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Observation of mirror-odd and mirror-even spin texture in ultrathin epitaxially strained RuO2 films

T0 review · 3 major / 5 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read Ultra-thin epitaxially strained RuO2 shows a momentum-dependent spin texture whose mirror-even component implies time-reversal symmetry breaking and the m′m2′ magnetic point group.

desk verdict Genuinely new spin-ARPES data on ultra-thin strained RuO2 with a solid symmetry analysis, but the abstract overstates the conclusion by glossing over the unaddressed multiple-scattering alternative. read the letter →

arxiv 2509.16361 v5 pith:26SK72N7 submitted 2025-09-19 cond-mat.mtrl-sci cond-mat.str-el

Yichen Zhang , Seung Gyo Jeong , Luca Buiarelli , Seungjun Lee , Yucheng Guo , Jiaqin Wen , Hang Li , Sreejith Nair
show 19 more authors
In Hyeok Choi Zheng Ren Ziqin Yue Jounghoon Hyun Tieqiong Zhang Alexei Fedorov Sung-Kwan Mo Hojoon Lim Adrian Hunt Iradwikanari Waluyo Junichiro Kono Jan Minar Jong Seok Lee Tony Low Turan Birol Rafael M. Fernandes Milan Radovic Bharat Jalan Ming Yi
This is my paper · ORCID
classification cond-mat.mtrl-scicond-mat.str-el
keywords RuO2altermagnetismspin-resolvedARPESspintextureepitaxialstrainmagneticpointgrouptime-reversalsymmetrybreakingultrathinfilms
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

Using spin-resolved ARPES on 2.7-nm epitaxially strained RuO2 films grown on a conducting TiO2 substrate, the paper reports a momentum-dependent photoelectron spin texture with two coexisting symmetry classes: a mirror-odd component expected from the polar, inversion-broken interface, and a mirror-even in-plane [001] component that the authors argue no nonmagnetic mechanism can produce. They conclude that the mirror-even component signals time-reversal symmetry breaking and that the observed pattern of spin-splitting terms is consistent with the magnetic point group m′m2′, with moments in the film plane. That magnetic point group admits both a ferromagnetic and a d-wave altermagnetic order parameter, so the phase would be a nonrelativistic spin structure stabilized by epitaxial strain in the ultra-thin limit, distinct from the nonmagnetic behavior established for bulk and strain-relaxed RuO2. The same measurements show strain-shifted narrow surface bands near the Fermi level, which accompany the new spin texture.

What carries the argument

The load-bearing machinery is the irreducible-representation classification of spin-splitting terms for the paramagnetic point group $mm2.1'$, up to quadratic order in momentum (Table 1). The classification shows which combinations of spin polarization components $\sigma_i$ and momentum products $k_i k_j$ transform under each irrep. The decisive move is treating the out-of-plane momentum $k_{110}$ as a constant in the ultra-thin film, so that the observed linear-looking $k_{001}\sigma_{110}$ term is reinterpreted as the quadratic term $k_{110}k_{001}\sigma_{110}$. Together with the mirror-even uniform ($\sigma_{001}$) or $k_{110}^{2}\sigma_{001}$ term and the Rashba term $k_{1\bar{1}0}\sigma_{001}$, all observed splittings then belong to the single irrep $B_1^-$, whose condensation gives the magnetic point group $m'm2'$. The spin-resolved ARPES measurements use very-low-energy electron diffraction spin detectors to select the in-plane [001] and out-of-plane [110] polarization directions.

What would settle it

A spin-resolved ARPES measurement of a nonmagnetic reference film with the same surface termination and measurement geometry, or a one-step photoemission calculation that includes spin-dependent final-state scattering, could settle it: if the mirror-even [001] polarization survives without magnetism, the magnetic conclusion collapses. A second check would be varying the photon energy to test whether the out-of-plane momentum $k_{110}$ is truly constant; if the $k_{001}\sigma_{110}$ term is a genuine linear term, the symmetry analysis would instead require a lower-symmetry magnetic group incompatible with the mm2 structural symmetry.

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Extended reading notes

Core claim

On its own terms, the paper's central discovery is that the photoelectron spin polarization of fully strained 2.7-nm RuO2 contains, near the Fermi level, an in-plane [001] component that is even under both the (1̄10) and (001) mirrors, in addition to the expected mirror-odd spin texture. Because such a mirror-even component is not allowed by any nonmagnetic spin-orbit mechanism in the polar point group mm2, the paper attributes it to time-reversal symmetry breaking. The symmetry analysis of the observed terms — the uniform $\sigma_{001}$ or quadratic $k_{110}^{2}\sigma_{001}$, the linear $k_{001}\sigma_{110}$, and the Rashba-type $k_{1\bar{1}0}\sigma_{001}$ — yields, under the assumption that $k_{110}$ is a constant, a single magnetic order parameter $B_1^-$ and the magnetic point group $m'm2'$ with in-plane moments. The paper states that this magnetic group is consistent with both ferromagnetism and d-wave altermagnetism, and presents the result as direct spectroscopic evidence of a nonrelativistic spin structure in the ultra-thin strained regime of RuO2.

Load-bearing premise

The conclusion rests on the assumption that the measured photoelectron spin polarization reflects the intrinsic spin of the initial electronic states, and not a spin polarization produced by spin-dependent scattering of the outgoing photoelectrons.

Editorial extensions

If this is right

  • The fully strained ultra-thin regime of RuO2 is a distinct electronic state: the nonrelativistic spin texture and broken time reversal appear below the roughly 4-nm fully strained thickness, while bulk and strain-relaxed films remain nonmagnetic.
  • The proposed magnetic point group $m'm2'$ has in-plane moments, distinguishing the low-temperature phase from the out-of-plane-moment $m'm'2$ phase inferred from room-temperature second-harmonic generation, even though both correspond to d-wave altermagnetism.
  • Because the mirror-odd Rashba-type component coexists with the mirror-even magnetic component, the system combines spin-orbit and nonrelativistic spin splittings, which could be exploited for spin-charge conversion.
  • A magnetic order parameter transforming as $B_1^-$ predicts additional spin-splitting terms beyond those measured, for example $k_{1\bar{1}0}k_{001}\sigma_{1\bar{1}0}$ and $(k_{1\bar{1}0}^{2}-k_{001}^{2})\sigma_{001}$, providing a checklist for future spin-resolved measurements.

