pith. sign in

arxiv: 2606.18657 · v1 · pith:WITA5IWPnew · submitted 2026-06-17 · ❄️ cond-mat.mes-hall

Bidirectional motion of antiferromagnetic skyrmions driven by competing spin torques

Laichuan Shen , Wang Kang , Xichao Zhang , Qiuping Huang , Yalin Lu , Zhifeng Zhu , Yan Zhou This is my paper

Pith reviewed 2026-06-26 20:11 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall
keywords antiferromagnetic skyrmionsspin-transfer torquespin-orbit torquebidirectional motionThiele equationlogic gatesracetrack memory
0
0 comments X

The pith

Antiferromagnetic skyrmions reverse their motion direction above a current threshold due to competing torques.

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

The paper computationally shows that antiferromagnetic skyrmions move in one direction under low current densities but reverse direction once current exceeds a threshold value. This reversal arises because the relative strengths of two effective forces, one from spin-transfer torque and one from spin-orbit torque, switch dominance. The authors analyze the effect with the Thiele equation and demonstrate that the same mechanism can be used to build programmable logic gates on a single racetrack.

Core claim

We computationally demonstrate that antiferromagnetic skyrmions moving in one direction at low current densities can reverse their motion direction when the driving current is above a threshold. Based on the Thiele approach analysis, we show that this bidirectional motion originates from a change in the relative strengths of two effective forces arising from spin-transfer and spin-orbit torques. Furthermore, exploiting this bidirectional motion on a single racetrack, we design programmable logic gates.

What carries the argument

Competing effective forces from spin-transfer torque and spin-orbit torque on rigid antiferromagnetic skyrmions, analyzed through the Thiele equation.

Load-bearing premise

The Thiele approach accurately models the skyrmion dynamics as rigid particles without significant deformation, pinning, or other unaccounted effects at the currents studied.

What would settle it

An experiment that tracks antiferromagnetic skyrmion velocity direction versus increasing current density and finds no reversal at the predicted threshold current would falsify the central claim.

Figures

Figures reproduced from arXiv: 2606.18657 by Laichuan Shen, Qiuping Huang, Wang Kang, Xichao Zhang, Yalin Lu, Yan Zhou, Zhifeng Zhu.

Figure 1
Figure 1. Figure 1: (a) Top panel: Sketch of the calculation model, composed of an antiferromagnet (AFM) and a heavy metal [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: (a)-(c) Calculated forces induced by STT ( [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: (a) Schematic of the skyrmion-based logic device. Two currents [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: (a) Snapshots of magnetic structures under different currents. The box in the middle indicates the detection [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
read the original abstract

Antiferromagnetic skyrmions are swirling topological spin textures with rich dynamics and intriguing transport properties, yet their bidirectional dynamics remain largely unexplored. Here, we investigate the dynamics of antiferromagnetic skyrmions driven by current-induced spin-transfer and spin-orbit torques. We computationally demonstrate that antiferromagnetic skyrmions moving in one direction at low current densities can reverse their motion direction when the driving current is above a threshold. Based on the Thiele approach analysis, we show that this bidirectional motion originates from a change in the relative strengths of two effective forces arising from spin-transfer and spin-orbit torques. Furthermore, exploiting this bidirectional motion on a single racetrack, we design programmable logic gates. Our results not only uncover a hidden mechanism for bidirectional skyrmion motion but also facilitate the development of antiferromagnet-based logic devices.

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 / 1 minor

Summary. The manuscript computationally demonstrates that antiferromagnetic skyrmions driven by combined spin-transfer torque (STT) and spin-orbit torque (SOT) exhibit bidirectional motion: they move in one direction at low current densities but reverse direction above a threshold current. Thiele-equation analysis attributes this reversal to a crossover in the relative magnitudes of two opposing effective forces arising from STT and SOT. The work further proposes exploiting the bidirectional motion to realize programmable logic gates on a single racetrack.

