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REVIEW 2 major objections 4 minor 66 references

A correlation-driven stripe spin-density wave can host d_xy-wave altermagnetism once a uniaxial staggered potential unlocks MT symmetry.

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Correlation-driven (π,0) SDW order plus a uniaxial staggered potential produces a d_xy-wave stripe-ordered altermagnetic insulator that survives finite-temperature DQMC scaling.

T0 review reviewed 2026-07-14 challenge →

load-bearing objection Solid HF+DQMC evidence that a (π,0) SDW plus a static USEP produces a d_xy SOAM insulator that survives finite-T scaling inside a controlled window; the novelty is real and the soft spots are exactly the ones already flagged (tuned hoppings, sign problem). the 2 major comments →

arxiv 2607.11532 v1 pith:CG5Z6GSY submitted 2026-07-13 cond-mat.str-el

Stripe-Ordered Altermagnetism Emerging from Correlation-Driven Spin-Density-Wave Instability

Zenghui Fan , Jingyao Meng , Tianxing Ma This is my paper
classification cond-mat.str-el PACS 75.10.Lp71.10.Fd75.30.Fv71.27.+a
keywords altermagnetismspin-density wavestripe orderHubbard modeliron pnictidesdeterminant quantum Monte Carlononrelativistic spin splitting
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.

The reading

Altermagnetism has so far been identified almost exclusively inside collinear antiferromagnets. This paper asks whether the same momentum-dependent spin splitting can appear inside a different magnetic instability—the (π,0) stripe spin-density wave that is the parent state of iron pnictides. Using a minimal Hubbard model on a square lattice with staggered next-nearest-neighbor hoppings, the authors show that a uniaxial staggered electric potential breaks the TdT symmetry that otherwise forces spin degeneracy, while preserving MT symmetry. Electron correlations then spontaneously open a stripe-ordered altermagnetic insulator whose spin splitting is d_xy-wave. Both Hartree–Fock and finite-temperature determinant quantum Monte Carlo finite-size scaling confirm that the long-range stripe order survives at accessible temperatures. The result widens the definition of altermagnetism beyond conventional antiferromagnets and points to a concrete, tunable platform—optical lattices with engineered charge modulation—where the phase could be realized.

Core claim

In a half-filled Hubbard model that captures the iron-pnictide Fermi surface and (π,0) SDW instability, a uniaxial staggered electric potential converts the pure spin-stripe state into a d_xy-wave stripe-ordered altermagnetic insulator: the potential breaks TdT while preserving MT, thereby unlocking nonrelativistic spin splitting whose magnitude is set by the competition between U and ε, and whose long-range order is stable under unbiased DQMC finite-size scaling.

What carries the argument

The uniaxial staggered electric potential ε that differentiates the four sublattices into charge-rich and hole-rich sites, breaking TdT while retaining MT; this symmetry change, together with the correlation-driven spin-stripe order parameter δm_S (or Os = S(π,0)), is what produces the d_xy spin splitting.

Load-bearing premise

The hoppings chosen to mimic iron-pnictide Fermi-surface topology, together with the assumption that a static uniaxial staggered potential can be imposed without destroying the stripe order or introducing competing phases, remain valid once thermal and quantum fluctuations are treated by sign-problem-limited quantum Monte Carlo.

What would settle it

A finite-size DQMC or cold-atom measurement of the spin-stripe structure factor Os/N that extrapolates to zero for the same U ≳ 4 and ε ≲ 0.4 where the paper reports a finite intercept, or a spectroscopic measurement showing that the predicted d_xy spin splitting is absent once the staggered potential is applied.

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

If this is right

  • Altermagnetism is no longer restricted to collinear antiferromagnets; any spin-density-wave instability that can be symmetry-tuned by charge modulation can host it.
  • The SOAM phase is insulating with a charge gap linear in U and suppressed by ε, so transport and optical probes can map the phase boundary.
  • Optical-lattice realizations with laser-engineered uniaxial potentials become a direct experimental route to the predicted d_xy spin splitting.
  • The same mechanism may operate in real iron pnictides once an external staggered potential or strain is applied.

