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Charge-Transfer Electronic Structure of NiX $_2$ (X = S, Se)

Using DFT+DMFT with optimized double-counting corrections to match experimental spectra, this study reveals that NiS $_2$ and NiSe $_2$ possess a smaller charge-transfer energy than previously thought, leading to significant ligand-to-Ni charge transfer, reduced Ni local moments, and a clarified evolution of low-energy electronic structures across the NiS $_{2-x}$ Se $_x$ series driven by the interplay between Ni upper Hubbard bands and antibonding chalcogen-dimer states.

Original authors: Atsushi Hariki, Takaki Okauchi, Daisuke Takegami, Naoki Ito, Mizuki Furo, Ayako Yamamoto, Tomoya Higo, Satoru Nakatsuji, Masato Yoshimura, Takashi Mizokawa, Jan Kunes

Published 2026-09-03

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Original authors: Atsushi Hariki, Takaki Okauchi, Daisuke Takegami, Naoki Ito, Mizuki Furo, Ayako Yamamoto, Tomoya Higo, Satoru Nakatsuji, Masato Yoshimura, Takashi Mizokawa, Jan Kunes

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

In the world of solid materials, the behavior of electrons often determines whether a substance conducts electricity like a metal or blocks it like an insulator. For decades, scientists have understood that in many transition-metal compounds, strong repulsion between electrons can trap them in place, creating a gap in energy that prevents current from flowing. This is known as a Mott insulator. However, a different scenario exists where the gap is not caused by electron repulsion alone, but by the energy cost of moving an electron from a surrounding atom to the central metal atom. This is called a charge-transfer insulator. The distinction matters because it changes how we predict a material's properties and how it might respond to pressure or chemical changes. Understanding the precise balance between these forces is crucial for designing new materials for electronics and energy technologies, yet the exact nature of this balance in certain nickel compounds has remained a subject of debate.

A team of researchers has now revisited the electronic structure of two specific nickel compounds, nickel disulfide and nickel diselenide, to resolve these uncertainties. These materials share the same crystal arrangement, featuring nickel atoms surrounded by pairs of sulfur or selenium atoms. While the sulfur-based compound is an insulator, the selenium-based one is a metal, and they can be mixed to create a material that switches between these two states. To understand why this happens, the scientists used a powerful combination of computer modeling and experimental data. They built a detailed simulation of the electrons in these crystals and then adjusted a specific parameter in their model until the simulated results matched real-world measurements taken with high-energy X-rays. This process allowed them to calibrate their model with high precision, ensuring it reflected the actual physical reality of the materials rather than just a theoretical guess.

The researchers found that the energy required to move an electron from the sulfur or selenium atoms to the nickel atom is significantly smaller than previously thought. This lower energy cost means that electrons are more easily shared between the nickel and its neighbors, a phenomenon known as charge transfer. This sharing reduces the magnetic strength of the nickel atoms, making them less magnetic than standard theories would predict. The study confirms that the electronic gap in the insulating sulfur compound is shaped by a delicate competition between the nickel atoms and the pairs of sulfur atoms. Specifically, the sulfur pairs have their own internal electronic states that sit just above the energy level where electrons can move freely. In the sulfur compound, these states sit high enough to maintain the insulating gap, but in the selenium compound, the corresponding states are lower in energy.

When the scientists applied this refined understanding to the selenium compound, they discovered that the lower energy of these selenium states allows them to overlap with the nickel states, effectively closing the gap and turning the material into a metal. The study rules out earlier ideas that suggested a much larger energy separation between these states, which would have implied a different mechanism for the material's behavior. Instead, the evidence points to a scenario where the specific arrangement of the selenium pairs pushes the material over the edge into a metallic state. By successfully reproducing not only the general electronic structure but also the detailed fingerprints of the nickel atoms' core electrons, the team has provided a realistic and consistent picture of how these materials work. This clarity helps explain how a simple change in the chemical composition, swapping sulfur for selenium, can drive a fundamental shift from an insulator to a metal without altering the underlying crystal structure.

Technical Summary: Charge-Transfer Electronic Structure of NiX2 (X = S, Se)

Problem Statement
The electronic nature of nickel dichalcogenides (NiS $_2$ and NiSe $_2$ ) remains a subject of debate regarding the interplay between electron correlations, covalent bonding, and the specific role of chalcogen dimers. While NiS $_2$ is traditionally classified as a charge-transfer (CT) insulator with a small gap (~0.2 eV) and NiSe $_2$ as a metal, the mechanism driving the metal-insulator transition (MIT) in the solid solution NiS $_{2-x}$ Se $_x$ is not fully resolved. Previous Density Functional Theory combined with Dynamical Mean-Field Theory (DFT+DMFT) studies placed the sulfur-selenium antibonding dimer states below the nickel 3d upper Hubbard band (UHB). However, recent experimental spectroscopic data suggest discrepancies with these models, hinting at a significantly smaller or even negative charge-transfer energy and a different ordering of electronic states. The precise relative position of the Ni 3d states and the chalcogen $p$ states, governed by the double-counting correction ( $\mu_{dc}$ ), requires re-evaluation to reconcile theory with experimental valence-band, core-level, and absorption spectra.

Methodology
The authors employed a DFT+DMFT framework to investigate the electronic structures of NiS $_2$ and NiSe $_2$ .

