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Quasi-symmetry Constrained Spin Ferromagnetism in Altermagnets

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Pith's one-line read A uniaxial spin space group decides the order in spin-orbit coupling at which an altermagnet's weak ferromagnetic moment appears, explaining the near-zero moments of RuO2 and MnTe.

desk verdict A genuinely useful symmetry principle for when weak ferromagnetism in altermagnets is large or tiny; the spin-channel caveat is real but the paper is honest about it. read the letter →

arxiv 2412.09338 v2 pith:J34KBR42 submitted 2024-12-12 cond-mat.str-el cond-mat.mes-hallcond-mat.mtrl-sci

Mercè Roig , Yue Yu , Rune C. Ekman , Andreas Kreisel , Brian M. Andersen , Daniel F. Agterberg This is my paper · ORCID
classification cond-mat.str-elcond-mat.mes-hallcond-mat.mtrl-sci
keywords altermagnetismspin-orbitcouplingweakferromagnetismquasi-symmetryuniaxialspinspacegroupLandautheoryanomalousHalleffectmagneticanisotropy
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

Altermagnets are collinear antiferromagnets whose spin-split bands are momentum-dependent; in the presence of spin-orbit coupling they can host both an anomalous Hall effect and a weak ferromagnetic moment. Density functional theory finds that some altermagnets (RuO2, MnTe) have a large Hall effect but a nearly vanishing magnetic moment, while others (FeSb2) have a sizable one. This paper argues that the size of the induced ferromagnetic spin moment is set by a symmetry that the normal state acquires when only one component of the spin-orbit coupling is present, called the uniaxial spin space group. Using microscopic models and Landau theory, it shows the moment is generated at linear, quadratic, or cubic order in spin-orbit coupling depending on the crystal point group and the symmetry of the altermagnetic spin splitting, and it derives analytic expressions for the magnetic anisotropy energy that fix the preferred Néel-vector orientation.

What carries the argument

The central object is the uniaxial spin space group: the quasi-symmetry of the normal state that appears when only one Cartesian component of the spin-orbit coupling is nonzero, e.g., $\lambda_z \neq 0$ with $\lambda_x = \lambda_y = 0$. In that limit the Hamiltonian acquires spin rotational symmetry about the SOC axis, a symmetry higher than the magnetic space group but lower than the full spin space group. The criterion is analyticity-based: a Landau coefficient or response function can host a contribution $\lambda_x^{n_x}\lambda_y^{n_y}\lambda_z^{n_z} X$ only if the corresponding product of SOC order parameters with $X$ is a spin-scalar in the trivial irreducible representation of the SOC-free system. Applied to the bilinear $M$–$N$ coupling, this produces Table I: linear in SOC for D2h and for D4h with A2g splitting, quadratic for D4h with B1g or B2g splitting, and cubic for D6h B1g/B2g and Oh A2g. The same machinery yields analytic formulas for the magnetic anisotropy coefficients $s_1$ and $s_2$ in terms of the itinerant susceptibility $L(k)$, showing that the Néel easy axis can switch with Fermi energy.

What would settle it

Run an exact diagonalization of the minimal model for a rutile altermagnet (D4h, B2g) such as RuO2 with the spin-orbit coupling strength scaled by a factor $\alpha_{\text{soc}}$; the paper predicts $|\mathbf{M}| \propto \alpha_{\text{soc}}^2$, so observing a linear dependence would falsify the central claim. Equivalently, for a D6h B1g altermagnet like MnTe or CrSb, the moment should scale as $\alpha_{\text{soc}}^3$; a lower-order scaling would refute the selection rule.

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Extended reading notes

Core claim

The paper's central claim is that a SOC-enabled quasi-symmetry, the uniaxial spin space group, determines the order in spin-orbit coupling at which a weak ferromagnetic spin moment is induced in an altermagnet. For a rutile altermagnet like RuO2, whose spin splitting belongs to the B2g irreducible representation of D4h, the bilinear coupling MxNy + MyNx is symmetry allowed, but the intrinsic crystal symmetry forces the two coefficients equal while the quasi-symmetry would require them to be opposite; the linear-in-SOC term therefore vanishes and the moment scales quadratically. In orthorhombic FeSb2 (B1g of D2h) the quasi-symmetry permits a linear term, giving the calculated moment of roughly 0.03 μB, while in hexagonal MnTe and CrSb (B1g of D6h) the leading term is cubic. The paper derives a general criterion by treating the three SOC components as order parameters in a SOC-free Landau theory, verifies the scaling by exact diagonalization of minimal models calibrated to DFT, and shows the same symmetry reasoning explains why the AHE is generically linear in SOC and tied to the SOC component parallel to the Néel vector.

