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arxiv: 2508.21673 · v2 · submitted 2025-08-29 · ❄️ cond-mat.supr-con · cond-mat.str-el

Odd-Parity Magnetism in Fe-Based Superconductors

Reuel Dsouza , Andreas Kreisel , Brian M. Andersen , Daniel F. Agterberg , Morten H. Christensen This is my paper

Pith reviewed 2026-05-18 20:26 UTC · model grok-4.3

classification ❄️ cond-mat.supr-con cond-mat.str-el
keywords odd-parity magnetismFe-based superconductorscoplanar magnetic orderh-wave spin splittinginversion symmetry breakingnon-linear anomalous Hall effectEdelstein effect
0
0 comments X p. Extension

The pith

Fe-based superconductors with coplanar magnetic order realize an odd-parity magnetic state with h-wave spin splitting along kz.

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

This paper shows that Fe-based superconductors displaying coplanar magnetic order host an odd-parity magnetic phase. The phase breaks inversion symmetry while keeping time-reversal symmetry intact. Low-energy modeling combined with density-functional theory reveals that, without spin-orbit coupling, electron spins polarize along the out-of-plane momentum direction and split according to an h-wave form factor. The size of this splitting is controlled by out-of-plane hopping amplitudes and the positions of the hole and electron Fermi pockets. A reader would care because these common materials thereby become a platform for studying odd-parity magnetism and its possible coexistence with superconductivity.

Core claim

The Fe-based superconductors exhibiting coplanar magnetic order realize an odd-parity magnetic state by combining low-energy modeling with density-functional theory. In the absence of spin-orbit coupling, the electronic spins are polarized along the kz-direction and the splitting of the up and down states exhibits an h-wave form-factor. The magnitude of the splitting depends sensitively on specific parameters of the low-energy model, including specific out-of-plane hopping parameters and the Fermi energies of the hole- and electron-pockets. Despite breaking inversion symmetry and exhibiting a finite out-of-plane Berry curvature and non-linear anomalous Hall effect, the Edelstein effect is a.

What carries the argument

Low-energy electronic model of the coplanar magnetic order, whose out-of-plane hopping terms produce the h-wave spin-splitting form factor when the Fermi energies of hole and electron pockets are appropriately placed.

If this is right

  • The state produces a finite out-of-plane Berry curvature and a non-linear anomalous Hall effect.
  • The Edelstein effect is absent without spin-orbit coupling but acquires in-plane components once spin-orbit coupling is included.
  • The odd-parity magnetic order can in principle coexist with the unconventional superconductivity already present in these compounds.
  • The strength of the spin splitting is tunable through changes in out-of-plane hopping or pocket energies.

Where Pith is reading between the lines

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

  • Pressure or doping that alters the out-of-plane hoppings could be used to switch the odd-parity splitting on and off.
  • The combination of broken inversion symmetry with preserved time-reversal symmetry may stabilize pairing states that are otherwise forbidden.
  • Similar coplanar orders in other layered compounds could be reexamined for hidden h-wave spin textures.

Load-bearing premise

The low-energy model parameters, specifically the out-of-plane hopping amplitudes and the Fermi energies of the hole and electron pockets, can be chosen such that a finite h-wave spin splitting occurs while remaining consistent with the known coplanar magnetic order and other experimental constraints.

What would settle it

Momentum-resolved spin-polarized spectroscopy or ARPES that either detects or rules out an h-wave spin splitting along kz in a material with established coplanar magnetic order.

Figures

Figures reproduced from arXiv: 2508.21673 by Andreas Kreisel, Brian M. Andersen, Daniel F. Agterberg, Morten H. Christensen, Reuel Dsouza.

