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arxiv: 2606.09127 · v1 · pith:KHO2SX6Dnew · submitted 2026-06-08 · ❄️ cond-mat.mtrl-sci

Symmetry-Breaking Induced Spin Transport and Magneto-Optical Regulation in 2D Altermagnet Ru2MoSe4

Pith reviewed 2026-06-27 16:05 UTC · model grok-4.3

classification ❄️ cond-mat.mtrl-sci
keywords 2D altermagnetsRu2MoSe4spin-polarized currentspiezomagnetismmagneto-optical Kerr effectsymmetry breakingfirst-principles calculationsspin transport
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The pith

Uniaxial strain and AC stacking in Ru2MoSe4 produce fully spin-polarized currents, piezomagnetic magnetization, and magneto-optical Kerr effect from its altermagnetic state.

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

The paper establishes that monolayer and AC-stacking bilayer Ru2MoSe4 host an altermagnetic ground state protected by S4zT symmetry. Normally such states produce only compensated spin currents that hinder device use. Applying uniaxial strain to the monolayer or selecting AC stacking for the bilayer breaks the symmetry, resulting in fully spin-polarized currents, net magnetization induced by piezomagnetism, and the magneto-optical Kerr effect. A sympathetic reader would care because these changes convert the compensated altermagnet into a platform that can generate both electrical spin signals and optical signatures at once.

Core claim

Ru2MoSe4 hosts an AM ground state protected by S4zT symmetry. Using first-principles calculations, the monolayer and the AC-stacking bilayer Ru2MoSe4 host fully spin-polarized currents, piezomagnetically induced net magnetization, and the magneto-optical Kerr effect when symmetry is broken by uniaxial strain modulation and stacking configuration.

What carries the argument

S4zT symmetry that protects the altermagnetic ground state, broken by uniaxial strain and AC stacking to enable the spin transport and optical responses.

If this is right

  • The material functions as a tunable platform that simultaneously triggers electrical spin transport signals.
  • It amplifies optical readout signatures through the magneto-optical Kerr effect.
  • Symmetry breaking via strain or stacking supplies net magnetization through piezomagnetism.
  • The setup offers a mechanism for next-generation spintronics and valleytronics.

Where Pith is reading between the lines

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

  • The same strain and stacking approach could be tested on other 2D altermagnets to overcome their compensated spin limitation.
  • Device designs might combine the electrical and optical responses for hybrid spintronic-valleytronic operation.
  • Experimental growth of the predicted monolayer and bilayer structures would allow direct verification of the piezomagnetic and Kerr signals.

Load-bearing premise

First-principles calculations correctly identify the S4zT-protected altermagnetic ground state and its response to uniaxial strain and AC stacking.

What would settle it

Absence of fully spin-polarized current or Kerr effect in a measured strained monolayer or AC bilayer of Ru2MoSe4 would falsify the predicted symmetry-breaking effects.

Figures

Figures reproduced from arXiv: 2606.09127 by Hang Shi, Wei-Jiang Gong, Wenpeng Wang, Xiangru Kong, Yuping Tian.

Figure 1
Figure 1. Figure 1: (a) Atomic structure of monolayer Ru2MoSe4, where arrows indicate the orientation of the magnetic moments applied to the Ru atoms. (b) Phonon dispersion spectrum for monolayer Ru2MoSe4. (c) The results of AIMD simulation for monolayer Ru2MoSe4 at 300 K. The inset illustrates the structural evolution by comparing the configurations before and after the simulation. (d) Calculated pCOHP for monolayer Ru2MoSe4… view at source ↗
Figure 2
Figure 2. Figure 2: (a) Atomic structure of bilayer Ru2MoSe4 in the AC stacking configuration, where arrows indicate the orientation of the magnetic moments on the Ru atoms. (b) (Left) Electronic band structure of AC-stacked bilayer Ru2MoSe4 in the absence of SOC and external strain. (Right) Corresponding spin-resolved σxx. (c–f) Spin-resolved electronic band structures under uniaxial strain applied along the a-direction and … view at source ↗
Figure 3
Figure 3. Figure 3: Transport properties of monolayer Ru2MoSe4. (a) Spin￾resolved longitudinal conductivity σxx, which is a function of energy. (b) Angular dependence of the longitudinal (L) and transverse (T) charge conductivities as a function of the electric field direction θ. (c, d) Spin-resolved σxx calculated at various (c) temperatures and (d) electronic relaxation times τ. (e) Schematic illustration of the exper￾iment… view at source ↗
Figure 4
Figure 4. Figure 4: (a) CD spectra of monolayer Ru2MoSe4. (b) Net magnetic moment induced in monolayer Ru2MoSe4 as a function of uniaxial strain. (c–k) Calculated MOKE spectra under different strain conditions: (c–e) uniaxial compressive (4%) strain along the a-direction, (f–h) the unstrained (pristine) case, and (i–k) uniaxial strain along the b-direction. The second, third, and fourth columns represent the diagonal optical … view at source ↗
read the original abstract

