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In the strongly correlated altermagnet NiS2, the spin splitting between bands also enforces a difference in their quasiparticle lifetimes.

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2026-08-03 15:21 UTC pith:EEUFHWE2

load-bearing objection Solid first DFT+DMFT treatment of NiS2 in its altermagnetic metallic phase; the spin-lifetime asymmetry is the main new result, but the claim that Hund's coupling amplifies it is under-tested and needs one more calculation. the 3 major comments →

arxiv 2512.17059 v1 pith:EEUFHWE2 submitted 2025-12-18 cond-mat.str-el cond-mat.mtrl-sci

Impact of strong electronic correlations on altermagnets: the case of NiS2

Ina Park , Turan Birol , Antoine Georges , Rafael M. Fernandes This is my paper
classification cond-mat.str-el cond-mat.mtrl-sci PACS 71.27.+a71.30.+h71.15.Mb75.50.Ee
keywords altermagnetismstrongly correlated electronsDFT+DMFTquasiparticle lifetimeHund's couplingNiS2spin splittingmetal–insulator transition
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper argues that strong electron correlations change how altermagnetic spin splitting works. In NiS2 near its pressure-driven metal–insulator transition, static correlations enlarge the local magnetic moment and uniformly boost the splitting between spin-up and spin-down bands, while dynamic correlations renormalize bands in an orbital- and energy-dependent way. The central new claim is that the two spin bands develop different quasiparticle lifetimes, with the lifetime difference roughly proportional to the spin splitting and amplified by Hund's coupling. If correct, this means an altermagnet can have one spin channel that is nearly coherent and another that is almost incoherent along a given direction, which matters for spin-based electronics.

Core claim

Using DFT, DFT+U, and DFT+DMFT calculations on NiS2 at P=4.3 GPa and T=50 K, the paper shows that static correlations uniformly enhance the altermagnetic spin splitting by increasing the local moment, while dynamic correlations renormalize bands in an orbital- and energy-dependent way. The central new claim is that the two spin bands acquire unequal quasiparticle lifetimes, with the lifetime difference roughly proportional to the momentum-dependent spin splitting. Hund's coupling amplifies this through a particle–hole asymmetry that increases scattering on the hole side. Additionally, sulfur-derived bands gain sizable splitting via hybridization with nickel states.

What carries the argument

The key machinery is the DFT+DMFT self-energy with a spin- and site-resolved structure that enforces altermagnetic relations: the majority-spin self-energy of one pair of Ni sites equals the minority-spin self-energy of the other pair. Projecting this local self-energy onto Bloch bands through orbital weights produces the momentum-dependent renormalization of the spin splitting, while the imaginary part of the same self-energy, extracted from the spectral function by Lorentzian fitting, yields the spin-resolved quasiparticle lifetimes.

Load-bearing premise

The calculation assumes that a simplified collinear magnetic structure faithfully represents the actual non-collinear altermagnetic order, and it imposes the altermagnetic spin relations by hand rather than letting the magnetic state emerge from the interactions.

What would settle it

Measure the momentum-resolved linewidths of the spin-split bands in metallic NiS2 near P ≈ 4.3 GPa using spin-resolved photoemission: if the difference in quasiparticle lifetime between the two spin species does not approximately follow the momentum-dependent spin splitting, or if the lifetimes are equal while the splitting is large, the central claim of lifetime locking is falsified.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

If this is right

  • Static correlations (DFT+U) uniformly enhance the altermagnetic spin splitting by increasing the local magnetic moment, with little effect on bandwidth.
  • Dynamic correlations (DFT+DMFT) change the spin splitting in a band-, momentum-, and energy-dependent way: some splittings increase, others decrease, depending on orbital character and particle–hole asymmetry.
  • Nominally nonmagnetic sulfur-derived bands develop a spin splitting of a few hundred meV through hybridization with nickel d-states, so altermagnetic properties can extend beyond the correlated orbitals.
  • The quasiparticle lifetime of the two spin species becomes strongly asymmetric, with the lifetime difference roughly proportional to the spin splitting, and this asymmetry is amplified by Hund's coupling.
  • The majority-spin quasiparticles are much heavier (effective mass ~6.25) than the minority-spin ones (~2.55), a direct consequence of the different self-energies.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If this lifetime contrast is generic, other correlated altermagnets near a metal–insulator transition should exhibit spin-selective coherence, which could be tuned by pressure or doping to make one spin channel nearly incoherent.
  • The lifetime asymmetry should be directly observable in spin-resolved photoemission linewidths or in spin-dependent transport measurements, offering a concrete experimental test beyond band-structure calculations.
  • Because the altermagnetic self-energy relations are imposed rather than derived, the paper does not prove that the asymmetry survives if altermagnetism is allowed to emerge self-consistently; an unbiased calculation would be a stronger test.
  • The Hund-assisted particle–hole asymmetry suggests that materials with stronger Hund's coupling should show a larger spin-lifetime contrast, providing a materials-design guideline.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