Figure 1
Figure 1. Figure 1: Coplanar magnetic order in Fe-based super￾conductors. (a) Crystal structure of a general Fe-based su￾perconductor in the P4/nmm space group with Pn/Ch de￾noting a pnictogen or chalcogen atom. The spacer layer can contain, e.g., lanthanides or alkali metals, or be empty. (b) Top-down view of the coplanar magnetic order. The gray square denotes the original unit cell while the black square denotes the magnet… view at source ↗
Figure 2
Figure 2. Figure 2: Momentum-space spin texture in the copla￾nar phase. (a) Fermi surface in the coplanar magnetic phase colored according to Sz(k). (b) and (c) show cuts of the Fermi surface at kz = 0 and kz = π/2, respectively, showing how the bands split away from the kz = 0 plane. Here, the mag￾netic order parameter ∆ = 60 meV. In (b) the Fermi surface is highlighted in black to make it visible. M, (ε1). Note that the fac… view at source ↗
Figure 3
Figure 3. Figure 3: Impact of spin-orbit coupling. Fermi sur￾face cross sections showing (a)–(b) [Sx(k) + Sy(k)] / √ 2, (c)– (d) [Sy(k) − Sx(k)] / √ 2, and (e)–(f) Sz(k) at kz = 0 and kz = π/2, respectively. The gray dashed lines denote the mirror planes with respect to which the spin projection is an￾tisymmetric; Sx(k) + Sy(k) transforms as px, Sy(k) − Sx(k) as py, and Sz(k) as h. Here, ∆ = 60 meV and λΓ = λM = 25 meV. In (e… view at source ↗
Figure 4
Figure 4. Figure 4: First-principles results. (a) Crystal struc￾ture of LaFeAsO. (b) Electronic structure of LaFeAsO ob￾tained from DFT along the cut Γ′ = (0, 0, 0.3)π to O = (0.28√ 2, 0.42√ 2, 0.3)π with coplanar magnetic order im￾posed. The electronic bands are plotted in blue while the spin splitting of the bands nearest the Fermi level is shown in red. (c) Spin splitting as a function of the magnetic or￾der parameter for … view at source ↗
Figure 5
Figure 5. Figure 5: Fermi surface of low-energy model. (a) shows the Fermi surface of the low-energy model using the parame￾ters listed in Table I including the weak out-of-plane disper￾sion. (b) shows a cut through the kz = 0 plane [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
read the original abstract

Odd-parity magnetism constitutes an intriguing phase of matter which breaks inversion symmetry while preserving time-reversal symmetry. Here we demonstrate that the Fe-based superconductors exhibiting coplanar magnetic order realize an odd-parity magnetic state by combining low-energy modeling with density-functional theory. In the absence of spin-orbit coupling, the electronic spins are polarized along the $k_z$-direction and the splitting of the up and down states exhibits an $h$-wave form-factor. The magnitude of the splitting depends sensitively on specific parameters of the low-energy model, including specific out-of-plane hopping parameters and the Fermi energies of the hole- and electron-pockets. Interestingly, despite this state breaking inversion symmetry and exhibiting a finite out-of-plane Berry curvature and non-linear anomalous Hall effect, the Edelstein effect vanishes. Incorporating spin-orbit coupling tilts the momentum-space electronic spins into the ($k_x,k_y$)-plane and imparts finite in-plane components to the Edelstein response. Our findings highlight the Fe-based superconductors as platforms for exploring odd-parity magnetism both on its own and coexisting with unconventional superconductivity.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript claims that Fe-based superconductors exhibiting coplanar magnetic order realize an odd-parity magnetic state. Combining a low-energy effective model with density-functional theory, the authors show that, in the absence of spin-orbit coupling, kz-polarized spins exhibit an h-wave spin splitting whose magnitude depends sensitively on out-of-plane hopping amplitudes and the Fermi energies of the hole and electron pockets. With spin-orbit coupling the spins tilt into the (kx,ky) plane, the Edelstein response acquires in-plane components, and a finite out-of-plane Berry curvature and nonlinear anomalous Hall effect are present. The work positions these materials as platforms for odd-parity magnetism, possibly coexisting with unconventional superconductivity.

Significance. If the low-energy parameters are shown to be robustly fixed by DFT and experiment rather than tuned to produce the desired splitting, the result would identify a concrete, experimentally accessible realization of odd-parity magnetism in a family of materials already known for superconductivity and magnetism. This would enable direct tests of inversion-symmetry breaking, Berry-curvature effects, and the interplay with superconducting order.

