Electronic structure of the chiral helimagnet and $3d$-intercalated transition metal dichalcogenide $\mathrm{C}{\mathrm{r}}_{1/3}\mathrm{Nb}{\mathrm{S}}_2$

The electronic structure of the chiral helimagnet $\mathrm{C}{\mathrm{r}}_{1/3}\mathrm{Nb}{\mathrm{S}}_2$ has been studied with core level and angle-resolved photoemission spectroscopy (ARPES). Intercalated Cr atoms are found to be effective in donating electrons to the $\mathrm{Nb}{\mathrm{S}}_2$ layers but also cause significant modifications of the electronic structure of the host $\mathrm{Nb}{\mathrm{S}}_2$ material. In particular, the data provide evidence that a description of the electronic structure of $\mathrm{C}{\mathrm{r}}_{1/3}\mathrm{Nb}{\mathrm{S}}_2$ on the basis of a simple rigid band picture is untenable. The data also reveal substantial inconsistencies with the predictions of standard density functional theory. The relevance of these results to the attainment of a correct description of the electronic structure of chiral helimagnets, magnetic thin films/multilayers, and transition metal dichalcogenides intercalated with $3d$ magnetic elements is discussed.

Figure 1

(a) $S2p$ core level spectrum taken at normal emission from in situ cleaved $\mathrm{C}{\mathrm{r}}_{1/3}\mathrm{Nb}{\mathrm{S}}_2$ with $h\nu =918\mathrm{eV}$. The BE separation between the doublet originating from the surface (solid line) and the deeper layers (dashed line) amounts to $\sim 1\mathrm{eV}$. (b) $\mathrm{Cr}2p$ core level recorded at normal emission with $h\nu =918\mathrm{eV}$. Key features include a spin-orbit split doublet (A and B) and a loss feature (C). The arrows indicate kinks in the line shape of features A and B.

Figure 2

(a) The STM image of in situ cleaved $\mathrm{C}{\mathrm{r}}_{1/3}\mathrm{Nb}{\mathrm{S}}_2$ single crystals taken with a bias voltage of −0.4 V illustrating the large-scale surface morphology. (b) Line profile along the broken line in (a) reveals a terrace step height of 0.61 nm with high corrugation near the step edge. (c) and (d) Atomic resolution images of the (c) “smooth” and (d) “rough” areas denoted by s and r, respectively.

Figure 3

(a) Unit cell of $\mathrm{C}{\mathrm{r}}_{1/3}\mathrm{Nb}{\mathrm{S}}_2$ taken from [29]. (b) Representative LEED image obtained from $\mathrm{C}{\mathrm{r}}_{1/3}\mathrm{Nb}{\mathrm{S}}_2$ with an electron beam energy of 215 eV. The unit cell of the 1×1 (solid) and (√3×√3)R30° (dotted) reciprocal lattice are indicated.

Figure 4

High resolution ARPES spectra taken from $\mathrm{C}{\mathrm{r}}_{1/3}\mathrm{Nb}{\mathrm{S}}_2$ with $\sigma$-polarized photons of energy $h\nu =48\mathrm{eV}$. Nondispersive surface states are indicated by arrows in both the (a) image plot and (b) stacked EDCs.

Figure 5

The ResPES measured from $\mathrm{C}{\mathrm{r}}_{1/3}\mathrm{Nb}{\mathrm{S}}_2$ across the $\mathrm{Cr}{\mathrm{L}}_3$ absorption edge with photon polarization contained entirely in the sample plane. (a) $\mathrm{Cr}{\mathrm{L}}_3$ XAS measured in total electron yield. (b) ResPES image plot and (c) representative line profiles extracted at the corresponding photon energies labeled in (a).

Figure 6

ARPES spectra measured from $\mathrm{C}{\mathrm{r}}_{1/3}\mathrm{Nb}{\mathrm{S}}_2$ along the $\Gamma K$ direction over a wide $\left(a_1-a_4\right)$ and narrower $\left(b_1-b_4\right)$ binding energy range using photon energies $h\nu =40\mathrm{eV} (a_1,b_1),h\nu =196\mathrm{eV} (a_2,b_2),h\nu =401\mathrm{eV} (a_3,b_3)$ and $h\nu =736\mathrm{eV} (a_4,b_4)$. Spectra at $h\nu =40\mathrm{eV}$ has been symmetrized with respect to the $\mathrm{\Gamma }$ point.

