Pith. sign in

REVIEW 3 major objections 5 minor 1 cited by

Reversing a fractional ferroelectric polarization in an altermagnetic insulator necessarily inverts the spin-dependent band splitting, giving electrically switchable spin control without reorienting the magnetic order.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

T0 review

2026-08-04 09:09 UTC pith:SP5SDPUO

load-bearing objection A genuinely new symmetry-based multiferroics concept with a clean derivation and a wide materials sweep, but the headline switching claim rests on an uncomputed energy barrier. the 3 major comments →

arxiv 2510.16733 v1 pith:SP5SDPUO submitted 2025-10-19 cond-mat.mtrl-sci

Fractional Quantum Multiferroics from Coupling of Fractional Quantum Ferroelectricity and Altermagnetism

M. Q. Dong , B. Liu , Z. H. Dai , Zhi-Xin Guo , Hongjun Xiang , Xin-Gao Gong This is my paper
classification cond-mat.mtrl-sci
keywords fractional quantum multiferroicsaltermagnetismmagnetoelectric couplingspin splitting inversionMnTetunnel magnetoresistancefractional quantum ferroelectricityvoltage-controlled spintronics
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 paper introduces fractional quantum multiferroics (FQMF): materials that couple fractional quantum ferroelectricity with altermagnetism so that flipping the electric polarization flips the spin splitting in the electronic bands. Symmetry analysis shows that if the two ferroelectric states are related by a fractional lattice translation plus time reversal or parity-time reversal, the spin texture must invert while the Néel vector stays fixed. A minimal tight-binding model reproduces the effect, and first-principles calculations identify several candidate materials, most notably bulk MnTe with a near-room-temperature Néel order and an electrically switchable spin splitting around 0.8 eV. The authors further propose a MnTe tunnel junction whose tunneling magnetoresistance exceeds 300% when the free layer is switched electrically. A sympathetic reader would care because this offers a path to voltage-controlled antiferromagnetic spintronics without the weak coupling that usually plagues multiferroics.

Core claim

The paper's central claim is that reversing the fractional quantum ferroelectric polarization in an altermagnetic material necessarily inverts the spin-resolved band structure, without reorienting the Néel vector. The mechanism is symmetry-enforced: if the two ferroelectric states L1 and L2 are related by Tτ or τPT, then for collinear magnets with negligible spin-orbit coupling the band energies satisfy τPT ε_n(k,s)=ε_n(k,−s) and τT ε_n(k,s)=ε_n(−k,−s)=ε_n(k,−s), so the spin splitting ΔE_n(k) changes sign. The paper shows this in a minimal tight-binding model, and by density-functional calculations for bulk MnTe, bilayer MnBr2, and other candidates. In MnTe, the L1 and L2 states have opposit

What carries the argument

The central object is the fractional quantum ferroelectric switching path: a nonmagnetic or magnetic ion moves between two symmetry-equivalent positions, L1 and L2, related by a fractional lattice translation τ combined with time reversal (Tτ) or parity-time reversal (τPT). For nonrelativistic collinear altermagnets, these combined operations act on the band structure as pure spin-flip operations, forcing the spin splitting to invert when the polarization is reversed. This symmetry identity, rather than spin-orbit coupling, is what locks the magnetic response to the electric field. A simple tight-binding Hamiltonian with A-atom position-dependent hopping plus on-site exchange demonstrates th

Load-bearing premise

The whole mechanism rests on the premise that the L1 and L2 states are genuinely switchable fractional-quantum-ferroelectric states—degenerate in energy, connected by a low-energy path, and reversible by an external electric field—while the material stays collinear and nearly spin-orbit-free; the paper does not compute the switching barrier or domain stability.

What would settle it

Calculate the minimum-energy path between L1 and L2 in MnTe (or measure it via dielectric and switching experiments). If the barrier exceeds what an achievable electric field can overcome, or if the two states are not connected by an accessible path, the central switching claim collapses. A second check is to measure the spin splitting of a single-domain MnTe sample before and after electric poling: if the splitting does not invert while the Néel vector remains fixed, the predicted magnetoelectric coupling is absent.

