pith. sign in

arxiv: 2509.05620 · v2 · submitted 2025-09-06 · ❄️ cond-mat.mes-hall · cond-mat.mtrl-sci· cond-mat.other

Quantization of spin circular photogalvanic effect in altermagnetic Weyl semimetals

Hiroki Yoshida , Jan Priessnitz , Libor \v{S}mejkal , Shuichi Murakami This is my paper

Pith reviewed 2026-05-18 18:22 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall cond-mat.mtrl-scicond-mat.other
keywords altermagnetsWeyl semimetalsphotogalvanic effectspin currentssymmetry groupsoptical responsemagnetic materials
0
0 comments X

The pith

Altermagnetic Weyl semimetals generate a quantized spin current under circularly polarized light, an effect forbidden by symmetry in antiferromagnets.

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

The paper establishes that a spin-current version of the circular photogalvanic effect can be quantized in certain Weyl semimetals. This response arises only when the magnetic order belongs to the altermagnetic class. Antiferromagnets lack the symmetry that permits the necessary second-order spin response. By using spin point groups to classify allowed responses, the authors show which crystal symmetries support the effect. They then build a model Hamiltonian and perform first-principles calculations to find a concrete material where the Weyl points and the quantized response coexist.

Core claim

In altermagnetic Weyl semimetals the spin circular photogalvanic effect is quantized because the spin space group symmetries both enforce Weyl points and allow a second-order spin current that is linear in the light intensity and circular polarization. This quantization is unique to altermagnets; the corresponding spin point group of antiferromagnets forbids the response altogether.

What carries the argument

Spin point group classification of second-order spin-current responses, which reveals that the quantized circular photogalvanic effect for spin is permitted solely in altermagnets.

If this is right

  • The classification identifies all symmetry-allowed second-order spin responses across magnetic groups.
  • A symmetry-guided tight-binding model explicitly realizes the quantized spin photocurrent.
  • First-principles calculations locate Weyl crossings in a specific altermagnetic material candidate.

Where Pith is reading between the lines

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

  • Detection of this spin current could serve as a direct optical readout of altermagnetic order.
  • Similar quantized responses might appear in other frequency regimes or under different light polarizations.
  • The approach could generalize to predict new spintronic phenomena in other symmetry-broken phases.

Load-bearing premise

That the spin point group analysis exhaustively lists every possible second-order term in the spin current without omissions from higher-order or extrinsic contributions.

What would settle it

A direct measurement showing that the spin photocurrent in an altermagnetic Weyl semimetal is either unquantized or absent when the light is circularly polarized.

Figures

Figures reproduced from arXiv: 2509.05620 by Hiroki Yoshida, Jan Priessnitz, Libor \v{S}mejkal, Shuichi Murakami.

Figure 1
Figure 1. Figure 1: FIG. 1. Schematic illustration of the quantized spin circular [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Calculation of the conductivity tensor for a tight [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: (c) shows the band structure along the same path as [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
read the original abstract

We theoretically predict a spin-current analog of the quantized circular photogalvanic effect in Weyl semimetals. This phenomenon is forbidden in antiferromagnets by symmetry but uniquely allowed in altermagnets, highlighting a novel and intrinsic characteristic of altermagnetism. To systematically explore second-order spin current responses, we classify all symmetry-allowed responses based on spin point groups. Furthermore, we provide a comprehensive classification of altermagnetic Weyl semimetals by identifying spin space groups that host symmetry-enforced Weyl points. Utilizing this classification, we construct a symmetry-guided tight-binding model and confirm our predictions. Finally, we identify Weyl crossings in a material candidate via first-principle calculations. Our work unveils a distinctive optical response of altermagnets, paving the way for a new frontier in altermagnetism.

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

1 major / 1 minor

Summary. The paper predicts a quantized spin-current analog of the circular photogalvanic effect (CPGE) in altermagnetic Weyl semimetals. This response is claimed to be forbidden by symmetry in antiferromagnets but uniquely allowed in altermagnets. The authors classify all symmetry-allowed second-order spin current responses using spin point groups, provide a classification of altermagnetic Weyl semimetals via spin space groups, construct a symmetry-guided tight-binding model to demonstrate the quantization, and identify Weyl crossings in a material candidate using first-principles calculations.

