Pith. sign in

REVIEW 4 major objections 5 minor 2 cited by

RuO2 films with (100) and (110) orientations become altermagnetic under epitaxial strain even without Hubbard U, producing a 15.3% spin Hall angle.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Strained (100) and (110) RuO2 films are predicted to show altermagnetic spin splitting and a strong spin Hall effect at U=0, while bulk and (001)/(101) films remain nonmagnetic.

T0 review reviewed 2026-08-03 challenge →

load-bearing objection A plausible, testable reconciliation of the RuO2 controversy, but the headline 15.3% SHA is built on parameters the paper doesn't state. the 4 major comments →

arxiv 2602.11602 v2 pith:CXNDCF7H submitted 2026-02-12 cond-mat.mtrl-sci

Strain-Driven Altermagnetic Spin Splitting Effect in RuO₂

Seungjun Lee , Seung Gyo Jeong , Jian-Ping Wang , Bharat Jalan , Tony Low This is my paper
classification cond-mat.mtrl-sci
keywords AltermagnetismRuO2spin Hall effectepitaxial strainHubbard Uspin-orbit torquefirst-principles DFTtime-reversal-odd
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The reading

This paper argues that the controversial altermagnetic order in RuO2 is not intrinsic to bulk or most film orientations, but can be stabilized purely by epitaxial strain in (100) and (110) oriented films. The authors show that, even with zero Hubbard U correction, these strained films develop a magnetic Néel vector and produce a time-reversal-odd spin Hall effect (ASSE). For (100) RuO2 at a specific crystal angle, the predicted spin Hall angle reaches 15.3%, comparable to heavy metals like Pt and Ta. This reconciles conflicting experimental reports: bulk and (001)/(101) films are nonmagnetic, while thin strained (100)/(110) films show strong signatures. The result frames RuO2 as a controllable platform for altermagnetic spintronics.

Core claim

The central claim is that the magnetic ground state and the altermagnetic spin-splitting effect (ASSE) in RuO2 depend critically on epitaxial strain, crystal orientation, and the Hubbard U parameter. For bulk RuO2 and (001)/(101) films on TiO2, the critical U for magnetism is above ~1.2 eV, but experimental evidence suggests U is smaller, so these systems remain nonmagnetic in the absence of extrinsic effects. In contrast, (100) and (110) oriented films exhibit a finite Néel vector even at U=0, driven by a strain-induced Fermi-surface instability. In (100) RuO2, this produces a large T-odd spin Hall conductivity of 4271 (ℏ/e) S/cm at φ=0, corresponding to a spin Hall angle of ~15.3% without

What carries the argument

The key machinery is a first-principles DFT framework that models epitaxial strain by fixing in-plane lattice constants to those of TiO2 while relaxing the out-of-plane lattice constant and atomic positions, combined with a Hubbard U sweep. The central observable is the Néel vector magnitude |N|=|μ_Ru1−μ_Ru2|/2, which tracks magnetic order. Spin transport is decomposed into T-even (σ) and T-odd (σ^A) spin Hall conductivity tensors, computed via Kubo-like formulas; symmetry analysis constrains which tensor components survive for each orientation and Néel vector direction. In (100) and (110) RuO2, a strain-induced Fermi-surface instability produces altermagnetic spin splitting of a few tens of

Load-bearing premise

The load-bearing premise is that the strain-induced magnetic solution at U=0 in (100) and (110) RuO2 is physical and not an artifact of the chosen exchange-correlation functional or the simplified strain model that pins in-plane lattice constants to TiO2.

What would settle it

Grow high-quality, fully strained (100) RuO2 films thinner than ~4 nm and measure the spin Hall effect as a function of in-plane angle; if no T-odd component (identified by sign reversal under Néel vector reversal and its specific φ-dependence) is observed, or if ARPES shows no spin splitting at U≈0, the central claim is falsified.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

If this is right

  • Bulk RuO2 and (001)/(101) films on TiO2 are nonmagnetic without extrinsic effects, so prior ASSE reports in those orientations likely arise from defects, doping, or interface magnetism rather than intrinsic bulk altermagnetism.
  • (100) and (110) films are a viable route to observe ASSE without large Hubbard U; (100) gives a ~15.3% spin Hall angle at φ=0, comparable to Pt and Ta, making it a promising spin-orbit torque material.
  • The T-odd spin Hall conductivity flips sign when the Néel vector is reversed, offering a clean experimental signature to distinguish ASSE from conventional spin Hall effect.
  • In (110) RuO2, in-plane strain lowers symmetry and lifts spin degeneracy over the entire momentum space, producing a non-compensated ferrimagnet rather than an ideal altermagnet.
  • For (100) films, the effect requires ultra-thin, high-crystallinity films because epitaxial strain relaxes above roughly 4 nm thickness.