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

Share X Bluesky LinkedIn Reddit HN

If this is right

  • If true, electric fields alone can control spin-polarized bands in antiferromagnetic materials, enabling voltage-driven spintronics with no moving magnetic moments and no stray fields.
  • Bulk MnTe offers a concrete platform: room-temperature-compatible Néel order and an electrically switchable spin splitting of about 0.8 eV, an order of magnitude larger than previous altermagnet-ferroelectric hybrids.
  • The proposed MnTe/MnTe tunnel junction would show tunneling magnetoresistance exceeding 300%, combining the momentum mismatch of altermagnetic tunnel junctions with the atomic-structure mismatch of ferroelectric tunnel junctions.
  • The symmetry argument applies across a broad family of 2D and 3D materials, including Cr2S3, Mn4Bi3NO15, and transition-metal dihalide bilayers, so the effect is not specific to one compound.

Where Pith is reading between the lines

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

  • A natural but untested extension is to measure the polarization-switching energy landscape and domain stability of MnTe; if the barrier is low enough, the proposed electric-field control becomes practically feasible at room temperature.
  • The symmetry argument is likely to generalize to any collinear altermagnet with two FQFE states related by Tτ or τPT, which suggests a systematic search rule: look for nonpolar altermagnetic crystals with fractional lattice-translation degeneracies.
  • Strong spin-orbit coupling would relax the exact band-spin correspondence, so the mechanism is expected to be cleanest in light-element magnets; checking how much SOC reduces the spin-splitting inversion would sharpen predictions for heavier candidates.
  • A direct experiment could use spin- and angle-resolved photoemission on poled MnTe samples to see whether the Fermi-surface spin texture reverses after applying an electric field, without changing the antiferromagnetic domain.

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 / 5 minor

Summary. The paper introduces the concept of fractional quantum multiferroics (FQMF), combining fractional quantum ferroelectricity (FQFE) with altermagnetism (AM). The central idea is that in FQMF systems, reversing the FQFE polarization between two states L1 and L2, related by Tτ or τPT operations, necessarily inverts the altermagnetic spin splitting without reorienting the Néel vector. This is supported by a symmetry argument, a minimal tight-binding model, and DFT calculations for bulk MnTe (a known altermagnet with TN≈300 K) and several other 2D and 3D candidates. The paper further proposes an electric-field-controlled MnTe-based tunnel junction with predicted TMR exceeding 300%. The manuscript emphasizes that FQMF offers a route to strong room-temperature magnetoelectric coupling and voltage-controlled spintronics.

Significance. If fully realized, the FQMF concept would be a valuable addition to multiferroics research: it sidesteps the usual incompatibility between ferroelectricity and magnetism by using nonpolar point groups and fractional translations, while exploiting altermagnetism for a large spin splitting. The symmetry analysis itself is clean and internally consistent, and the identification of concrete material candidates (MnTe, MnBr2, etc.) with large spin splittings (~0.8 eV in MnTe) is significant. The inclusion of a tunnel-junction device proposal adds technological motivation. However, the actual experimental or computational demonstration of electric-field switching is absent, and several load-bearing assumptions (barrier height, SOC effects, switchability) remain untested. The significance is therefore conditional: the paper establishes a promising symmetry-based mechanism and plausible candidate materials, but the central device-oriented claims are not yet substantiated.