Significance. If the quantization and the symmetry-based distinction hold, the result would establish a distinctive optical signature of altermagnetism that is absent in conventional antiferromagnets, with potential implications for spintronic detection of altermagnetic order. The symmetry-guided model construction and first-principles support are positive elements that strengthen the work when the central symmetry argument is independently verified.

major comments (1)
  1. The central claim that the quantized spin CPGE is forbidden in antiferromagnets but permitted only in altermagnets rests on the spin point group classification of second-order spin current responses. The manuscript does not report an independent cross-check against full magnetic space group tables or the Bilbao Crystallographic Server to confirm that the relevant tensor components identically vanish under AFM symmetries. If any operation retained in the complete magnetic group is missed by the spin-group reduction, the prohibition fails and the uniqueness to altermagnets does not hold.
minor comments (1)
  1. The distinction between spin point groups and spin space groups is introduced in the abstract and classification sections but could be explained more explicitly in the main text for readers outside the immediate subfield.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading and constructive feedback on our manuscript. We address the major comment regarding the symmetry classification below and outline the revisions we will make to strengthen the presentation.

read point-by-point responses

  1. Referee: The central claim that the quantized spin CPGE is forbidden in antiferromagnets but permitted only in altermagnets rests on the spin point group classification of second-order spin current responses. The manuscript does not report an independent cross-check against full magnetic space group tables or the Bilbao Crystallographic Server to confirm that the relevant tensor components identically vanish under AFM symmetries. If any operation retained in the complete magnetic group is missed by the spin-group reduction, the prohibition fails and the uniqueness to altermagnets does not hold.

    Authors: We thank the referee for raising this important point on verification. Spin point groups provide the natural and minimal symmetry framework for classifying spin-dependent responses in altermagnets, as they encode the coupled spin-lattice symmetries that distinguish altermagnetism from conventional antiferromagnetism. In the latter, the presence of effective time-reversal symmetry (arising from combined operations in the full magnetic space group) forces the relevant second-order spin-current tensor components to vanish, which is already captured by the spin-point-group reduction used in our classification. Nevertheless, to directly address the concern and eliminate any ambiguity, we will add an explicit cross-check in the revised manuscript. This will include representative examples drawn from magnetic space group tables and the Bilbao Crystallographic Server, confirming that the quantized spin CPGE tensor is identically zero under standard AFM symmetries while remaining allowed under the spin space groups of altermagnets. These additions will be placed in a new subsection or supplementary note and will not alter the central conclusions or the tight-binding and first-principles results. revision: yes

Circularity Check

0 steps flagged

Symmetry classification and explicit model construction yield independent verification of the quantized spin CPGE

full rationale

The derivation begins with a symmetry classification of second-order spin-current responses under spin point groups, followed by identification of symmetry-enforced Weyl points in altermagnetic spin space groups. A tight-binding model is then constructed to respect these symmetries, and the spin CPGE is computed directly from it, producing the quantized value as a consequence of the allowed tensor components and topological properties. First-principles calculations independently locate candidate Weyl crossings. No equation or result reduces by construction to a fitted parameter, self-citation chain, or renamed input; the central claim follows from standard group-theoretic enumeration and explicit Hamiltonian diagonalization rather than tautological re-expression of the premises.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The paper rests on spin point group classifications and symmetry-enforced Weyl points whose validity is assumed from domain knowledge; no explicit free parameters or invented entities are stated in the abstract.

axioms (1)
  • domain assumption Spin point groups classify all symmetry-allowed second-order spin current responses.
    Invoked to systematically explore responses and identify those unique to altermagnets.

pith-pipeline@v0.9.0 · 5692 in / 1282 out tokens · 55614 ms · 2026-05-18T18:22:49.714913+00:00 · methodology

discussion (0)

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

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

85 extracted references · 85 canonical work pages · 1 internal anchor

  1. [1]

    ˇZuti´ c, J

    I. ˇZuti´ c, J. Fabian, and S. Das Sarma, Spintronics: Fun- damentals and applications, Rev. Mod. Phys.76, 323 (2004)

    work page 2004

  2. [2]

    Bader and S

    S. Bader and S. Parkin, Spintronics, Annu. Rev. Con- dens. Matter Phys.1, 71 (2010)

    work page 2010

  3. [3]