major comments (2)
  1. [Abstract and low-energy model] Abstract and the low-energy modeling section: the central claim that coplanar order realizes odd-parity magnetism requires a finite h-wave spin splitting of kz-polarized states. The abstract states that this splitting 'depends sensitively' on out-of-plane hopping parameters and the Fermi energies of the hole- and electron-pockets. The manuscript must demonstrate that the specific values obtained from the DFT fit (or other independent constraints) produce a nonzero splitting while remaining consistent with the observed coplanar order; otherwise the realization is not established and the result reduces to a parameter-tuned possibility.
  2. [DFT + low-energy model comparison] The weakest assumption identified in the stress-test note is load-bearing: if the DFT-derived out-of-plane hoppings and pocket energies instead yield vanishing or negligible h-wave splitting, the odd-parity state is not realized. The paper should report the numerical value of the splitting obtained with the unconstrained DFT parameters and show that it remains finite under reasonable variations.
minor comments (2)
  1. [Results section] Clarify the precise definition of the h-wave form factor (e.g., the angular dependence in the Brillouin zone) and provide an explicit expression or plot in the main text rather than only in supplementary material.
  2. [Edelstein effect discussion] The statement that the Edelstein effect vanishes without SOC should be accompanied by a brief symmetry argument or explicit calculation showing why the in-plane components are forbidden.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the thoughtful and constructive report. The comments correctly identify the need to explicitly demonstrate that the DFT-constrained parameters produce a finite h-wave splitting, rather than leaving the result dependent on unverified tuning. We address each major comment below and will revise the manuscript accordingly.

read point-by-point responses

  1. Referee: [Abstract and low-energy model] Abstract and the low-energy modeling section: the central claim that coplanar order realizes odd-parity magnetism requires a finite h-wave spin splitting of kz-polarized states. The abstract states that this splitting 'depends sensitively' on out-of-plane hopping parameters and the Fermi energies of the hole- and electron-pockets. The manuscript must demonstrate that the specific values obtained from the DFT fit (or other independent constraints) produce a nonzero splitting while remaining consistent with the observed coplanar order; otherwise the realization is not established and the result reduces to a parameter-tuned possibility.

    Authors: We agree that the central claim requires explicit verification with the DFT-derived parameters. The low-energy model parameters, including out-of-plane hoppings and pocket Fermi energies, were obtained by fitting to DFT calculations performed on Fe-based superconductors known to exhibit coplanar magnetic order. With these parameters the h-wave splitting is finite and the spin polarization remains along kz in the absence of spin-orbit coupling, consistent with the observed magnetic structure. In the revised manuscript we will add the explicit numerical value of the splitting (obtained directly from the unconstrained DFT fit) together with a brief discussion confirming consistency with the coplanar order. revision: yes

  2. Referee: [DFT + low-energy model comparison] The weakest assumption identified in the stress-test note is load-bearing: if the DFT-derived out-of-plane hoppings and pocket energies instead yield vanishing or negligible h-wave splitting, the odd-parity state is not realized. The paper should report the numerical value of the splitting obtained with the unconstrained DFT parameters and show that it remains finite under reasonable variations.

    Authors: We accept this criticism. The present manuscript highlights the sensitivity of the splitting but does not tabulate the concrete value obtained from the DFT fit. We will revise the text to report this numerical value and to show that the splitting remains finite (and of appreciable magnitude) under small variations of the out-of-plane hoppings and pocket energies that are still compatible with experimental Fermi-surface data and the stability of the coplanar magnetic phase. revision: yes

Circularity Check

0 steps flagged

Derivation self-contained via symmetry and DFT-constrained low-energy model

full rationale

The paper constructs a low-energy model informed by density-functional theory to examine the electronic structure under coplanar magnetic order. The odd-parity character and h-wave spin splitting follow directly from the symmetry-allowed terms in the model Hamiltonian once the magnetic order is imposed, with out-of-plane hoppings and pocket Fermi energies entering as standard tight-binding parameters constrained by DFT bands and known experimental order. No equation or result is shown to reduce by construction to a fitted input renamed as prediction, a self-citation chain, or an ansatz smuggled from prior work; the central demonstration remains independent of its inputs and externally falsifiable against DFT and experiment.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 0 invented entities

The central claim depends on the validity of a low-energy effective model whose parameters are tuned to the electronic structure of the real materials; no new particles or forces are postulated.

free parameters (2)
  • out-of-plane hopping parameters
    The magnitude of the spin splitting depends sensitively on these parameters.
  • Fermi energies of the hole- and electron-pockets
    These energies control the size of the h-wave splitting.
axioms (1)
  • domain assumption The low-energy model derived from DFT accurately captures the electronic states near the Fermi level in the presence of coplanar magnetic order.
    Invoked when combining low-energy modeling with density-functional theory.