Load-bearing premise

The load-bearing premise is that altermagnetism is driven purely by exchange interactions in the spin channel with no orbital angular momentum contribution, and that response functions are analytic in the spin-orbit coupling away from band crossings; if either fails, the quasi-symmetry selection rules for the spin moment need not hold.

Editorial extensions

If this is right

  • Rutile altermagnets (D4h, B2g spin splitting) such as RuO2, MnF2, NiF2 and CoF2 have a weak ferromagnetic spin moment that is at least quadratic in spin-orbit coupling, explaining the near-zero DFT moments while the anomalous Hall effect remains large.
  • Hexagonal altermagnets with B1g splitting (MnTe, CrSb) acquire a ferromagnetic moment only at cubic order in spin-orbit coupling, so their weak spin moment should be far below the linear-in-SOC scale.
  • Orthorhombic (D2h) and tetragonal A2g (Nb2FeB2, Ta2FeB2) altermagnets have a moment linear in spin-orbit coupling, with FeSb2's calculated 0.03 μB as a concrete example.
  • The analytic magnetic anisotropy coefficients s1 and s2 imply that the Néel-vector easy axis can switch between out-of-plane and in-plane as the Fermi energy moves, as previously reported for RuO2's c-axis to in-plane switch.
  • Because the quasi-symmetry criterion is independent of the microscopic model, it applies to any altermagnet whose ordering is driven purely by exchange interactions.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The same uniaxial spin space group reasoning should constrain other SOC-induced linear responses (for instance spin Hall or magneto-optical coefficients), since those responses are also even or odd under spin rotations in a component-wise way.
  • If a material is found whose altermagnetic ordering involves orbital angular momentum (a violation of the spin-channel assumption), the predicted linear/quadratic/cubic hierarchy could be disrupted; measuring the orbital versus spin part of the weak moment would test this.
  • The anisotropy-energy expressions suggest a practical tuning knob: doping or gating an altermagnet to shift the Fermi energy across the sign change of L(k) should reorient the Néel vector, an experimentally testable extension the paper does not pursue.
  • The quasi-symmetry argument relies on analytic response functions, so near Fermi-surface band crossings the scaling could break down; materials tuned to such crossings may show anomalously large weak ferromagnetism at SOC orders the symmetry would otherwise forbid.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

1 major / 5 minor

Summary. The paper addresses the material-dependent size of the weak ferromagnetic spin moment induced by spin-orbit coupling in altermagnets. Starting from the two-band minimal models of Ref. [35] and the Landau free energy of Eq. (1), the authors derive the one-loop bilinear coupling between the magnetization and the Néel order (Eq. (8)), the magnetic anisotropy coefficients s1 and s2 (Eqs. (11)-(12)), and Table I of lowest-order M-N invariants for the relevant point groups and altermagnetic irreps. They then introduce a 'uniaxial spin space-group' quasi-symmetry, generated when two SOC components vanish, and use it to determine the leading power of SOC at which the spin moment can appear. The criterion is applied to explain why RuO2 (D4h, B2g) and MnTe (D6h, B1g) have nearly vanishing FM spin moments despite large anomalous Hall responses, while FeSb2 (D2h, B1g) has a sizable moment, and to identify the Néel easy axis. The central claim is that this SOC power counting is fixed by the SOC-enabled quasi-symmetry for any altermagnet whose instability is purely in the spin channel.

Significance. The paper offers a clear and useful organizing principle: the ratio between the anomalous Hall conductivity and the weak FM spin moment in altermagnets is controlled by the point group and the altermagnetic irrep, with falsifiable predictions for the SOC power (linear for D2h B1g, quadratic for D4h B2g, cubic for D6h B1g and Oh A2g). The one-loop derivation of Eq. (8) and the analytic anisotropy expressions are clean, and the End Matter quasi-symmetry criterion is a coherent model-independent argument. The exact-diagonalization results of Fig. 1 support the predicted scalings, and the target DFT moments are not used as fit parameters, even though the model parameters are inherited from a prior DFT-calibrated study. The anisotropy formulas and the predicted easy-axis switch as a function of chemical potential are concrete and testable. The main weakness is that the generality of the central claim is explicitly conditional on the spin-channel assumption, which the paper does not verify for the specific materials.