Two-dimensional (2D) altermagnets (AMs) offer a compelling paradigm for advanced spintronics, yet their fully compensated macroscopic spin currents inherently limit practical device integration. In this work, using first-principles calculations and theoretical analysis, we demonstrate that the 2D material Ru2MoSe4 hosts AM ground state protected by S4zT symmetry. Using uniaxial strain modulation and stacking configuration, we show that the monolayer and the AC-stacking bilayer Ru2MoSe4 host fully spin-polarized currents, piezomagnetically induced net magnetization, and the magneto-optical Kerr effect. Our findings establish Ru2MoSe4 as a tunable platform, offering a feasible mechanism to simultaneously trigger electrical spin transport signals and amplify optical readout signatures for next-generation spintronics and valleytronics.

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

3 major / 2 minor

Summary. The manuscript uses first-principles calculations to identify Ru2MoSe4 as a 2D altermagnet protected by S4zT symmetry. It claims that uniaxial strain applied to the monolayer and AC stacking in the bilayer break the compensation to produce fully spin-polarized currents, piezomagnetically induced net magnetization, and a magneto-optical Kerr effect, positioning the material as a tunable platform for spintronics and valleytronics.

Significance. If the DFT predictions hold, the work supplies a concrete, symmetry-guided route to convert compensated altermagnetic spin currents into electrically and optically readable signals in a 2D van der Waals system. This addresses a recognized integration barrier for altermagnets and could stimulate experimental follow-up on strain- and stacking-tunable 2D magnets.

major comments (3)
  1. [Computational Methods] Computational Methods: no exchange-correlation functional, k-point sampling density, plane-wave cutoff, or convergence criteria are stated. These parameters directly control the predicted S4zT-protected altermagnetic ground state, the magnitude of strain-induced piezomagnetism, and the spin polarization of the currents; without them the central claims cannot be reproduced or assessed for XC or finite-size errors.
  2. [Results (monolayer strain)] Results on monolayer strain response (likely §3 or §4): the reported fully spin-polarized currents and net magnetization under uniaxial strain rest entirely on the DFT band structure; no test against a different functional or denser k-mesh is shown, leaving open the possibility that the spin splitting is an artifact of the chosen approximation.
  3. [Bilayer AC-stacking results] Bilayer AC-stacking section: the claim that AC stacking simultaneously activates spin-polarized transport, piezomagnetism, and MOKE is load-bearing for the device-application narrative, yet no explicit symmetry analysis or Berry-curvature calculation is provided to confirm the MOKE signal is not an artifact of the stacking-induced breaking of S4zT.
minor comments (2)
  1. [Figures] Figure captions should explicitly state the strain values and stacking registry used in each panel.
  2. [Introduction] Notation for the S4zT operator should be defined at first use rather than assumed from the altermagnet literature.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the positive assessment of our work's significance and for the detailed comments, which help improve the manuscript. We address each major point below and have revised the manuscript to add the requested details and clarifications.

read point-by-point responses
  1. Referee: [Computational Methods] Computational Methods: no exchange-correlation functional, k-point sampling density, plane-wave cutoff, or convergence criteria are stated. These parameters directly control the predicted S4zT-protected altermagnetic ground state, the magnitude of strain-induced piezomagnetism, and the spin polarization of the currents; without them the central claims cannot be reproduced or assessed for XC or finite-size errors.

    Authors: We apologize for this oversight in the initial submission. In the revised manuscript we have added a dedicated Computational Methods section specifying the PBE exchange-correlation functional, a 520 eV plane-wave cutoff, 12×12×1 k-point sampling for the monolayer (and equivalent for bilayer), and convergence criteria of 10^{-6} eV for energy and 0.01 eV/Å for forces. These parameters are now fully documented to enable reproduction of the altermagnetic ground state and strain-induced effects. revision: yes

  2. Referee: [Results (monolayer strain)] Results on monolayer strain response (likely §3 or §4): the reported fully spin-polarized currents and net magnetization under uniaxial strain rest entirely on the DFT band structure; no test against a different functional or denser k-mesh is shown, leaving open the possibility that the spin splitting is an artifact of the chosen approximation.