Computational Setup: DFT calculations were performed using the WIEN2k package within the Local Density Approximation (LDA) for experimental crystal structures. A tight-binding (TB) model was constructed using wien2wannier and wannier90, incorporating Ni 3d, chalcogen $p_\pi$ , and $p_\sigma$ orbitals.
Interaction Parameters: The Ni 3d shell interactions were treated with a Hubbard $U = 5.0$ eV and Hund's coupling $J = 1.0$ eV. The impurity problem was solved using the hybridization-expansion continuous-time quantum Monte Carlo (CT-QMC) solver at 580 K.
Double-Counting Correction Strategy: Unlike previous studies that used fixed schemes, the authors treated the double-counting correction ( $\mu_{dc}$ ) as an adjustable parameter. They optimized $\mu_{dc}$ by systematically varying the energy difference parameter $\Delta_{dp}$ (defined as the energy difference between Ni 3d and chalcogen $p$ orbitals) to reproduce experimental valence-band photoemission spectroscopy (PES) data.
Experimental Validation: The theoretical spectra were compared against:
- Hard X-ray PES (HX-PES, $h\nu = 6.5$ keV) and Soft X-ray PES (SX-PES, $h\nu = 1.2$ keV) measured at SPring-8 and Photon Factory.
- Ni 2p core-level X-ray Photoelectron Spectroscopy (XPS) and X-ray Absorption Spectroscopy (XAS) at the Ni $L_{2,3}$ edges.
Model Variations: The study compared "full models" (including chalcogen $p_\sigma$ orbitals) with reduced "Ni- $p_\pi$ " models (excluding $p_\sigma$ ) to isolate the role of dimer antibonding states.

Key Results

Optimized Charge-Transfer Energy: By matching the calculated valence-band spectra to experimental PES data, the optimal $\Delta_{dp}$ was determined to be 1.82 eV for NiS $_2$ and 1.58 eV for NiSe $_2$ . These values indicate a smaller charge-transfer energy than previously assumed in early DFT+DMFT studies, consistent with recent cluster-model analyses.
Reproduction of Spectral Features: The refined model successfully reproduces:
- The valence-band spectra for both HX-PES and SX-PES, correctly capturing the orbital-dependent cross-section variations.
- The Ni 2p core-level PES and XAS spectra of NiS $_2$ , including the specific satellite features (St1 and St2) in the Ni 2 $p_{3/2}$ component, which were only captured near the optimal $\Delta_{dp}$ values.
Electronic Structure and Charge Transfer:
- The optimized parameters reveal substantial ligand-to-Ni charge transfer, resulting in a Ni 3d occupancy of approximately 8.5 (significantly higher than the 8.2 found in NiO).
- This increased mixing between $|t_6e_2\rangle$ and $|t_6e_3p_\pi\rangle$ configurations leads to a reduction of the Ni local moment to a screened value of 1.38 $\mu_B$ , consistent with low-temperature experimental observations.
Mechanism of the Metal-Insulator Transition (MIT):
- NiS $_2$ : The system is an insulator where the UHB is separated from the CT band. The S-S antibonding dimer states ( $p_\sigma$ ) lie above the Fermi level ( $E_F$ ) and act largely as passive spectators in the optimal deep Ni $d$ -state scenario.
- NiSe $_2$ : The Se-Se dimer splitting is weaker, placing the antibonding $p_\sigma$ state at a lower energy compared to NiS $_2$ . While the Ni- $p_\pi$ subsystem alone might remain gapped for certain parameters, the weak hybridization with the Se $p_\sigma$ antibonding band provides the necessary "nudge" to push the system metallic. The Se $p_\sigma$ band crosses $E_F$ , closing the gap.
- The study clarifies that the MIT in the NiS $_{2-x}$ Se $_x$ series is driven by the relative position and interaction between the Ni upper Hubbard band and the antibonding chalcogen-dimer states, rather than a simple bandwidth control alone.

Significance and Claims
The paper claims to resolve discrepancies between earlier theoretical models and recent experimental spectroscopic data by establishing a realistic electronic structure through the optimization of the double-counting correction. The authors assert that their model provides a unified description of the low-energy electronic structure, core-level excitations, and magnetic moments for both NiS $_2$ and NiSe $_2$ .

The primary significance lies in:

Correcting the CT Energy Scale: Establishing a smaller charge-transfer energy that aligns with experimental core-level and valence-band data, challenging earlier assumptions about the energy separation between the UHB and the valence band top.
Clarifying the MIT Mechanism: Demonstrating that the transition from insulating NiS $_2$ to metallic NiSe $_2$ is governed by the specific energy alignment of the chalcogen dimer antibonding states relative to the Ni 3d UHB. The study highlights that the metallic nature of NiSe $_2$ arises from the overlap of the Se $p_\sigma$ antibonding band with the Fermi level, facilitated by the reduced dimer splitting and the specific charge-transfer energy.
Methodological Validation: Proving that tuning $\mu_{dc}$ against experimental PES is a robust strategy for determining the electronic structure of correlated materials, as evidenced by the simultaneous reproduction of valence-band, core-level, and absorption spectra.

The authors conclude that NiS $_2$ and NiSe $_2$ possess very similar Ni-chalcogen hybridization strengths, with NiS $_2$ situated close to the MIT on the insulating side, while the specific positioning of the Se antibonding states drives NiSe $_2$ into the metallic regime.

Technical Summary: Charge-Transfer Electronic Structure of NiX2 (X = S, Se)

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