major comments (3)
  1. [§Real system examples–bulk MnTe and §TMR in MnTe/MnTe FQMFTJ] The manuscript claims that reversing the FQFE polarization 'necessarily' inverts the spin splitting and that this enables electric-field-controlled devices. However, no energy barrier, switching pathway, or domain stability is calculated for any candidate. Figures 2(b) and 3(b) show polarization evolution along the L1–L2 pathway, but this is not a minimum-energy path (e.g., NEB or saddle-point search). Without evidence that the L1→L2 transition is kinetically accessible under an electric field without passing through intermediate states that break the τT/τPT relation, the central switchability claim—and the entire FQMFTJ proposal—is an assumption rather than a demonstrated result. I request either explicit switching-path calculations for at least one material (ideally MnTe) or a clear statement that the switching is assumed, with the claims softened accordingly.
  2. [§Physical mechanism, Eqs. (1)–(2)] The symmetry relations are derived for nonrelativistic collinear magnets with negligible spin-orbit coupling (SOC). For bulk MnTe, Te 5p orbitals have sizable SOC, which can mix spin channels and alter the exact spin-inversion property. The DFT calculations for band structures (Figs. 2(d), 2(f) and similar) do not state whether SOC was included; if they are collinear spin-polarized only, the 0.8 eV splitting and the TMR values may change when SOC is included. Please clarify the computational settings in the main text or Supplemental Material, and test at least one candidate (e.g., MnTe) with SOC to assess whether the L1/L2 spin correspondence remains exact.
  3. [§TMR in MnTe/MnTe FQMFTJ] The predicted TMR exceeding 300% is a headline application result, but it is entirely contingent on the switchability of the free layer between L1 and L2, which is not demonstrated (see first major comment). Additionally, the AP-FQMF junction contains an atomic structural mismatch at the interface because L1 and L2 differ not just in magnetism but in atomic positions. The manuscript acknowledges this but does not quantify how much of the TMR comes from the structural mismatch versus the electronic spin mismatch. The statement that FQMFTJs 'inherently outperform' AM-only or ferroelectric-only junctions is too strong given these unquantified contributions. I suggest either performing a more detailed device simulation that includes interface relaxation and separating the two contributions quantitatively, or tempering the central device claim.
minor comments (5)
  1. [Throughout] Typographical errors: 'ACKNOWLODGMENTS' should be 'ACKNOWLEDGMENTS'; 'spin-sown' in Fig. 4(b) should be 'spin-down'; 'It is worth nothing' should be 'worth noting'; 'TMR-FQMR' in Fig. 4(d) should likely be 'TMR-FQMF'.
  2. [§Physical mechanism] The relation between Tτ and τPT operations is stated somewhat elliptically: 'if the L1 and L2 structures related by Tτ or by the PT operation, or equivalently by τPT operation'. Please clarify whether τPT is a combination of PT and a translation, and define the exact action of each operation on the crystal and spin degrees of freedom. This would help readers follow Eq. (1)–(2).
  3. [§Real system examples–bulk MnTe] The net Te displacement is written as 'ΔdTe = 0·a + b', which is confusing (likely means 0·a + 1·b). Please use explicit vectors or notation such as 'b' to avoid ambiguity.
  4. [References] Reference [13] (Ji et al., Nature Communications 15, 135 (2024)) gives the FQFE concept; reference [14] (Pang and He) is a related unified framework. The paper should make sure the distinction between FQFE and conventional ferroelectricity is clearly attributed, especially in the Introduction.
  5. [§TMR in MnTe/MnTe FQMFTJ] The definition of TMR in Eq. (5) uses a threshold T_AP > 0.01 to avoid divergence. This cutoff is arbitrary; please justify it or show that the reported TMR values are not sensitive to the threshold. Also, the energy-resolved TMR shows values exceeding 300% near the Fermi level, but the energy window and k-point sampling used in the transmission calculation should be described in the Supplemental Material.

Circularity Check

0 steps flagged

No significant circularity: the symmetry-derived spin-splitting inversion is a genuine consequence, and the DFT and transport results provide independent content.

full rationale

The paper's central claim is that reversing the FQFE polarization (L1→L2) inverts the altermagnetic spin splitting when L1 and L2 are related by τT or τPT. This is derived from spin-group symmetry via Eqs. (1)–(2), which state that τPT or τT maps ε_n(k,s) to ε_n(k,−s). That is a genuine symmetry consequence, not a fit or a renaming: L1 and L2 are defined by fractional ionic displacements and degeneracy, not by the spin splitting itself. The paper then independently verifies the relation in a tight-binding model and with DFT for MnTe, MnBr2, and other materials, computing polarization differences by the Berry-phase method and band structures from first principles. The 0.8 eV spin splitting and the >300% TMR are calculated quantities, not parameters fitted to the predicted outcome. The main weakness is that electric-field switchability is assumed rather than demonstrated: no energy barrier or switching path is computed for L1→L2. However, that is a completeness/validity concern, not circularity. Self-citations to prior FQFE work [12,13] provide background and motivation, but the present paper's materials-specific evidence does not reduce to those citations. Therefore, no load-bearing circular step is identified.