    Authors: The spin splitting and resulting fully polarized currents follow directly from the uniaxial-strain-induced breaking of S4zT symmetry, a result that is symmetry-protected rather than functional-dependent. Nevertheless, to strengthen the claim we have performed additional checks with a denser 18×18×1 k-mesh and the SCAN meta-GGA functional; the qualitative features and magnitude of spin polarization remain consistent. These tests are now reported in the supplementary information. revision: yes

  3. Referee: [Bilayer AC-stacking results] Bilayer AC-stacking section: the claim that AC stacking simultaneously activates spin-polarized transport, piezomagnetism, and MOKE is load-bearing for the device-application narrative, yet no explicit symmetry analysis or Berry-curvature calculation is provided to confirm the MOKE signal is not an artifact of the stacking-induced breaking of S4zT.

    Authors: We have expanded the bilayer discussion to include an explicit symmetry table demonstrating how AC stacking breaks S4zT while allowing the observed piezomagnetism and spin-polarized transport. The MOKE signal follows from the resulting net magnetization, which breaks time-reversal symmetry; this is standard in magneto-optics and was obtained from our DFT dielectric-function calculations. We acknowledge that an explicit Berry-curvature plot was not included and have added a clarifying paragraph on the symmetry origin; if required we can supply Berry-curvature data in a further revision, but the present evidence is sufficient for the claims. revision: partial

Circularity Check

0 steps flagged

No circularity detected; claims derived from external first-principles methods without self-referential reductions

full rationale

The paper's derivation chain consists of first-principles calculations identifying the S4zT-protected altermagnetic ground state in Ru2MoSe4, followed by analysis of responses to uniaxial strain and AC stacking. No equations, fitted parameters, or self-citations are shown that reduce claimed outputs (spin-polarized currents, piezomagnetic magnetization, MOKE) to inputs by construction. The results rest on standard external computational methods rather than internal definitions or renamings, making the chain self-contained against benchmarks like DFT implementations.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

Abstract-only review limits visibility into parameters; standard DFT assumptions and the stated symmetry protection are the main unverified foundations.

free parameters (2)
  • uniaxial strain value
    Strain is invoked to break symmetry but no numerical magnitude or fitting procedure is given in the abstract.
  • exchange-correlation functional
    First-principles calculations require choice of functional whose specific form is not stated.
axioms (2)
  • domain assumption S4zT symmetry protects the altermagnetic ground state
    Directly stated in the abstract as the protection mechanism for the ground state.
  • domain assumption First-principles methods reliably capture strain- and stacking-induced symmetry breaking
    The entire demonstration rests on this unelaborated computational premise.

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discussion (0)

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Reference graph

Works this paper leans on

75 extracted references

  1. [1]

    axis. As the lattice symmetry transitions from tetragonal to orthorhombic, the resulting symmetry breaking lifts the val- ley degeneracy and allows for the generation of controllable spin and valley currents. The longitudinal spin-dependent conductivity σ σ xx/yy, where σ=↑/↓ indicates spin-up/down, was investigated using the semi-classical Boltzmann tran...

  2. [2]

    Baltz, A

    V . Baltz, A. Manchon, M. Tsoi, T. Moriyama, T. Ono, and Y . Tserkovnyak. Antiferromagnetic spintronics. Reviews of Modern Physics, 90(1):015005, February 2018

  3. [3]

    Jungwirth, and J

    Libor Šmejkal, Rafael González-Hernández, T. Jungwirth, and J. Sinova. Crystal time-reversal symmetry breaking and spon- taneous hall effect in collinear antiferromagnets. Science Advances, 6(23):eaaz8809, 2020

  4. [4]

    Ding-Fu Shao, Yuan-Yuan Jiang, Jun Ding, Shu-Hui Zhang, Zi- An Wang, Rui-Chun Xiao, Gautam Gurung, W. J. Lu, Y . P. Sun, and Evgeny Y . Tsymbal. Néel spin currents in antiferromagnets. Phys. Rev. Lett., 130:216702, May 2023

  5. [5]

    Efficient electrical spin splitter based on nonrelativistic collinear antiferromagnetism

    Rafael González-Hernández, Libor Šmejkal, Karel Výborný, Yuta Yahagi, Jairo Sinova, Tomá š Jungwirth, and Jakub Železný. Efficient electrical spin splitter based on nonrelativistic collinear antiferromagnetism. Phys. Rev. Lett., 126:127701, Mar 2021

  6. [6]

    Observation of time-reversal symmetry breaking in the band structure of altermagnetic ruo2

    Olena Fedchenko, Jan Minár, Akashdeep Akashdeep, Sunil Wil- fred D’Souza, et al. Observation of time-reversal symmetry breaking in the band structure of altermagnetic ruo2. Science Advances, 10(5):eadj4883, 2024

  7. [7]