Reading between the lines

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

  • A decisive test the paper leaves implicit: a one-step photoemission calculation with spin-dependent final-state scattering, or a spin-resolved ARPES control on a nonmagnetic sample with identical geometry, would determine whether the mirror-even [001] polarization survives without magnetism.
  • If $m'm2'$ is the true magnetic group, the in-plane [001] moments should show up as a characteristic crystalline-axis dependence in magneto-optical Kerr rotation and planar Hall transport, which could also help distinguish ferromagnetism from d-wave altermagnetism.
  • A photon-energy-dependent spin-resolved ARPES scan on a series of strained film thicknesses could test the assumption that $k_{110}$ is a good constant; if the $k_{001}\sigma_{110}$ term is genuinely linear in momentum, the magnetic point group assignment would have to be revised.
  • The strain-shifted surface-derived $\alpha$ narrow bands sit at the same energies as the mirror-even polarization; spin-polarized slab calculations that include the surface $d_{z^2}$ states could reveal whether those bands enhance the magnetic instability.
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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

3 major / 5 minor

Summary. The manuscript reports spin-resolved ARPES measurements on 2.7 nm fully strained epitaxial RuO2 films grown on TiO2/Nb:TiO2(110) by hybrid molecular beam epitaxy. The authors observe narrow bands near the Fermi level and a photoelectron spin polarization that combines a mirror-odd component (consistent with inversion-symmetry breaking) and a mirror-even in-plane [001] component that is not expected for the paramagnetic state. Using a group-theory classification of spin-splitting terms for the paramagnetic point group mm2.1', they show that the observed mirror-even terms can be accommodated by a magnetic order parameter transforming as B1-, which would correspond to the magnetic point group m'm2' with in-plane moments, compatible with either ferromagnetism or d-wave altermagnetism. The magnetic conclusion is explicitly stated to hold only if the mirror-even photoelectron spin polarization is an intrinsic initial-state property and not a final-state multiple-scattering artifact. The paper is an experimental first look at the spin structure in the ultra-thin, fully strained regime of RuO2.

Significance. If the central claim holds, the paper provides direct spectroscopic evidence for a nonrelativistic spin texture stabilized by epitaxial strain in ultra-thin RuO2, a material whose bulk and thick-film forms have increasingly been argued to be nonmagnetic. This would be an important advance for the altermagnetism debate and for oxide heterostructure spintronics. The authors should be credited for the careful sample characterization (XRD, XRR, RHEED, AFM, SHG), the two-photon-energy internal consistency checks of the spin polarization, the propagated Poisson error bars, and the transparent group-theory classification in Table 1, which does not fit any parameter and is a genuine symmetry analysis. The main weakness is that the load-bearing premise—that the mirror-even polarization reflects the intrinsic initial-state spin texture rather than spin-dependent final-state multiple scattering—is explicitly conditional and is not independently tested. This limits the strength of the conclusions as currently worded.

major comments (3)
  1. [Abstract and Discussion] The abstract claims that 'a comprehensive symmetry analysis rules out nonmagnetic origins of this spin texture,' but the symmetry analysis in the Discussion and Table 1 only classifies spin-splitting terms of the initial-state Hamiltonian. It does not constrain spin-dependent final-state multiple scattering, which is known to produce momentum-dependent photoelectron spin polarization even for nonmagnetic surfaces (refs. 66-72). The manuscript itself acknowledges this condition, stating that the magnetic conclusion holds 'if the observed mirror-even spin polarization arises from intrinsic magnetism regardless of photoemission multiple scattering,' and notes 'potential complications on the photoelectron spin polarization from multiple scattering.' No one-step photoemission calculation or nonmagnetic control measurement is provided. The abstract's unconditional wording therefore overstates the evidence. This is a load-bearing issue because the mirror-even [001] polarization is the sole basis for the time-reversal-symmetry-broken conclusion.
  2. [Discussion, paragraph 4] The assignment of the observed k001*sigma110 term to the B1- irrep rests on the assumption that the out-of-plane momentum k110 can be treated as a constant, allowing the term to be reinterpreted as the quadratic k110*k001*sigma110 term. The manuscript states this assumption but does not provide quantitative justification, such as an estimate of the kz broadening from the 2.7 nm film thickness or a photon-energy dependence test. If kz conservation is not fully suppressed, the term would transform as B1+ under mm2.1', which the authors themselves note would require a different magnetic point group (m.1') incompatible with the structural mm2 symmetry. Because this assumption directly determines the proposed m'm2' magnetic point group, it needs either additional experimental support or an explicit sensitivity analysis showing that the qualitative conclusion is robust to partial kz coherence.
  3. [Fig. 4, panels K-L and Results section] The text states 'Judging from the calculated spin polarization presented in Fig. 4 (K and L)' in reference to data-derived spin polarization curves. The curves in Fig. 4(K,L) are converted from measured spin-resolved EDCs, not from a calculation. This appears to be a typo (likely 'measured' instead of 'calculated'), but because the figure is central to the mirror-even claim, the wording should be corrected to avoid ambiguity about whether any theoretical spin-resolved simulation is being shown.
minor comments (5)
  1. [Abstract] The abstract says '2-nanometer-thick' while the main text and Methods consistently state 2.7 nm; this should be harmonized.
  2. [Methods, Eq. (1)] The Sherman function is quoted as S = 0.2 without an uncertainty. Since the absolute polarization values are not central to the symmetry classification, this is acceptable, but adding a nominal systematic uncertainty would improve the error discussion.
  3. [Methods, normalization paragraph] The spin-resolved EDCs are normalized using counts in kinetic-energy windows that are assumed to be background-dominated. It would be helpful to state explicitly whether those windows were checked to have negligible spin polarization, since a spin-polarized background would bias the normalized asymmetry.
  4. [Fig. 4D] The arrows marking the alpha, gamma, and delta bands are described in the text and figure caption, but the figure panel itself is busy; adding the labels directly on the panel would improve readability.
  5. [Discussion, last paragraph] The phrase 'could be associated with time-reversal-symmetry breaking' is appropriately cautious, but the earlier sentence in the same paragraph ('is beyond intrinsically nonmagnetic origins') is stronger; aligning these two statements would help the reader track the level of certainty.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity found: the mm2.1' spin-splitting classification is an independent group-theory table, and the m'm2' assignment is a conditional inference from the observed spin terms, not a fit or self-citation-derived equivalence.