Figure 7

Stacked EDCs $\left(a_1\text{−}{a}_4\right)$ and MDCs $\left(b_1\text{−}{b}_4\right)$ along the $\Gamma K$ direction extracted from the corresponding image plots depicted in Fig. 6, $b_1,b_4$. Tick marks tracing the dispersion of the two bands in proximity to $E_{\mathrm{F}}$ have been added to the EDC stacks in $a_1\text{−}{a}_4$ as a guide to the eye. In the MDC stacks, the MDC at $E_{\mathrm{F}}$ is denoted with a thicker line.

Figure 8

Direct comparison of MDCs extracted at $E_{\mathrm{F}}$ for $h\nu =40,$ 196, 401, and 736 eV depicting $k_{\mathrm{F}}$ crossings about $\Gamma$. Features from the $h\nu =40\mathrm{eV}$ spectra are labeled $\alpha$, ${\beta }_1$, and ${\beta }_2$ for the purpose of comparisons. For a description of this notation, see text.

Figure 9

Comparison of (a) valence band and (b) Nb $3d$ PES spectra for $\mathrm{Nb}{\mathrm{S}}_2$ (top) and $\mathrm{C}{\mathrm{r}}_{1/3}\mathrm{Nb}{\mathrm{S}}_2$ (bottom) as measured at normal emission with $h\nu =750\mathrm{eV}$. From (a), a comparison of similar features in the VB as well as the shallow $S3s$ core level demonstrates a 0.4 eV shift towards higher binding energy. The suppression of the higher BE peaks of the Nb $3d$ doublet (solid line) observed in $\mathrm{C}{\mathrm{r}}_{1/3}\mathrm{Nb}{\mathrm{S}}_2$ is visible in (b).

Figure 10

The FSs of (a) $\mathrm{Nb}{\mathrm{S}}_2$ and (b) $\mathrm{C}{\mathrm{r}}_{1/3}\mathrm{Nb}{\mathrm{S}}_2$ measured along the $\Gamma K$ direction using photons of energy $h\nu =40\mathrm{eV}$. The solid and broken lines indicate the 1×1 and √3×√3 BZ, respectively.

Figure 11

Band dispersion of $(a_1,a_2) \mathrm{Nb}{\mathrm{S}}_2$ and $(b_1,b_2) \mathrm{C}{\mathrm{r}}_{1/3}\mathrm{Nb}{\mathrm{S}}_2$ measured along the $\Gamma K$ direction over a wide BE range using $h\nu =40\mathrm{eV}$ photons having a polarization horizontal $(a_1,b_1)$ or vertical $(a_2,b_2)$ with respect to the scattering plane.

Figure 12

Stacked EDCs of the corresponding image plots in Fig. 11 shown within $\sim 1\mathrm{eV}$ from $E_{\mathrm{F}}$. Tick marks tracing the dispersion of the bonding (red) and antibonding (black) bilayer split Nb-bands have been added as a guide to the eye. The Nb-derived bonding band is found to sink $\sim 200\mathrm{meV}$ below $E_{\mathrm{F}}$ (b).

Figure 13

Stacked MDCs of the corresponding image plots in Fig. 11 shown within $\sim 1\mathrm{eV}$ from $E_{\mathrm{F}}$. The MDC at $E_{\mathrm{F}}$ is denoted with a thicker line.

Figure 14

Direct comparison of MDCs at $E_{\mathrm{F}}$ extracted from the data shown in Fig. 13. In the fit of the MDCs, shown in $\left(a_1\right)$ and $\left(b_1\right)$, the broken lines denote spectral weight originating from the background. The main features of the MDCs in $\mathrm{C}{\mathrm{r}}_{1/3}\mathrm{Nb}{\mathrm{S}}_2$ ($b_1$ and $b_2$) are likewise denoted in $\mathrm{Nb}{\mathrm{S}}_2 \left(a_1\right)$. In $\left({\mathrm{a}}_1\right)$, peak S (red) sinks below $E_{\mathrm{F}}$ in $\mathrm{C}{\mathrm{r}}_{1/3}\mathrm{Nb}{\mathrm{S}}_2$. A slight misalignment of the sample is responsible for an asymmetry with respect to $\Gamma$ of the MDCs in $\left(a_2\right)$ and $\left(b_2\right)$.

Figure 15

The FSs of $\mathrm{C}{\mathrm{r}}_{1/3}\mathrm{Nb}{\mathrm{S}}_2$ measured along the ($a_1$ and $b_1$) $\Gamma K$ and ($a_2$ and $b_2$) $\Gamma M$ direction using $\pi$-polarized ($a_1$ and $a_2$) and $\sigma$-polarized ($b_1$ and $b_2$) photons of energy $h\nu =40\mathrm{eV}$. Solid and broken lines denote the 1×1 and √3×√3 BZ, respectively.