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Works this paper leans on

67 extracted references · 67 canonical work pages

  1. [1]

    S. Ran, C. Eckberg, Q.-P. Ding, Y. Furukawa, T. Metz, S. R. Saha, I.-L. Liu, M. Zic, H. Kim, J. Paglione, and N. P. Butch, Nearly ferromagnetic spin-triplet supercon- ductivity, Science 365, 684 (2019)

    work page 2019

  2. [2]

    Ran, I.-L

    S. Ran, I.-L. Liu, Y. S. Eo, D. J. Campbell, P. M. Neves, W. T. Fuhrman, S. R. Saha, C. Eckberg, H. Kim, D. Graf, F. Balakirev, J. Singleton, J. Paglione, and N. P. Butch, Extreme magnetic field-boosted superconductiv- ity, Nature Physics 15, 1250 (2019)

    work page 2019

  3. [3]

    Zhang, L.-H

    S.-B. Zhang, L.-H. Hu, and T. Neupert, Finite- momentum Cooper pairing in proximitized altermagnets, Nature Communications 15, 1801 (2024)

    work page 2024

  4. [4]

    Pientka, L

    F. Pientka, L. I. Glazman, and F. von Oppen, Topological 6 superconducting phase in helical Shiba chains, Phys. Rev. B 88, 155420 (2013)

    work page 2013

  5. [5]

    Fulde and R

    P. Fulde and R. A. Ferrell, Superconductivity in a strong spin-exchange field, Phys. Rev. 135, A550 (1964)

    work page 1964

  6. [6]

    A. I. Larkin and Y. N. Ovchinnikov, Nonuniform state of superconductors, Zh. Eksp. Teor. Fiz. 47, 1136 (1964)

    work page 1964

  7. [7]

    D. J. Scalapino, A common thread: The pairing inter- action for unconventional superconductors, Rev. Mod. Phys. 84, 1383 (2012)

    work page 2012

  8. [8]

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

    work page 2022

  9. [9]

    Monthoux, D

    P. Monthoux, D. Pines, and G. G. Lonzarich, Supercon- ductivity without phonons, Nature 450, 1177 (2007)

    work page 2007

  10. [10]

    A. T. Rømer, T. A. Maier, A. Kreisel, I. Eremin, P. J. Hirschfeld, and B. M. Andersen, Pairing in the two- dimensional Hubbard model from weak to strong cou- pling, Phys. Rev. Res. 2, 013108 (2020)

    work page 2020

  11. [11]

    C. Wu, K. Sun, E. Fradkin, and S.-C. Zhang, Fermi liquid instabilities in the spin channel, Phys. Rev. B 75, 115103 (2007)

    work page 2007

  12. [12]

    Hayami, Y

    S. Hayami, Y. Yanagi, and H. Kusunose, Momentum- Dependent Spin Splitting by Collinear Antiferromagnetic Ordering, Journal of the Physical Society of Japan 88, 123702 (2019)

    work page 2019

  13. [13]

    I. I. Mazin, K. Koepernik, M. D. Johannes, R. Gonz´ alez- Hern´ andez, and L.ˇSmejkal, Prediction of unconventional magnetism in doped FeSb 2, Proceedings of the National Academy of Sciences 118, e2108924118 (2021)

    work page 2021

  14. [14]

    ˇSmejkal, J

    L. ˇSmejkal, J. Sinova, and T. Jungwirth, Beyond Con- ventional Ferromagnetism and Antiferromagnetism: A Phase with Nonrelativistic Spin and Crystal Rotation Symmetry, Phys. Rev. X 12, 031042 (2022)

    work page 2022

  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. X 12, 040002 (2022)

    work page 2022

  16. [16]

    Bhowal and N

    S. Bhowal and N. A. Spaldin, Ferroically Ordered Mag- netic Octupoles in d-Wave Altermagnets, Phys. Rev. X 14, 011019 (2024)

    work page 2024

  17. [17]

    P-wave magnets

    A. Birk Hellenes, T. Jungwirth, R. Jaeschke-Ubiergo, A. Chakraborty, J. Sinova, and L. ˇSmejkal, P-wave mag- nets, arXiv e-prints , arXiv:2309.01607 (2023)

    work page Pith review arXiv 2023

  18. [18]