full rationale

The derivation chain is: (i) measure photoelectron spin polarization; (ii) classify all spin-splitting terms allowed for the paramagnetic point group mm2.1' in Table 1; (iii) identify which observed terms appear; (iv) conclude that, under the explicitly stated condition that the mirror-even polarization is intrinsic, the simplest magnetic point group is m'm2'. Step (ii) is not derived from the data: Table 1 is a general irrep decomposition with no free parameters fitted to the spin-resolved EDCs, so the conclusion is not encoded in the input. Step (iv) is conditional, and the paper explicitly states that 'lower-symmetry groups cannot be ruled out', so there is no uniqueness claim imported from the authors' prior work. The reinterpretation of the observed k001 sigma110 term as k110 k001 sigma110 is supported by the physical statement that the ultra-thin film 'does not have a well-defined kz', not by a circular redefinition of the observation. The same-group citations (refs 57, 60) are used as independent corroboration from SHG, MOKE, and Hall transport, not as the origin of the spin-resolved observation, and the structural mm2 assignment is also re-measured here by RA-SHG. No fitted parameter is renamed as a prediction, and no ansatz is smuggled in by citation. The unresolved multiple-scattering alternative is a genuine evidence gap and a correctness risk, but not a circularity: the abstract's 'comprehensive symmetry analysis rules out nonmagnetic origins' is stronger than the Discussion's conditional 'if the observed mirror-even spin polarization arises from intrinsic magnetism regardless of photoemission multiple scattering', yet this overstatement does not make any equation or conclusion equivalent to its own input by construction.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The central magnetic interpretation rests on three fitted or assumed inputs: U=0 and the -200 meV rigid shift to match bands (which do not directly fix the spin-texture conclusion), and the crucial assumption that the spin polarization is intrinsic rather than a final-state scattering artifact. The group-theory step itself is parameter-free once the input terms are selected.

free parameters (3)
  • Hubbard U = 0 eV
    U was tuned to match measured band dispersions; authors state the best match is achieved with no U, which also gives the uncompensated altermagnetic ground state used in the band comparison.
  • DFT Fermi-level shift = -200 meV
    Slab DFT bands are rigidly shifted by -200 meV to align with ARPES; the authors argue it is a global shift, but it is still a fitted parameter.
  • Fixed kz in bulk DFT = kz = 2π/6d
    Bulk band structure plotted at a fixed kz chosen to mimic quantum confinement in the ultra-thin film; used for comparing with film data.
assumptions (4)
  • domain assumption Density functional theory in the PBE-GGA approximation (without Hubbard U) describes the relevant bands and the magnetic ground state of strained RuO2 sufficiently for the comparison.
    Used throughout the Ab-initio calculations section and Fig. 3; the choice of no U is justified only by matching measured dispersions, and the magnetic ground state is delicate.
  • domain assumption The measured photoelectron spin polarization is an intrinsic property of the initial electronic states; final-state multiple scattering does not generate the observed mirror-even pattern.
    Explicitly hedged in the Discussion: 'if the observed mirror-even spin polarization arises from intrinsic magnetism regardless of photoemission multiple scattering'. This is the decisive unproven premise.
  • ad hoc to paper The out-of-plane momentum k110 is a constant (not a good quantum number) in the ultra-thin film, allowing reclassification of the observed k001σ110 term as k110k001σ110.
    Stated in the Discussion: 'because of the ultra-thin character of the film, we assume that the out-of-plane momentum k110 can be simply treated as a constant.' This is needed for the B1- irrep assignment.
  • domain assumption The paramagnetic point group of the film is mm2.1' (from SHG and structural data) and the spin texture can be described by a single magnetic order parameter irrep at second order in k.
    Basis of Table 1 and the search for the 'simplest combinations of irreps'; the minimality assumption is acknowledged: 'lower-symmetry groups cannot be ruled out'.

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Cite this review

Pith. "Pith review of Observation of mirror-odd and mirror-even spin texture in ultrathin epitaxially strained RuO2 films." pith.science (2026). https://pith.science/paper/26SK72N7

@misc{pith2026250916361,
  author       = {Pith},
  title        = {Pith review of: Observation of mirror-odd and mirror-even spin texture in ultrathin epitaxially strained RuO2 films},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/26SK72N7}},
  note         = {Machine review of arXiv:2509.16361}
}
abstract

Recently, rutile ruthenium dioxide (RuO$_2$) has attracted renewed interest due to expectations of prominent altermagnetic spin splitting. However, accumulating experimental evidence suggests that, in its bulk and thick-film forms, RuO$_2$ does not display any form of magnetic ordering. Despite this, the spin structure of RuO$_2$ remains largely unexplored in the ultrathin limit, where substrate-imposed epitaxial strain can be substantial. Here, we use spin-resolved angle-resolved photoemission spectroscopy, supported by ab initio calculations, to reveal the electronic structure of 2-nanometer-thick epitaxial RuO$_2$ heterostructures. We observe an unconventional spin texture characterized by the coexistence of mirror-even and mirror-odd momentum-dependent components. A comprehensive symmetry analysis rules out nonmagnetic origins of this spin texture. These findings suggest an emergent nonrelativistic spin structure enabled by epitaxial strain in the ultrathin limit, marking a distinct departure from the behavior of relaxed or bulk RuO$_2$. Our work opens previously unexplored perspectives for exploring symmetry-breaking mechanisms and spin textures in oxide heterostructures.