Where Pith is reading between the lines

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

  • If the SOAM phase is confirmed, altermagnetic spintronics could be built on existing iron-based platforms rather than requiring new collinear antiferromagnets.
  • The competition between U and ε suggests a continuous tuning knob for the spin-splitting amplitude that could be used to switch spin-current responses on and off.
  • Sign-problem-free reformulations or larger-scale methods that reach lower temperatures would test whether the extrapolated long-range order persists to T = 0.
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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

2 major / 4 minor

Summary. The manuscript studies a minimal four-sublattice Hubbard model with staggered next-nearest-neighbor hoppings chosen to reproduce the iron-pnictide Fermi-surface topology (hole pocket at Γ, electron pocket at X). Using Hartree–Fock mean-field theory and determinant quantum Monte Carlo, the authors show that a correlation-driven (π,0) spin-density-wave (stripe) order, once a uniaxial staggered electric potential ε is introduced, spontaneously realizes a d_xy-wave stripe-ordered altermagnetic (SOAM) insulator. The potential breaks the original TdT symmetry while preserving MT, unlocking nonrelativistic spin splitting whose momentum-space pattern is mapped in Fig. 1(e). The HF phase diagram (Fig. 2) and DQMC structure-factor peaks at (π,0) together with finite-size extrapolations of Os/N to a nonzero intercept for U ≳ 4 and ε ≲ 0.4 at β = 6 (Fig. 4) are presented as evidence that the phase survives at accessible finite temperatures.

Significance. If the result holds, the work supplies a concrete microscopic route by which altermagnetism can emerge from a correlation-driven SDW rather than from a conventional collinear antiferromagnet. The combination of a transparent symmetry argument (TdT o MT), a self-consistent HF phase diagram, and unbiased DQMC finite-size scaling constitutes a solid advance for the strongly correlated community and for the growing literature on altermagnetism in iron-based systems. The explicit proposal that the required uniaxial potential can be engineered by laser interference or in optical lattices further strengthens the experimental relevance.

major comments (2)
  1. [Model and Method / SM S1] Model and Method / SM S1: The hoppings are fixed at the specific values t1 = 0.3, t2 = 1.4, t'2 = −0.6 that reproduce the iron-pnictide Fermi surface. While this choice is physically motivated, the manuscript does not demonstrate that the SOAM phase remains stable under modest variations of the NNN hoppings or under a more generic band structure that still supports a (π,0) SDW. A brief robustness check (or an explicit statement of the limited scope) is needed before the claim can be regarded as generic for SDW-driven altermagnetism.
  2. [Fig. 4 / SM S3] Fig. 4 and SM S3: The sign problem restricts the accessible temperatures and system sizes; the finite-size extrapolations of Os/N are performed only at β = 6. Although the data show a clear tendency toward long-range order for selected (U,ε), the manuscript should quantify more carefully how far the extrapolated intercepts remain stable when the lowest reliable eta is varied, or at least discuss the possible influence of residual finite-temperature effects on the claimed thermodynamic stability of the SOAM phase.
minor comments (4)
  1. [Fig. 1(e)] Fig. 1(e) caption and main text: the phrase “unconventional d_xy-wave” is used without a quantitative multipole decomposition; a short sentence clarifying that the nodal structure alone is taken as diagnostic would improve precision.
  2. [Eq. (2)] Eq. (2) and surrounding text: the parameterization ⟨nilσ⟩ = 1/2 + (−1)^{l+σ} δmS assumes half-filling and a pure stripe; a parenthetical remark that other collinear channels were checked and found to vanish would make the MF procedure fully transparent.
  3. [SM Fig. S2] SM Fig. S2: the average-sign curves are useful; adding the corresponding average-sign values next to the data points of Fig. 4(e,f) would allow readers to assess statistical reliability at a glance.
  4. [References] References: a few recent experimental reports on altermagnetic SDW order (e.g., CsCr3Sb5) are cited; ensuring that the most recent arXiv versions are updated before publication would be helpful.

Circularity Check

0 steps flagged

No significant circularity; SOAM phase and its finite-T survival are computed outcomes of HF self-consistency and DQMC structure-factor scaling on a fixed microscopic Hubbard model, not forced by definition or self-citation.