Significance. If the central claim is robust, the result identifies a current-density-controlled mechanism for reversing AFM skyrmion velocity without polarity reversal, which could be useful for antiferromagnetic spintronic devices. The combination of micromagnetic simulations with Thiele collective-coordinate analysis is a strength, as it supplies both numerical evidence and an analytic explanation of the force competition.

major comments (2)
  1. [Thiele approach analysis] Thiele analysis section: the derivation of opposing effective forces and the predicted reversal threshold treats the skyrmion as a rigid particle whose collective coordinates obey a closed set of ODEs. The manuscript does not report quantitative checks (e.g., time evolution of the Néel-vector profile, breathing-mode amplitude, or topological charge conservation) confirming that the texture remains rigid at currents above the reversal threshold; without such validation the observed reversal in simulations could arise from unaccounted deformation or magnon coupling rather than the STT–SOT force crossover alone.
  2. [Micromagnetic results] Micromagnetic results section: the central claim that reversal occurs precisely where the Thiele-derived force ratio changes sign requires a direct, quantitative comparison between the simulated velocity-versus-current curve and the analytic threshold. No such overlay or parameter table is provided, leaving open whether the numerical reversal matches the rigid-particle prediction or is influenced by pinning, damping, or discretization effects.
minor comments (1)
  1. Figure captions and axis labels should explicitly state the current-density units and the sign convention for velocity to allow immediate comparison with the Thiele force expressions.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed and constructive report. The two major comments highlight important aspects of validating the Thiele analysis and its connection to the micromagnetic results. We address each point below and indicate the revisions we will make.

read point-by-point responses

  1. Referee: [Thiele approach analysis] Thiele analysis section: the derivation of opposing effective forces and the predicted reversal threshold treats the skyrmion as a rigid particle whose collective coordinates obey a closed set of ODEs. The manuscript does not report quantitative checks (e.g., time evolution of the Néel-vector profile, breathing-mode amplitude, or topological charge conservation) confirming that the texture remains rigid at currents above the reversal threshold; without such validation the observed reversal in simulations could arise from unaccounted deformation or magnon coupling rather than the STT–SOT force crossover alone.

    Authors: We agree that explicit validation of the rigid-particle assumption strengthens the Thiele analysis. In the revised manuscript we will add supplementary figures showing the time evolution of the Néel-vector profile and the breathing-mode amplitude for currents both below and above the reversal threshold, together with confirmation that the topological charge remains conserved. These checks will be performed on the same parameter sets used for the velocity curves. revision: yes

  2. Referee: [Micromagnetic results] Micromagnetic results section: the central claim that reversal occurs precisely where the Thiele-derived force ratio changes sign requires a direct, quantitative comparison between the simulated velocity-versus-current curve and the analytic threshold. No such overlay or parameter table is provided, leaving open whether the numerical reversal matches the rigid-particle prediction or is influenced by pinning, damping, or discretization effects.

    Authors: We accept that a direct overlay is necessary for quantitative validation. The revised version will include a new figure (or panel) that overlays the simulated velocity-versus-current data with the analytic threshold obtained from the Thiele force balance, using the exact material parameters of the simulations. A supplementary table will also list the damping, pinning, and discretization parameters to allow readers to assess their influence. revision: yes

Circularity Check

0 steps flagged

No circularity: standard Thiele analysis applied to simulation results

full rationale

The paper reports micromagnetic simulations demonstrating current-dependent reversal of antiferromagnetic skyrmion velocity and invokes the Thiele collective-coordinate equation to attribute the reversal to the crossing of opposing STT and SOT force terms. Both steps are independent of the target result: the simulations are direct numerical integration of the Landau-Lifshitz-Gilbert equation, and the Thiele framework is a long-established rigid-particle reduction whose force expressions are derived from the same micromagnetic energy without reference to the reversal phenomenon itself. No fitted parameters are relabeled as predictions, no self-citation supplies a uniqueness theorem, and no ansatz is smuggled through prior work by the same authors. The derivation chain therefore remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review provides no information on free parameters, axioms, or invented entities.