Figures

Figures reproduced from arXiv: 2509.16361 by the authors.

Figure 1
Figure 1. Proposed spin texture relevant in epitaxially-strained RuO2. (A) Schematic illustration of the charge dipole produced at the (110) RuO2/TiO2 interface and the associated Rashba-type spin splitting within the (110)-plane. (B) Decorated local chemical environment of the two Ru sublattices in RuO2 related by a C4 rotational symmetry and the schematic illustration of nonrelativistic altermagnetic spin splitting in k-spa… view at source ↗
Figure 2
Figure 2. Design and structural characterization of fully strained metallic RuO2 (110) het￾erostructures grown by hMBE. (A) XRR and (B) XRD 2θ-θ scans of RuO2 heterostructures. Scattered symbols and solid lines in (A) represent the experimental data and corresponding fitting results, respectively. The inset in (A) shows a schematic illustration of the heterostructure archi￾tecture comprising of 2.7 nm RuO2/ 2 nm TiO2/ Nb:TiO2… view at source ↗
Figure 3
Figure 3. Narrow bands (NBs) in the ultra-thin epitaxially-strained RuO2. (A) Constant energy contour (CEC) at E - EF = -0.1 eV measured by 62 eV p-polarized (indicated on the left top) photons, with an energy integration window of 20 meV, emphasizing the α narrow bands (α-NB) and β narrow bands (β-NB) denoted by the red and blue arrows. (B) CEC at E - EF = -0.3 eV showing the β-NB. (C) Measured electronic band dispersions al… view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: Measured photoelectron spin polarization along the in-plane [001] direction with respect to the (1¯10)-mirror plane. (A) Fermi surface probed by 55 eV photons. (B) Band dispersions along the Γ¯ − M¯ direction indicated by the horizontal dashed double-arrow in (A). (C a…
Figure 5
Figure 5. Figure 5: Out-of-plane and in-plane photoelectron spin polarization with respect to the (001)- mirror plane. (A) Fermi surface reproduced from Fig. 4A but highlighting the (001)-mirror and the momentum positions of the measured spin-resolved energy distribution curves (EDCs) usi…

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Works this paper leans on

83 extracted references · 35 canonical work pages

  1. [1]

    & Jungwirth, T

    ˇSmejkal, L., Sinova, J. & Jungwirth, T. Beyond Conventional Ferromagnetism and Antifer- romagnetism: A Phase with Nonrelativistic Spin and Crystal Rotation Symmetry.Phys. Rev. X12, 031042 (2022). URL https://link.aps.org/doi/10.1103/PhysRevX.12. 031042

    doi:10.1103/physrevx.12 2022

  2. [2]

    & Jungwirth, T

    ˇSmejkal, L., Sinova, J. & Jungwirth, T. Emerging Research Landscape of Altermagnetism.Phys. Rev. X12, 040501 (2022). URL https://link.aps.org/doi/10.1103/PhysRevX. 12.040501

    doi:10.1103/physrevx 2022

  3. [3]

    M., Sinova, J

    Jungwirth, T., Fernandes, R. M., Sinova, J. & Smejkal, L. Altermagnets and beyond: Nodal magnetically-ordered phases.arXiv1–17 (2024). URL https://arxiv.org/abs/2409. 10034

    2024

  4. [4]

    & Zhang, S.-C

    Wu, C. & Zhang, S.-C. Dynamic Generation of Spin-Orbit Coupling.Phys. Rev. Lett.93, 036403 (2004). URL https://link.aps.org/doi/10.1103/PhysRevLett.93. 036403

    doi:10.1103/physrevlett.93 2004

  5. [5]

    & Zhang, S.-C

    Wu, C., Sun, K., Fradkin, E. & Zhang, S.-C. Fermi liquid instabilities in the spin channel.Phys. Rev. B75, 115103 (2007). URL https://link.aps.org/doi/10.1103/PhysRevB. 75.115103

    doi:10.1103/physrevb 2007

  6. [6]

    & Song, Z.-D

    Xiao, Z., Zhao, J., Li, Y ., Shindou, R. & Song, Z.-D. Spin Space Groups: Full Classification and Applications.Phys. Rev. X14, 031037 (2024). URL https://link.aps.org/doi/ 25 10.1103/PhysRevX.14.031037

    doi:10.1103/physrevx.14.031037 2024

  7. [7]

    Chen, X.et al.Enumeration and Representation Theory of Spin Space Groups.Phys. Rev. X14, 031038 (2024). URL https://link.aps.org/doi/10.1103/PhysRevX.14. 031038

    doi:10.1103/physrevx.14 2024

  8. [8]

    Jiang, Y .et al.Enumeration of Spin-Space Groups: Toward a Complete Description of Symmetries of Magnetic Orders.Phys. Rev. X14, 031039 (2024). URL https://link. aps.org/doi/10.1103/PhysRevX.14.031039

    doi:10.1103/physrevx.14.031039 2024

Show all 83 references
  1. [9]

    B.et al.P-wave magnets.arXiv1–6 (2023)

    Hellenes, A. B.et al.P-wave magnets.arXiv1–6 (2023). URL https://arxiv.org/ abs/2309.01607

    2023 arXiv

  2. [10]

    & Liu, Q

    Liu, P., Li, J., Han, J., Wan, X. & Liu, Q. Spin-Group Symmetry in Magnetic Materials with Negligible Spin-Orbit Coupling.Phys. Rev. X12, 021016 (2022). URL https://link. aps.org/doi/10.1103/PhysRevX.12.021016

    2022 doi

  3. [11]