full rationale

The derivation chain begins with a Hubbard Hamiltonian whose hoppings (t1=0.3, t2=1.4, t'2=-0.6) and USEP term ε are fixed inputs chosen to reproduce iron-pnictide Fermi-surface topology (SM S1) and to break TdT while preserving MT. Collinear order parameters δmS, δmN, δmT are defined from microscopic spin operators and solved self-consistently in Hartree-Fock (Eqs. 2-4 and SM S2); the resulting phase diagram (Fig. 2a), spin-splitting map ΔE (Fig. 1e), and charge gap are direct numerical outputs, not fitted to a target altermagnetic spectrum. Unbiased DQMC then measures the independent spin structure factor S(k) and Os ≡ S(π,0), whose finite-size extrapolations Os/N o finite intercept (Fig. 4e,f) establish long-range stripe order at accessible eta=6. Self-citations ([48,49] and methodological DQMC papers) supply only the model class and algorithmic details; they do not contain a uniqueness theorem, ansatz, or prior SOAM result that forces the present claim. No parameter is fitted to spin-splitting data and then re-used as a prediction, and the dxy character follows from the computed band eigenvalues under the imposed MT symmetry rather than from a definitional renaming. The calculation is therefore self-contained against its own microscopic operators and numerical methods.

Axiom & Free-Parameter Ledger

3 free parameters · 4 axioms · 1 invented entities

The claim rests on a standard Hubbard Hamiltonian with three hand-chosen hoppings that encode iron-pnictide phenomenology, the Hartree-Fock decoupling, the DQMC algorithm (including HS transformation and reweighting under a mild sign problem), and the assertion that a static uniaxial staggered potential is a legitimate experimental knob. No new particles or forces are postulated; the SOAM phase is an emergent many-body state of the given Hamiltonian.

free parameters (3)
  • t1, t2, t′2 = 0.3, 1.4, −0.6
    Nearest- and next-nearest-neighbor hoppings fixed by hand (t1=0.3, t2=1.4, t′2=−0.6) to reproduce the iron-pnictide Fermi-surface topology; not derived from first principles within the paper.
  • U and ε ranges
    Interaction and staggered-potential strengths scanned to locate the SOAM lobe; critical values (Uc≈3.25, εc≈0.6) are outputs of the calculation but the scanned window is chosen by the authors.
  • chemical potential μ
    Tuned at each (U,ε,β,L) to enforce half-filling once particle-hole symmetry is broken by NNN hoppings; required for the sign-problem-managed DQMC runs.
axioms (4)
  • domain assumption The four-sublattice Hubbard model with the chosen hoppings captures the essential (π,0) SDW instability of iron pnictides.
    Stated in Model and Method and SM S1; taken from earlier S4-symmetric models without re-derivation.
  • domain assumption Hartree-Fock decoupling in the density channel plus self-consistent solution of collinear order parameters (δmS, δmN, δmT) correctly identifies the ground-state magnetic instability.
    Standard mean-field procedure detailed in SM S2; used to construct the phase diagram of Fig. 2.
  • standard math Determinant QMC with discrete HS transformation and reweighting yields unbiased finite-temperature observables when the average sign remains tolerable.
    Standard algorithm (White et al., Assaad & Evertz); sign averages reported in SM S3 for the parameter window used.
  • ad hoc to paper A static uniaxial staggered electric potential ε can be imposed experimentally (e.g., by laser interference) without introducing additional terms that destroy the SDW.
    Introduced in the Hamiltonian and justified only by reference to optical-lattice proposals; no microscopic derivation of its stability is given.
invented entities (1)
  • stripe-ordered altermagnetic (SOAM) phase no independent evidence
    purpose: Name and characterize the novel insulating state that combines (π,0) stripe order with d_xy-wave non-relativistic spin splitting under MT symmetry.
    Emergent many-body phase of the given Hamiltonian; not an elementary particle or new force. Independent evidence would be experimental observation of the predicted spin splitting or optical-lattice realization.

reviewed 2026-07-14 · how reviews work

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Cite this review

Pith. "Pith review of Stripe-Ordered Altermagnetism Emerging from Correlation-Driven Spin-Density-Wave Instability." pith.science (2026). https://pith.science/paper/CG5Z6GSY

@misc{pith2026260711532,
  author       = {Pith},
  title        = {Pith review of: Stripe-Ordered Altermagnetism Emerging from Correlation-Driven Spin-Density-Wave Instability},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/CG5Z6GSY}},
  note         = {Machine review of arXiv:2607.11532}
}
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abstract