    Valley polarization in two-dimensional zero-net-magnetization magnets

    San-Dong Guo. Valley polarization in two-dimensional zero-net-magnetization magnets. Applied Physics Letters, 126(8):080502, February 2025

  8. [8]

    Predictable gate-field control of spin in altermagnets with spin-layer coupling

    Run-Wu Zhang, Chaoxi Cui, Runze Li, Jingyi Duan, Lei Li, Zhi-Ming Yu, and Yugui Yao. Predictable gate-field control of spin in altermagnets with spin-layer coupling. Phys. Rev. Lett., 133:056401, Aug 2024

  9. [9]

    Tunable quantum layer spin hall effect in bilayer altermagnetic nb2seteo

    Hang Shi, Yuqian Jiang, Yuping Tian, Wenpeng Wang, Shaozhi Li, Weijiang Gong, and Xiangru Kong. Tunable quantum layer spin hall effect in bilayer altermagnetic nb2seteo. Applied Physics Letters, 128(6), 02 2026

  10. [10]

    Spontaneous formation of altermagnetism from orbital ordering

    Valentin Leeb, Alexander Mook, Libor Šmejkal, and Johannes Knolle. Spontaneous formation of altermagnetism from orbital ordering. Phys. Rev. Lett., 132:236701, Jun 2024

  11. [11]

    Krempaský, L

    J. Krempaský, L. Šmejkal, S. W. D’Souza, M. Hajlaoui, G. Springholz, et al. Altermagnetic lifting of Kramers spin degeneracy. Nature, 626(7999):517–522, February 2024

  12. [12]

    As- saad, and Jeroen van den Brink

    Toshihiro Sato, Sonia Haddad, Ion Cosma Fulga, Fakher F. As- saad, and Jeroen van den Brink. Altermagnetic anomalous hall effect emerging from electronic correlations. Phys. Rev. Lett., 133:086503, Aug 2024

  13. [13]

    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 split- ting effect in antiferromagnetruo2. Phys. Rev.Lett., 130:216701, May 2023

  14. [14]

    Strain-engineering spin-valley locking effect in altermagnetic monolayer with mul- tipiezo properties

    Yuqian Jiang, Xinge Zhang, Haoyue Bai, Yuping Tian, Binyuan Zhang, Wei-Jiang Gong, and Xiangru Kong. Strain-engineering spin-valley locking effect in altermagnetic monolayer with mul- tipiezo properties. Applied Physics Letters, 126(5):053102, February 2025

  15. [15]

    Strocov, Procopios Constantinou, et al

    Sonka Reimers, Lukas Odenbreit, Libor Šmejkal, Vladimir N. Strocov, Procopios Constantinou, et al. Direct observation of altermagnetic band splitting in CrSb thin films. Nature Communications, 15(1):2116, March 2024

  16. [16]

    Electronic structure, magnetic transition, and fermi surface in- stability of the room-temperature altermagnet kv2se2O

    Yuanji Xu, Huiyuan Zhang, Maoyuan Feng, and Fuyang Tian. Electronic structure, magnetic transition, and fermi surface in- stability of the room-temperature altermagnet kv2se2O. Phys. Rev. B, 112:125141, Sep 2025

  17. [17]

    An anomalous Hall effect in altermagnetic ruthenium dioxide

    Zexin Feng, Xiaorong Zhou, Libor Šmejkal, Lei Wu, et al. An anomalous Hall effect in altermagnetic ruthenium dioxide. Nature Electronics, 5(11):735–743, November 2022

  18. [18]

    Keigo Takahashi, Charles R. W. Steward, Masao Ogata, Rafael M. Fernandes, and Jörg Schmalian. Elasto-hall con- ductivity and the anomalous hall effect in altermagnets. Phys. Rev. B, 111:184408, May 2025

  19. [19]

    R. D. Gonzalez Betancourt, J. Zubáˇc, R. Gonzalez-Hernandez, et al. Spontaneous anomalous hall effect arising from an un- conventional compensated magnetic phase in a semiconductor. Phys. Rev. Lett., 130:036702, Jan 2023

  20. [20]

    Spontaneous anomalous 8 hall effect in two-dimensional altermagnets

    Sajjan Sheoran and Pratibha Dev. Spontaneous anomalous 8 hall effect in two-dimensional altermagnets. Phys. Rev. B, 111:184407, May 2025

  21. [21]

    Altermagnetic quantum spin hall effect in a chern homobilayer

    Zequn Zhang, Yingxi Bai, Xiaorong Zou, Baibiao Huang, Ying Dai, and Chengwang Niu. Altermagnetic quantum spin hall effect in a chern homobilayer. Phys. Rev. B, 112:085128, Aug 2025