pith-pipeline@v0.9.1-grok · 5687 in / 1113 out tokens · 47278 ms · 2026-06-26T20:11:39.488585+00:00 · methodology

discussion (0)

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

Reference graph

Works this paper leans on

174 extracted references · 109 canonical work pages

  1. [1]

    Science , author =

    Skyrmion. Science , author =. 2009 , pages =. doi:10.1126/science.1166767 , abstract =

    work page doi:10.1126/science.1166767 2009

  2. [2]

    Beyond skyrmions:. Phys. Rep. , author =. 2021 , pages =. doi:10.1016/j.physrep.2020.10.001 , abstract =

    work page doi:10.1016/j.physrep.2020.10.001 2021

  3. [3]

    Topological properties and dynamics of magnetic skyrmions , volume =. Nat. Nanotechnol. , author =. 2013 , pages =. doi:10.1038/nnano.2013.243 , number =

    work page doi:10.1038/nnano.2013.243 2013

  4. [4]

    Static and. Phys. Rev. Lett. , author =. 2016 , pages =. doi:10.1103/PhysRevLett.116.147203 , number =

    work page doi:10.1103/physrevlett.116.147203 2016

  5. [5]

    Direct observation of the skyrmion. Nat. Phys. , author =. 2017 , pages =. doi:10.1038/nphys3883 , language =

    work page doi:10.1038/nphys3883 2017

  6. [6]

    Antiferromagnetic. Sci. Rep. , author =. 2016 , pages =. doi:10.1038/srep24795 , language =

    work page doi:10.1038/srep24795 2016

  7. [7]

    Dynamics of antiferromagnetic skyrmion driven by the spin. Appl. Phys. Lett. , author =. 2016 , pages =. doi:10.1063/1.4967006 , language =

    work page doi:10.1063/1.4967006 2016

  8. [8]

    Magnetic skyrmions: advances in physics and potential applications , volume =. Nat. Rev. Mater. , author =. 2017 , pages =. doi:10.1038/natrevmats.2017.31 , abstract =

    work page doi:10.1038/natrevmats.2017.31 2017

  9. [9]

    Perspective:. J. Appl. Phys. , author =. 2018 , pages =. doi:10.1063/1.5048972 , number =

    work page doi:10.1063/1.5048972 2018

  10. [10]

    Nucleation, stability and current-induced motion of isolated magnetic skyrmions in nanostructures , volume =. Nat. Nanotechnol. , author =. 2013 , pages =. doi:10.1038/nnano.2013.210 , number =

    work page doi:10.1038/nnano.2013.210 2013

  11. [11]

    Magnetic skyrmion logic gates: conversion, duplication and merging of skyrmions , volume =. Sci. Rep. , author =. 2015 , pages =. doi:10.1038/srep09400 , language =

    work page doi:10.1038/srep09400 2015

  12. [12]

    Current-. Phys. Rev. Applied , author =. 2019 , pages =. doi:10.1103/PhysRevApplied.12.064033 , language =

    work page doi:10.1103/physrevapplied.12.064033 2019

  13. [13]

    Current-driven dynamics and inhibition of the skyrmion. Nat. Commun. , author =. 2018 , pages =. doi:10.1038/s41467-018-03378-7 , language =

    work page doi:10.1038/s41467-018-03378-7 2018

  14. [14]

    Steady-. Phys. Rev. Lett. , author =. 1973 , pages =. doi:10.1103/PhysRevLett.30.230 , language =

    work page doi:10.1103/physrevlett.30.230 1973

  15. [15]

    A thermodynamic theory of “weak” ferromagnetism of antiferromagnetics , volume =. J. Phys. Chem. Solids , author =. 1958 , pages =. doi:10.1016/0022-3697(58)90076-3 , abstract =

    work page doi:10.1016/0022-3697(58)90076-3 1958

  16. [16]