Altermagnetism is conventionally identified within the paradigm of collinear antiferromagnets. Its potential realization within other spin instabilities, such as a spin-density wave (SDW), remains a fundamentally compelling open question. Here, we combine Hartree-Fock mean-field and unbiased determinant quantum Monte Carlo methods to investigate a minimal Hubbard model relevant to iron pnictides. We reveal a novel $d_{xy}$-wave stripe-ordered altermagnetic (SOAM) insulating phase driven fundamentally by the correlation-induced $(\pi,0)$ SDW instability. Within this phase, an introduced uniaxial staggered electric potential alters the underlying symmetry: it breaks the original combined time-reversal and spatial translation symmetry ($T_{d}\mathcal{T}$) and retains a combined time-reversal and mirror invariance ($M\mathcal{T}$), thereby unlocking the pronounced nonrelativistic spin splitting. Crucially, the exact finite-size scaling from our determinant quantum Monte Carlo simulations confirms that this correlation-driven SOAM phase stably survives at accessible finite temperatures. Our study pushes the frontier of altermagnetism beyond the conventional antiferromagnetic paradigm into the realm of SDW instability, advancing the fundamental understanding of altermagnetism in strongly correlated electron systems.

Figures

Figures reproduced from arXiv: 2607.11532 by Jingyao Meng, Tianxing Ma, Zenghui Fan.

Figure 1
Figure 1. Figure 1: FIG. 1. Real-space spin-stripe configurations (a) without and (b) with the USEP. Yellow and blue spheres represent spin-up and [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. (a) Mean-field ground-state phase diagram at half [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Finite-size scaling analysis of the spin-stripe structure [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗

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Reference graph

Works this paper leans on

66 extracted references · 3 canonical work pages

  1. [1]

    As sketched in Fig. 1(a), these NNN hoppings alternate witht 2 andt ′ 2 as follows: along the (1,1)/(1,−1) directions, the hopping element ist 2/t′ 2 for sublatticesl= 1 and 4, andt ′ 2/t2 for sublatticesl= 2 and 3. The parameterεquantifies the USEP, which in- troduces charge inhomogeneity on sublattices, whileµis the chemical potential andUdenotes the on...

  2. [2]

    ThisT dTsymmetry strictly prohibits any AM spin splitting

    While this collinear spin stripe configuration ensures a vanishing net magnetization, it remains invariant under the combined operation of time-reversal (T) and a diagonal translation (Td). ThisT dTsymmetry strictly prohibits any AM spin splitting. Consequently, although a substantial electron correlationUopens a SDW gap, the spin bands remain completely ...

  3. [3]

    Hayami, Y

    S. Hayami, Y. Yanagi, and H. Kusunose, Momentum- dependent spin splitting by collinear antiferromagnetic ordering, Journal of the Physical Society of Japan88, 123702 (2019)

    2019

  4. [4]

    ˇSmejkal, J

    L. ˇSmejkal, J. Sinova, and T. Jungwirth, Beyond conven- tional ferromagnetism and antiferromagnetism: A phase with nonrelativistic spin and crystal rotation symmetry, Phys. Rev. X12, 031042 (2022)

    2022

  5. [5]

    ˇSmejkal, J

    L. ˇSmejkal, J. Sinova, and T. Jungwirth, Emerging re- search landscape of altermagnetism, Phys. Rev. X12, 040501 (2022)

    2022

  6. [6]

    Gomonay, V

    O. Gomonay, V. P. Kravchuk, R. Jaeschke-Ubiergo, K. V. Yershov, T. Jungwirth, L. ˇSmejkal, J. v. d. Brink, and J. Sinova, Structure, control, and dynamics of altermag- netic textures, npj Spintronics2, 35 (2024)

    2024

  7. [7]

    H.-Y. Ma, M. Hu, N. Li, J. Liu, W. Yao, J.-F. Jia, and J. Liu, Multifunctional antiferromagnetic materials with giant piezomagnetism and noncollinear spin current, Na- ture communications12, 2846 (2021)

    2021

  8. [8]

    X. Duan, J. Zhang, Z. Zhu, Y. Liu, Z. Zhang, I. ˇZuti´ c, and T. Zhou, Antiferroelectric altermagnets: Antiferro- electricity alters magnets, Phys. Rev. Lett.134, 106801 (2025)

    2025

  9. [9]

    P. A. McClarty and J. G. Rau, Landau theory of alter- magnetism, Phys. Rev. Lett.132, 176702 (2024)

    2024

  10. [10]

