Discovery of Van Hove Singularities: Electronic Fingerprints of 3Q Magnetic Order in a van der Waals Quantum Magnet

Abstract

Magnetically intercalated transition metal dichalcogenides are emerging as a rich platform for exploring exotic quantum states in van der Waals magnets. Among them, CoxTaS2 has attracted intense interest following the recent discovery of a distinctive 3Q magnetic ground state and a pronounced anomalous Hall effect below a critical doping of x=1/3, both intimately tied to cobalt concentration. To date, direct signatures of this enigmatic 3Q magnetic order in the electronic structure remain elusive. Here we report a comprehensive doping dependent angle resolved photoemission spectroscopy study that unveils these long-sought fingerprints. Our data reveal an unexpected "inverse Mexican hat" dispersion along the K-M-K direction, accompanied by two van Hove singularities. These features are consistent with theoretical predictions for a 3Q magnetic order near three-quarters band filling on a cobalt triangular lattice. These results provide evidence of 3Q magnetic order in the electronic structure, establishing TMD van der Waals magnets as tunable materials to explore the interplay between magnetism and topology.

Figures (4)

• Figure 1: Electronic Structure Comparison between Undoped and Co-Doped 2$\it{H}$-TaS$_2$.a, Crystal structure of Co$_{1/3}$TaS$_2$. Adjacent TaS$_2$ layers with opposite in-plane orientations are highlighted in orange and yellow. b, Top view of the crystal structure. The solid and dashed black lines represent the unit cells of Co$_{1/3}$TaS$_2$ and 2$\it{H}$-TaS$_2$, respectively. c, Phase diagram of Co$_{1/3}$TaS$_2$, adapted from PPark2024JPark. d, Top view of the 3$\bf{Q}$ magnetic order on a triangular lattice system. The black lines indicate the magnetic unit cell. e, f, Low temperature (10 K) Fermi surfaces mapping of 2$\it{H}$-TaS$_2$ and Co$_{0.32}$TaS$_2$. The solid (dashed) lines denote the Brillouin zone of 2$\it{H}$-TaS$_2$ (Co$_{1/3}$TaS$_2$). High-symmetry points are labeled as $\Gamma_0$, K$_0$, and M$_0$ for 2$\it{H}$-TaS$2$, and $\Gamma$, K, and M for Co$_{1/3}$TaS$_2$. The gapped portions indicated by an arrow signifies the charge density wave (CDW) gap in 2$\it{H}$-TaS$_2$. In both panels, the fitted Fermi surface obtained from the raw data are overlaid in the upper-left quadrant. Observed Fermi surface sheets are marked with $\mathrm{\upalpha}$ (dark blue curves), $\mathrm{\upbeta}$ (light blue curves) and $\mathrm{\upgamma}$ (magenta curves). g-i, Energy-momentum intensity plots of 2$\it{H}$-TaS$_2$ (panel g) and Co$_{0.32}$TaS$_2$ (panels h,i), measured along the $\rm{M_0}$-$\Gamma_0$-$\rm{K_0}$ high-symmetry direction. Data in panels g,h/i are acquired using linearly horizontal (LH)/linearly vertical (LV) polarized light. j, k, Extracted band dispersions for 2$\it{H}$-TaS$_2$ ($\mathrm{\upalpha}$, $\mathrm{\upbeta}$ and $\mathrm{\updelta}$) and Co$_{0.32}$TaS$_2$ ($\mathrm{\upalpha}$, $\mathrm{\upbeta}$, $\mathrm{\upgamma}_{\mathrm{K}}$, $\mathrm{\upgamma}_{\mathrm{M}}$ and $\mathrm{\upepsilon}$), along with their corresponding momentum distribution curves (MDCs) at the Fermi level (E$\rm{_F}$). Filled and open circles represent the peak positions of MDCs and energy distribution curves (EDCs), respectively, extracted from Supplementary Fig. S2. l, Calculated band structures including spin-orbit coupling along $\rm{M_0}$-$\Gamma_0$-$\rm{K_0}$ at the $\it k_z$ = 0 plane for bulk 2$\it{H}$-TaS$_2$ crystal. The Fermi level of Co$_{0.32}$TaS$_2$ is referenced by shifting 300 meV above the original E$\rm{_F}$.