3 major / 4 minor

Summary. The manuscript presents a comparative DFT, DFT+U, and DFT+DMFT study of metallic NiS2 in its altermagnetic phase near the pressure-driven metal–insulator transition. The authors argue that static correlations enhance the local moment and produce a nearly uniform enhancement of the altermagnetic spin splitting, whereas dynamic correlations renormalize the bandwidth in a momentum-, band-, and energy-dependent way, causing non-rigid modifications of the splitting. They further report that the spin-up and spin-down quasiparticles acquire different lifetimes, with the lifetime difference roughly proportional to the altermagnetic splitting, and attribute an additional enhancement of this effect near the Fermi level to Hund's-coupling-induced particle–hole asymmetry. The calculations are benchmarked against the experimental local moment (1.11 vs 1.15 μB) and effective mass (6.25 vs 5.8).

Significance. If the central claims hold, this is a valuable contribution: it identifies NiS2 as a strongly correlated metallic altermagnet and provides a systematic decomposition of static versus dynamic correlation effects on the spin splitting, including a previously underappreciated spin-resolved lifetime asymmetry. The work combines state-of-the-art DFT+DMFT with careful cross-checks against DFT+U and experimental anchors, and the qualitative mechanism—dynamic correlations converting energy splitting into a coherence contrast—is physically appealing and potentially important for altermagnetic spintronics. The paper is also honest about the imposed collinear magnetic structure and the constrained form of the self-energy, though, as detailed below, those choices limit the strength of the quantitative conclusions.

major comments (3)
  1. [Sec. V and Appendix E (Figs. 5 and 8)] The claim that Hund's coupling amplifies the lifetime asymmetry is asserted but not directly tested. Appendix E shows that reducing J from 1.0 to 0.8 eV weakens the particle–hole asymmetry and the shoulder in ImΣ(ω), but the authors do not recompute the quasiparticle lifetimes or Δτ for J = 0.8 using the Lorentzian extraction of Appendix D. Since a smaller J also reduces the local moment and the altermagnetic splitting ΔAM, the observed change in ImΣ(ω) alone cannot distinguish the proposed many-body amplification from the trivial kinematic scaling τ ∝ [−ImΣ(ε)]^{-1}, which would produce Δτ ∝ ΔAM regardless of Hund's coupling. This is load-bearing because the paper's novelty rests on a correlation-specific mechanism. Please compute Δτ at J = 0.8 and compare it with the expected scaling from the reduced ΔAM; alternatively, state explicitly why the existing data already rule out the kinema
  2. [Sec. II / Appendix C (Eq. C4)] The DMFT calculation is performed for the collinear magnetic structure of Fig. 1(e), not the experimentally observed non-collinear structure of Fig. 1(d). The authors justify this with group-theoretic arguments and the similar form of Eqs. (1)–(2), but they do not test whether the collinear approximation changes the magnitude or energy dependence of the self-energy, the local moment, or the lifetime asymmetry. Moreover, Eq. C4 explicitly imposes the altermagnetic relations among the site-resolved self-energies, meaning the altermagnetic order is an input rather than an emergent result. A nonlocal self-energy component could alter the momentum-dependent renormalization and the predicted Δτ. Please provide a quantitative check—for example, a DFT+U or DFT+DMFT calculation of the non-collinear phase, or at least a comparison of the collinear versus non-collinear DFT+U local moments and split
  3. [Sec. V (Fig. 5(e)–(l))] The central statement that 'the AM splitting ... effectively lock[s] the energy splitting to the lifetime difference' is supported only by visual comparison of the panels in Fig. 5. No quantitative measure of the correlation between ΔAM(k) and Δτ(k) is given, and the relationship appears to hold only for bands that do not cross the Fermi level; band #2 and the Γ–R1 band show qualitatively different behavior. Given that the extraction procedure (Appendix D) fixes peak centers from a coherent reference spectrum and then fits widths, it is important to quantify the correlation (e.g., a scatter plot of Δτ versus ΔAM with a correlation coefficient or a scaling exponent) and to state explicitly where the proportionality holds and where it fails. Without this, the 'locking' claim is stronger than the presented evidence.
minor comments (4)
  1. [Sec. IV / Sec. V text] The manuscript repeatedly refers to 'Se-p' orbitals and 'Se-p' bands (e.g., 'nominally non-magnetic Se-p states' in Sec. IV and 'Se-p' in Sec. V). Since the compound is NiS2 and Fig. 4 labels the states as S-p, these appear to be typos for 'S-p'.
  2. [Sec. VI] In the concluding paragraph, 'very difference' should read 'very different'.
  3. [Fig. 5] The multi-panel layout of Fig. 5 is difficult to parse: the color scale for τ is defined only in the first row, and the axis labels are cramped. Please enlarge the panels and add explicit labels to each row/column.
  4. [Appendix D] The Lorentzian fitting procedure fixes peak centers from A0(k,ω) with ImΣ=0. For strongly overlapping or heavily damped bands, this may bias the extracted widths. A brief discussion of the sensitivity of τ and Δτ to the fitting procedure would strengthen the quantitative claims.