    Ji, Z.-Y

    J.-H. Ji, Z.-Y. Shao, Y.-B. Liu, and F. Yang, N´ eel or- dered magnetic phases in bipartite quasicrystals (2025), arXiv:2511.22204 [cond-mat.str-el]

    arXiv 2025

  11. [11]

    ˇSmejkal, A

    L. ˇSmejkal, A. H. MacDonald, J. Sinova, S. Nakatsuji, and T. Jungwirth, Anomalous hall antiferromagnets, Na- ture Reviews Materials7, 482 (2022)

    2022

  12. [12]

    T. Sato, S. Haddad, I. C. Fulga, F. F. Assaad, and J. van den Brink, Altermagnetic anomalous hall effect emerging from electronic correlations, Phys. Rev. Lett. 133, 086503 (2024)

    2024

  13. [13]

    A. D. Vita, C. Bigi, D. Romanin, M. D. Watson, V. Polewczyk, M. Zonno, F. Bertran, M. B. Petersen, F. Motti, G. Vinai, M. Tuniz, F. Cilento, M. Cuoco, B. M. Andersen, A. Kreisel, L. J. D’Onofrio, O. J. Clark, M. T. Edmonds, C. Candelora, M. Xu, S. Cheng, A. LaFleur, T. Antonelli, G. Sangiovanni, L. D. Re, I. Vobornik, J. Fujii, F. M. Granozio, A. Sambri, ...

    arXiv 2026

  14. [14]

    Sicheler, R

    N. Sicheler, R. Raimondi, G. Sangiovanni, and L. D. Re, Optically tunable spin transport in bilayer altermagnetic mott insulators (2025), arXiv:2508.06938 [cond-mat.str- el]

    Pith/arXiv arXiv 2025

  15. [15]

    Mazin (The PRX Editors), Editorial: Altermagnetism—a new punch line of fundamental magnetism, Phys

    I. Mazin (The PRX Editors), Editorial: Altermagnetism—a new punch line of fundamental magnetism, Phys. Rev. X12, 040002 (2022)

    2022

  16. [16]

    L. Bai, W. Feng, S. Liu, L. ˇSmejkal, Y. Mokrousov, and Y. Yao, Altermagnetism: Exploring new frontiers in mag- netism and spintronics, Advanced Functional Materials 34, 2409327 (2024)

    2024

  17. [17]

    C. Song, H. Bai, Z. Zhou, L. Han, H. Reichlova, J. H. Dil, J. Liu, X. Chen, and F. Pan, Altermagnets as a new class of functional materials, Nature Reviews Materials 10, 473 (2025)

    2025

  18. [18]

    Y. Che, H. Lv, X. Wu, and J. Yang, Engineering alter- magnetic states in two-dimensional square tessellations, Phys. Rev. Lett.135, 036701 (2025)

    2025

  19. [19]

    V. Leeb, A. Mook, L. ˇSmejkal, and J. Knolle, Sponta- neous formation of altermagnetism from orbital ordering, Phys. Rev. Lett.132, 236701 (2024)

    2024

  20. [20]

    Giuli, C

    S. Giuli, C. Mejuto-Zaera, and M. Capone, Alter- magnetism from interaction-driven itinerant magnetism, Phys. Rev. B111, L020401 (2025)

    2025

  21. [21]

    P. Das, V. Leeb, J. Knolle, and M. Knap, Realizing al- termagnetism in fermi-hubbard models with ultracold atoms, Phys. Rev. Lett.132, 263402 (2024)

    2024

  22. [22]

    Kaushal and M

    N. Kaushal and M. Franz, Altermagnetism in modified lieb lattice hubbard model, Phys. Rev. Lett.135, 156502 (2025)

    2025

  23. [23]

    H. Q. Lin and J. E. Hirsch, Two-dimensional hubbard model with nearest- and next-nearest-neighbor hopping, Phys. Rev. B35, 3359 (1987)

    1987

  24. [24]

    C. Wu, K. Sun, E. Fradkin, and S.-C. Zhang, Fermi liquid instabilities in the spin channel, Phys. Rev. B75, 115103 (2007)

    2007

  25. [25]

    Reimers, L

    S. Reimers, L. Odenbreit, L. ˇSmejkal, V. N. Strocov, P. Constantinou, A. B. Hellenes, R. Jaeschke Ubiergo, W. H. Campos, V. K. Bharadwaj, A. Chakraborty,et al., Direct observation of altermagnetic band splitting in crsb thin films, Nature Communications15, 2116 (2024)