    Baltz, A

    V. Baltz, A. Manchon, M. Tsoi, T. Moriyama, T. Ono, and Y. Tserkovnyak, Antiferromagnetic spintronics, Rev. Mod. Phys.90, 015005 (2018)

    work page 2018

  4. [4]

    Jungwirth, X

    T. Jungwirth, X. Marti, P. Wadley, and J. Wunderlich, Antiferromagnetic spintronics, Nat. Nanotechnol.11, 231 (2016)

    work page 2016

  5. [5]

    V. M. Edelstein, Spin polarization of conduction elec- trons induced by electric current in two-dimensional asymmetric electron systems, Solid State Commun.73, 233 (1990). 6

    work page 1990

  6. [6]

    S. D. Ganichev, E. L. Ivchenko, V. V. Bel’kov, S. A. Tarasenko, M. Sollinger, D. Weiss, W. Wegscheider, and W. Prettl, Spin-galvanic effect, Nature417, 153 (2002)

    work page 2002

  7. [7]

    Dyakonov and V

    M. Dyakonov and V. Perel, Current-induced spin orien- tation of electrons in semiconductors, Phys. Lett.35A, 459 (1971)

    work page 1971

  8. [8]

    J. E. Hirsch, Spin Hall Effect, Phys. Rev. Lett.83, 1834 (1999)

    work page 1999

  9. [9]

    Murakami, N

    S. Murakami, N. Nagaosa, and S.-C. Zhang, Dissipation- less Quantum Spin Current at Room Temperature, Sci- ence301, 1348 (2003)

    work page 2003

  10. [10]

    Sinova, D

    J. Sinova, D. Culcer, Q. Niu, N. A. Sinitsyn, T. Jung- wirth, and A. H. MacDonald, Universal Intrinsic Spin Hall Effect, Phys. Rev. Lett.92, 126603 (2004)

    work page 2004

  11. [11]

    Y. K. Kato, R. C. Myers, A. C. Gossard, and D. D. Awschalom, Observation of the Spin Hall Effect in Semi- conductors, Science306, 1910 (2004)

    work page 1910

  12. [12]

    Wunderlich, B

    J. Wunderlich, B. Kaestner, J. Sinova, and T. Jung- wirth, Experimental Observation of the Spin-Hall Effect in a Two-Dimensional Spin-Orbit Coupled Semiconduc- tor System, Phys. Rev. Lett.94, 047204 (2005)

    work page 2005

  13. [13]

    Uchida, S

    K. Uchida, S. Takahashi, K. Harii, J. Ieda, W. Koshibae, K. Ando, S. Maekawa, and E. Saitoh, Observation of the spin Seebeck effect, Nature455, 778 (2008)

    work page 2008

  14. [14]

    Uchida, T

    K.-i. Uchida, T. Nonaka, T. Ota, and E. Saitoh, Lon- gitudinal spin-Seebeck effect in sintered polycrystalline (Mn,Zn)Fe2O4, Appl. Phys. Lett.97, 262504 (2010)

    work page 2010

  15. [15]

    C. M. Jaworski, J. Yang, S. Mack, D. D. Awschalom, J. P. Heremans, and R. C. Myers, Observation of the spin- Seebeck effect in a ferromagnetic semiconductor, Nature Mater.9, 898 (2010)

    work page 2010

  16. [16]

    J. Xiao, G. E. W. Bauer, K.-c. Uchida, E. Saitoh, and S. Maekawa, Theory of magnon-driven spin Seebeck ef- fect, Phys. Rev. B81, 214418 (2010)

    work page 2010

  17. [17]

    Cheng, Y

    S.-g. Cheng, Y. Xing, Q.-f. Sun, and X. C. Xie, Spin Nernst effect and Nernst effect in two-dimensional elec- tron systems, Phys. Rev. B78, 045302 (2008)

    work page 2008

  18. [18]

    Liu and X

    X. Liu and X. C. Xie, Spin Nernst effect in the absence of a magnetic field, Solid State Commun.150, 471 (2010)

    work page 2010

  19. [19]

    Tauber, M

    K. Tauber, M. Gradhand, D. V. Fedorov, and I. Mertig, Extrinsic Spin Nernst Effect from First Principles, Phys. Rev. Lett.109, 026601 (2012)

    work page 2012

  20. [20]