major comments (1)
  1. [Main text, paragraph following Fig. 2; Conclusions] The claimed model-independent universality is explicitly conditional on the assumption stated in the main text: 'The only assumption ... is that AM is an instability purely in the spin-channel.' This assumption is load-bearing: the End Matter criterion is constructed for order parameters that are spin vectors with orbital labels, and it requires the relevant Landau term to be a spin scalar and orbitally trivial. A spin-singlet orbital component of the AM order in the same irrep Γ_N would not transform under the uniaxial spin rotations, so it could in principle couple to the magnetization at a lower order in SOC than the spin-channel criterion predicts. The paper does not verify that the AM order in RuO2, MnTe, or FeSb2 is dominated by the spin channel. I ask the authors to provide such verification (for example, by estimating the orbital contribution to the AM order parameter in their DFT calculations) or to explicitly state in the abstract and title that the result applies only to exchange-driven, spin-only altermagnets and that an orbital AM component can alter the SOC power of the total induced moment.
minor comments (5)
  1. [Table I caption] The last column uses only a check or cross for whether Mi is linear in SOC; for the crosses, the actual leading SOC order (quadratic versus cubic) is stated in the text and End Matter but would be much more useful if added directly to the table.
  2. [Eq. (9)] The notation df(ε)/dε evaluated at ε = E^±_k is nonstandard; please use f'(E^±_k) or define the derivative symbol in the text.
  3. [Introduction, first paragraph] The phrase 'the AHE and the ferromagnetic spin moment share the same symmetry and hence are usually proportional' is potentially misleading, since the paper demonstrates that the SOC power can differ; 'share the same symmetry selection rules' would be more accurate.
  4. [End Matter, analyticity caveat] The End Matter caveat that response functions are assumed to be analytic in λx, λy, λz, excluding band crossings at the Fermi level, is important enough to be restated in the main text where the universal quasi-symmetry claim is made.
  5. [Supplementary Material S4] The table of secondary order parameters is stated without showing the one-loop calculation that produces the listed SOC powers; please include the derivation or explicitly identify the table as a summary of calculations presented elsewhere.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity; the central SOC-scaling law is derived from independent group theory and a self-contained microscopic calculation.

full rationale

The paper's derivation chain runs as follows. First, standard Landau symmetry analysis (Table I) determines which bilinear M-N invariants are allowed at linear order in SOC, using the antisymmetric-direct-product criterion of McClarty and Rau (Ref. 23, an external reference). Second, a one-loop calculation in the minimal model yields Eq. (8), whose (M x N) form reproduces the group-theoretic selection rule and gives the explicit SOC power; this is a genuine derivation, not a re-statement of the target DFT moments. Third, a separate quasi-symmetry argument (End Matter) treats the SOC components as symmetry-breaking order parameters in the SOC-free spin-space group and derives the same linear/quadratic/cubic selections from first principles, again without invoking any fitted FM moment. The model parameters (hoppings and SOC strengths) are taken from the authors' prior minimal-model paper (Ref. 35) and from DFT band splittings, but the FM spin moment itself is computed, not fitted to the DFT FM moments quoted in the introduction; the agreement with DFT (RuO2 nearly zero, FeSb2 ~0.03 mu_B) is therefore a nontrivial consistency check rather than a built-in result. The only stated microscopic assumption, that altermagnetism is purely a spin-channel instability driven solely by exchange interactions, is explicitly announced in the quasi-symmetry section and is acknowledged in the Conclusions as a caveat for orbital moments. That is a limitation on the universality claim, not a circular reduction, and the paper flags it. The load-bearing self-citation to Ref. 35 supplies the starting Hamiltonian, but the new results (the SOC power of the induced moment, the anisotropy coefficients s1 and s2, and the quasi-symmetry criterion) are derived, not assumed. No equation or claim reduces to its own input by construction, so the paper is not significantly circular.

Assumptions & free parameters 4 free parameters · 4 assumptions · 0 invented entities

The central scaling results are derived from a microscopic model whose parameters are fixed by DFT band structures, not by the target FM moments. The quasi-symmetry criterion itself is model-independent, resting on group theory and analyticity. The main circularity burden comes from using the authors' own minimal model and DFT-estimated inputs to 'confirm' DFT phenomenology.

free parameters (4)
  • RuO2 SOC parameters (λx, λy, λz) = (0.05, 0.05, 0.17) eV
    Estimated from DFT calculations (SM S5) by reading off SOC-induced splittings at high-symmetry points; used as input to the minimal model in Fig. 1 and anisotropy calculations.
  • FeSb2 SOC parameters (λx, λy, λz) = (2.7, 6.6, 75) meV
    Estimated from DFT calculations (SM S5) using Wien2k; used as input for the FeSb2 model.
  • Néel order magnitude Nx = 0.2 eV (RuO2), 0.05 eV (FeSb2)
    Chosen based on DFT estimates; sets the size of the order parameter in the numerical calculations of Fig. 1.
  • Hopping parameters = Tables S3-S4 (from Ref [35])
    Tight-binding hoppings for rutile and FeSb2 taken from the authors' prior minimal-model paper; not fitted in this work but required for the numerical results.
assumptions (4)
  • domain assumption Altermagnetic order is purely spin-channel (exchange-driven, no orbital angular momentum contribution)
    Stated explicitly in the main text as the only assumption underlying the quasi-symmetry analysis; if orbital moments are present, the selection rules for the spin FM moment may change.
  • domain assumption Response functions are analytic in the SOC components λx, λy, λz
    Invoked in the End Matter (General SOC-enabled quasi-symmetry) to justify that the leading SOC power is determined by the lowest-order allowed Landau term; requires the density of states not to be concentrated at band crossings.
  • domain assumption The minimal model of Ref [35] captures the DFT phenomenology of altermagnets
    The microscopic Hamiltonian in Eq. (2) is inherited from the authors' prior work and is assumed to faithfully represent the band structure and SOC of real altermagnets.
  • standard math Landau free-energy expansion near Tc is valid
    The derivation of cij and s1,s2 uses a one-loop expansion of the free energy close to the critical temperature, a standard approach.