    2024

  26. [26]

    G. Yang, Z. Li, S. Yang, J. Li, H. Zheng, W. Zhu, Z. Pan, Y. Xu, S. Cao, W. Zhao,et al., Three-dimensional map- ping of the altermagnetic spin splitting in crsb, Nature Communications16, 1442 (2025)

    2025

  27. [27]

    W. Lu, S. Feng, Y. Wang, D. Chen, Z. Lin, X. Liang, S. Liu, W. Feng, K. Yamagami, J. Liu,et al., Signa- ture of topological surface bands in altermagnetic weyl semimetal crsb, Nano Letters25, 7343 (2025)

    2025

  28. [28]

    Zeng, M.-Y

    M. Zeng, M.-Y. Zhu, Y.-P. Zhu, X.-R. Liu, X.-M. Ma, Y.- J. Hao, P. Liu, G. Qu, Y. Yang, Z. Jiang, K. Yamagami, M. Arita, X. Zhang, T.-H. Shao, Y. Dai, K. Shimada, Z. Liu, M. Ye, Y. Huang, Q. Liu, and C. Liu, Observation of spin splitting in room-temperature metallic antiferro- magnet crsb, Advanced Science11, 2406529 (2024)

    2024

  29. [29]

    J. Ding, Z. Jiang, X. Chen, Z. Tao, Z. Liu, T. Li, J. Liu, J. Sun, J. Cheng, J. Liu, Y. Yang, R. Zhang, L. Deng, 7 W. Jing, Y. Huang, Y. Shi, M. Ye, S. Qiao, Y. Wang, Y. Guo, D. Feng, and D. Shen, Large band splitting in g-wave altermagnet crsb, Phys. Rev. Lett.133, 206401 (2024)

    2024

  30. [30]

    Krempask` y, L

    J. Krempask` y, L. ˇSmejkal, S. D’souza, M. Hajlaoui, G. Springholz, K. Uhl´ ıˇ rov´ a, F. Alarab, P. Constantinou, V. Strocov, D. Usanov,et al., Altermagnetic lifting of kramers spin degeneracy, Nature626, 517 (2024)

    2024

  31. [31]

    S. Lee, S. Lee, S. Jung, J. Jung, D. Kim, Y. Lee, B. Seok, J. Kim, B. G. Park, L. ˇSmejkal, C.-J. Kang, and C. Kim, Broken kramers degeneracy in altermagnetic mnte, Phys. Rev. Lett.132, 036702 (2024)

    2024

  32. [32]

    Osumi, S

    T. Osumi, S. Souma, T. Aoyama, K. Yamauchi, A. Honma, K. Nakayama, T. Takahashi, K. Ohgushi, and T. Sato, Observation of a giant band splitting in alter- magnetic mnte, Phys. Rev. B109, 115102 (2024)

    2024

  33. [33]

    Jiang, M

    B. Jiang, M. Hu, J. Bai, Z. Song, C. Mu, G. Qu, W. Li, W. Zhu, H. Pi, Z. Wei,et al., A metallic room- temperature d-wave altermagnet, Nature Physics21, 754 (2025)

    2025

  34. [34]

    Zhang, X

    F. Zhang, X. Cheng, Z. Yin, C. Liu, L. Deng, Y. Qiao, Z. Shi, S. Zhang, J. Lin, Z. Liu,et al., Crystal-symmetry- paired spin–valley locking in a layered room-temperature metallic altermagnet candidate, Nature Physics21, 760 (2025)

    2025

  35. [35]

    N. Ni, E. Climent-Pascual, S. Jia, Q. Huang, and R. J. Cava, Physical properties and magnetic structure of the layered oxyselenide la 2o3mn2se2, Phys. Rev. B82, 214419 (2010)

    2010

  36. [36]

    C.-C. Wei, X. Li, S. Hatt, X. Huai, J. Liu, B. Singh, K.-M. Kim, R. M. Fernandes, P. Cardon, L. Zhao, T. T. Tran, B. A. Frandsen, K. S. Burch, F. Liu, and H. Ji, la2o3mn2se2: A correlated insulating layered d-wave al- termagnet, Phys. Rev. Mater.9, 024402 (2025)

    2025

  37. [37]