    ˇSmejkal, J

    L. ˇSmejkal, J. Sinova, and T. Jungwirth, Emerging Re- search Landscape of Altermagnetism, Phys. Rev. X 12, 040501 (2022)

    work page 2022

  19. [19]

    ˇSmejkal, A

    L. ˇSmejkal, A. B. Hellenes, R. Gonz´ alez-Hern´ andez, J. Sinova, and T. Jungwirth, Giant and Tunneling Mag- netoresistance in Unconventional Collinear Antiferro- magnets with Nonrelativistic Spin-Momentum Coupling, Phys. Rev. X 12, 011028 (2022)

    work page 2022

  20. [20]

    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 Physics 32, 100991 (2023)

    work page 2023

  21. [21]

    Sødequist and T

    J. Sødequist and T. Olsen, Two-dimensional altermag- nets from high throughput computational screening: Symmetry requirements, chiral magnons, and spin-orbit effects, Applied Physics Letters 124, 182409 (2024)

    work page 2024

  22. [22]

    Y. Yu, M. B. Lyngby, T. Shishidou, M. Roig, A. Kreisel, M. Weinert, B. M. Andersen, and D. F. Agterberg, Odd- parity magnetism driven by antiferromagnetic exchange, Phys. Rev. Lett. 135, 046701 (2025)

    work page 2025

  23. [23]

    Lee and P

    C. Lee and P. M. R. Brydon, Inversion-asymmetric itiner- ant antiferromagnets by the space group symmetry, arXiv e-prints , arXiv:2502.16417 (2025)

    work page arXiv 2025

  24. [24]

    Krempask´ y, L.ˇSmejkal, S

    J. Krempask´ y, L.ˇSmejkal, S. W. D’Souza, M. Hajlaoui, G. Springholz, K. Uhl´ ıˇ rov´ a, F. Alarab, P. C. Constanti- nou, V. Strocov, D. Usanov, W. R. Pudelko, R. Gonz´ alez- Hern´ andez, A. Birk Hellenes, Z. Jansa, H. Reichlov´ a, et al. , Altermagnetic lifting of Kramers spin degeneracy, Nature 626, 517 (2024)

    work page 2024

  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, T. Denneulin, W. Shi, R. E. Dunin-Borkowski, S. Das, M. Kl¨ aui,et al., Direct observation of altermagnetic band splitting in CrSb thin films, Nature Communications 15, 2116 (2024)

    work page 2024

  26. [26]

    Reichlova, R

    H. Reichlova, R. Lopes Seeger, R. Gonz´ alez-Hern´ andez, I. Kounta, R. Schlitz, D. Kriegner, P. Ritzinger, M. Lammel, M. Leivisk¨ a, A. Birk Hellenes, K. Olejn´ ık, V. Petˇ riˇ cek, P. Doleˇ zal, L. Horak, E. Schmoranzerova, et al. , Observation of a spontaneous anomalous Hall re- sponse in the Mn5Si3 d-wave altermagnet candidate, Na- ture Communications...

    work page 2024

  27. [27]

    R. B. Regmi, H. Bhandari, B. Thapa, Y. Hao, N. Sharma, J. McKenzie, X. Chen, A. Nayak, M. El Gazzah, B. G. M´ arkus, L. Forr´ o, X. Liu, H. Cao, J. F. Mitchell, I. I. Mazin, and N. J. Ghimire, Altermagnetism in the layered intercalated transition metal dichalcogenide CoNb 4Se8, Nature Communications 16, 4399 (2025)

    work page 2025

  28. [28]

    Candelora, M

    C. Candelora, M. Xu, S. Cheng, A. De Vita, D. Ro- manin, C. Bigi, M. Bang Petersen, A. LaFleur, M. Ca- landra, J. Miwa, Y. Hwang, Z. Wang, F. Mazzola, and I. Zeljkovic, Discovery of intertwined spin and charge density waves in a layered altermagnet, arXiv e-prints , arXiv:2503.03716 (2025)

    work page arXiv 2025

  29. [29]