Where Pith is reading between the lines

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

  • If correct, the orientation- and strain-dependent magnetism suggests that other rutile-structure transition-metal oxides may show similar strain-tunable altermagnetism, extending the material base beyond RuO2.
  • The prediction of small or zero U in RuO2 could be directly tested by ARPES on fully strained (100) films: the few-tens-of-meV spin splitting should be observable, and its absence would contradict the claim.
  • The distinct φ-dependence of T-odd versus T-even SHC could serve as a fingerprint in spin-torque ferromagnetic resonance experiments, where measuring the angular dependence isolates the altermagnetic contribution.
  • A testable extension: thickness-dependent spin Hall measurements on (100) RuO2 should show a sharp drop in ASSE once strain relaxes above ~4 nm.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 5 minor

Summary. The paper uses DFT+U calculations to study how epitaxial strain, crystallographic orientation, and the Hubbard U parameter affect the magnetic ground state and spin Hall response of RuO2. Symmetry analysis is used to classify T-even and T-odd spin Hall conductivity tensors for (001), (101), (110), and (100) films on TiO2. The authors report a critical U of about 1.0–1.2 eV for bulk RuO2, and find that fully strained (100) and (110) films are magnetic even at U = 0, whereas bulk and (001)/(101) remain nonmagnetic. For (100) RuO2, they compute a dominant T-odd SHC component of 4271 (ℏ/e) S/cm at φ = 0, quoted as a spin Hall angle of ~15.3%, and argue that this reconciles conflicting experimental reports on ASSE in RuO2.

Significance. If the central result holds, the paper provides a concrete design rule: ultra-thin, highly strained (100) RuO2 films should exhibit a strong time-reversal-odd spin Hall effect even in the absence of a Hubbard U, while bulk and (001)/(101) samples should be nonmagnetic. This would help settle the current controversy over RuO2's magnetic ground state and spin-transport properties. The systematic U scan, orientation-dependent tensor analysis, and comparison with recent experiments are strengths. However, the quantitative headline depends on several unreported or assumed computational and material parameters, so the result is not yet reproducible or robust as presented.

major comments (4)
  1. [Sec. 'To investigate the U- and strain-dependent electronic structure'; Fig. 2(a)] The central claim that (100) and (110) RuO2 are magnetic at U = 0 is not supported by sufficient computational evidence. The manuscript does not state the exchange-correlation functional, k-point sampling, smearing, plane-wave cutoff, or the energy difference between the magnetic and nonmagnetic solutions. The statement 'All other computational details are provided in Supplementary Information' is not checkable from the manuscript, and the U = 0 state sits near a magnetic/nonmagnetic boundary (the critical U is only ~1.0–1.2 eV). A GGA-type functional may overstabilize Stoner magnetism near such a boundary; the authors should report the total-energy difference and test at least one alternative functional or a convergence check on the magnetic moment.
  2. [Eqs. (1)–(2) and Sec. 'We begin with our discussion...'] The constant-broadening parameter Γ entering the SHC formulas is never specified. Values such as 4271 (ℏ/e) S/cm and the resulting 15.3% SHA depend quantitatively on Γ, especially for Fermi-surface-dominated T-odd terms. The manuscript must state the Γ value used and show that the reported SHC values are converged with respect to Γ, or provide a physically motivated choice (e.g., from experimental scattering rate). Without this, the quantitative predictions are not reproducible.
  3. [Fig. 4(b) and Sec. 'Through the previous discussion...'] The 15.3% spin Hall angle is obtained by dividing the computed SHC by an assumed charge conductivity. The text cites the bulk room-temperature experimental conductivity of RuO2 (2.8×10^4 Ω^-1 cm^-1, Ref. [47]), but the target system is a fully strained, ultra-thin (100) film. Strain, defects, and finite thickness can change the charge conductivity substantially. The authors should either calculate the film's conductivity from the same DFT electronic structure, use a measured film value, or explicitly label the 15.3% as an upper-bound estimate based on the bulk conductivity. This is load-bearing for the paper's headline number.
  4. [Sec. 'Figure 2(b-d) show electronic band structures...'] The text states that for (110) RuO2, in-plane strain 'lifts spin-degeneracy over the entire momentum space, indicating that it becomes non-compensated ferrimagnet instead of ideal altermagnet.' This contradicts the abstract and summary, which group (100) and (110) together as exhibiting 'strain-induced altermagnetic spin splitting.' If (110) is a non-compensated ferrimagnet, its T-odd SHC is not a pure ASSE. The authors should clarify whether the (110) T-odd response is an altermagnetic effect or a ferrimagnet spin-current effect, and quantify any net magnetization. This affects the reconciliation narrative and the design guidelines.
minor comments (5)
  1. [Throughout] Typos and grammatical errors: 'unsetteled' should be 'unsettled'; 'it is importantly note' should be 'it is important to note'; 'lager' should be 'larger'; 'meither' should be 'neither'; 'four times lager' should be 'four times larger'.
  2. [Fig. 1 and Fig. 2 captions] The caption of Fig. 1 lists panels (e–h) for U-dependent Néel vector and band structures, but the main text refers to Fig. 2 for these panels. Please renumber the figures/captions consistently.
  3. [Sec. 'Figure 4(b) shows...'] The sentence contains a duplicated phrase: 'With non-zero φ, an unconventional component, At φ = 90°...' Please revise for clarity.
  4. [References [32] and SI] Reference [32] is listed as 'See supplemental material'; please provide a full citation or description of the SI, and ensure Tables S1–S3 are either included or properly referenced.
  5. [Eq. (1)] It would help to state explicitly which terms correspond to the Fermi-sea and Fermi-surface contributions, since the text refers to them but the decomposition is not shown in the equation.