    Wimmer, D

    S. Wimmer, D. K¨ odderitzsch, K. Chadova, and H. Ebert, First-principles linear response description of the spin Nernst effect, Phys. Rev. B88, 201108 (2013)

    work page 2013

  21. [21]

    Meyer, Y.-T

    S. Meyer, Y.-T. Chen, S. Wimmer, M. Altham- mer, T. Wimmer, R. Schlitz, S. Gepr¨ ags, H. Huebl, D. K¨ odderitzsch, H. Ebert, G. E. W. Bauer, R. Gross, and S. T. B. Goennenwein, Observation of the spin Nernst effect, Nature Mater.16, 977 (2017)

    work page 2017

  22. [22]

    Sheng, Y

    P. Sheng, Y. Sakuraba, Y.-C. Lau, S. Takahashi, S. Mi- tani, and M. Hayashi, The spin Nernst effect in tungsten, Sci. Adv.3, e1701503 (2017)

    work page 2017

  23. [23]

    S. M. Young, F. Zheng, and A. M. Rappe, Prediction of a Linear Spin Bulk Photovoltaic Effect in Antiferromag- nets, Phys. Rev. Lett.110, 057201 (2013)

    work page 2013

  24. [24]

    Xiao, D.-F

    R.-C. Xiao, D.-F. Shao, Y.-H. Li, and H. Jiang, Spin photogalvanic effect in two-dimensional collinear antifer- romagnets, npj Quantum Mater.6, 1 (2021)

    work page 2021

  25. [25]

    R. Fei, W. Song, L. Pusey-Nazzaro, and L. Yang,P T- Symmetry-Enabled Spin Circular Photogalvanic Effect in Antiferromagnetic Insulators, Phys. Rev. Lett.127, 207402 (2021)

    work page 2021

  26. [26]

    H. Xu, H. Wang, J. Zhou, and J. Li, Pure spin photocur- rent in non-centrosymmetric crystals: bulk spin photo- voltaic effect, Nat. Commun.12, 4330 (2021)

    work page 2021

  27. [27]

    R.-C. Xiao, Y. J. Jin, and H. Jiang, Spin photovoltaic effect in antiferromagnetic materials: Mechanisms, sym- metry constraints, and recent progress, APL Mater.11, 070903 (2023)

    work page 2023

  28. [28]

    R. D. R. Bhat and J. E. Sipe, Optically Injected Spin Currents in Semiconductors, Phys. Rev. Lett.85, 5432 (2000)

    work page 2000

  29. [29]

    R. D. R. Bhat, F. Nastos, A. Najmaie, and J. E. Sipe, Pure Spin Current from One-Photon Absorption of Lin- early Polarized Light in Noncentrosymmetric Semicon- ductors, Phys. Rev. Lett.94, 096603 (2005)

    work page 2005

  30. [30]

    H. Zhao, X. Pan, A. L. Smirl, R. D. R. Bhat, A. Najmaie, J. E. Sipe, and H. M. van Driel, Injection of ballistic pure spin currents in semiconductors by a single-color linearly polarized beam, Phys. Rev. B72, 201302 (2005)

    work page 2005

  31. [31]

    Kraut and R

    W. Kraut and R. von Baltz, Anomalous bulk photo- voltaic effect in ferroelectrics: A quadratic response the- ory, Phys. Rev. B19, 1548 (1979)

    work page 1979

  32. [32]

    V. I. Belinicher and B. I. Sturman, The photogalvanic effect in media lacking a center of symmetry, Sov. Phys. Usp.23, 199 (1980)

    work page 1980

  33. [33]

    von Baltz and W

    R. von Baltz and W. Kraut, Theory of the bulk pho- tovoltaic effect in pure crystals, Phys. Rev. B23, 5590 (1981)

    work page 1981

  34. [34]

    Aversa and J

    C. Aversa and J. E. Sipe, Nonlinear optical susceptibili- ties of semiconductors: Results with a length-gauge anal- ysis, Phys. Rev. B52, 14636 (1995)

    work page 1995

  35. [35]

    J. E. Sipe and A. I. Shkrebtii, Second-order optical re- sponse in semiconductors, Phys. Rev. B61, 5337 (2000)

    work page 2000

  36. [36]