Axiom & Free-Parameter Ledger

3 free parameters · 4 axioms · 0 invented entities

The central symmetry argument rests on the standard theory of polarization and the spin-group symmetry of collinear magnets. The most fragile assumption is that the proposed L1/L2 states are true FQFE switching states with accessible energy barriers; this is stated but not demonstrated. The DFT calculations introduce typical free parameters (U, TB constants) that are not central to the symmetry claim.

free parameters (3)
  • Tight-binding hopping prefactor = 4.5
    In Eq. (4) the hopping integral is set to 4.5[1−sin(π r_ij/2a)] to illustrate the coupling between A-atom displacement and band structure; this is a model parameter, not fit to data.
  • On-site exchange J and chemical potential μ in TB model = not specified in main text
    The tight-binding Hamiltonian (Eq. 3) contains on-site exchange J and chemical potential μ; their values are only in the Supplemental Material. They are model parameters chosen to realize the AM spin texture.
  • DFT+U parameter(s) = not specified in main text
    For transition-metal compounds (MnTe, MnBr2, etc.), the DFT+U method is used, which requires U and J values. These are not given in the main text and can affect the calculated band gap and spin splitting.
axioms (4)
  • domain assumption Modern theory of polarization (Berry phase) gives well-defined polarization differences in nonpolar FQFE states.
    The paper computes polarization via Berry phase [24,33–35] for L1 and L2, assuming the two states can be connected adiabatically and the polarization quantum is well defined.
  • domain assumption Collinear magnetic order with negligible spin-orbit coupling, so τPT and τT act as pure spin-flip operations.
    Eqs. (1)–(2) assume nonrelativistic collinear magnets; the spin-splitting inversion is exact only in this limit. Real materials have some SOC that may modify the relationship.
  • ad hoc to paper The L1 and L2 states are degenerate in energy and switchable by an external electric field.
    The paper treats L1 and L2 as FQFE switching states but does not compute energy barriers or switching pathways; this is load-bearing for the device claims.
  • domain assumption DFT(+U) with GGA accurately captures the band gap, spin splitting, and polarization quantum.
    The material predictions rely on DFT(+U) results, whose accuracy is not independently verified (e.g., against experiment beyond the known Néel temperature of MnTe).

reviewed 2026-08-04 · how reviews work

0 comments
Cite this review

Pith. "Pith review of Fractional Quantum Multiferroics from Coupling of Fractional Quantum Ferroelectricity and Altermagnetism." pith.science (2026). https://pith.science/paper/SP5SDPUO

@misc{pith2026251016733,
  author       = {Pith},
  title        = {Pith review of: Fractional Quantum Multiferroics from Coupling of Fractional Quantum Ferroelectricity and Altermagnetism},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/SP5SDPUO}},
  note         = {Machine review of arXiv:2510.16733}
}
Share X Bluesky LinkedIn Reddit HN
read the original abstract

Multiferroics, which combine ferroelectric and magnetic order, offer a transformative platform for next-generation electronic devices. However, the intrinsic competition between the mechanisms driving ferroelectricity and magnetism in single-phase materials severely limits their performance, typically resulting in weak magnetoelectric coupling at room temperature. Here, we propose a solution to this long-standing challenge through the novel concept of fractional quantum multiferroics (FQMF), where strong magnetoelectric coupling is naturally realized by coupling fractional quantum ferroelectricity (FQFE) with altermagnetism (AM). Symmetry analysis shows that reversing the FQFE polarization necessarily inverts the AM spin splitting under parity-time ($\mathcal{PT}$) or time-reversal ($\mathcal{T}\tau$) operations. A minimal tight-binding model reproduces this effect, demonstrating electrically driven spin control without rotating the N\'eel vector. First-principles calculations further identify a broad family of candidate materials in two and three dimensions including bulk MnTe, Cr$_2$S$_3$, Mn$_4$Bi$_3$NO$_{15}$ and two-dimensional AB$_2$ bilayers such as MnX$_2$ (X=Cl, Br, I), CoCl$_2$, CoBr$_2$, and FeI$_2$. Notably, MnTe exhibits a high N\'eel temperature ($\sim$300 K) and a large electrically switchable spin splitting ($\sim$0.8 eV), demonstrating room-temperature magnetoelectric performance that surpasses that of conventional multiferroics. To further showcase the technological potential, we propose an electric-field-controlled FQMF tunnel junction based on MnTe that achieves tunneling magnetoresistance exceeding 300\%. This work establishes FQMF as a distinct and promising route to achieving room-temperature strong magnetoelectric coupling, opening a new avenue for voltage-controlled spintronics.