    S., Fernandes, R

    Antonenko, D. S., Fernandes, R. M. & Venderbos, J. W. F. Mirror Chern Bands and Weyl Nodal Loops in Altermagnets.Phys. Rev. Lett.134, 096703 (2025). URL https://link. aps.org/doi/10.1103/PhysRevLett.134.096703

    2025 doi

  4. [12]

    & and, K

    Gao, X.-J., Sun, Z.-T., Yu, R.-P., Guo, X.-Y . & and, K. T. L. Heesch Weyl Fermions in inadmissible chiral antiferromagnets.arXiv1–10 (2023). URL https://arxiv.org/ abs/2305.15876. 26

    2023 arXiv

  5. [13]

    M., de Carvalho, V

    Fernandes, R. M., de Carvalho, V . S., Birol, T. & Pereira, R. G. Topological transition from nodal to nodeless zeeman splitting in altermagnets.Phys. Rev. B109, 024404 (2024). URL https://link.aps.org/doi/10.1103/PhysRevB.109.024404

    2024 doi

  6. [14]

    URLhttps://arxiv.org/pdf/2410.17993

    Hu, M.et al.Spin Hall and Edelstein Effects in Novel Chiral Noncollinear Altermagnets.arXiv 1–22 (2024). URLhttps://arxiv.org/pdf/2410.17993

    2024

  7. [15]

    Radaelli, P. G. & Gurung, G. Colour symmetry and non-collinear altermagnetism.arXiv1–17 (2025). URLhttps://arxiv.org/pdf/2501.02947

    2025 arXiv

  8. [16]

    ˇSmejkal, L.et al.Chiral Magnons in Altermagnetic RuO2.Phys. Rev. Lett.131, 256703 (2023). URLhttps://link.aps.org/doi/10.1103/PhysRevLett.131.256703

    2023 doi

  9. [17]

    & Masuda, T

    Liu, Z., Ozeki, M., Asai, S., Itoh, S. & Masuda, T. Chiral Split Magnon in Altermagnetic MnTe. Phys. Rev. Lett.133, 156702 (2024). URL https://link.aps.org/doi/10.1103/ PhysRevLett.133.156702

    2024

  10. [18]

    & Cao, K

    Zhang, Y .-F., Ni, X.-S., Ke, C. & Cao, K. Chiral magnon splitting in altermagnetic CrSb from first principles.arXiv1–8 (2025). URLhttps://arxiv.org/pdf/2503.12920

    2025 arXiv

  11. [19]

    & Sinova, J

    ˇSmejkal, L., Gonz ´alez-Hern´andez, R., Jungwirth, T. & Sinova, J. Crystal time-reversal symmetry breaking and spontaneous Hall effect in collinear antiferromagnets.Sci. Adv.6, eaaz8809 (2020). URL https://www.science.org/doi/abs/10.1126/sciadv. aaz8809. 27

    2020 doi

  12. [20]

    C., Assaad, F

    Sato, T., Haddad, S., Fulga, I. C., Assaad, F. F. & van den Brink, J. Altermagnetic Anomalous Hall Effect Emerging from Electronic Correlations.Phys. Rev. Lett.133, 086503 (2024). URL https://link.aps.org/doi/10.1103/PhysRevLett.133.086503

    2024 doi

  13. [21]

    Takahashi, K., Steward, C. R. W., Ogata, M., Fernandes, R. M. & Schmalian, J. Elasto-Hall conductivity and the anomalous Hall effect in altermagnets.Phys. Rev. B111, 184408 (2025). URLhttps://link.aps.org/doi/10.1103/PhysRevB.111.184408

    2025 doi

  14. [22]

    & Manchon, A

    Gonz´alez-Hern´andez, R., Ritzinger, P., V ´yborn´y, K., ˇZelezn´y, J. & Manchon, A. Non- relativistic torque and Edelstein effect in non-collinear magnets.Nat. Commun.15, 7663 (2024). URLhttps://www.nature.com/articles/s41467-024-51565-6

    2024

  15. [23]

    B., Gonz ´alez-Hern´andez, R., Sinova, J

    ˇSmejkal, L., Hellenes, A. B., Gonz ´alez-Hern´andez, R., Sinova, J. & Jungwirth, T. Giant and Tunneling Magnetoresistance in Unconventional Collinear Antiferromagnets with Non- relativistic Spin-Momentum Coupling.Phys. Rev. X12, 011028 (2022). URL https: //link.aps.org/doi/10...

    2022 doi

  16. [24]

    J., Wadley, P

    Dal Din, A., Amin, O. J., Wadley, P. & Edmonds, K. W. Antiferromagnetic spintronics and beyond.npj Spintronics2, 25 (2024). URL https://www.nature.com/articles/ s44306-024-00029-0

    2024

  17. [25]

    & Bl¨ugel, S

    Liu, Q., Dai, X. & Bl¨ugel, S. Different facets of unconventional magnetism.Nat. Phys.21, 329 (2025). URLhttp://dx.doi.org/10.1038/s41567-024-02750-3. 28

    2025 doi

  18. [26]

    & Marmodoro, A

    Weißenhofer, M. & Marmodoro, A. Atomistic spin dynamics simulations of magnonic spin Seebeck and spin Nernst effects in altermagnets.Phys. Rev. B110, 094427 (2024). URL https://link.aps.org/doi/10.1103/PhysRevB.110.094427

    2024 doi

  19. [27]

    URL https://arxiv

    Jungwirth, T.et al.Altermagnetic spintronics.arXiv1–15 (2025). URL https://arxiv. org/abs/2508.09748

    2025 arXiv

  20. [28]

    H.et al.Anomalous Antiferromagnetism in Metallic RuO2 Determined by Resonant X-ray Scattering.Phys

    Zhu, Z. H.et al.Anomalous Antiferromagnetism in Metallic RuO2 Determined by Resonant X-ray Scattering.Phys. Rev. Lett.122, 017202 (2019). URL https://link.aps.org/ doi/10.1103/PhysRevLett.122.017202

    2019 doi

  21. [29]