    V. M. Fridkin, Bulk photovoltaic effect in noncentrosym- metric crystals, Crystallogr. Rep.46, 654 (2001)

    work page 2001

  37. [37]

    Morimoto and N

    T. Morimoto and N. Nagaosa, Topological aspects of non- linear excitonic processes in noncentrosymmetric crys- tals, Phys. Rev. B94, 035117 (2016)

    work page 2016

  38. [38]

    Morimoto and N

    T. Morimoto and N. Nagaosa, Topological nature of non- linear optical effects in solids, Sci. Adv.2, e1501524 (2016)

    work page 2016

  39. [39]

    Q. Ma, A. G. Grushin, and K. S. Burch, Topology and geometry under the nonlinear electromagnetic spotlight, Nat. Mater.20, 1601 (2021)

    work page 2021

  40. [40]

    Ahn, G.-Y

    J. Ahn, G.-Y. Guo, N. Nagaosa, and A. Vishwanath, Riemannian geometry of resonant optical responses, Nat. Phys.18, 290 (2022)

    work page 2022

  41. [41]

    Hsu, J.-S

    H.-C. Hsu, J.-S. You, J. Ahn, and G.-Y. Guo, Nonlin- ear photoconductivities and quantum geometry of chiral multifold fermions, Phys. Rev. B107, 155434 (2023)

    work page 2023

  42. [42]

    Morimoto, S

    T. Morimoto, S. Kitamura, and N. Nagaosa, Geometric Aspects of Nonlinear and Nonequilibrium Phenomena, J. Phys. Soc. Jpn.92, 072001 (2023)

    work page 2023

  43. [43]

    W. J. Jankowski, A. S. Morris, Z. Davoyan, A. Bouhon, F. N. ¨Unal, and R.-J. Slager, Non-Abelian Hopf-Euler insulators, Phys. Rev. B110, 075135 (2024)

    work page 2024

  44. [44]

    Alexandradinata, Quantization of intraband and in- terband Berry phases in the shift current, Phys

    A. Alexandradinata, Quantization of intraband and in- terband Berry phases in the shift current, Phys. Rev. B 110, 075159 (2024)

    work page 2024

  45. [45]

    W. J. Jankowski and R.-J. Slager, Quantized Integrated Shift Effect in Multigap Topological Phases, Phys. Rev. Lett.133, 186601 (2024)

    work page 2024

  46. [46]

    Avdoshkin, J

    A. Avdoshkin, J. Mitscherling, and J. E. Moore, Multi- state Geometry of Shift Current and Polarization, Phys. Rev. Lett.135, 066901 (2025). 7

    work page 2025

  47. [47]

    Mitscherling, A

    J. Mitscherling, A. Avdoshkin, and J. E. Moore, Gauge- invariant projector calculus for quantum state geometry and applications to observables in crystals, Phys. Rev. B 112, 085104 (2025)

    work page 2025

  48. [48]

    de Juan, A

    F. de Juan, A. G. Grushin, T. Morimoto, and J. E. Moore, Quantized circular photogalvanic effect in Weyl semimetals, Nat. Commun.8, 15995 (2017)

    work page 2017

  49. [49]

    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. X12, 031042 (2022)

    work page 2022

  50. [50]

    ˇSmejkal, J

    L. ˇSmejkal, J. Sinova, and T. Jungwirth, Emerging Re- search Landscape of Altermagnetism, Phys. Rev. X12, 040501 (2022)

    work page 2022

  51. [51]

    ˇSmejkal, R

    L. ˇSmejkal, R. Gonz´ alez-Hern´ andez, T. Jungwirth, and J. Sinova, Crystal time-reversal symmetry breaking and spontaneous Hall effect in collinear antiferromagnets, Sci. Adv.6, eaaz8809 (2020)

    work page 2020

  52. [52]

    Z. Feng, X. Zhou, L. ˇSmejkal, L. Wu, Z. Zhu, H. Guo, R. Gonz´ alez-Hern´ andez, X. Wang, H. Yan, P. Qin, X. Zhang, H. Wu, H. Chen, Z. Meng, L. Liu, Z. Xia, J. Sinova, T. Jungwirth, and Z. Liu, An anomalous Hall effect in altermagnetic ruthenium dioxide, Nat. Electron. 5, 735 (2022)

    work page 2022

  53. [53]