Circularity Check

0 steps flagged

No significant circularity: the AM order is an input, and the spin-splitting renormalization and lifetime asymmetry are outputs of the DFT+DMFT calculation, not fitted to the quantities they explain.

full rationale

The paper does not derive altermagnetism from the calculation; it takes the experimentally established AM order as input and imposes the corresponding self-energy relations in Eq. C4. Its actual claims concern how static and dynamic correlations renormalize that imposed order, and these effects are computed, not assumed. The DFT+DMFT results (M_DMFT = 1.11 μB, m_eff ≈ 6.25, the spin-resolved spectra, and the k-dependent lifetimes) are compared with experiment or with DFT/DFT+U calculations, not fitted to the quantities they explain. The relation between ΔAM(k) and Δτ(k) emerges from the frequency dependence of ImΣ and the Lorentzian extraction described in Appendix D; it is not an identity built into the definitions. The self-citations used for the AM classification (Ref. [7]) and for previous NiS2 DMFT studies (Ref. [72]) are corroborated by external references and by the explicit symmetry analysis in Sec. II, so they are not load-bearing in a circular way. The Appendix E J = 0.8 comparison shows a reduced particle-hole asymmetry but does not recompute Δτ; this is a robustness limitation, not a circular reduction. The U and J values are inherited from prior published calculations, so the quantitative agreement with experiment is not a free prediction, but the central qualitative results are not equivalent to the inputs by construction.

Axiom & Free-Parameter Ledger

4 free parameters · 5 axioms · 0 invented entities

No new particles or fields are introduced. The central claims rest on standard DFT/DMFT approximations plus two material-specific modeling choices: the collinear proxy for the magnetic order and the externally imposed altermagnetic form of the self-energy. The DFT+U comparison is anchored by tuning U to match the DMFT moment, which is transparent but adds a fitted parameter to the static-dynamic decomposition.