Circularity Check

0 steps flagged

No significant circularity: the predicted SHC values are direct DFT outputs, and the small-U choice is grounded in external experiments rather than fitted to the paper's own predictions.

full rationale

The paper's derivation chain is self-contained for the central quantitative claims. The T-even and T-odd spin Hall conductivities are computed from the linear-response formulas in Eqs. (1)-(2) using DFT eigenstates of the strained RuO2 unit cells. The Hubbard-U scan is a parameter study: U is not fitted to any target SHC value. The conclusion that U is small is argued from independent experimental evidence (muSR, ARPES, optics; refs. 18-21, 45), and the U=0 result for (100)/(110) is a genuinely new DFT prediction for those strained orientations. The bulk U=0 SHC values are benchmarked against an independent prior DFT calculation (ref. 46), and the U=2 eV ASSE value is checked against a previous prediction (ref. 7). The self-citations (refs. 23, 24, 44) support contextual claims about epitaxial strain and thickness relaxation, but these are not load-bearing for the computed spin Hall tensors; removing them would not alter the SHC numbers. The possible fragility of the U=0 Stoner-type magnetism and the absence of detailed convergence/functional tests in the main text are robustness concerns, not circularity.

Axiom & Free-Parameter Ledger

3 free parameters · 5 axioms · 0 invented entities

The paper adds no new entities or forces. Its numerical predictions rest on DFT approximations (functional, strain model, constant-broadening) and on the external experimental inference that U is small. The main free parameters are U, Gamma, and the conductivity used for the SHA; none are fitted to the target SHC values, but their unstated values affect the headline numbers.

free parameters (3)
  • Hubbard U parameter for Ru 4d = 0 (for the main prediction; critical value ~1.0-1.2 eV)
    Scanned in DFT. The central ASSE claim uses U=0, chosen because the authors argue experiments rule out large U. This is an input assumption, not fitted to SHC data.
  • Broadening constant Gamma = not specified in main text
    Appears in Eqs. 1-2 and directly affects the magnitude of the computed SHC. Its value is not stated in the main text (presumably in SI).
  • Charge conductivity sigma used for spin Hall angle = 2.8e4 Ohm^-1 cm^-1 (bulk, room temperature, ref [47])
    Used to convert SHC to spin Hall angle. The same bulk value may be used for strained thin films, which is an approximation that is not flagged.
axioms (5)
  • domain assumption DFT with a standard exchange-correlation functional (presumably PBE) captures the itinerant magnetism of RuO2 at U=0.
    The U=0 magnetism in (100)/(110) is a DFT result; if the functional overstabilizes magnetic solutions, the central prediction fails. Invoked in Sec. on U-dependent magnetism and Fig. 2.
  • domain assumption The constant-broadening model for the spin Hall conductivity (Eqs. 1-2) is applicable to RuO2.
    All SHC values are computed with this model; the broadening parameter Gamma is an unstated input.
  • domain assumption The epitaxial strain model (in-plane lattice fixed to bulk TiO2, full relaxation of out-of-plane lattice and atomic positions) represents realistic ultra-thin films.
    The central strain-driven magnetism depends on this model. Introduced in the paragraph beginning 'To model epitaxial strain effects...'.
  • domain assumption Recent experimental reports of nonmagnetic bulk RuO2 and small U are correct.
    The paper uses refs [18-22] to argue U is small; this external evidence underpins the negative predictions for bulk/(001)/(101) and the choice U=0.
  • standard math Tensor rotation via D matrix (sigma'^k_ij = sum D_i^l D_j^m D_k^n sigma^n_lm) correctly describes SHC for rotated crystal orientations.
    Used to derive the symmetry-restricted tensors for (101), (110), and (100) films. Standard group-theoretic result.