    Berlijn, T.et al.Itinerant Antiferromagnetism in RuO2.Phys. Rev. Lett.118, 077201 (2017). URLhttps://link.aps.org/doi/10.1103/PhysRevLett.118.077201

    2017 doi

  22. [30]

    & Kune ˇs, J

    Ahn, K.-H., Hariki, A., Lee, K.-W. & Kune ˇs, J. Antiferromagnetism in RuO2 as d-wave Pomeranchuk instability.Phys. Rev. B99, 184432 (2019). URL https://link.aps. org/doi/10.1103/PhysRevB.99.184432

    2019 doi

  23. [31]

    URL https://www.sciencedirect.com/science/ article/pii/S2542529323000275

    Guo, Y .et al.Spin-split collinear antiferromagnets: A large-scale ab-initio study.Materials To- day Physics32, 100991 (2023). URL https://www.sciencedirect.com/science/ article/pii/S2542529323000275

    2023

  24. [32]

    Electron5, 735 (2022)

    Feng, Z.et al.An anomalous Hall effect in altermagnetic ruthenium dioxide.Nat. Electron5, 735 (2022). URL https://www.nature.com/articles/s41928-022-00866-z. 29

    2022

  25. [33]

    URL https://doi.org/10.1063/5

    Tschirner, T.et al.Saturation of the anomalous Hall effect at high magnetic fields in alter- magnetic RuO2.APL Mater .11, 101103 (2023). URL https://doi.org/10.1063/5. 0160335

    2023 doi

  26. [34]

    Small21, 2407722 (2025)

    Song, J.et al.Spin-Orbit Coupling Driven Magnetic Response in Altermagnetic RuO 2. Small21, 2407722 (2025). URL https://onlinelibrary.wiley.com/doi/abs/ 10.1002/smll.202407722

    2025 doi

  27. [35]

    URL https://advanced.onlinelibrary.wiley.com/ doi/abs/10.1002/adma.202507764

    Chen, H.et al.Spin-Splitting Magnetoresistance in Altermagnetic RuO 2 Thin Films.Advanced Materials2025, 2507764. URL https://advanced.onlinelibrary.wiley.com/ doi/abs/10.1002/adma.202507764

    doi

  28. [36]

    Bai, H.et al.Observation of Spin Splitting Torque in a Collinear Antiferromagnet RuO2. Phys. Rev. Lett.128, 197202 (2022). URL https://link.aps.org/doi/10.1103/ PhysRevLett.128.197202

    2022

  29. [37]

    Karube, S.et al.Observation of Spin-Splitter Torque in Collinear Antiferromagnetic RuO2. Phys. Rev. Lett.129, 137201 (2022). URL https://link.aps.org/doi/10.1103/ PhysRevLett.129.137201

    2022

  30. [38]

    Electron5, 267 (2022)

    Bose, A.et al.Tilted spin current generated by the collinear antiferromagnet ruthenium dioxide.Nat. Electron5, 267 (2022). URL https://www.nature.com/articles/ s41928-022-00744-8

    2022

  31. [39]

    Zhang, Y .et al.Simultaneous High Charge-Spin Conversion Efficiency and Large Spin Diffusion Length in Altermagnetic RuO 2.Adv. Funct. Mater .34, 2313332 30 (2024). URL https://advanced.onlinelibrary.wiley.com/doi/abs/10. 1002/adfm.202313332

    2024

  32. [40]

    Feng, X.et al.Incommensurate Spin Density Wave in Antiferromagnetic RuO2 Evinced by Abnormal Spin Splitting Torque.Phys. Rev. Lett.132, 086701 (2024). URL https: //link.aps.org/doi/10.1103/PhysRevLett.132.086701

    2024 doi

  33. [41]

    Bai, H.et al.Efficient Spin-to-Charge Conversion via Altermagnetic Spin Splitting Effect in Antiferromagnet RuO2.Phys. Rev. Lett.130, 216701 (2023). URL https://link.aps. org/doi/10.1103/PhysRevLett.130.216701

    2023 doi

  34. [42]

    Liao, C.-T., Wang, Y .-C., Tien, Y .-C., Huang, S.-Y . & Qu, D. Separation of Inverse Alter- magnetic Spin-Splitting Effect from Inverse Spin Hall Effect in RuO2.Phys. Rev. Lett.133, 056701 (2024). URL https://link.aps.org/doi/10.1103/PhysRevLett.133. 056701

    2024 doi

  35. [43]

    Adv.10, eadj4883 (2024)

    Fedchenko, O.et al.Observation of time-reversal symmetry breaking in the band structure of altermagnetic RuO2.Sci. Adv.10, eadj4883 (2024). URL https://www.science.org/ doi/abs/10.1126/sciadv.adj4883

    2024 doi

  36. [44]

    URL https://arxiv.org/abs/2402.04995

    Lin, Z.et al.Observation of Giant Spin Splitting and d-wave Spin Texture in Room Temperature Altermagnet RuO2.arXiv1–32 (2024). URL https://arxiv.org/abs/2402.04995

    2024 arXiv

  37. [45]

    URL https://www.nature.com/ articles/s44306-024-00055-y

    Keßler, P.et al.Absence of magnetic order in RuO 2: insights from µSR spectroscopy and neutron diffraction.npj Spintronics2, 50 (2024). URL https://www.nature.com/ articles/s44306-024-00055-y. 31

    2024

  38. [46]

    Hiraishi, M.et al.Nonmagnetic Ground State in RuO2 Revealed by Muon Spin Rotation. Phys. Rev. Lett.132, 166702 (2024). URL https://link.aps.org/doi/10.1103/ PhysRevLett.132.166702

    2024

  39. [47]

    Kiefer, L.et al.Crystal structure and absence of magnetic order in single-crystalline RuO 2. J. Phys. Condens. Matter37, 135801 (2025). URL https://dx.doi.org/10.1088/ 1361-648X/adad2a

    2025

  40. [48]