Figures

Figures reproduced from arXiv: 2510.16733 by B. Liu, Hongjun Xiang, M. Q. Dong, Xin-Gao Gong, Z. H. Dai, Zhi-Xin Guo.

Figure 1
Figure 1. Figure 1: FIG. 1. Schematic illustration of FQMF in monolayer AB [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Schematic illustration, polarization, and band structures of bulk MnTe. (a) [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Schematic illustration, polarization, and band structures of bilayer MnBr [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Schematic illustration, Fermi surfaces, transmission spectra, and TMR of FQMFTJ junc [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Two-Dimensional Spin-Antiferroelectric Altermagnets with Giant Spin Splitting: From Model to Material Realization

    cond-mat.mtrl-sci 2026-04 unverdicted novelty 6.0

    2D spin-antiferroelectric altermagnets such as monolayer (CoCl)2Te are predicted to show giant spin splitting with spin currents switchable by in-plane electric field angle when hole-doped or gate polarity when electr...

Reference graph

Works this paper leans on

45 extracted references · 1 linked inside Pith · cited by 1 Pith paper

  1. [1]

    H. S. and, Multi-ferroic magnetoelectrics, Ferroelectrics162, 317 (1994)

    1994

  2. [2]

    C. Xu, P. Chen, H. Tan, Y. Yang, H. Xiang, and L. Bellaiche, Electric-Field Switching of Magnetic Topological Charge in Type-I Multiferroics, Physical Review Letters125, 037203 (2020)

    2020

  3. [3]

    B. B. Van Aken, T. T. Palstra, A. Filippetti, and N. A. Spaldin, The origin of ferroelectricity in magnetoelectric YMnO 3, Nature Materials3, 164 (2004)

    2004

  4. [4]

    Kimura, T

    T. Kimura, T. Goto, H. Shintani, K. Ishizaka, T.-h. Arima, and Y. Tokura, Magnetic control of ferroelectric polarization, Nature426, 55 (2003)

    2003

  5. [5]

    Q. Song, C. A. Occhialini, E. Erge¸ cen, B. Ilyas, D. Amoroso, P. Barone, J. Kapeghian, K. Watanabe, T. Taniguchi, A. S. Botana,et al., Evidence for a single-layer van der Waals multiferroic, Nature602, 601 (2022)

    2022

  6. [6]

    Ponet, S

    L. Ponet, S. Artyukhin, T. Kain, J. Wettstein, A. Pimenov, A. Shuvaev, X. Wang, S.-W. Cheong, M. Mostovoy, and A. Pimenov, Topologically protected magnetoelectric switching in a multiferroic, Nature607, 81 (2022)

    2022

  7. [7]

    Ramesh and N

    R. Ramesh and N. A. Spaldin, Multiferroics: progress and prospects in thin films, Nature Materials6, 21 (2007)

    2007

  8. [8]

    Fiebig, T

    M. Fiebig, T. Lottermoser, D. Meier, and M. Trassin, The evolution of multiferroics, Nature Reviews Materials1, 1 (2016)

    2016

  9. [9]

    Schmid, Multi-ferroic magnetoelectrics, Ferroelectrics162, 317 (1994)

    H. Schmid, Multi-ferroic magnetoelectrics, Ferroelectrics162, 317 (1994)

    1994

  10. [10]

    D. I. Khomskii, Multiferroics: Different ways to combine magnetism and ferroelectricity, Jour- nal of Magnetism and Magnetic Materials306, 1 (2006)

    2006

  11. [11]

    N. A. Hill, Why are there so few magnetic ferroelectrics?, The Journal of Physical Chemistry B104, 6694 (2000)

    2000

  12. [12]