    Anisotropic. Phys. Rev. , author =. 1960 , pages =. doi:10.1103/PhysRev.120.91 , number =

    work page doi:10.1103/physrev.120.91 1960

  17. [17]

    Skyrmion dynamics in chiral ferromagnets , volume =. Phys. Rev. B , author =. 2015 , pages =. doi:10.1103/PhysRevB.92.064412 , number =

    work page doi:10.1103/physrevb.92.064412 2015

  18. [18]

    Skyrmion fractionalization and merons in chiral magnets with easy-plane anisotropy , volume =. Phys. Rev. B , author =. 2015 , pages =. doi:10.1103/PhysRevB.91.224407 , number =

    work page doi:10.1103/physrevb.91.224407 2015

  19. [19]

    Skyrmion-electronics: writing, deleting, reading and processing magnetic skyrmions toward spintronic applications , volume =. J. Phys.: Condens. Matter. , author =. 2020 , pages =. doi:10.1088/1361-648X/ab5488 , abstract =

    work page doi:10.1088/1361-648x/ab5488 2020

  20. [20]

    , year =

    Zhou, Y. , year =. Magnetic skyrmions: intriguing physics and new spintronic device concepts , volume =. doi:https://doi.org/10.1093/nsr/nwy109 , journal =

    work page doi:10.1093/nsr/nwy109

  21. [21]

    Magnetic skyrmion bundles and their current-driven dynamics , volume =. Nat. Nanotechnol. , author =. 2021 , pages =. doi:10.1038/s41565-021-00954-9 , number =

    work page doi:10.1038/s41565-021-00954-9 2021

  22. [22]

    The design and verification of. AIP Adv. , author =. 2014 , pages =. doi:10.1063/1.4899186 , number =

    work page doi:10.1063/1.4899186 2014

  23. [23]

    Skyrmion-. Phys. Rev. Applied , author =. 2021 , pages =. doi:10.1103/PhysRevApplied.15.064004 , language =

    work page doi:10.1103/physrevapplied.15.064004 2021

  24. [24]

    Skyrmions-based logic gates in one single nanotrack completely reconstructed via chirality barrier , volume =. Natl. Sci. Rev. , author =. 2022 , pages =. doi:10.1093/nsr/nwac021 , abstract =

    work page doi:10.1093/nsr/nwac021 2022

  25. [25]

    Nano Lett

    Reconfigurable. Nano Lett. , author =. 2018 , pages =. doi:10.1021/acs.nanolett.7b04722 , abstract =

    work page doi:10.1021/acs.nanolett.7b04722 2018

  26. [26]

    Stochastic. Phys. Rev. Applied , author =. 2020 , pages =. doi:10.1103/PhysRevApplied.13.054049 , language =

    work page doi:10.1103/physrevapplied.13.054049 2020

  27. [27]

    IEEE Trans

    A. IEEE Trans. Magn. , author =. 2004 , pages =. doi:10.1109/TMAG.2004.836740 , abstract =

    work page doi:10.1109/tmag.2004.836740 2004

  28. [28]

    Skyrmion. Nat. Phys. , author =. 2017 , pages =. doi:10.1038/nphys4000 , number =

    work page doi:10.1038/nphys4000 2017

  29. [29]

    Nano Lett

    Helium. Nano Lett. , author =. 2021 , pages =. doi:10.1021/acs.nanolett.1c00136 , abstract =

    work page doi:10.1021/acs.nanolett.1c00136 2021

  30. [30]

    Spin torque nano-oscillators based on antiferromagnetic skyrmions , volume =. Appl. Phys. Lett. , author =. 2019 , pages =. doi:10.1063/1.5080302 , abstract =

    work page doi:10.1063/1.5080302 2019

  31. [31]

    A theory on skyrmion size , volume =. Commun. Phys. , author =. 2018 , pages =. doi:10.1038/s42005-018-0029-0 , language =

    work page doi:10.1038/s42005-018-0029-0 2018

  32. [32]