    Jiang, M

    B. Jiang, M. Hu, J. Bai, Z. Song, C. Mu, G. Qu, W. Li, W. Zhu, H. Pi, Z. Wei, Y.-J. Sun, Y. Huang, X. Zheng, Y. Peng, L. He, et al. , A metallic room-temperature d- wave altermagnet, Nature Physics 21, 754 (2025)

    work page 2025

  30. [30]

    Yamada, M

    R. Yamada, M. T. Birch, P. R. Baral, S. Okumura, R. Nakano, S. Gao, Y. Ishihara, K. K. Kolincio, I. Be- lopolski, H. Sagayama, H. Nakao, K. Ohishi, T. Naka- jima, Y. Tokura, T.-h. Arima, Y. Motome, M. M. Hirschmann, and M. Hirschberger, Gapping the spin- nodal planes of an anisotropic p-wave magnet to in- duce a large anomalous Hall effect, arXiv e-prints...

    work page arXiv 2025

  31. [31]

    Q. Song, S. Stavri´ c, P. Barone, A. Droghetti, D. S. An- tonenko, J. W. F. Venderbos, C. A. Occhialini, B. Ilyas, E. Erge¸ cen, N. Gedik, S.-W. Cheong, R. M. Fernandes, S. Picozzi, and R. Comin, Electrical switching of ap-wave magnet, Nature 642, 64 (2025)

    work page 2025

  32. [32]

    D. H. Lu, M. Yi, S.-K. Mo, A. S. Erickson, J. Analytis, J.-H. Chu, D. J. Singh, Z. Hussain, T. H. Geballe, I. R. Fisher, and Z.-X. Shen, Electronic structure of the iron- based superconductor LaOFeP, Nature 455, 81 (2008)

    work page 2008

  33. [33]

    Eschrig and K

    H. Eschrig and K. Koepernik, Tight-binding models for the iron-based superconductors, Phys. Rev. B 80, 104503 (2009)

    work page 2009

  34. [34]

    Cvetkovic and O

    V. Cvetkovic and O. Vafek, Space group symmetry, spin- orbit coupling, and the low-energy effective Hamiltonian for iron-based superconductors, Phys. Rev. B 88, 134510 (2013)

    work page 2013

  35. [35]

    R. M. Fernandes and A. V. Chubukov, Low-energy micro- scopic models for iron-based superconductors: a review, 7 Reports on Progress in Physics 80, 014503 (2016)

    work page 2016

  36. [36]

    Kreisel, P

    A. Kreisel, P. J. Hirschfeld, and B. M. Andersen, On the Remarkable Superconductivity of FeSe and Its Close Cousins, Symmetry 12, 10.3390/sym12091402 (2020)

    work page doi:10.3390/sym12091402 2020

  37. [37]

    G. R. Stewart, Superconductivity in iron compounds, Rev. Mod. Phys. 83, 1589 (2011)

    work page 2011

  38. [38]

    Stadel, D

    R. Stadel, D. D. Khalyavin, P. Manuel, K. Yokoyama, S. Lapidus, M. H. Christensen, R. M. Fernandes, D. Phelan, D. Y. Chung, R. Osborn, S. Rosenkranz, and O. Chmaissem, Multiple magnetic orders in LaFeAs1−xPxO uncover universality of iron-pnictide su- perconductors, Communications Physics 5, 146 (2022)

    work page 2022

  39. [39]

    J. M. Allred, K. M. Taddei, D. E. Bugaris, M. J. Krogstad, S. H. Lapidus, D. Y. Chung, H. Claus, M. G. Kanatzidis, D. E. Brown, J. Kang, R. M. Fernandes, I. Eremin, S. Rosenkranz, O. Chmaissem, and R. Os- born, Double-q spin-density wave in iron arsenide super- conductors, Nature Physics 12, 493 (2016)

    work page 2016

  40. [40]

    Lorenzana, G

    J. Lorenzana, G. Seibold, C. Ortix, and M. Grilli, Com- peting Orders in FeAs Layers, Phys. Rev. Lett. 101, 186402 (2008)

    work page 2008

  41. [41]

    J. Kang, X. Wang, A. V. Chubukov, and R. M. Fernan- des, Interplay between tetragonal magnetic order, stripe magnetism, and superconductivity in iron-based materi- als, Phys. Rev. B 91, 121104 (2015)

    work page 2015

  42. [42]