• Figure 2: Co doping and potassium-deposition effects on the electronic structure of Co$_{x}$TaS$_2$.a, ARPES spectra along the $\rm{M_0}$–$\Gamma_0$–$\rm{K_0}$ high-symmetry direction for Co$_x$TaS$2$ samples with $x$ = 0.29, 0.31, 0.33, 0.34, and 0.36. b, ARPES spectra of Co$_{0.29}$TaS$_2$ along the $\Gamma_0$–$\rm{K_0}$ direction before and after successive potassium (K) depositions. c, EDCs at the M point for Co$_{x}$TaS$_2$ samples with $x$ = 0.29, 0.31, 0.33, 0.34 and 0.36, obtained from panel a. d, EDCs at the M point for Co$_{0.29}$TaS$_2$ before and after different rounds of K-deposition, obtained from panel b. EDC peaks corresponding to the $\mathrm{\upalpha}$, $\mathrm{\upbeta}$, and $\mathrm{\upgamma}_{\mathrm{M}}$ bands are labeled accordingly. e, Evolution of the band bottoms of the $\mathrm{\upalpha}$, $\mathrm{\upbeta}$, $\mathrm{\upgamma}_{\mathrm{K}}$, and $\mathrm{\upgamma}_{\mathrm{M}}$ bands as a function of Co doping and K deposition. Black and orange curves labeled M($\mathrm{\upgamma}_{\mathrm{M}}$), M($\mathrm{\upbeta}$), and M($\mathrm{\upalpha}$) represent the energy positions of peaks $\mathrm{\upgamma}_{\mathrm{M}}$, $\mathrm{\upbeta}$, and $\mathrm{\upalpha}$, respectively, obtained from panels c and d. The curve labeled K ($\mathrm{\upgamma}_{\mathrm{K}}$) shows the Co doping dependence of the $\mathrm{\upgamma}_{\mathrm{K}}$ band bottom, extracted from EDCs at the K point (see Supplementary Fig. S8). Error bars are determined based on the fitting error of the EDC peak position.
• Figure 3: Doping-dependent Fermi surfaces of Co$_x$TaS$_2$ and signature of a phase transition across $x_{\rm{c}}$.a, Calculated Fermi surface of a triangular lattice at 3/4-filling, without the 3$\bf{Q}$ magnetic order. The edge centers of the hexagonal Fermi surface are connected by three nesting wave vectors. Van Hove singularities (VHSs) located at the M points are marked by magenta dots. b, Calculated Fermi surface of a triangular lattice slightly away from 3/4-filling, incorporating 3$\bf{Q}$ magnetic order. In this case, the VHSs are located at the tips of the triangular Fermi pockets. Original and folded Fermi surface sheets are shown as solid and dashed magenta curves, respectively. Computational details are provided in the Methods section. c, The nesting wave vector (($\pi$,0)-$\mathbf{G}$) connects the edges of the hexagonal Fermi surface at 3/4-filling, and is equivalent to ($\pi$, 0) up to a reciprocal lattice vector $\mathbf{G}$. The corresponding 3$\bf{Q}$ magnetic order in real space and the reconstructed Brillouin zone are illustrated in Supplementary Fig. S9. d-f, Experimental Fermi surface mappings for samples with $x$=0.29, $x$=0.32 and $x$=0.34, respectively. g, Evolution of the triangular Fermi pockets as a function of doping level $x$, extracted from the raw spectra (Supplementary Fig. S10). MDCs obtained along the K-M direction for $x$=0.29 and $x$=0.36 samples are shown on the right. h, Ratio of spectral weight on the Fermi surface between the tip of the $\mathrm{\upgamma}$ pocket and the M point as a function of Co composition ($x$).
• Figure 4: Doping-dependent band structure along K-M-K and signature of the 3Q states for $x$$\textless$$x_{\rm{c}}$.a, Second derivative images, with respect to energy, along the K-M-K direction as a function of Co doping, derived from the raw data shown in Supplementary Fig. S11). The blue and red arrows indicate the momenta corresponding to the Fermi momentum of the $\mathrm{\upgamma}_{\mathrm{K}}$ band and the M point in the $x=0.29$ sample. b, Intensity ratio of EDC peaks obtained at the momenta indicated by the blue and red arrows in panel (a), plotted as a function of Co composition ($x$). c, d, Experimental band structures for the $x=0.29$ (c) and $x=0.36$ (d) samples along the K-M-K direction. e, f, Representative EDCs extracted at three selected momenta (k1, k2, and k3), as marked by black lines in panels (c) and (d). g, h, Experimentally extracted band dispersion along the K-M-K direction for the $x=0.29$ (g) and $x=0.36$ (h) samples, obtained from EDC stacks provided in Supplementary Fig. S11. The dot size reflects the relative intensity of the EDC peaks, highlighting the distribution of spectral weight. i, j, Calculated band structures along the K-M-K direction for a triangular lattice with (i) and without (j) 3$\bf{Q}$ order. In the presence of 3$\bf{Q}$ order, two VHSs appear on either side of the M point, accompanied by a band dip at M. In contrast, without 3$\bf{Q}$ order, a single VHS is located at M. Calculated band structures along the $\Gamma$-M-$\Gamma$ direction are provided in Supplementary Fig. S13. Details of the computational parameters are provided in the Methods section.