    Garcia-Gassull, A

    L. Garcia-Gassull, A. Razpopov, P. P. Stavropoulos, I. I. Mazin, and R. Valent´ ı, Microscopic origin of the magnetic interactions and their experimental signa- tures in altermagnetic La 2O3Mn2Se2, npj Spintronics4, 10.1038/s44306-025-00125-9 (2026)

    work page doi:10.1038/s44306-025-00125-9 2026

  38. [38]

    Y. Guo, H. Liu, O. Janson, I. C. Fulga, J. van den Brink, and J. I. Facio, Spin-split collinear antiferromagnets: A large-scale ab-initio study, Materials Today Physics32, 100991 (2023)

    2023

  39. [39]

    L.-D. Yuan, Z. Wang, J.-W. Luo, and A. Zunger, Predic- tion of low-z collinear and noncollinear antiferromagnetic compounds having momentum-dependent spin splitting even without spin-orbit coupling, Phys. Rev. Mater.5, 014409 (2021)

    2021

  40. [40]

    Zheng, C.-M

    B.-X. Zheng, C.-M. Chung, P. Corboz, G. Ehlers, M.-P. Qin, R. M. Noack, H. Shi, S. R. White, S. Zhang, and G. K.-L. Chan, Stripe order in the underdoped region of the two-dimensional hubbard model, Science358, 1155 (2017)

    2017

  41. [41]

    Xu, C.-M

    H. Xu, C.-M. Chung, M. Qin, U. Schollw¨ ock, S. R. White, and S. Zhang, Coexistence of superconductivity with par- tially filled stripes in the hubbard model, Science384, eadh7691 (2024)

    2024

  42. [42]

    R. M. Z. F. H. L. Y. Y. T. M. H.-Q. Lin, Charge stripe and superconductivity tuned by interlayer interaction in a sign-problem-free bilayer extended hubbard model, Frontiers of Physics21, 115202 (2026)

    2026

  43. [43]

    Parthenios, P

    N. Parthenios, P. M. Bonetti, R. Gonz´ alez-Hern´ andez, W. H. Campos, L. ˇSmejkal, and L. Classen, Spin and pair density waves in two-dimensional altermagnetic metals, Phys. Rev. B112, 214410 (2025)

    2025

  44. [44]

    Huang, C

    Z. Huang, C. Xu, Y. Que, Y. Liu, Y. Wang, S. Zhu, R. Shivajirao, Z. J. Tong, A. Kumar, C. Cao,et al., Controlling an altermagnetic spin density wave in the kagome magnet cscr3sb5, Nature Communications 10.1038/s41467-026-73976-3 (2026)

    work page doi:10.1038/s41467-026-73976-3 2026

  45. [45]

    Y.-K. Wang, S. Li, and S. A. Yang, Two-dimensional altermagnetic iron oxyhalides: Real chern topol- ogy and valley–spin–lattice coupling, Nano Letters 10.1021/acs.nanolett.5c05461 (2026)

    work page doi:10.1021/acs.nanolett.5c05461 2026

  46. [46]

    J. Li, X. Fu, Z. Zeng, W. He, C. Zheng, C. Chen, L. Zhang, W. Liu, R. Wu, T. Wang,et al., Uncovering a novel Al 2Li2FeO5 structure as a candidate altermagnet in ancient yaozhou sauce wares (960-1279 ce), Journal of the European Ceramic Society , 118325 (2026)

    2026

  47. [47]

    J.-X. Zhu, R. Yu, H. Wang, L. L. Zhao, M. D. Jones, J. Dai, E. Abrahams, E. Morosan, M. Fang, and Q. Si, Band narrowing and mott localization in iron oxychalco- genides la2o2fe2O(Se,S) 2, Phys. Rev. Lett.104, 216405 (2010)

    2010

  48. [48]

    Fan, Y.-K

    A.-D. Fan, Y.-K. Wang, J.-Y. Li, and S. Li, Valley- dependent electronic properties in two-dimensional al- termagnetic iron-based transition metal chalcogenides, Phys. Rev. B112, 235135 (2025)

    2025

  49. [49]

    R. M. Fernandes, A. V. Chubukov, and J. Schmalian, What drives nematic order in iron-based superconduc- tors?, Nature physics10, 97 (2014)

    2014

  50. [50]

    Hu and N

    J. Hu and N. Hao,S 4 symmetric microscopic model for iron-based superconductors, Phys. Rev. X2, 021009 (2012)

    2012

  51. [51]