reviewed 2026-08-03 · how reviews work

0 comments
Cite this review

Pith. "Pith review of Strain-Driven Altermagnetic Spin Splitting Effect in RuO$_2$." pith.science (2026). https://pith.science/paper/CXNDCF7H

@misc{pith2026260211602,
  author       = {Pith},
  title        = {Pith review of: Strain-Driven Altermagnetic Spin Splitting Effect in RuO$_2$},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/CXNDCF7H}},
  note         = {Machine review of arXiv:2602.11602}
}
Share X Bluesky LinkedIn Reddit HN
read the original abstract

The non-relativistic spin-momentum locking in altermagnets gives rise to a time-reversal-odd spin Hall effect, known as the altermagnetic spin-splitting effect (ASSE). Although ASSE was first reported in RuO$_2$, subsequent experiments have yielded inconsistent results, leaving its spin-transport mechanism unclear. Here, we systematically investigate how strain, crystal orientation, and the Hubbard $U$ parameter influence the magnetic ground state and spin Hall response of RuO$_2$. Guided by recent experimental observations, we find that $U$ is likely smaller than the value required to induce intrinsic magnetism, suggesting that bulk RuO$_2$ and (001)/(101) RuO$_2$ thin films grown on TiO$_2$ are nonmagnetic in the absence of extrinsic effects. In contrast, (100) and (110) films exhibit strain-induced altermagnetic spin splitting, leading to a strong ASSE even without Hubbard $U$ corrections. These results reconcile previous experimental discrepancies and provide design guidelines for RuO$_2$-based spintronic devices.

Figures

Figures reproduced from arXiv: 2602.11602 by Bharat Jalan, Jian-Ping Wang, Seung Gyo Jeong, Seungjun Lee, Tony Low.

Figure 1
Figure 1. Figure 1: FIG. 1. (a–d) Top views of the crystal structures of RuO [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: (a) summarizes the Hubbard U-dependent lo￾cal magnetic moments of bulk, (001), (101), (110) and (100) RuO2, respectively. Without SOC, a critical Hub￾bard U value for nonmagnetic to magnetic phase tran￾sition is predicted between 1.0 and 1.2 eV for Ru 4d in a good agreement with the previous DFT calcula￾tion. [17] Including SOC slightly increases the critical U value (∼1.2 eV). The (101) RuO2 case shows ne… view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. (a-c) Hubbard [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. The representative (a-b) [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗

discussion (0)

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

Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Nonmagnetic-magnetic Transitions in Rutile RuO2

    cond-mat.mtrl-sci 2026-04 unverdicted novelty 5.0

    DFT calculations show RuO2 undergoes transitions between nonmagnetic and altermagnetic ground states as a function of Hubbard U and strain that changes cell volume.

  2. Nonmagnetic-magnetic Transitions in Rutile RuO2

    cond-mat.mtrl-sci 2026-04 conditional novelty 5.0

    Correlation strength and volume-changing strain can switch bulk rutile RuO2 between nonmagnetic and multiple altermagnetic phases with spin splitting.

Reference graph

Works this paper leans on

55 extracted references · 4 linked inside Pith · cited by 1 Pith paper

  1. [1]

    [23, 24] These strain effects are significant in (001), (100), and (110) RuO 2, but are relatively weak in (101) RuO 2 (+0.2% for [10 ¯1])

    (−4.7%) and [100]=[010] (+2.2%) directions, re- spectively. [23, 24] These strain effects are significant in (001), (100), and (110) RuO 2, but are relatively weak in (101) RuO 2 (+0.2% for [10 ¯1]). Such strain can signifi- cantly modify the electronic structure and SHC tensors of RuO 2 and must be carefully considered when analyz- ing experimental resul...

