Evidence for Many-Body States in NiPS$_3$ Revealed by Angle-Resolved Photoelectron Spectroscopy

TL;DR

This work shows that NiPS$_3$ exhibits many-body final-state physics in ARPES beyond mean-field band theory. By combining high-resolution μ-ARPES with DFT$+U$ and a multiplet-resolved NiS$_6$ cluster ED model, the authors identify a weakly dispersive near-VBM feature arising from mixed $d^7$ and $d^8 ext{$ackslash$L}$ final states, while the rest of the spectrum aligns with mean-field expectations. The cluster analysis explains the ARPES feature as local multiplet physics and highlights strong Ni–S covalency driving bonding–antibonding and ligand-hole configurations. The results emphasize that a genuine quantum many-body description is essential to capture both single- and two-particle spectroscopies in this 2D correlated material, positioning NiPS$_3$ as a model system for covalent, low-dimensional magnets. Together, these findings motivate future theoretical efforts that merge DFT with cluster-DMFT or beyond, to fully describe the correlated spectral function in NiPS$_3$ and related materials.

Abstract

We present $μ$-ARPES spectra of the Mott-insulating van der Waals antiferromagnet NiPS$_3$. Signatures of strong correlations- such as the onset of atomic or atomic-ligand multiplets and spin-orbit-entangled exciton have been observed in this material by various two-particle spectroscopies, but not previously in photoemission. Our measurements reveal a weakly dispersive feature at the valence-band edge that is absent in DFT+$U$ calculations and remains unchanged across the Néel transition. After critically examining and ruling out alternative interpretations, we show that an exact diagonalization of a NiS$_6$ cluster yields low-energy final-state configurations of mixed multiplet $d^7$ and $d^8\underline{L}$ character, whose energy differences are consistent with the observed additional feature. This implies that ARPES directly accesses local Ni-S multiplet physics in NiPS$_3$, revealing a many-body structure beyond mean-field theory. Our results confirm that NiPS$_3$ is an excellent model platform in which strong correlations, reduced dimensionality, and covalent metal-ligand bonding jointly shape both two- and single-particle spectroscopies, underscoring the need for a genuinely quantum many-body description of two-dimensional quantum materials.

Figures (13)

• Figure 1: MPX$_3$ crystal structure and ARPES results: (a) Geometrical structure of MPS$_3$ compounds, illustrating the honeycomb sublattice of MS$_6$ octahedra (top and side views). The yellow-shaded area marks one representative MS$_6$ cluster. (b) Comparison of experimental ARPES spectra for MnPS$_3$Strasdas2023, FePS$_3$Koitzsch2023, CoPS$_3$VOLOSHINA2023140511, and NiPS$_3$ -- along the M-$\Gamma$-M direction. The dashed boxes refer to the orbital contribution depicted in (c). A characteristic weakly dispersive feature at low binding energy is highlighted by a red box and is not captured by DFT+$U$ calculations. It emerges only for NiPS$_3$, indicating an additional Ni–S–derived spectroscopic feature. (c) Schematic summary of the generic DFT+$U$ band structure of all three MPS$_3$ systems. The states at highest binding energy originate predominantly from P $3p$ orbitals (blue box) followed by a mixture of P and S $3p$ levels (violet box), while the mid-lying manifold arises from hybridized transition-metal $3d$ and chalcogen $3p$ orbitals (green box). The highest-lying states near the Fermi energy correspond to hybridized M ($e_{\rm g}$) levels, whose occupation evolves systematically from Mn ($3d^5$) to Ni ($3d^8$) (orange box).
• Figure 2: (a) Schematic illustration of the Brillouin zone of NiPS$_3$, showing the high-symmetry points and the measured momentum path ($\overline{\Gamma}-\overline{\rm K}-\overline{\rm M}$) within the basal plane. (b) ARPES intensity map of NiPS$_3$ measured along the $\Gamma$-K-M-$\Gamma$ direction at T < T$_{\rm N}$ (45K and 220K). The additional spectral feature centered around –1.3 eV and not captured by DFT+U calculations displays a discernable, weak dispersion and a maximum intensity near K. (c) Photon-energy-dependent ARPES spectra collected for h$\nu$ = 55–70 eV, usually corresponding to different k$_z$ values. A distinct variation of the band position and curvature appears indicating a dispersion along all three momentum directions. Above the Néel temperature, the dispersion and strength of the spectral feature remains unchanged within experimental accuracy, indicating that the electronic structure associated with this spectral feature is largely insensitive to the magnetic ordering.
• Figure 3: (a) Effective band structure of NiPS$_3$ obtained from DFT+$U$ calculations and unfolded onto the primitive (non-magnetic) Brillouin zone to enable direct comparison with the experimental spectra. The details of the unfolding procedure and its justification are provided in Pestka2025. (b) Atom-projected density of states (pDOS) for Ni, P, and S, showing the dominant Ni–S hybridization within the valence manifold. (c) Crystal-field-resolved Ni 3$d$ pDOS highlighting the separation between $t{_{2g}}$ and $e_{\rm g}$ states, with the latter forming the upper valence band. (d) Simplified schematic of the NiPS$_3$ band structure, illustrating the correspondence between the calculated DFT+$U$ results and the characteristic arrangement of metal $e_{\rm g}$/$t_{\rm 2 g}$ levels and ligand-derived bands.
• Figure 4: Evolution of the spin-dependent DOS with an increasing value of Hubbard $U$ in the DFT$+U$ approach. Calculations performed for NiPS$_3$ at $J_H=0$ eV, see text for further details. The calculated spin-dependent DOS is additionally projected to the Ni e$_{\rm g}$ orbitals (red), the Ni t$_{\rm 2g}$ orbitals (black) and the s and p orbitals of the ligand atoms S and P (lilac grey). Note that the left-most panel is obtained for $U=0$ eV and a non-magnetic ground state.
• Figure 5: Spin-dependent DOS in the DFT$+U$ approach: (a) nickel (black) and sulfur (lilac grey) orbitals [equivalent to the panel at $U_{\rm H}=1.6$ eV in Fig. \ref{['fig:evolutionU']}]; (b) only sulfur orbitals, showing DOS for spin-up polarized (left panel), unpolarized (middle panel), and spin-down polarized (right panel) sites as depicted in (c); (c) Cartoon showing polarization of sulfur atoms depending on the location with respect to the spin-polarized nickel atoms in the zigzag AF-ordered state. Calculations performed for NiPS$_3$ at $U=1.6$ eV and $J_H=0$ eV, see text for further details.