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Pith. "Pith review of Quasi-symmetry Constrained Spin Ferromagnetism in Altermagnets." pith.science (2026). https://pith.science/paper/J34KBR42

@misc{pith2026241209338,
  author       = {Pith},
  title        = {Pith review of: Quasi-symmetry Constrained Spin Ferromagnetism in Altermagnets},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/J34KBR42}},
  note         = {Machine review of arXiv:2412.09338}
}
read the original abstract

Altermagnets break time-reversal symmetry and their spin-orbit coupling (SOC) allow for an anomalous Hall effect (AHE) that depends on the direction of the N\'eel ordering vector. The AHE and the ferromagnetic spin moment share the same symmetry and hence are usually proportional. However, density functional theory (DFT) calculations find that the AHE exists with negligible ferromagnetic spin moment for some compounds, whereas it reaches sizable values for other altermagnets. By examining realistic minimal models for altermagnetism in which the DFT phenomenology is captured, we uncover a general SOC-enabled quasi-symmetry, the uniaxial spin space-group, that provides a natural explanation for the amplitude of the ferromagnetic spin moment across the vast range of different altermagnetic materials. Additionally, we derive analytic expressions for the magnetic anisotropy energy, providing a simple means to identify the preferred N\'eel vector orientation for altermagnets.

Figures

Figures reproduced from arXiv: 2412.09338 by the authors.

Figure 1
Figure 1. FIG. 1. Minimal model band structures and induced mag [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. SOC-enabled quasi-symmetry in a tetragonal system [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Classification scheme of the spin space group and [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗

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Works this paper leans on

51 extracted references · 45 canonical work pages · cited by 1 Pith paper

  1. [35]

    Minimal models for al- termagnetism,

    Mercè Roig, Andreas Kreisel, Yue Yu, Brian M. Ander- sen, and Daniel F. Agterberg, “Minimal models for al- termagnetism,” Phys. Rev. B110, 144412 (2024)

    work page 2024

  2. [1]

    Anomalous Hall effect,

    Naoto Nagaosa, Jairo Sinova, Shigeki Onoda, A. H. Mac- Donald, and N. P. Ong, “Anomalous Hall effect,” Rev. Mod. Phys. 82, 1539–1592 (2010)

    work page 2010

  3. [2]

    Quantum Nonlinear Hall Effect Induced by Berry Curvature Dipole in Time- Reversal Invariant Materials,

    Inti Sodemann and Liang Fu, “Quantum Nonlinear Hall Effect Induced by Berry Curvature Dipole in Time- Reversal Invariant Materials,” Phys. Rev. Lett. 115, 216806 (2015)

    work page 2015

  4. [3]

    Quantum metric nonlinear Hall ef- fect in a topological antiferromagnetic heterostructure,

    Anyuan Gao, Yu-Fei Liu, Jian-Xiang Qiu, Barun Ghosh, Thaís V. Trevisan, Yugo Onishi, Chaowei Hu, Tiema Qian, Hung-Ju Tien, Shao-Wen Chen, Mengqi Huang, Damien Bérubé, Houchen Li, Christian Tzschaschel, Thao Dinh, et al., “Quantum metric nonlinear Hall ef- fect in a topological antiferromagnetic heterostructure,” Science 381, 181–186 (2023)

    work page 2023

  5. [4]

    Uni- fication of Nonlinear Anomalous Hall Effect and Nonre- ciprocal Magnetoresistance in Metals by the Quantum Geometry,

    Daniel Kaplan, Tobias Holder, and Binghai Yan, “Uni- fication of Nonlinear Anomalous Hall Effect and Nonre- ciprocal Magnetoresistance in Metals by the Quantum Geometry,” Phys. Rev. Lett.132, 026301 (2024)

    work page 2024

  6. [5]

    Quantum Geometry Induced Nonlinear Transport in Altermagnets,

    Yuan Fang, Jennifer Cano, and Sayed Ali Akbar Gho- rashi, “Quantum Geometry Induced Nonlinear Transport in Altermagnets,” Phys. Rev. Lett.133, 106701 (2024)

    work page 2024

  7. [6]

    Nonlinear Hall effects,

    Z. Z. Du, Hai-Zhou Lu, and X. C. Xie, “Nonlinear Hall effects,” Nature Reviews Physics3, 744–752 (2021)

    work page 2021

  8. [7]