free parameters (4)
  • U (DMFT) = 8 eV
    Slater F0 parameter in the density-density interaction; inherited from prior paramagnetic-phase DMFT studies of NiS2, not fit in this paper.
  • J (DMFT) = 1 eV
    Hund's coupling in the density-density interaction; also from previous work. The authors also run J=0.8 eV as a control, but the main results use J=1 eV.
  • U (DFT+U) = 2 eV
    Chosen so that the DFT+U local magnetic moment (1.10 μB) matches the DFT+DMFT and experimental values, to enable a controlled static-vs-dynamic comparison.
  • Lattice parameter a = 5.599 Å
    Interpolated from experimental volume at P=4.3 GPa (Ref. 87), not fitted.
axioms (5)
  • domain assumption The experimentally realized non-collinear AM order can be approximated by the collinear spin configuration of Fig. 1(e) for the DFT and DFT+DMFT calculations.
    The paper uses this collinear structure throughout; group symmetry arguments are given, but no direct numerical comparison between the collinear and non-collinear self-energies is presented.
  • domain assumption The DFT+DMFT self-energy is purely local (k-independent before upfolding) and is constrained to obey the altermagnetic relations of Eq. C4.
    The entire comparison of static vs. dynamic correlation effects and the lifetime anisotropy rests on this local self-energy and on the imposed AM symmetry structure.
  • standard math PBE-GGA provides a sufficient starting point for the DFT and embedded DMFT calculations.
    The exact exchange-correlation functional is not tested; PBE is a standard choice for this type of material.
  • ad hoc to paper The density-density form of the Coulomb interaction (Slater parametrization) is adequate for NiS2 with four Ni impurities per cell.
    The authors use the density-density form in the CTQMC solver. Full rotation-invariant interactions could alter quantitative lifetimes and the particle-hole asymmetry.
  • domain assumption The effective low-energy spin-splitting Hamiltonian can be written in the k-cubic forms given in Eqs. (1) and (2).
    Used for the group-theory classification of the altermagnetic splitting; it follows from the irrep analysis of the magnetic order parameter.

pith-pipeline@v1.3.0-alltime-deepseek · 182 in / 10504 out tokens · 155099 ms · 2026-08-03T15:21:27.938686+00:00 · methodology

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read the original abstract

One of the distinguishing features of an altermagnet is that its spin-up and spin-down bands display a nodal momentum-dependent splitting even in the absence of spin-orbit coupling. While this property has been investigated in many weakly-correlated altermagnetic materials, the impact of strong electron-electron interactions on the spin-dependent electronic structure has remained little explored, particularly in metals. Here, we propose NiS2 as a prototypical strongly correlated metallic altermagnet. While at ambient pressure this compound is an altermagnetic Mott insulator, it undergoes a pressure-driven metal-insulator transition (MIT) while maintaining its altermagnetic ordered phase. By systematically comparing DFT, DFT+U, and DFT+DMFT calculations on the metallic altermagnetic phase near the MIT, we disentangle how strong static and dynamic correlations modify the electronic structure. Specifically, the spin splitting of the bands is modified not only through the enhancement of the local magnetic moment caused by static correlations, but also by the momentum-dependent bandwidth renormalization caused by dynamic correlations. Moreover, dynamic electronic correlations cause a pronounced lifetime asymmetry between the spin-up and spin-down quasiparticles, an effect that is amplified by the particle-hole asymmetry promoted by Hund's correlations. Our results not only shed light on the rich landscape of correlation effects in metallic altermagnets, but also establishes NiS2 as a platform to investigate the interplay between Mott and Hund physics and altermagnetic order.

Figures

Figures reproduced from arXiv: 2512.17059 by Antoine Georges, Ina Park, Rafael M. Fernandes, Turan Birol.

Figure 1
Figure 1. Figure 1: (a) [53, 60–66]. Therefore, NiS2 provides an ideal framework to investigate the electronic properties of a strongly-correlated metallic altermagnet. In this paper, we systematically analyze the altermag￾netic electronic structure of NiS2 in the correlated metal￾lic phase near the pressure-induced MIT. To disentangle the effects of static and dynamic correlations, we perform a comparative analysis using DFT… view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. (a) Non-relativistic DFT band structure for the [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. (a) Projected density of states (PDOS) of Ni [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Comparison between (a)-(d) DFT, (b)-(e) DFT+ [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. (a)-(d) DFT+DMFT band structures, with the corresponding quasiparticle lifetime marked by colored circles along [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. (a) Band structure from DFT calculations (gray thick lines) and the [PITH_FULL_IMAGE:figures/full_fig_p011_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Band structure projected on the sublattices of the Ni atoms (see Fig. [PITH_FULL_IMAGE:figures/full_fig_p011_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. DFT+DMFT self-energy for different [PITH_FULL_IMAGE:figures/full_fig_p012_8.png] view at source ↗

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