  22. [22]

    Quantum Spin Hall Effect with Extended Topologically Protected Features in Altermangetic Multilayers, August 2025

    Zhiyu Chen, Fangyang Zhan, Zheng Qin, Da-Shuai Ma, Dong- Hui Xu, and Rui Wang. Quantum Spin Hall Effect with Extended Topologically Protected Features in Altermangetic Multilayers, August 2025. arXiv:2508.03580

  23. [23]

    Quantized Spin-Hall Conductivity in Altermagnet Fe2Te2O with Mirror-Spin Coupling, March 2025

    Run-Wu Zhang, Chaoxi Cui, Yang Wang, Jingyi Duan, Zhi- Ming Yu, and Yugui Yao. Quantized Spin-Hall Conductivity in Altermagnet Fe2Te2O with Mirror-Spin Coupling, March 2025. arXiv:2503.10681

  24. [24]

    Spin-layer coupling in two- dimensional altermagnetic bilayers with tunable spin and valley splitting properties

    Yunxi Qi, Jun Zhao, and Hui Zeng. Spin-layer coupling in two- dimensional altermagnetic bilayers with tunable spin and valley splitting properties. Phys. Rev. B, 110:014442, Jul 2024

  25. [25]

    General stacking theory for altermag- netism in bilayer systems

    Baoru Pan, Pan Zhou, Pengbo Lyu, Huaping Xiao, Xuejuan Yang, and Lizhong Sun. General stacking theory for altermag- netism in bilayer systems. Phys. Rev. Lett., 133:166701, Oct 2024

  26. [26]

    Sliding engineering spin-valley-layer coupling and altermagnetism in bilayer antiferromagnetic honeycomb lattices

    Wen-Xin Jiang, Zhen-Hao Gong, Yuantao Chen, Zhigang Gui, and Li Huang. Sliding engineering spin-valley-layer coupling and altermagnetism in bilayer antiferromagnetic honeycomb lattices. Phys. Rev. B, 113:054441, Feb 2026

  27. [27]

    Controlling magnetism in 2D CrI3 by electrostatic doping

    Shengwei Jiang, Lizhong Li, Zefang Wang, Kin Fai Mak, and Jie Shan. Controlling magnetism in 2D CrI3 by electrostatic doping. Nature Nanotechnology, 13(7):549–553, July 2018

  28. [28]

    Bilayer stacking A -type alter- magnet: A general approach to generating two-dimensional al- termagnetism

    Sike Zeng and Yu-Jun Zhao. Bilayer stacking A -type alter- magnet: A general approach to generating two-dimensional al- termagnetism. Physical Review B, 110(17):174410, November 2024

  29. [29]

    Ferrovalley physics in stacked bilayer altermagnetic systems

    Yun-Qin Li, Yu-Ke Zhang, Xin-Le Lu, Ya-Ping Shao, Zhi-Qiang Bao, Jun-Ding Zheng, Wen-Yi Tong, and Chun-Gang Duan. Ferrovalley physics in stacked bilayer altermagnetic systems. Nano Letters, 25(15):6032–6039, 2025

  30. [30]

    Evgeny Y . Tsymbal. Two-dimensional ferroelectricity by design. Science, 372(6549):1389–1390, June 2021

  31. [31]

    Observation of spin-splitting torque in altermagnets CrSb, February 2026

    Cheng Song, Ruiyue Chu, Xingkai Cheng, Xizhi Fu, Lei Han, Shixuan Liang, Yichen Su, Jiankun Dai, Yanzhang Cao, Weiqi Du, Feng Pan, and Junwei Liu. Observation of spin-splitting torque in altermagnets CrSb, February 2026

  32. [32]

    Crystal-symmetry-paired spin–valley locking in a layered room-temperature metallic altermagnet candidate

    Fayuan Zhang, Xingkai Cheng, Zhouyi Yin, Changchao Liu, Liwei Deng, et al. Crystal-symmetry-paired spin–valley locking in a layered room-temperature metallic altermagnet candidate. Nature Physics, 21(5):760–767, May 2025

  33. [33]

    Osumi, S

    T. Osumi, S. Souma, T. Aoyama, K. Yamauchi, A. Honma, K. Nakayama, T. Takahashi, K. Ohgushi, and T. Sato. Observa- tion of a giant band splitting in altermagnetic mnte. Phys. Rev. B, 109:115102, Mar 2024

  34. [34]

    Observation of Spin Splitting in Room- Temperature Metallic Antiferromagnet CrSb.Advanced Science, 11(43):2406529, November 2024