    Quantum-metric-induced nonlinear transport in a topological antiferromagnet,

    Naizhou Wang, Daniel Kaplan, Zhaowei Zhang, To- bias Holder, Ning Cao, Aifeng Wang, Xiaoyuan Zhou, Feifei Zhou, Zhengzhi Jiang, Chusheng Zhang, Shihao Ru, Hongbing Cai, Kenji Watanabe, Takashi Taniguchi, BinghaiYan, andWeiboGao,“Quantum-metric-induced nonlinear transport in a topological antiferromagnet,” Nature 621, 487–492 (2023)

    work page 2023

Show all 51 references
  1. [8]

    Broken Kramers Degen- eracy in Altermagnetic MnTe,

    Suyoung Lee, Sangjae Lee, Saegyeol Jung, Jiwon Jung, Donghan Kim, Yeonjae Lee, Byeongjun Seok, Jaeyoung Kim, Byeong Gyu Park, Libor Šmejkal, Chang-Jong Kang, and Changyoung Kim, “Broken Kramers Degen- eracy in Altermagnetic MnTe,” Phys. Rev. Lett. 132, 036702 (2024)

    2024

  2. [9]

    Altermagnetic lifting of Kramers spin degeneracy,

    J. Krempaský, L. Šmejkal, S. W. D’Souza, M. Ha- jlaoui, G. Springholz, K. Uhlířová, F. Alarab, P. C. Constantinou, V. Strocov, D. Usanov, W. R. Pudelko, R. González-Hernández, A. Birk Hellenes, Z. Jansa, H. Reichlová, Z. Šobáň, R. D. Gonzalez Betancourt, P. Wadley, J. Sinova, ...

    2024

  3. [10]

    Observation of a giant band splitting in altermagnetic MnTe,

    T. Osumi, S. Souma, T. Aoyama, K. Yamauchi, A. Honma, K. Nakayama, T. Takahashi, K. Ohgushi, and T. Sato, “Observation of a giant band splitting in altermagnetic MnTe,” Phys. Rev. B109, 115102 (2024)

    2024

  4. [11]

    Topological Weyl Altermagnetism in CrSb,

    Cong Li, Mengli Hu, Zhilin Li, Yang Wang, Wanyu Chen, Balasubramanian Thiagarajan, Mats Leandersson, Craig Polley, Timur Kim, Hui Liu, Cosma Fulga, Maia G. 6 Vergniory, Oleg Janson, Oscar Tjernberg, and Jeroen van den Brink, “Topological Weyl Altermagnetism in CrSb,” arXiv (20...

    2024 doi arXiv

  5. [12]

    Three-dimensional map- ping of the altermagnetic spin splitting in CrSb,

    Guowei Yang, Zhanghuan Li, Sai Yang, Jiyuan Li, Hao Zheng, Weifan Zhu, Ze Pan, Yifu Xu, Saizheng Cao, Wenxuan Zhao, Anupam Jana, Jiawen Zhang, Mao Ye, Yu Song, Lun-Hui Hu, Lexian Yang, Jun Fujii, Ivana Vobornik, Ming Shi, Huiqiu Yuan, Yongjun Zhang, Yuanfeng Xu, and Yang Liu, ...

    2025

  6. [13]

    Direct observation of altermagnetic band splitting in CrSb thin films,

    Sonka Reimers, Lukas Odenbreit, Libor Šmejkal, Vladimir N. Strocov, Procopios Constantinou, Anna B. Hellenes, Rodrigo Jaeschke Ubiergo, Warlley H. Cam- pos, VenkataK.Bharadwaj, AtasiChakraborty, Thibaud Denneulin, Wen Shi, Rafal E. Dunin-Borkowski, Suvadip Das, Mathias Kläui, ...

    2024

  7. [14]

    Large Band Splitting in g-Wave Altermagnet CrSb,

    Jianyang Ding, Zhicheng Jiang, Xiuhua Chen, Zicheng Tao, Zhengtai Liu, Tongrui Li, Jishan Liu, Jianping Sun, Jinguang Cheng, Jiayu Liu, Yichen Yang, Runfeng Zhang, Liwei Deng, Wenchuan Jing, Yu Huang, Yum- ing Shi, Mao Ye, Shan Qiao, Yilin Wang, Yanfeng Guo, Donglai Feng, and ...

    2024

  8. [15]

    An anomalous Hall effect in altermagnetic ruthenium diox- ide,

    Zexin Feng, Xiaorong Zhou, Libor Šmejkal, Lei Wu, Zengwei Zhu, Huixin Guo, Rafael González-Hernández, Xiaoning Wang, Han Yan, Peixin Qin, Xin Zhang, Hao- jiang Wu, Hongyu Chen, Ziang Meng, Li Liu, Zhengcai Xia, Jairo Sinova, Tomáš Jungwirth, and Zhiqi Liu, “An anomalous Hall e...