    M. N. Gastiasoro and B. M. Andersen, Competing mag- netic double- Q phases and superconductivity-induced reentrance of C2 magnetic stripe order in iron pnictides, Phys. Rev. B 92, 140506 (2015)

    work page 2015

  43. [43]

    M. H. Christensen, J. Kang, B. M. Andersen, I. Eremin, and R. M. Fernandes, Spin reorientation driven by the in- terplay between spin-orbit coupling and Hund’s rule cou- pling in iron pnictides, Phys. Rev. B 92, 214509 (2015)

    work page 2015

  44. [44]

    M. H. Christensen, D. D. Scherer, P. Kotetes, and B. M. Andersen, Role of multiorbital effects in the magnetic phase diagram of iron pnictides, Phys. Rev. B 96, 014523 (2017)

    work page 2017

  45. [45]

    M. D. Lumsden and A. D. Christianson, Magnetism in Fe-based superconductors, Journal of Physics: Con- densed Matter 22, 203203 (2010)

    work page 2010

  46. [46]

    Dai, Antiferromagnetic order and spin dynamics in iron-based superconductors, Rev

    P. Dai, Antiferromagnetic order and spin dynamics in iron-based superconductors, Rev. Mod. Phys. 87, 855 (2015)

    work page 2015

  47. [47]

    S. Avci, O. Chmaissem, J. M. Allred, S. Rosenkranz, I. Eremin, A. V. Chubukov, D. E. Bugaris, D. Y. Chung, M. G. Kanatzidis, J.-P. Castellan, J. A. Schlueter, H. Claus, D. D. Khalyavin, P. Manuel, A. Daoud- Aladine, and R. Osborn, Magnetically driven suppression of nematic order in an iron-based superconductor, Nature Communications 5, 3845 (2014)

    work page 2014

  48. [48]

    W. R. Meier, Q.-P. Ding, A. Kreyssig, S. L. Bud’ko, A. Sapkota, K. Kothapalli, V. Borisov, R. Valent´ ı, C. D. Batista, P. P. Orth, R. M. Fernandes, A. I. Gold- man, Y. Furukawa, A. E. B¨ ohmer, and P. C. Canfield, Hedgehog spin-vortex crystal stabilized in a hole-doped iron-based superconductor, npj Quantum Materials 3, 5 (2018)

    work page 2018

  49. [49]

    S. Wu, W. A. Phelan, L. Liu, J. R. Morey, J. A. Tutma- her, J. C. Neuefeind, A. Huq, M. B. Stone, M. Feygenson, D. W. Tam, B. A. Frandsen, B. Trump, C. Wan, S. R. Dunsiger, T. M. McQueen, Y. J. Uemura, and C. L. Bro- holm, Incommensurate Magnetism Near Quantum Criti- cality in CeNiAsO, Phys. Rev. Lett. 122, 197203 (2019)

    work page 2019

  50. [50]

    A. V. Chubukov, D. V. Efremov, and I. Eremin, Mag- netism, superconductivity, and pairing symmetry in iron- based superconductors, Phys. Rev. B 78, 134512 (2008)

    work page 2008

  51. [51]

    Si and E

    Q. Si and E. Abrahams, Strong correlations and magnetic frustration in the high Tc iron pnictides, Phys. Rev. Lett. 101, 076401 (2008)

    work page 2008

  52. [52]

    Yin, C.-C

    W.-G. Yin, C.-C. Lee, and W. Ku, Unified Picture for Magnetic Correlations in Iron-Based Superconductors, Phys. Rev. Lett. 105, 107004 (2010)

    work page 2010

  53. [53]

    W. Lv, F. Kr¨ uger, and P. Phillips, Orbital ordering and unfrustrated ( π, 0) magnetism from degenerate double exchange in the iron pnictides, Phys. Rev. B 82, 045125 (2010)

    work page 2010

  54. [54]

    P. Dai, J. Hu, and E. Dagotto, Magnetism and its micro- scopic origin in iron-based high-temperature supercon- ductors, Nature Physics 8, 709 (2012)

    work page 2012

  55. [55]

    Supplementary Material containing details of the pertur- bative calculation of the spin splitting and the calcula- tion of the Edelstein and anomalous Hall effects within the low energy model, as well as additional DFT results

    work page

  56. [56]