    Wenzel, M.et al.Fermi-liquid behavior of nonaltermagnetic RuO2.Phys. Rev. B111, L041115 (2025). URLhttps://link.aps.org/doi/10.1103/PhysRevB.111.L041115

    2025 doi

  41. [49]

    URLhttps://arxiv.org/abs/2503.20621

    Wu, Z.et al.The Fermi surface of RuO 2 measured by quantum oscillations.arXiv1–11 (2025). URLhttps://arxiv.org/abs/2503.20621

    2025 arXiv

  42. [50]

    URLhttps://arxiv.org/abs/2504.21138

    Qian, T.et al.Determining the Nature of Magnetism in Altermagnetic Candidate RuO 2.arXiv 1–7 (2025). URLhttps://arxiv.org/abs/2504.21138

    2025 arXiv

  43. [51]

    URL https://arxiv.org/pdf/2505

    Yumnam, G.et al.Constraints on magnetism and correlations in RuO 2 from lattice dynamics and M¨ossbauer spectroscopy.arXiv1–8 (2025). URL https://arxiv.org/pdf/2505. 03250

    2025

  44. [52]

    URLhttps://arxiv.org/pdf/2503.07985

    Wang, Y .-C.et al.Robust Anisotropic Spin Hall Effect in Rutile RuO 2.arXiv1–17 (2025). URLhttps://arxiv.org/pdf/2503.07985

    2025

  45. [53]

    T.et al.Revisiting altermagnetism in RuO 2: a study of laser-pulse induced charge dynamics by time-domain terahertz spectroscopy.npj Spintronics3, 17 (2025)

    Plouff, D. T.et al.Revisiting altermagnetism in RuO 2: a study of laser-pulse induced charge dynamics by time-domain terahertz spectroscopy.npj Spintronics3, 17 (2025). URL https: //www.nature.com/articles/s44306-025-00083-2. 32

    2025

  46. [54]

    Liu, J.et al.Absence of Altermagnetic Spin Splitting Character in Rutile Oxide RuO2. Phys. Rev. Lett.133, 176401 (2024). URL https://link.aps.org/doi/10.1103/ PhysRevLett.133.176401

    2024

  47. [55]

    I., Garcia-Gassull, L

    Smolyanyuk, A., Mazin, I. I., Garcia-Gassull, L. & Valent ´ı, R. Fragility of the magnetic order in the prototypical altermagnet RuO2.Phys. Rev. B109, 134424 (2024). URL https: //link.aps.org/doi/10.1103/PhysRevB.109.134424

    2024 doi

  48. [56]

    Qian, Z., Yang, Y ., Liu, S. & Wu, C. Fragile unconventional magnetism inRuO2 by proximity to Landau-Pomeranchuk instability.Phys. Rev. B111, 174425 (2025). URL https://link. aps.org/doi/10.1103/PhysRevB.111.174425

    2025 doi

  49. [57]

    G.et al.Altermagnetic Polar Metallic phase in Ultra-Thin Epitaxially-Strained RuO 2 Films.arXiv1–23 (2024)

    Jeong, S. G.et al.Altermagnetic Polar Metallic phase in Ultra-Thin Epitaxially-Strained RuO 2 Films.arXiv1–23 (2024). URLhttps://arxiv.org/pdf/2405.05838

    2024 arXiv

  50. [58]

    K.et al.Thickness-dependent insulator-to-metal transition in epitaxial Ruo2 films.Phys

    Rajapitamahuni, A. K.et al.Thickness-dependent insulator-to-metal transition in epitaxial Ruo2 films.Phys. Rev. Mater .8, 075002 (2024). URL https://link.aps.org/doi/ 10.1103/PhysRevMaterials.8.075002

    2024 doi

  51. [59]

    URLhttps://arxiv.org/pdf/2408.05187

    Weber, M.et al.All optical excitation of spin polarization in d-wave altermagnets.arXiv1–26 (2024). URLhttps://arxiv.org/pdf/2408.05187

    2024 arXiv

  52. [60]

    G.et al.Metallicity and anomalous Hall effect in epitaxially strained, atomically thin RuO2 films.Proceedings of the National Academy of Sciences122, e2500831122 (2025)

    Jeong, S. G.et al.Metallicity and anomalous Hall effect in epitaxially strained, atomically thin RuO2 films.Proceedings of the National Academy of Sciences122, e2500831122 (2025). URL https://www.pnas.org/doi/abs/10.1073/pnas.2500831122. 33

    2025 doi

  53. [61]

    URLhttps://doi.org/10.1063/5.0062726

    Nunn, W.et al.Solid-source metal–organic molecular beam epitaxy of epitaxial RuO 2.APL Materials9, 091112 (2021). URLhttps://doi.org/10.1063/5.0062726

    2021 doi

  54. [62]

    Physical Review B98, 241101 (2018)

    Jovic, V .et al.Dirac nodal lines and flat-band surface state in the functional oxide RuO 2. Physical Review B98, 241101 (2018). URL https://journals.aps.org/prb/ abstract/10.1103/PhysRevB.98.241101

    2018 doi

  55. [63]

    P.et al.Strain-stabilized superconductivity.Nat

    Ruf, J. P.et al.Strain-stabilized superconductivity.Nat. Commun.12, 59 (2021). URL http://dx.doi.org/10.1038/s41467-020-20252-7

    2021 doi

  56. [64]

    URL https://doi.org/10.1021/ acscatal.0c04871

    Jovic, V .et al.Momentum for Catalysis: How Surface Reactions Shape the RuO 2 Flat Surface State.ACS Catalysis11, 1749–1757 (2021). URL https://doi.org/10.1021/ acscatal.0c04871

    2021

  57. [65]

    URL http://arxiv.org/abs/2507.05047

    Keßler, P.et al.Moir ´e-assisted charge instability in ultrathin RuO2.arXiv1–14 (2025). URL http://arxiv.org/abs/2507.05047

    2025 arXiv

  58. [66]

