction at the Fermi level. The MDCs are taken at the same photon energies as in Fig. 8. The same normalization applies as in Fig. 4. (b) ARPES intensity plot of the $k_z\text{−}{k}_{\mathrm{\Gamma }{K}_0}$ band dispersion at Fermi level. The labels ${\mathrm{\Gamma }}_n$ and $A_n$ have been defined in relation to Fig. 7. Two vertical-dashed lines shown in cyan in both panels represent the boundary of the Brillouin zone of ${\mathrm{Co}}_{1/3}{\mathrm{NbS}}_2$ and correspond to the M point at $k_z=0$.

Figure 12

(a) DFT-calculated electronic bands of 2H-${\mathrm{NbS}}_2$ with DFT-relaxed lattice parameters. (b) DFT-calculated electronic bands of 2H-${\mathrm{NbS}}_2$ with additional 2/3 electrons per Nb atom and the lattice parameters borrowed form DFT-relaxed ${\mathrm{Co}}_{1/3}{\mathrm{NbS}}_2$ structure. Blue and yellow colors reflect the relative weights of niobium and sulfur orbitals in particular states. (c) DFT-calculated electronic bands of ${\mathrm{Co}}_{1/3}{\mathrm{NbS}}_2$ in antiferromagnetically ordered state. The colors mark the dominant character of electronic states: blue indicates that the electronic state is predominantly composed of niobium orbitals, yellow represents the dominance of sulfur orbitals, and red specifies the dominance of cobalt orbitals in the electronic state.