    2022

  9. [16]

    Coexistence of anomalous Hall effect and weak magne- tization in a nominally collinear antiferromagnet MnTe,

    K. P. Kluczyk, K. Gas, M. J. Grzybowski, P. Skupiński, M. A. Borysiewicz, T. Fas, J. Suffczyński, J. Z. Do- magala, K. Grasza, A. Mycielski, M. Baj, K. H. Ahn, K. Výborný, M. Sawicki, and M. Gryglas-Borysiewicz, “Coexistence of anomalous Hall effect and weak magne- tization in...

    2024

  10. [17]

    Spontaneous Anomalous Hall Effect Arising from an Unconventional Compensated Magnetic Phase in a Semiconductor,

    R. D. Gonzalez Betancourt, J. Zubáč, R. Gonzalez- Hernandez, K. Geishendorf, Z. Šobáň, G. Springholz, K. Olejník, L. Šmejkal, J. Sinova, T. Jungwirth, S. T. B. Goennenwein, A. Thomas, H. Reichlová, J. Železný, and D. Kriegner, “Spontaneous Anomalous Hall Effect Arising from an...

    2023

  11. [18]

    Crystal time-reversal symmetry breaking and spontaneous Hall effect in collinear antifer- romagnets,

    Libor Šmejkal, Rafael González-Hernández, T. Jung- wirth, and J. Sinova, “Crystal time-reversal symmetry breaking and spontaneous Hall effect in collinear antifer- romagnets,” Sci. Adv.6 (2020), 10.1126/sciadv.aaz8809

    2020 doi

  12. [19]

    Be- yond Conventional Ferromagnetism and Antiferromag- netism: A Phase with Nonrelativistic Spin and Crystal Rotation Symmetry,

    Libor Šmejkal, Jairo Sinova, and Tomas Jungwirth, “Be- yond Conventional Ferromagnetism and Antiferromag- netism: A Phase with Nonrelativistic Spin and Crystal Rotation Symmetry,” Phys. Rev. X12, 031042 (2022)

    2022

  13. [20]

    Emerging Research Landscape of Altermagnetism,

    Libor Šmejkal, Jairo Sinova, and Tomas Jungwirth, “Emerging Research Landscape of Altermagnetism,” Phys. Rev. X12, 040501 (2022)

    2022

  14. [21]

    Anomalous Hall an- tiferromagnets,

    LiborŠmejkal, AllanH.MacDonald, JairoSinova, Satoru Nakatsuji, and Tomas Jungwirth, “Anomalous Hall an- tiferromagnets,” Nat. Rev. Mater.7, 482–496 (2022)

    2022

  15. [22]

    Multifunctional an- tiferromagnetic materials with giant piezomagnetism and noncollinearspincurrent,

    Hai-Yang Ma, Mengli Hu, Nana Li, Jianpeng Liu, Wang Yao, Jin-Feng Jia, and Junwei Liu, “Multifunctional an- tiferromagnetic materials with giant piezomagnetism and noncollinearspincurrent,” Nat.Commun. 12,1–8(2021)

    2021

  16. [23]

    Landau Theory of Altermagnetism,

    Paul A. McClarty and Jeffrey G. Rau, “Landau Theory of Altermagnetism,” Phys. Rev. Lett.132, 176702 (2024)

    2024

  17. [24]

    Anomalous-Hall Neel textures in altermagnetic materials,

    Rui-Chun Xiao, Hui Li, Hui Han, Wei Gan, Meng- meng Yang, Ding-Fu Shao, Shu-Hui Zhang, Yang Gao, Mingliang Tian, and Jianhui Zhou, “Anomalous-Hall Neel textures in altermagnetic materials,” arXiv (2024), 10.48550/arXiv.2411.10147, 2411.10147

    2024 doi arXiv

  18. [25]

    Topological transition from nodal to nodeless Zeeman splitting in altermag- nets,

    Rafael M. Fernandes, Vanuildo S. de Carvalho, Turan Birol, and Rodrigo G. Pereira, “Topological transition from nodal to nodeless Zeeman splitting in altermag- nets,” Phys. Rev. B109, 024404 (2024)

    2024

  19. [26]

    Altermag- netism with non-collinear spins,

    Sang-Wook Cheong and Fei-Ting Huang, “Altermag- netism with non-collinear spins,” npj Quantum Mater. 9, 1–6 (2024)

    2024

  20. [27]

    Origin of the gos- samer ferromagnetism in MnTe,

    I. I. Mazin and K. D. Belashchenko, “Origin of the gos- samer ferromagnetism in MnTe,” Phys. Rev. B 110, 214436 (2024)

    2024

  21. [28]