    Robust and. Phys. Rev. Applied , author =. 2022 , pages =. doi:10.1103/PhysRevApplied.18.014025 , language =

    work page doi:10.1103/physrevapplied.18.014025 2022

  33. [33]

    Nature , author =

    Spontaneous skyrmion ground states in magnetic metals , volume =. Nature , author =. 2006 , pages =. doi:10.1038/nature05056 , language =

    work page doi:10.1038/nature05056 2006

  34. [34]

    Science , author =

    Magnetic. Science , author =. 2008 , pages =. doi:10.1126/science.1145799 , abstract =

    work page doi:10.1126/science.1145799 2008

  35. [35]

    Skyrmion-. Proc. IEEE , author =. 2016 , pages =. doi:10.1109/JPROC.2016.2591578 , language =

    work page doi:10.1109/jproc.2016.2591578 2016

  36. [36]

    Magnetic skyrmions: from fundamental to applications , volume =. J. Phys. D: Appl. Phys. , author =. 2016 , pages =. doi:10.1088/0022-3727/49/42/423001 , abstract =

    work page doi:10.1088/0022-3727/49/42/423001 2016

  37. [37]

    Statics and dynamics of skyrmions interacting with disorder and nanostructures , volume =. Rev. Mod. Phys. , author =. 2022 , pages =. doi:10.1103/RevModPhys.94.035005 , language =

    work page doi:10.1103/revmodphys.94.035005 2022

  38. [38]

    The 2020 skyrmionics roadmap , volume =. J. Phys. D: Appl. Phys. , author =. 2020 , pages =. doi:10.1088/1361-6463/ab8418 , abstract =

    work page doi:10.1088/1361-6463/ab8418 2020

  39. [39]

    Current-. Phys. Rev. Lett. , author =. 2020 , pages =. doi:10.1103/PhysRevLett.124.037202 , language =

    work page doi:10.1103/physrevlett.124.037202 2020

  40. [40]

    Programmable skyrmion-based logic gates in a single nanotrack , volume =. Phys. Rev. B , author =. 2023 , pages =. doi:10.1103/PhysRevB.107.054437 , language =

    work page doi:10.1103/physrevb.107.054437 2023

  41. [41]

    Science , author =

    Fast current-induced skyrmion motion in synthetic antiferromagnets , volume =. Science , author =. 2024 , pages =. doi:10.1126/science.add5751 , abstract =

    work page doi:10.1126/science.add5751 2024

  42. [42]

    vortices

    Thermodynamically stable “vortices” in magnetically ordered crystals. Sov. Phys. JETP , author =. 1989 , pages =

    1989

  43. [43]

    A reversible conversion between a skyrmion and a domain-wall pair in a junction geometry , volume =. Nat. Commun. , author =. 2014 , pages =. doi:10.1038/ncomms5652 , language =

    work page doi:10.1038/ncomms5652 2014

  44. [44]

    Realization of skyrmion shift register , volume =. Sci. Bull. , author =. 2024 , pages =. doi:10.1016/j.scib.2024.05.035 , language =

    work page doi:10.1016/j.scib.2024.05.035 2024

  45. [45]

    High-frequency spin transfer nano-oscillator based on the motion of skyrmions in an annular groove , volume =. New J. Phys. , author =. 2020 , pages =. doi:10.1088/1367-2630/ab7258 , abstract =

    work page doi:10.1088/1367-2630/ab7258 2020

  46. [46]

    Positive and negative drag, dynamic phases, and commensurability in coupled one-dimensional channels of particles with. Phys. Rev. E , author =. 2011 , pages =. doi:10.1103/PhysRevE.83.061404 , language =

    work page doi:10.1103/physreve.83.061404 2011

  47. [47]

    npj Spintronics , author =

    Structure, control, and dynamics of altermagnetic textures , volume =. npj Spintronics , author =. 2024 , pages =. doi:10.1038/s44306-024-00042-3 , abstract =

    work page doi:10.1038/s44306-024-00042-3 2024

  48. [48]