    & Feder, R

    Tamura, E., Piepke, W. & Feder, R. New spin-polarization effect in photoemission from nonmagnetic surfaces.Phys. Rev. Lett.59, 934–937 (1987). URL https://link.aps. org/doi/10.1103/PhysRevLett.59.934

    1987 doi

  59. [67]

    & Feder, R

    Tamura, E. & Feder, R. Spin Polarization in Normal Photoemission by Linearly Polarized Light from Nonmagnetic (001) Surfaces.Europhysics Letters16, 695 (1991). URL https: //dx.doi.org/10.1209/0295-5075/16/7/015. 34

    1991 doi

  60. [68]

    & Feder, R

    Henk, J. & Feder, R. Spin Polarization in Normal Photoemission by Linearly Polarized Light from Non-Magnetic (110) Surfaces.Europhysics Letters28, 609 (1994). URLhttps: //dx.doi.org/10.1209/0295-5075/28/8/012

    1994 doi

  61. [69]

    & Heinzmann, U

    Schmiedeskamp, B., V ogt, B. & Heinzmann, U. Experimental verification of a new spin- polarization effect in photoemission: Polarized photoelectrons from Pt(111) with linearly polarized radiation in normal incidence and normal emission.Phys. Rev. Lett.60, 651–654 (1988). URLht...

    1988 doi

  62. [70]

    & Heinzmann, U

    Irmer, N., David, R., Schmiedeskamp, B. & Heinzmann, U. Experimental verification of a spin effect in photoemission: Polarized electrons due to phase-shift differences in the normal emission from Pt(100) by unpolarized radiation.Phys. Rev. B45, 3849–3852 (1992). URL https://li...

    1992 doi

  63. [71]

    & Heinzmann, U

    Irmer, N., Frentzen, F., Yu, S.-W., Schmiedeskamp, B. & Heinzmann, U. A new effect in spin-resolved photoemission from Pt(110) in normal emission by linearly polarized VUV- radiation.J. Electron Spectrosc. Relat. Phenom.78, 321 (1996). URL https://www. sciencedirect.com/scienc...

    1996

  64. [72]

    & Kirschner, J

    Feder, R. & Kirschner, J. Spin polarization in directional photoemission from non-magnetic crystals by unpolarized light.Solid State Commun.40, 547 (1981). URL https://www. sciencedirect.com/science/article/pii/0038109881905706

    1981

  65. [73]

    M.et al.Kramers nodal line metals.Nature Communications12, 3064 (2021)

    Xie, Y . M.et al.Kramers nodal line metals.Nature Communications12, 3064 (2021). URL http://dx.doi.org/10.1038/s41467-021-22903-9. 35

    2021 doi

  66. [74]

    Phys.6, 134 (2023)

    Zhang, Y .et al.Kramers nodal lines and Weyl fermions in SmAlSi.Commun. Phys.6, 134 (2023). URLhttps://www.nature.com/articles/s42005-023-01257-2

    2023

  67. [75]

    URL https://www.nature.com/articles/ s41467-025-60020-z

    Zhang, Y .et al.Kramers nodal lines in intercalated TaS 2 superconductors.Nature Communications16, 4984 (2025). URL https://www.nature.com/articles/ s41467-025-60020-z

    2025

  68. [76]

    URLhttps://arxiv.org/abs/2503.08571

    Domaine, G.et al.Tunable Octdong and Spindle-Torus Fermi Surfaces in Kramers Nodal Line Metals.arXiv1–25 (2025). URLhttps://arxiv.org/abs/2503.08571

    2025

  69. [77]

    & Sham, L

    Kohn, W. & Sham, L. J. Self-Consistent Equations Including Exchange and Correlation Effects.Phys. Rev.140, A1133–A1138 (1965). URL https://journals.aps.org/ pr/abstract/10.1103/PhysRev.140.A1133

    1965 doi

  70. [78]

    & Furthm¨uller, J

    Kresse, G. & Furthm¨uller, J. Efficient Iterative Schemes forabinitio Total-Energy Calculations Using a Plane-Wave Basis Set.Phys. Rev. B54, 11169–11186 (1996). URL https:// journals.aps.org/prb/abstract/10.1103/PhysRevB.54.11169

    1996 doi

  71. [79]

    Bl¨ochl, P. E. Projector Augmented-Wave Method.Phys. Rev. B50, 17953– 17979 (1994). URL https://journals.aps.org/prb/abstract/10.1103/ PhysRevB.50.17953

    1994

  72. [80]

    & Joubert, D

    Kresse, G. & Joubert, D. From Ultrasoft Pseudopotentials to the Projector Augmented-Wave Method.Phys. Rev. B59, 1758–1775 (1999). URL https://journals.aps.org/prb/ abstract/10.1103/PhysRevB.59.1758. 36

    1999 doi

  73. [81]

    P., Burke, K

    Perdew, J. P., Burke, K. & Ernzerhof, M. Generalized Gradient Approximation Made Sim- ple.Phys. Rev. Lett.77, 3865–3868 (1996). URL https://journals.aps.org/prl/ abstract/10.1103/PhysRevLett.77.3865

    1996 doi

  74. [82]

    K.et al.Engineering Carrier Effective Masses in Ultrathin Quantum Wells of IrO2.Physical Review Letters121, 176802 (2018)

    Kawasaki, J. K.et al.Engineering Carrier Effective Masses in Ultrathin Quantum Wells of IrO2.Physical Review Letters121, 176802 (2018). URL https://journals.aps.org/ prl/abstract/10.1103/PhysRevLett.121.176802

    2018 doi

  75. [83]

    Journal of Chemical Physics152, 074101 (2020)

    Blaha, P.et al.WIEN2k: An APW+lo program for calculating the properties of solids. Journal of Chemical Physics152, 074101 (2020). URL https://doi.org/10.1063/1. 5143061. 37 Figure 1:Proposed spin texture relevant in epitaxially-strained RuO2.(A) Schematic illustration of the c...

    2020 doi

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