    R. D. Gonzalez Betancourt, J. Zub´ aˇ c, R. Gonzalez- Hernandez, K. Geishendorf, Z. ˇSob´ aˇ n, G. Springholz, K. Olejn´ ık, L.ˇSmejkal, J. Sinova, T. Jungwirth, S. T. B. Goennenwein, A. Thomas, H. Reichlov´ a, J.ˇZelezn´ y, and D. Kriegner, Spontaneous Anomalous Hall Effect Arising from an Unconventional Compensated Magnetic Phase in a Semiconductor, Phy...

    work page 2023

  54. [54]

    M. Wang, K. Tanaka, S. Sakai, Z. Wang, K. Deng, Y. Lyu, C. Li, D. Tian, S. Shen, N. Ogawa, N. Kanazawa, P. Yu, R. Arita, and F. Kagawa, Emergent zero-field anomalous Hall effect in a reconstructed rutile antifer- romagnetic metal, Nat. Commun.14, 8240 (2023)

    work page 2023

  55. [55]

    H. Jin, Z. Tan, Z. Gong, and J. Wang, Anomalous Hall effect in two-dimensional vanadium tetrahalogen with al- termagnetic phase, Phys. Rev. B110, 155125 (2024)

    work page 2024

  56. [56]

    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, A. Badura, S. Bertaina, A. Thomas, V. Baltz, L. Michez, J. Sinova, S. T. B. Goennenwein, T. Jungwirth, and L. ˇSmejkal, Observation...

    work page 2024

  57. [57]

    Gonz´ alez-Hern´ andez, L.ˇSmejkal, K

    R. Gonz´ alez-Hern´ andez, L.ˇSmejkal, K. V´ yborn´ y, Y. Ya- hagi, J. Sinova, T. Jungwirth, and J. ˇZelezn´ y, Effi- cient Electrical Spin Splitter Based on Nonrelativistic Collinear Antiferromagnetism, Phys. Rev. Lett.126, 127701 (2021)

    work page 2021

  58. [58]

    Karube, T

    S. Karube, T. Tanaka, D. Sugawara, N. Kadoguchi, M. Kohda, and J. Nitta, Observation of Spin-Splitter Torque in Collinear Antiferromagnetic RuO2, Phys. Rev. Lett.129, 137201 (2022)

    work page 2022

  59. [59]

    H. Bai, L. Han, X. Y. Feng, Y. J. Zhou, R. X. Su, Q. Wang, L. Y. Liao, W. X. Zhu, X. Z. Chen, F. Pan, X. L. Fan, and C. Song, Observation of Spin Splitting Torque in a Collinear Antiferromagnet RuO2, Phys. Rev. Lett.128, 197202 (2022)

    work page 2022

  60. [60]

    H. Bai, Y. C. Zhang, Y. J. Zhou, P. Chen, C. H. Wan, L. Han, W. X. Zhu, S. X. Liang, Y. C. Su, X. F. Han, F. Pan, and C. Song, Efficient Spin-to-Charge Conversion via Altermagnetic Spin Splitting Effect in Antiferromag- net RuO2, Phys. Rev. Lett.130, 216701 (2023)

    work page 2023

  61. [61]

    H. G. Giil, B. Brekke, J. Linder, and A. Brataas, Qua- siclassical theory of superconducting spin-splitter effects and spin-filtering via altermagnets, Phys. Rev. B110, L140506 (2024)

    work page 2024

  62. [62]

    Y. Guo, J. Zhang, Z. Zhu, Y.-y. Jiang, L. Jiang, C. Wu, J. Dong, X. Xu, W. He, B. He, Z. Huang, L. Du, G. Zhang, K. Wu, X. Han, D.-f. Shao, G. Yu, and H. Wu, Direct and Inverse Spin Splitting Effects in Altermag- netic RuO2, Adv. Sci.11, 2400967 (2024)

    work page 2024

  63. [63]

    Adamantopoulos, M

    T. Adamantopoulos, M. Merte, F. Freimuth, D. Go, L. Zhang, M. Leˇ zai´ c, W. Feng, Y. Yao, J. Sinova, L. ˇSmejkal, S. Bl¨ ugel, and Y. Mokrousov, Spin and or- bital magnetism by light in rutile altermagnets, npj Spin- tronics2, 1 (2024)

    work page 2024

  64. [64]