    Skyrmion. Phys. Rev. Lett. , author =. 2024 , pages =

    2024

  49. [49]

    and Gurung, Shivraj and Rai, D

    Tamang, R. and Gurung, Shivraj and Rai, D. P. and Brahimi, Samy and Lounis, Samir , month = dec, year =. Newly discovered magnetic phase:. doi:10.48550/arXiv.2412.05377 , abstract =

    work page doi:10.48550/arxiv.2412.05377

  50. [50]

    Nat Commun , author =

    Spin current generation in organic antiferromagnets , volume =. Nat Commun , author =. 2019 , pages =. doi:10.1038/s41467-019-12229-y , abstract =

    work page doi:10.1038/s41467-019-12229-y 2019

  51. [51]

    Efficient. Phys. Rev. Lett. , author =. 2021 , pages =. doi:10.1103/PhysRevLett.126.127701 , language =

    work page doi:10.1103/physrevlett.126.127701 2021

  52. [52]

    Observation of. Phys. Rev. Lett. , author =. 2022 , pages =. doi:10.1103/PhysRevLett.129.137201 , language =

    work page doi:10.1103/physrevlett.129.137201 2022

  53. [53]

    Spontaneous. Phys. Rev. Lett. , author =. 2023 , pages =. doi:10.1103/PhysRevLett.130.036702 , language =

    work page doi:10.1103/physrevlett.130.036702 2023

  54. [54]

    Beyond. Phys. Rev. X , author =. 2022 , pages =. doi:10.1103/PhysRevX.12.031042 , language =

    work page doi:10.1103/physrevx.12.031042 2022

  55. [55]

    Emerging. Phys. Rev. X , author =. 2022 , pages =. doi:10.1103/PhysRevX.12.040501 , language =

    work page doi:10.1103/physrevx.12.040501 2022

  56. [56]

    Giant and. Phys. Rev. X , author =. 2022 , pages =. doi:10.1103/PhysRevX.12.011028 , language =

    work page doi:10.1103/physrevx.12.011028 2022

  57. [57]

    Skyrmion-based chaotic oscillator driven by a constant current , volume =. Phys. Rev. B , author =. 2024 , pages =. doi:10.1103/PhysRevB.109.014422 , language =

    work page doi:10.1103/physrevb.109.014422 2024

  58. [58]

    and Yershov, Kostiantyn V

    Kravchuk, Volodymyr P. and Yershov, Kostiantyn V. and Facio, Jorge I. and Guo, Yaqian and Janson, Oleg and Gomonay, Olena and Sinova, Jairo and Brink, Jeroen van den , month = may, year =. Chiral magnetic excitations and domain textures of g-wave altermagnets , url =. doi:10.48550/arXiv.2504.05241 , abstract =

    work page doi:10.48550/arxiv.2504.05241

  59. [59]

    Curvature-. Phys. Rev. Lett. , author =. 2025 , pages =. doi:10.1103/PhysRevLett.134.116701 , abstract =

    work page doi:10.1103/physrevlett.134.116701 2025

  60. [60]

    Spin-. Phys. Rev. Lett. , author =. 2025 , pages =. doi:10.1103/PhysRevLett.134.176401 , language =

    work page doi:10.1103/physrevlett.134.176401 2025

  61. [61]

    Physica D , author =

    A practical method for calculating largest. Physica D , author =. 1993 , pages =. doi:10.1016/0167-2789(93)90009-P , language =

    work page doi:10.1016/0167-2789(93)90009-p 1993

  62. [62]

    Current Biology , author =

    Bidirectional. Current Biology , author =. 2004 , pages =. doi:10.1016/j.cub.2004.06.045 , language =

    work page doi:10.1016/j.cub.2004.06.045 2004

  63. [63]

    Altermagnets as a new class of functional materials , volume =. Nat. Rev. Mater. , author =. 2025 , pages =. doi:10.1038/s41578-025-00779-1 , language =

    work page doi:10.1038/s41578-025-00779-1 2025

  64. [64]