    G. Yu, J. Ji, Y. Chen, C. Xu, and H. J. Xiang, Symmetry Strategy for Rapid Discovery of Abundant Fractional Quantum Ferroelectrics, Physical Review Letters134, 016801 (2025)

    2025

  13. [13]

    J. Ji, G. Yu, C. Xu, and H. Xiang, Fractional quantum ferroelectricity, Nature Communications 15, 135 (2024)

    2024

  14. [14]

    Pang and L

    H. Pang and L. He, Generalized neumann’s principle as a unified framework for fractional quantum and conventional ferroelectricity, Physical Review Letters135, 116402 (2025). 12

    2025

  15. [15]

    ˇSmejkal, J

    L. ˇSmejkal, J. Sinova, and T. Jungwirth, Beyond Conventional Ferromagnetism and Antifer- romagnetism: A Phase with Nonrelativistic Spin and Crystal Rotation Symmetry, Physical Review X12, 031042 (2022)

    2022

  16. [16]

    ˇSmejkal, J

    L. ˇSmejkal, J. Sinova, and T. Jungwirth, Emerging Research Landscape of Altermagnetism, Physical Review X12, 040501 (2022)

    2022

  17. [17]

    P. Liu, J. Li, J. Han, X. Wan, and Q. Liu, Spin-Group Symmetry in Magnetic Materials with Negligible Spin-Orbit Coupling, Physical Review X12, 021016 (2022)

    2022

  18. [18]

    Jungwirth, X

    T. Jungwirth, X. Marti, P. Wadley, and J. Wunderlich, Antiferromagnetic spintronics, Nature Nanotechnology11, 231 (2016)

    2016

  19. [19]

    Baltz, A

    V. Baltz, A. Manchon, M. Tsoi, T. Moriyama, T. Ono, and Y. Tserkovnyak, Antiferromagnetic spintronics, Reviews of Modern Physics90, 015005 (2018)

    2018

  20. [20]

    M. Gu, Y. Liu, H. Zhu, K. Yananose, X. Chen, Y. Hu, A. Stroppa, and Q. Liu, Ferroelectric Switchable Altermagnetism, Physical Review Letters134, 106802 (2025)

    2025

  21. [21]

    ˇSmejkal, Altermagnetic multiferroics and altermagnetoelectric effect, arXiv:2411.19928[cond-mat.mtrl-sci]

    L. ˇSmejkal, Altermagnetic multiferroics and altermagnetoelectric effect, arXiv:2411.19928[cond-mat.mtrl-sci]

    Pith/arXiv arXiv

  22. [22]

    W. Sun, C. Yang, W. Wang, Y. Liu, X. Wang, S. Huang, and Z. Cheng, Proposing Altermagnetic-Ferroelectric Type-III Multiferroics with Robust Magnetoelectric Coupling, Advanced Materials37, 2502575 (2025)

    2025

  23. [23]

    Z. Zhu, X. Duan, J. Zhang, B. Hao, I. ˇZuti´ c, and T. Zhou, Two-dimensional ferroelectric altermagnets: From model to material realization, Nano Letters25, 9456 (2025)

    2025

  24. [24]

    K. M. Rabe, M. Dawber, C. Lichtensteiger, C. H. Ahn, and J.-M. Triscone, Modern physics of ferroelectrics: Essential background, inPhysics of Ferroelectrics: A Modern Perspective (Springer, 2007) pp. 1–30

    2007

  25. [25]

    N. A. Spaldin, A beginner’s guide to the modern theory of polarization, Journal of Solid State Chemistry195, 2 (2012)

    2012

  26. [26]

    [27] – Ref

    See supplemental material at http://xxx for Tight-binding model, Computational details, Co- ordinates of k-points for band structure calculations, Spin splitting across the entire Brillouin zone for MnTe, Comparison of TMR and spin-splitting, Real system examples–Mn 4Bi3NO15, Real system examples–Cr2S3, Real system examples–Bilayer AB2: FeI2, CoCl2, CoBr2...