    Ma, H.-Q

    T. Ma, H.-Q. Lin, and J. Hu, Quantum monte carlo study of a dominants-wave pairing symmetry in iron-based su- perconductors, Phys. Rev. Lett.110, 107002 (2013)

    2013

  52. [52]

    Y. Gu, Z. Liu, T. Xie, W. Zhang, D. Gong, D. Hu, X. Ma, C. Li, L. Zhao, L. Lin, Z. Xu, G. Tan, G. Chen, Z. Y. Meng, Y.-f. Yang, H. Luo, and S. Li, Unified phase di- agram for iron-based superconductors, Phys. Rev. Lett. 119, 157001 (2017)

    2017

  53. [53]

    Shibauchi, A

    T. Shibauchi, A. Carrington, and Y. Matsuda, A quan- tum critical point lying beneath the superconducting dome in iron pnictides, Annu. Rev. Condens. Matter Phys.5, 113 (2014)

    2014

  54. [54]

    R. M. Fernandes, A. I. Coldea, H. Ding, I. R. Fisher, P. Hirschfeld, and G. Kotliar, Iron pnictides and chalco- genides: a new paradigm for superconductivity, Nature 601, 35 (2022)

    2022

  55. [55]

    Z. P. Yin, K. Haule, and G. Kotliar, Spin dynamics and orbital-antiphase pairing symmetry in iron-based super- conductors, Nature Physics10, 845 (2014)

    2014

  56. [56]

    S. R. White, D. J. Scalapino, R. L. Sugar, E. Y. Loh, J. E. Gubernatis, and R. T. Scalettar, Numerical study of the two-dimensional hubbard model, Phys. Rev. B40, 506 (1989)

    1989

  57. [57]

    T. Ma, L. Zhang, C.-C. Chang, H.-H. Hung, and R. T. Scalettar, Localization of interacting dirac fermions, Phys. Rev. Lett.120, 116601 (2018)

    2018

  58. [58]

    R. Ma, Z. Fan, T. Ma, and C. Wu, Parameter- dependent superconducting transition temperature in a sign-problem-free bilayer model, Chinese Physics Letters 42, 110705 (2025)

    2025

  59. [59]

    Xiong, H

    Y. Xiong, H. Ma, H. Liu, R. Ma, and T. Ma, Com- parison of superconducting pairing in doped cuprates and nickelates within the hubbard model including the third-nearest neighbor hopping terms, Phys. Rev. B111, 8 045151 (2025)

    2025

  60. [60]

    J. Meng, Z. Fan, M. Ye, and T. Ma, Strain tuning of the transport gap and magnetic order in dirac fermion systems, Chinese Physics B34, 098101 (2025)

    2025

  61. [61]

    F. F. Assaad and I. F. Herbut, Pinning the order: The nature of quantum criticality in the hubbard model on honeycomb lattice, Phys. Rev. X3, 031010 (2013)

    2013

  62. [62]

    C. Chin, R. Grimm, P. Julienne, and E. Tiesinga, Fesh- bach resonances in ultracold gases, Rev. Mod. Phys.82, 1225 (2010)

    2010

  63. [63]

    P. J. Hirschfeld, M. M. Korshunov, and I. I. Mazin, Gap symmetry and structure of fe-based superconductors, Re- ports on Progress in Physics74, 124508 (2011)

    2011

  64. [64]

    Chubukov, Pairing mechanism in fe-based supercon- ductors, Annu

    A. Chubukov, Pairing mechanism in fe-based supercon- ductors, Annu. Rev. Condens. Matter Phys.3, 57 (2012)

    2012

  65. [65]

    Thomale, C

    R. Thomale, C. Platt, W. Hanke, J. Hu, and B. A. Bernevig, Exoticd-wave superconducting state of strongly hole-dopedk xba1−xfe2as2, Phys. Rev. Lett. 107, 117001 (2011)

    2011

  66. [66]

    Stripe-Ordered Altermagnetism Emerging from Correlation-Driven Spin-Density-Wave Instability

    F. Assaad and H. Evertz, World-line and determinan- tal quantum monte carlo methods for spins, phonons and electrons, inComputational Many-Particle Physics, edited by H. Fehske, R. Schneider, and A. Weiße (Springer Berlin Heidelberg, Berlin, Heidelberg, 2008) pp. 277–356. 9 Supplementary Materials for “Stripe-Ordered Altermagnetism Emerging from Correlati...

    2008

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