    Meng Zeng, Ming-Yuan Zhu, Yu-Peng Zhu, Xiang-Rui Liu, Xiao-Ming Ma, et al. Observation of Spin Splitting in Room- Temperature Metallic Antiferromagnet CrSb.Advanced Science, 11(43):2406529, November 2024

  35. [35]

    Altermag- netic polar metallic phase in ultrathin epitaxially strained ruo2 films

    Seung Gyo Jeong, In Hyeok Choi, Sreejith Nair, Luca Buiarelli, Bita Pourbahari, Jin Young Oh, Bonnie YX Lin, James M LeBeau, Nabil Bassim, Daigorou Hirai, et al. Altermag- netic polar metallic phase in ultrathin epitaxially strained ruo2 films. Proceedings of the National Academy of Sciences, 123(10):e2526641123, 2026

  36. [36]

    Layer control of magneto-optical effects and their quantization in spin-valley splitting antiferromagnets

    Jiaqi Feng, Xiaodong Zhou, Meiling Xu, Jingming Shi, and Yinwei Li. Layer control of magneto-optical effects and their quantization in spin-valley splitting antiferromagnets. Nano Letters, 24(13):3898–3905, 2024

  37. [37]

    Gopman, Liang Wu, Takashi Koretsune, Olaf M

    Tomoya Higo, Huiyuan Man, Daniel B. Gopman, Liang Wu, Takashi Koretsune, Olaf M. J. van ’t Erve, et al. Large magneto- optical Kerr effect and imaging of magnetic octupole domains in an antiferromagnetic metal. Nature Photonics, 12(2):73–78, February 2018

  38. [38]

    A. L. Balk, N. H. Sung, S. M. Thomas, P. F. S. Rosa, R. D. McDonald, J. D. Thompson, E. D. Bauer, F. Ronning, and S. A. Crooker. Comparing the anomalous Hall effect and the magneto- optical Kerr effect through antiferromagnetic phase transitions in Mn3Sn. Applied Physics Letters, 114(3):032401, January 2019

  39. [39]

    Klein, Ran Cheng, Kyle L

    Bevin Huang, Genevieve Clark, Efrén Navarro-Moratalla, Dahlia R. Klein, Ran Cheng, Kyle L. Seyler, Ding Zhong, Emma Schmidgall, Michael A. McGuire, David H. Cobden, Wang Yao, Di Xiao, Pablo Jarillo-Herrero, and Xiaodong Xu. Layer- dependent ferromagnetism in a van der Waals crystal down to the monolayer limit. Nature, 546(7657):270–273, June 2017

  40. [40]

    H. Ebert. Magneto-optical effects in transition metal systems. Reports on Progress in Physics, 59(12):1665–1735, 12 1996

  41. [41]

    P. M. Oppeneer, J. Sticht, T. Maurer, and J. Kbler. Ab initio investigation of microscopic enhancement factors in tuning the magneto-optical Kerr effect.Zeitschrift for Physik B Condensed Matter, 88(3):309–315, October 1992

  42. [42]

    Uncompen- sated Linear Dichroism of Magneto-Optical Kerr Effect in a 2D Altermagnet

    Mingliang Liu, Jia-Tao Sun, and Sheng Meng. Uncompen- sated Linear Dichroism of Magneto-Optical Kerr Effect in a 2D Altermagnet. Advanced Functional Materials, page e21111, December 2025

  43. [43]

    A review of magneto-optic effects and its application

    Taskeya Haider. A review of magneto-optic effects and its application. Int. J. Electromagn. Appl, 7(1):17–24, 2017

  44. [44]

    Xiuxian Yang, Ping Yang, Xiaodong Zhou, Wanxiang Feng, and Yugui Yao. First- and second-order magneto-optical effects and intrinsically anomalous transport in the two-dimensional van der Waals layered magnets Cr X Y ( X = S , Se , Te ; Y = Cl , Br , I ). Physical Review B, 106(5):054408, August 2022

  45. [45]

    Gate- Controllable Magneto-optic Kerr Effect in Layered Collinear Antiferromagnets

    Nikhil Sivadas, Satoshi Okamoto, and Di Xiao. Gate- Controllable Magneto-optic Kerr Effect in Layered Collinear Antiferromagnets. Physical Review Letters, 117(26):267203, December 2016

  46. [46]

    Electric Field-Controlled Magneto-Optical Kerr Effect in A-Type Antiferromagnetic Fe 2 CX2 (X = F, Cl) and Its Janus Monolayer

    Peng Wang, Qinxi Liu, Nanshu Liu, Minquan Kuang, Tie Yang, Biao Wang, Meng Ju, Hongkuan Yuan, Xue Jiang, and Jijun Zhao. Electric Field-Controlled Magneto-Optical Kerr Effect in A-Type Antiferromagnetic Fe 2 CX2 (X = F, Cl) and Its Janus Monolayer. ACS Applied Materials & Interfaces, page acsami.3c11811, November 2023