    Itin- erant Antiferromagnetism in RuO2,

    T. Berlijn, P. C. Snijders, O. Delaire, H.-D. Zhou, T. A. Maier, H.-B. Cao, S.-X. Chi, M. Matsuda, Y. Wang, M. R. Koehler, P. R. C. Kent, and H. H. Weitering, “Itin- erant Antiferromagnetism in RuO2,” Phys. Rev. Lett. 118, 077201 (2017)

    2017

  22. [29]

    Nonmagnetic Ground State in RuO2 Revealed by Muon Spin Rotation,

    M. Hiraishi, H. Okabe, A. Koda, R. Kadono, T. Muroi, D. Hirai, and Z. Hiroi, “Nonmagnetic Ground State in RuO2 Revealed by Muon Spin Rotation,” Phys. Rev. Lett. 132, 166702 (2024)

    2024

  23. [30]

    Absence of magnetic order in RuO2: insights from µSR spectroscopy and neutron diffraction,

    Philipp Keßler, Laura Garcia-Gassull, Andreas Suter, Thomas Prokscha, Zaher Salman, Dmitry Khalyavin, Pascal Manuel, Fabio Orlandi, Igor I. Mazin, Roser Va- lentí, and Simon Moser, “Absence of magnetic order in RuO2: insights from µSR spectroscopy and neutron diffraction,” npj...

    2024 doi

  24. [31]

    Staggered Dzyaloshinskii-Moriya interaction inducing weak ferro- magnetism in centrosymmetric altermagnets and weak ferrimagnetism in noncentrosymmetric altermagnets,

    Carmine Autieri, Raghottam M. Sattigeri, Giuseppe Cuono, and Amar Fakhredine, “Staggered Dzyaloshinskii-Moriya interaction inducing weak ferro- magnetism in centrosymmetric altermagnets and weak ferrimagnetism in noncentrosymmetric altermagnets,” Phys. Rev. B111, 054442 (2025)

    2025

  25. [32]

    Pre- diction of unconventional magnetism in doped FeSb2,

    Igor I. Mazin, Klaus Koepernik, Michelle D. Johannes, Rafael González-Hernández, and Libor Šmejkal, “Pre- diction of unconventional magnetism in doped FeSb2,” Proc. Natl. Acad. Sci. U.S.A.118, e2108924118 (2021)

    2021

  26. [33]

    In- trinsic anomalous hall effect in altermagnets,

    Lotan Attias, Alex Levchenko, and Maxim Khodas, “In- trinsic anomalous hall effect in altermagnets,” Phys. Rev. B 110, 094425 (2024)

    2024

  27. [34]

    Interplay of alter- magnetism and weak ferromagnetism in two-dimensional RuF4,

    Marko Milivojević, Marko Orozović, Silvia Picozzi, Mar- tin Gmitra, and Srđan Stavrić, “Interplay of alter- magnetism and weak ferromagnetism in two-dimensional RuF4,” 2D Mater.11, 035025 (2024)

    2024

  28. [36]

    Group Theory on Quasisymmetry and Protected Near Degeneracy,

    Jiayu Li, Ao Zhang, Yuntian Liu, and Qihang Liu, “Group Theory on Quasisymmetry and Protected Near Degeneracy,” Phys. Rev. Lett.133, 026402 (2024)

    2024

  29. [37]

    Quasi- 7 symmetry-protected topology in a semi-metal,

    Chunyu Guo, Lunhui Hu, Carsten Putzke, Jonas Diaz, Xiangwei Huang, Kaustuv Manna, Feng-Ren Fan, Chan- dra Shekhar, Yan Sun, Claudia Felser, Chaoxing Liu, B. Andrei Bernevig, and Philip J. W. Moll, “Quasi- 7 symmetry-protected topology in a semi-metal,” Nature Physics 18, 813–8...

    2022

  30. [38]

    Large intrinsic anomalous Hall effect in bothNb2FeB2 and Ta2FeB2 with collinear antiferromagnetism,

    Xiao-Yao Hou, Huan-Cheng Yang, Zheng-Xin Liu, Peng- Jie Guo, and Zhong-Yi Lu, “Large intrinsic anomalous Hall effect in bothNb2FeB2 and Ta2FeB2 with collinear antiferromagnetism,” Phys. Rev. B107, L161109 (2023)

    2023

  31. [39]

    Supple- mentary Material for: Quasi-symmetry Constrained Spin Ferromagnetism in Altermagnets,

    Mercè Roig, Yue Yu, Rune C. Ekman, Andreas Kreisel, Brian M. Andersen, and Daniel F. Agterberg, “Supple- mentary Material for: Quasi-symmetry Constrained Spin Ferromagnetism in Altermagnets,”

  32. [40]

    Classification of electronic ne- maticity in three-dimensional crystals and quasicrystals,