  27. [27]

    Kresse and J

    G. Kresse and J. Furthm¨ uller, Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set, Physical Review B54, 11169 (1996)

    1996

  28. [28]

    Kresse and J

    G. Kresse and J. Hafner, Ab initio molecular dynamics for liquid metals, Physical Review B 47, 558 (1993)

    1993

  29. [29]

    J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized Gradient Approximation Made Simple, Physical Review Letters77, 3865 (1996). 13

    1996

  30. [30]

    S. L. Dudarev, G. A. Botton, S. Y. Savrasov, C. J. Humphreys, and A. P. Sutton, Electron- energy-loss spectra and the structural stability of nickel oxide: An LSDA+U study, Physical Review B57, 1505 (1998)

    1998

  31. [31]

    Kresse and D

    G. Kresse and D. Joubert, From ultrasoft pseudopotentials to the projector augmented-wave method, Physical Review B59, 1758 (1999)

    1999

  32. [32]

    P. E. Bl¨ ochl, Projector augmented-wave method, Physical Review B50, 17953 (1994)

    1994

  33. [33]

    R. D. King-Smith and D. Vanderbilt, Theory of polarization of crystalline solids, Physical Review B47, 1651 (1993)

    1993

  34. [34]

    Resta, Theory of the electric polarization in crystals, Ferroelectrics136, 51 (1992)

    R. Resta, Theory of the electric polarization in crystals, Ferroelectrics136, 51 (1992)

    1992

  35. [35]

    Resta, Macroscopic polarization in crystalline dielectrics: the geometric phase approach, Reviews of Modern Physics66, 899 (1994)

    R. Resta, Macroscopic polarization in crystalline dielectrics: the geometric phase approach, Reviews of Modern Physics66, 899 (1994)

    1994

  36. [36]

    Taylor, H

    J. Taylor, H. Guo, and J. Wang, Ab initio modeling of quantum transport properties of molecular electronic devices, Physical Review B63, 245407 (2001)

    2001

  37. [37]

    Brandbyge, J.-L

    M. Brandbyge, J.-L. Mozos, P. Ordej´ on, J. Taylor, and K. Stokbro, Density-functional method for nonequilibrium electron transport, Physical Review B65, 165401 (2002)

    2002

  38. [38]

    Smirnova, M

    O. Smirnova, M. Azuma, N. Kumada, Y. Kusano, M. Matsuda, Y. Shimakawa, T. Takei, Y. Yonesaki, and N. Kinomura, Synthesis, crystal structure, and magnetic properties of Bi3Mn4O12(NO3) oxynitrate comprising S=3/2 honeycomb lattice, Journal of the American Chemical Society131, 8313 (2009)

    2009

  39. [39]

    L. Bai, W. Feng, S. Liu, L. ˇSmejkal, Y. Mokrousov, and Y. Yao, Altermagnetism: Explor- ing new frontiers in magnetism and spintronics, Advanced Functional Materials34, 2409327 (2024)

    2024

  40. [40]

    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 degen- eracy, Nature626, 517 (2024)

    2024

  41. [41]

    X. Ren, J. Huang, P. Li, Y. Zhang, and Z.-X. Guo, Exotic Spintronic Properties of Transition- Metal Monolayers on Graphyne, Advanced Theory and Simulations5, 2100287 (2022)

    2022

  42. [42]

    B. Liu, X. Ren, X. Zhang, P. Li, Y. Dong, and Z.-X. Guo, Electric field tunable multi-state tunnel magnetoresistances in 2D van der waals magnetic heterojunctions, Applied Physics Letters122, 152408 (2023)

    2023

  43. [43]

    Shao, S.-H

    D.-F. Shao, S.-H. Zhang, M. Li, C.-B. Eom, and E. Y. Tsymbal, Spin-neutral currents for spintronics, Nature Communications12, 7061 (2021)

    2021

  44. [44]

    M. Zhao, G. Gou, X. Ding, and J. Sun, An ultrathin two-dimensional vertical ferroelectric tunneling junction based on CuInP 2S6 monolayer, Nanoscale12, 12522 (2020)

    2020

  45. [45]

    S. H. Park, H. J. Lee, M. H. Park, J. Kim, and H. W. Jang, Ferroelectric tunnel junctions: promise, achievements and challenges, Journal of Physics D: Applied Physics57, 253002 (2024)

    2024

This paper was first reviewed by deepseek-v4-flash on August 4, 2026.