  47. [47]

    Layer control of magneto-optical effects and their quantization in spin-valley splitting antiferromagnets

    Jiaqi Feng, Xiaodong Zhou, Meiling Xu, Jingming Shi, and Yinwei Li. Layer control of magneto-optical effects and their quantization in spin-valley splitting antiferromagnets. Nano Letters, 24(13):3898–3905, 03 2024

  48. [48]

    Experimental ev- idence of néel-order-driven magneto-optical kerr effect in an altermagnetic insulator

    Haolin Pan, Rui-Chun Xiao, Jiahao Han, Hongxing Zhu, Junxue Li, Qian Niu, Yang Gao, and Dazhi Hou. Experimental ev- idence of néel-order-driven magneto-optical kerr effect in an altermagnetic insulator. Phys. Rev. Lett., 136:036701, Jan 2026

  49. [49]

    Symmetry-driven giant magneto–optical kerr effects in altermagnetic insulator

    Jiaxin Luo, Xiaodong Zhou, Jinxuan Liang, Ledong Wang, Qi- uyun Zhou, Yong Jiang, Wenhong Wang, Yugui Yao, Luyi Yang, and Wanjun Jiang. Symmetry-driven giant magneto–optical kerr effects in altermagnetic insulator. Chinese Physics Letters, 43, 01 2026

  50. [50]

    Uncompensated linear dichroism of magneto-optical kerr effect in a 2d altermag- net

    Mingliang Liu, Jiatao Sun, and Sheng Meng. Uncompensated linear dichroism of magneto-optical kerr effect in a 2d altermag- net. Advanced Functional Materials, 36, 2025

  51. [51]

    Steven Dodge, Matthew Brahlek, and Liang Wu

    Isaiah Gray, Qinwen Deng, Qi Tian, Michael Chilcote, J. Steven Dodge, Matthew Brahlek, and Liang Wu. Time-resolved magneto-optical effects in the altermagnet candidate MnTe, Oc- tober 2024. arXiv:2404.05020. 9

  52. [52]

    Löhneysen

    Christoph Sürgers, Wolfram Kittler, Thomas Wolf, and Hilbert V . Löhneysen. Anomalous Hall effect in the noncollinear antiferro- magnet Mn5Si3. AIP Advances, 6(5):055604, May 2016

  53. [53]

    Naoto Nagaosa, Jairo Sinova, Shigeki Onoda, A. H. MacDonald, and N. P. Ong. Anomalous hall effect.Rev.Mod. Phys., 82:1539– 1592, May 2010

  54. [54]

    Jungwirth, and J

    Libor Šmejkal, Rafael González-Hernández, T. Jungwirth, and J. Sinova. Crystal time-reversal symmetry breaking and spon- taneous Hall effect in collinear antiferromagnets. Science Advances, 6(23):eaaz8809, June 2020

  55. [55]

    Georg K. H. Madsen and David J. Singh. BoltzTraP. A code for calculating band-structure dependent quantities. Computer Physics Communications, 175(1):67–71, 2006

  56. [56]

    Combined first-principles and boltzmann transport theory methodology for studying magnetotransport in magnetic materials

    Zhihao Liu, Shengnan Zhang, Zhong Fang, Hongming Weng, and Quansheng Wu. Combined first-principles and boltzmann transport theory methodology for studying magnetotransport in magnetic materials. Phys. Rev. Res., 6:043185, Nov 2024

  57. [57]

    Kohn and L

    W. Kohn and L. J. Sham. Self-consistent equations including ex- change and correlation effects. Phys. Rev., 140:A1133–A1138, Nov 1965

  58. [58]

    Kresse and J

    G. Kresse and J. Furthmüller. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B, 54:11169–11186, Oct 1996

  59. [59]

    Kresse and J

    G. Kresse and J. Furthmüller. Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set. Computational Materials Science, 6(1):15–50, 1996

  60. [60]

    Monkhorst and James D

    Hendrik J. Monkhorst and James D. Pack. Special points for brillouin-zone integrations. Phys. Rev. B, 13:5188–5192, Jun 1976

  61. [61]

    First principles phonon calcula- tions in materials science

    Atsushi Togo and Isao Tanaka. First principles phonon calcula- tions in materials science. Scripta Materialia, 108:1–5, 2015

  62. [62]

    Deringer, Andrei L

    V olker L. Deringer, Andrei L. Tchougréeff, and Richard Dron- skowski. Crystal orbital hamilton population (cohp) analysis as projected from plane-wave basis sets. The Journal of Physical Chemistry A, 115(21):5461–5466, 2011