    Sodemann and L

    I. Sodemann and L. Fu, Quantum Nonlinear Hall Effect Induced by Berry Curvature Dipole in Time-Reversal In- variant Materials, Phys. Rev. Lett. 115, 216806 (2015)

    work page 2015

  57. [57]

    Z. Z. Du, H.-Z. Lu, and X. C. Xie, Nonlinear Hall effects, Nature Reviews Physics 3, 744 (2021)

    work page 2021

  58. [58]

    A. I. Coldea and M. D. Watson, The key ingredients of the electronic structure of FeSe, Annual Review of Con- densed Matter Physics 9, 125 (2018)

    work page 2018

  59. [59]

    S. V. Borisenko, D. V. Evtushinsky, Z.-H. Liu, I. Moro- zov, R. Kappenberger, S. Wurmehl, B. B¨ uchner, A. N. Yaresko, T. K. Kim, M. Hoesch, T. Wolf, and N. D. Zhi- gadlo, Direct observation of spin–orbit coupling in iron- based superconductors, Nature Physics 12, 311 (2016)

    work page 2016

  60. [60]

    M. H. Christensen, J. Kang, and R. M. Fernandes, In- tertwined spin-orbital coupled orders in the iron-based superconductors, Phys. Rev. B 100, 014512 (2019)

    work page 2019

  61. [61]

    Koepernik and H

    K. Koepernik and H. Eschrig, Full-potential nonorthog- onal local-orbital minimum-basis band-structure scheme, Phys. Rev. B 59, 1743 (1999)

    work page 1999

  62. [62]

    Miyake, K

    T. Miyake, K. Nakamura, R. Arita, and M. Imada, Com- parison of Ab initio Low-Energy Models for LaFePO, LaFeAsO, BaFe2As2, LiFeAs, FeSe, and FeTe: Electron Correlation and Covalency, Journal of the Physical Soci- ety of Japan 79, 044705 (2010)

    work page 2010

  63. [63]

    K. Iida, Y. Nagai, S. Ishida, M. Ishikado, N. Murai, A. D. Christianson, H. Yoshida, Y. Inamura, H. Nakamura, A. Nakao, K. Munakata, D. Kagerbauer, M. Eisterer, K. Kawashima, Y. Yoshida, H. Eisaki, and A. Iyo, Co- existing spin resonance and long-range magnetic order of Eu in EuRbFe4As4, Phys. Rev. B 100, 014506 (2019)

    work page 2019

  64. [64]

    J. M. Wilde, A. Kreyssig, D. Vaknin, N. S. Sangeetha, B. Li, W. Tian, P. P. Orth, D. C. Johnston, B. G. Ue- land, and R. J. McQueeney, Helical magnetic ordering in Sr(Co1−xNix)2As2, Phys. Rev. B 100, 161113 (2019)

    work page 2019

  65. [65]

    Nedi´ c, M

    A.-M. Nedi´ c, M. H. Christensen, Y. Lee, B. Li, B. G. Ueland, R. M. Fernandes, R. J. McQueeney, L. Ke, and P. P. Orth, Competing magnetic fluctuations and orders in a multiorbital model of doped SrCo 2As2, Phys. Rev. B 108, 245149 (2023)

    work page 2023

  66. [66]

    B. Li, Y. Sizyuk, N. S. Sangeetha, J. M. Wilde, P. Das, W. Tian, D. C. Johnston, A. I. Goldman, A. Kreyssig, P. P. Orth, R. J. McQueeney, and B. G. Ueland, Antifer- romagnetic stacking of ferromagnetic layers and doping- controlled phase competition in Ca 1−xSrxCo2−yAs2, Phys. Rev. B 100, 024415 (2019). 8 εΓ ε1 ε3 1/(2mΓ) 1 /(2m1) 1 /(2m3) 132 −400 −647 −...

    work page 2019

  67. [67]

    Cvetkovic and Z

    V. Cvetkovic and Z. Tesanovic, Multiband magnetism and superconductivity in Fe-based compounds, Euro- physics Letters 85, 37002 (2009). END MA TTER A. Low-energy model The parameters used in the low-energy model are given in Table I. The parameters controlling the in-plane dispersion are obtained from fitting the k · p-model of Ref. [34] to the tight-bind...

    work page 2009