    Magnetism , author =

    Altermagnetism and. Magnetism , author =. 2025 , pages =. doi:10.3390/magnetism5030017 , abstract =

    work page doi:10.3390/magnetism5030017 2025

  65. [65]

    Nat Rev Mater , author =

    Anomalous. Nat Rev Mater , author =. 2022 , pages =. doi:10.1038/s41578-022-00430-3 , abstract =

    work page doi:10.1038/s41578-022-00430-3 2022

  66. [66]

    Advanced Materials , author =

    Emerging. Advanced Materials , author =. 2024 , pages =. doi:10.1002/adma.202310379 , abstract =

    work page doi:10.1002/adma.202310379 2024

  67. [67]

    Altermagnetism:. Adv. Funct. Mater. , author =. 2024 , pages =. doi:10.1002/adfm.202409327 , abstract =

    work page doi:10.1002/adfm.202409327 2024

  68. [68]

    Tunneling. Phys. Rev. Lett. , author =. 2025 , pages =. doi:10.1103/nrk5-5zrj , language =

    work page doi:10.1103/nrk5-5zrj 2025

  69. [69]

    Spin-neutral currents for spintronics , volume =. Nat. Commun. , author =. 2021 , pages =. doi:10.1038/s41467-021-26915-3 , abstract =

    work page doi:10.1038/s41467-021-26915-3 2021

  70. [70]

    Terahertz. Adv. Sci. , author =. 2023 , pages =. doi:10.1002/advs.202300512 , abstract =

    work page doi:10.1002/advs.202300512 2023

  71. [71]

    Spin-. Phys. Rev. Lett. , author =. 2025 , pages =. doi:10.1103/l8d1-gpgr , language =

    work page doi:10.1103/l8d1-gpgr 2025

  72. [72]

    Observation of. Phys. Rev. Lett. , author =. 2022 , pages =. doi:10.1103/PhysRevLett.128.197202 , language =

    work page doi:10.1103/physrevlett.128.197202 2022

  73. [73]

    Observation of time-reversal symmetry breaking in the band structure of altermagnetic. Sci. Adv. , author =. 2024 , pages =. doi:10.1126/sciadv.adj4883 , abstract =

    work page doi:10.1126/sciadv.adj4883 2024

  74. [74]

    Nature , author =

    Manipulation of the altermagnetic order in. Nature , author =. 2025 , pages =. doi:10.1038/s41586-024-08436-3 , language =

    work page doi:10.1038/s41586-024-08436-3 2025

  75. [75]

    Nature , author =

    Unconventional magnons in collinear magnets dictated by spin space groups , volume =. Nature , author =. 2025 , pages =. doi:10.1038/s41586-025-08715-7 , language =

    work page doi:10.1038/s41586-025-08715-7 2025

  76. [76]

    Ferroelectric. Phys. Rev. Lett. , author =. 2025 , pages =. doi:10.1103/PhysRevLett.134.106802 , language =

    work page doi:10.1103/physrevlett.134.106802 2025

  77. [77]

    Nature , author =

    Altermagnetic lifting of. Nature , author =. 2024 , pages =. doi:10.1038/s41586-023-06907-7 , abstract =

    work page doi:10.1038/s41586-023-06907-7 2024

  78. [78]

    Three-dimensional mapping of the altermagnetic spin splitting in. Nat. Commun. , author =. 2025 , pages =. doi:10.1038/s41467-025-56647-7 , abstract =

    work page doi:10.1038/s41467-025-56647-7 2025

  79. [79]

    Nature , author =

    Nanoscale imaging and control of altermagnetism in. Nature , author =. 2024 , pages =. doi:10.1038/s41586-024-08234-x , abstract =

    work page doi:10.1038/s41586-024-08234-x 2024

  80. [80]

    Altermagnet skyrmions:. Phys. Rev. B , author =. 2025 , pages =. doi:10.1103/xtcd-t47t , language =

    work page doi:10.1103/xtcd-t47t 2025

Showing first 80 references.