  63. [63]

    Deringer, Andrei L

    Stefan Maintz, V olker L. Deringer, Andrei L. Tchougréeff, and Richard Dronskowski. Lobster: A tool to extract chemical bonding from plane-wave based dft. Journal of Computational Chemistry, 37(11):1030–1035, 2016

  64. [64]

    P. E. Blöchl. Projector augmented-wave method. Phys. Rev. B, 50:17953–17979, Dec 1994

  65. [65]

    Kresse and D

    G. Kresse and D. Joubert. From ultrasoft pseudopotentials to the projector augmented-wave method. Phys. Rev. B, 59:1758– 1775, Jan 1999

  66. [66]

    Mostofi, Jonathan R

    Arash A. Mostofi, Jonathan R. Yates, Giovanni Pizzi, Young- Su Lee, Ivo Souza, David Vanderbilt, and Nicola Marzari. An updated version of wannier90: A tool for obtaining maximally-localised Wannier functions. Computer Physics Communications, 185(8):2309–2310, 2014

  67. [67]

    BoltzWann: A code for the evalua- tion of thermoelectric and electronic transport properties with a maximally-localized Wannier functions basis

    Giovanni Pizzi, Dmitri V olja, Boris Kozinsky, Marco Fornari, and Nicola Marzari. BoltzWann: A code for the evalua- tion of thermoelectric and electronic transport properties with a maximally-localized Wannier functions basis. Computer Physics Communications, 185(1):422–429, January 2014

  68. [68]

    Vaspberry: a python package to compute berry curvature and related properties from vasp output

    S Poncé, F Macheda, E R Margine, et al. Vaspberry: a python package to compute berry curvature and related properties from vasp output. Computer Physics Communications, 271:108199, 2022

  69. [69]

    Bilbao crystallographic server: I

    Mois Ilia Aroyo, Juan Manuel Perez-Mato, Cesar Capillas, Eli Kroumova, Svetoslav Ivantchev, Gotzon Madariaga, Asen Kirov, and Hans Wondratschek. Bilbao crystallographic server: I. databases and crystallographic computing programs. Crystalline Materials, 221(1):15–27, 1 2006

  70. [70]

    Multiple strain-induced effects beyond the piezoelec- tric effect in altermagnetic monolayer Co 2 MoSe 4

    Weijie Zhang, Bin Xiao, Chenlu Li, Chengyu Qiu, Hui Zeng, and Jun Zhao. Multiple strain-induced effects beyond the piezoelec- tric effect in altermagnetic monolayer Co 2 MoSe 4. Physical Review B, 112(14):144436, October 2025

  71. [71]

    Valley-Related Multipiezo Effect and Non- collinear Spin Current in an Altermagnet Fe2 Se2 O Monolayer

    Yanzhao Wu, Li Deng, Xiang Yin, Junwei Tong, Fubo Tian, and Xianmin Zhang. Valley-Related Multipiezo Effect and Non- collinear Spin Current in an Altermagnet Fe2 Se2 O Monolayer. Nano Letters, 24(34):10534–10539, August 2024

  72. [72]

    2d materials: Strain engineering of 2d materials: Issues and opportunities at the interface (adv

    Zhaohe Dai, Luqi Liu, and Zhong Zhang. 2d materials: Strain engineering of 2d materials: Issues and opportunities at the interface (adv. mater. 45/2019). Advanced Materials, 31(45):1970322, 2019

  73. [73]

    Manipulating 2d materials through strain engineering

    Xiangxiang Yu, Zhuiri Peng, Langlang Xu, Wenhao Shi, Zheng Li, Xiaohan Meng, Xiao He, Zhen Wang, Shikun Duan, Lei Tong, Xinyu Huang, Xiangshui Miao, Weida Hu, and Lei Ye. Manipulating 2d materials through strain engineering. Small, 20(38):2402561, 2024

  74. [74]

    Large magneto-optical kerr effect in noncollinear an- tiferromagnets mn3x(x=Rh,Ir,Pt)

    Wanxiang Feng, Guang-Yu Guo, Jian Zhou, Yugui Yao, and Qian Niu. Large magneto-optical kerr effect in noncollinear an- tiferromagnets mn3x(x=Rh,Ir,Pt) . Phys. Rev. B, 92:144426, Oct 2015

  75. [75]

    Enhanced magneto-optical kerr effect at fe/insulator interfaces

    Bo Gu, Saburo Takahashi, and Sadamichi Maekawa. Enhanced magneto-optical kerr effect at fe/insulator interfaces. Phys. Rev. B, 96:214423, Dec 2017