Figure 16

Band dispersion measured along the ($a_1$ and $b_1$) $\Gamma K$ and ($a_2$ and $b_2) \Gamma M$ direction using $\pi$-polarized ($a_1$ and $a_2$) and $\sigma$-polarized $(b_1$ and $b_2$) photons of energy $h\nu =40\mathrm{eV}$.

Figure 17

Stacked EDCs of the corresponding image plots in Fig. 16 shown within $\sim 1\mathrm{eV}$ from $E_{\mathrm{F}}$. Tick marks tracing the dispersion of the backfolded band (green) and Nb-derived bonding band (red) in $\left(b_1\right)$ and $\left(b_2\right)$ have been added as a guide to the eye.

Figure 18

Stacked MDCs of the corresponding image plots in Fig. 16 shown within $\sim 1\mathrm{eV}$ from $E_{\mathrm{F}}$. The MDC at $E_{\mathrm{F}}$ are denoted with the thicker line. Tick marks tracing the dispersion of the backfolded band (green) and Nb-derived bonding band (red) in $\left(b_1\right)$ and $\left(b_2\right)$ have been added as a guide to the eye. Additional tick marks tracing the dispersion of the split $\alpha$ band (black) have been added in $\left(a_1\right)$ as a guide to the eye.

Figure 19

(a) Sketch of the 1×1 BZ illustrating how the hole-like band at $K$ folds due to a √3×√3 superlattice potential. (b) Band dispersion taken along the $\Gamma K$ direction with $\sigma$-polarized photons of $h\nu =40\mathrm{eV}$. Superimposed on the image plot is a trace of the MDC peak positions of the band at $K$ (solid) translated by a √3×√3 lattice vector (broken line). (c) The MDC stacks having a negative offset taken from 300 meV to $E_{\mathrm{F}}$ from the image plot in (b). Broken lines have been translated by a √3×√3 lattice vector and rescaled so as to directly compare the dispersion. (d) Band dispersion measured along the $\Gamma K$ direction with LV polarized photons of energy $h\nu =196\mathrm{eV}$.

Figure 20

Band dispersion measured along the $\left(a_1\right)$ and $\left(b_1\right)$ $\Gamma K$ and $\left(a_2\right)$ and $\left(b_2\right)$ $\Gamma M$ direction using $\pi$-polarized $\left(a_1\right)$ and $\left(a_2\right)$ and $\sigma$-polarized $\left(b_1\right)$ and $\left(b_2\right)$ photons of energy $h\nu =48\mathrm{eV}$.

Figure 21

Stacked EDCs of the corresponding image plots in Fig. 20 shown within $\sim 1\mathrm{eV}$ from $E_{\mathrm{F}}$. Tick marks tracing the dispersion of the Nb-derived bonding band (red) in $\left(b_1\right)$ and $\left(b_2\right)$ have been added as a guide to the eye.

Figure 22

Stacked MDCs of the corresponding image plots in Fig. 20 shown within $\sim 1\mathrm{eV}$ from $E_{\mathrm{F}}$. The MDC at $E_{\mathrm{F}}$ are denoted with a thicker line. Tick marks tracing the dispersion of the Nb-derived bonding band (red) in $\left(b_1\right)$ and $\left(b_2\right)$ and the split $\alpha$ band (black) in $\left(a_1\right)$ have been added as a guide to the eye.

Figure 23

Direct comparison of MDCs extracted at $E_{\mathrm{F}}$ from Fig. 16 and Fig. 20. The main features of the MDCs are labeled using the same convention as used in Fig. 14.

Figure 24

MDCs extracted at $E_{\mathrm{F}}$ along the $\Gamma K$ direction using (a) $\pi$-polarized and (b) $\sigma$-polarized photons. The photon energy was varied from $h\nu =40\mathrm{eV}$ to $h\nu =60\mathrm{eV}$ in steps of 1 eV (a) or 2 eV (b).

Figure 25

Calculated spin-polarized DOS of ${\mathrm{Cr}}_{1/3}{\mathrm{NbS}}_2$ in units of inverse electron volts per unit cell. Note the lower values of the DOS for the spin down channel for energies of $\sim \pm 250\mathrm{meV}$ from $E_{\mathrm{F}}$.