    Matthias Hecker, Anant Rastogi, Daniel F. Agterberg, and Rafael M. Fernandes, “Classification of electronic ne- maticity in three-dimensional crystals and quasicrystals,” Phys. Rev. B109, 235148 (2024)

    2024

  33. [41]

    Classification of atomic-scale multi- poles under crystallographic point groups and applica- tion to linear response tensors,

    Satoru Hayami, Megumi Yatsushiro, Yuki Yanagi, and Kusunose Hiroaki, “Classification of atomic-scale multi- poles under crystallographic point groups and applica- tion to linear response tensors,” Phys. Rev. B98, 165110 (2018)

    2018

  34. [42]

    Ferroically Ordered Magnetic Octupoles in d-Wave Altermagnets,

    Sayantika Bhowal and Nicola A. Spaldin, “Ferroically Ordered Magnetic Octupoles in d-Wave Altermagnets,” Phys. Rev. X14, 011019 (2024)

    2024

  35. [43]

    Berry curvature and quantum metric in N-band systems: An eigenprojector approach,

    Ansgar Graf and Frédéric Piéchon, “Berry curvature and quantum metric in N-band systems: An eigenprojector approach,” Phys. Rev. B104, 085114 (2021)

    2021

  36. [44]

    Weak Ferromagnetism in Altermagnets from Alternating g-Tensor Anisotropy,

    Daegeun Jo, Dongwook Go, Yuriy Mokrousov, Pe- ter M. Oppeneer, Sang-Wook Cheong, and Hyun- Woo Lee, “Weak Ferromagnetism in Altermagnets from Alternating g-Tensor Anisotropy,” arXiv (2024), 10.48550/arXiv.2410.17386, (accepted in PRL). End Matter Appendix: General SOC-enabled ...

    2024 doi arXiv

  37. [45]

    Ferromagnetic order is ⃗MA1g, and altermagnetic order is⃗NP, with altermagnetic symmetry ΓN = P

    In the SOC-free tetragonalD4h systems, the SOC order parameters are: ⃗OEg,1 = (Λxy, 0, 0), ⃗OEg,2 = (0, Λxy, 0) and ⃗OA2g = (0 , 0, Λz). Ferromagnetic order is ⃗MA1g, and altermagnetic order is⃗NP, with altermagnetic symmetry ΓN = P. To have a SOC- linear coupling between an a...

  38. [46]

    To have a SOC-linear coupling between altermagnet and ferromagnet, ⃗O · ( ⃗M × ⃗N ) must be allowed

    In the SOC-free hexagonal D6h systems, the SOC order parameters are: ⃗OE1g,1 = (Λ xy, 0, 0), ⃗OE1g,2 = (0 , Λxy, 0) and ⃗OA2g = (0 , 0, Λz). To have a SOC-linear coupling between altermagnet and ferromagnet, ⃗O · ( ⃗M × ⃗N ) must be allowed. Thus, ΓN = A2g or E1g. For two atom...

  39. [47]

    For ΓN = A2g, M N3 coupling has no SOC-linear contribution since A2g ⊗ A2g ⊗ A2g ⊗ T1g has no trivial IR

    In the SOC-free cubic Oh systems, the SOC or- der parameters are: ⃗OT1g,1 = (Λ , 0, 0), ⃗OT1g,2 = (0, Λ, 0) and ⃗OT1g,3 = (0 , 0, Λ). For ΓN = A2g, M N3 coupling has no SOC-linear contribution since A2g ⊗ A2g ⊗ A2g ⊗ T1g has no trivial IR. Sim- ilarly, a SOC-quadratic contribu...

    2013

  40. [48]

    Classification of electronic nematicity in three-dimensional crystals and quasicrystals,

    Matthias Hecker, Anant Rastogi, Daniel F. Agterberg, and Rafael M. Fernandes, “Classification of electronic nematicity in three-dimensional crystals and quasicrystals,” Phys. Rev. B 109, 235148 (2024)

    2024

  41. [49]

    Berry curvature and quantum metric inN-band systems: An eigenprojector approach,

    Ansgar Graf and Fr´ ed´ eric Pi´ echon, “Berry curvature and quantum metric inN-band systems: An eigenprojector approach,” Phys. Rev. B 104, 085114 (2021)

    2021

  42. [50]

    Minimal models for altermagnetism,

    Merc` e Roig, Andreas Kreisel, Yue Yu, Brian M. Andersen, and Daniel F. Agterberg, “Minimal models for altermagnetism,” Phys. Rev. B 110, 144412 (2024)

    2024

  43. [51]

    Blaha, K

    P. Blaha, K. Schwarz, G. K. Madsen, D. Kvasnicka, and J. Luitz, WIEN2k an Augmented Plane Wave Plus Local Orbitals Program for Calculating Crystal Properties (Technische Universit¨ at Wien, 2001)

    2001

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