    Y. Noda, K. Ohno, and S. Nakamura, Momentum- dependent band spin splitting in semiconducting MnO 2: a density functional calculation, Phys. Chem. Chem. Phys.18, 13294 (2016)

    work page 2016

  65. [65]

    Okugawa, K

    T. Okugawa, K. Ohno, Y. Noda, and S. Nakamura, Weakly spin-dependent band structures of antiferromag- netic perovskite LaMO3 (M = Cr, Mn, Fe), J. Phys. Con- dens. Matter30, 075502 (2018)

    work page 2018

  66. [66]

    K.-H. Ahn, A. Hariki, K.-W. Lee, and J. Kuneˇ s, Antifer- romagnetism in RuO 2 asd-wave Pomeranchuk instabil- ity, Phys. Rev. B99, 184432 (2019)

    work page 2019

  67. [67]

    M. Naka, S. Hayami, H. Kusunose, Y. Yanagi, Y. Mo- tome, and H. Seo, Spin current generation in organic an- tiferromagnets, Nat. Commun.10, 4305 (2019)

    work page 2019

  68. [68]

    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, J. Sinova, and M. Jourdan, Direct observation of altermagnetic band splitting in CrSb thin films, Nat. Commun.15, 2116 (2024)

    work page 2024

  69. [69]

    Hariki, A

    A. Hariki, A. Dal Din, O. J. Amin, T. Yamaguchi, A. Badura, D. Kriegner, K. W. Edmonds, R. P. Cam- pion, P. Wadley, D. Backes, L. S. I. Veiga, S. S. Dhesi, G. Springholz, L. ˇSmejkal, K. V´ yborn´ y, T. Jungwirth, and J. Kuneˇ s, X-Ray Magnetic Circular Dichroism in Altermagneticα-MnTe, Phys. Rev. Lett.132, 176701 (2024)

    work page 2024

  70. [70]

    R. Dong, R. Cao, D. Tan, and R. Fei, Crystal Symmetry Selected Pure Spin Photocurrent in Altermagnetic Insu- lators (2024), arXiv:2412.09216

    work page internal anchor Pith review arXiv 2024

  71. [71]

    Ezawa, Bulk photovoltaic effects in altermagnets, Phys

    M. Ezawa, Bulk photovoltaic effects in altermagnets, Phys. Rev. B111, L201405 (2025)

    work page 2025

  72. [72]

    Litvin and W

    D. Litvin and W. Opechowski, Spin Groups, Physica (Amsterdam)76, 538 (1974)

    work page 1974

  73. [73]

    D. B. Litvin, Spin Point Groups, Acta Crystallogr. A33, 279 (1977)

    work page 1977

  74. [74]

    Ahn, G.-Y

    J. Ahn, G.-Y. Guo, and N. Nagaosa, Low-Frequency Di- vergence and Quantum Geometry of the Bulk Photo- voltaic Effect in Topological Semimetals, Phys. Rev. X 10, 041041 (2020)

    work page 2020

  75. [75]

    I, symmetry restricted form of spin conduc- tivity tensor for all 27 non-centrosymmetric altermag- netic spin point groups

    See Supplemental Material at url comes here for deriva- tion of Tab. I, symmetry restricted form of spin conduc- tivity tensor for all 27 non-centrosymmetric altermag- netic spin point groups

    work page

  76. [76]

    Z.-M. Yu, Z. Zhang, G.-B. Liu, W. Wu, X.-P. Li, R.-W. Zhang, S. A. Yang, and Y. Yao, Encyclopedia of emergent 1 particles in three-dimensional crystals, Science Bulletin 67, 375 (2022)

    work page 2022

  77. [77]

    A. M. Ar´ evalo-L´ opez and J. P. Attfield, Weak ferro- magnetism and domain effects in multiferroic linbo3-type mntio3-ii, Phys. Rev. B88, 104416 (2013)

    work page 2013

  78. [78]

    Kresse and J

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

    work page 1996

  79. [79]

    Kresse and D

    G. Kresse and D. Joubert, From ultrasoft pseudopoten- tials to the projector augmented-wave method, Phys. Rev. B59, 1758 (1999)

    work page 1999

  80. [80]

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

    work page 1994

Showing first 80 references.