    2000

  2. [2]

    We emphasize this clear angular dependence inT-even SHE must be care- fully considered in analyzing experimental data

    and [010] or [ ¯110] directions. We emphasize this clear angular dependence inT-even SHE must be care- fully considered in analyzing experimental data. For both orientations, meitherϕ= 0 ◦ orϕ= 90 ◦, unconventional component,σ x zx becomes non-zero due to the lack of in- plane mirror operation corresponding to the charge cur- rent direction. [38] Figure 4...

    2000

  3. [3]

    & 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)

    2020

  4. [4]

    & Jungwirth, T

    ˇSmejkal, L., Sinova, J. & Jungwirth, T. Emerging re- search landscape of altermagnetism.Phys. Rev. X12, 040501 (2022)

    2022

  5. [5]

    & Jungwirth, T

    ˇSmejkal, L., Sinova, J. & Jungwirth, T. Beyond conven- tional ferromagnetism and antiferromagnetism: A phase with nonrelativistic spin and crystal rotation symmetry. Phys. Rev. X12, 031042 (2022)

    2022

  6. [6]

    & Tsym- bal, E

    Shao, D.-F., Zhang, S.-H., Li, M., Eom, C.-B. & Tsym- bal, E. Y. Spin-neutral currents for spintronics.Nat. Commun.12, 7061 (2021)

    2021

  7. [7]

    & Yao, Y

    Zhou, X., Feng, W., Yang, X., Guo, G.-Y. & Yao, Y. Crystal chirality magneto-optical effects in collinear an- tiferromagnets.Phys. Rev. B104, 024401 (2021)

    2021

  8. [8]

    Electron.5, 735–743 (2022)

    Feng, Z.et al.An anomalous hall effect in altermagnetic ruthenium dioxide.Nat. Electron.5, 735–743 (2022)

    2022

  9. [9]

    Gonz´ alez-Hern´ andez, R.et al.Efficient electrical spin splitter based on nonrelativistic collinear antiferromag- netism.Phys. Rev. Lett.126, 127701 (2021)

    2021

  10. [10]

    Elec- tron.5, 267–274 (2022)

    Bose, A.et al.Tilted spin current generated by the collinear antiferromagnet ruthenium dioxide.Nat. Elec- tron.5, 267–274 (2022)

    2022

  11. [11]

    Bai, H.et al.Observation of spin splitting torque in a collinear antiferromagnet RuO 2.Phys. Rev. Lett.128, 197202 (2022)

    2022

  12. [12]

    Weber, M.et al.All optical excitation of spin polarization in d-wave altermagnets.arXiv preprint arXiv:2408.05187 (2024)

    Pith/arXiv arXiv 2024

  13. [13]

    Berlijn, T.et al.Itinerant antiferromagnetism in RuO 2. Phys. Rev. Lett.118, 077201 (2017)

    2017

  14. [14]

    Zhu, Z.et al.Anomalous antiferromagnetism in metallic RuO2 determined by resonant x-ray scattering.Phys. Rev. Lett.122, 017202 (2019)

    2019

  15. [15]

    & Kuneˇ s, J

    Ahn, K.-H., Hariki, A., Lee, K.-W. & Kuneˇ s, J. Antifer- romagnetism in RuO 2 as d-wave Pomeranchuk instabil- ity.Phys. Rev. B99, 184432 (2019). 6

    2019

  16. [16]

    Tschirner, T.et al.Saturation of the anomalous Hall ef- fect at high magnetic fields in altermagnetic RuO 2.APL Mater.11(2023)

    2023

  17. [17]

    Song, J.et al.Spin-Orbit Coupling Driven Magnetic Response in Altermagnetic RuO 2.Small21, 2407722 (2025)

    2025

  18. [18]

    adv.10, eadj4883 (2024)

    Fedchenko, O.et al.Observation of time-reversal sym- metry breaking in the band structure of altermagnetic RuO2.Sci. adv.10, eadj4883 (2024)

    2024

  19. [19]

    I., Garcia-Gassull, L

    Smolyanyuk, A., Mazin, I. I., Garcia-Gassull, L. & Va- lent ´ ı, R. Fragility of the magnetic order in the proto- typical altermagnet RuO 2.Phys. Rev. B109, 134424 (2024)

    2024

  20. [20]

    Hiraishi, M.et al.Nonmagnetic ground state in RuO 2 revealed by muon spin rotation.Phys. Rev. Lett.132, 166702 (2024)

    2024

  21. [21]

    npj Spintronics2, 50 (2024)

    Keßler, P.et al.Absence of magnetic order in RuO 2: insights fromµSR spectroscopy and neutron diffraction. npj Spintronics2, 50 (2024)

    2024

  22. [22]

    Liu, J.et al.Absence of altermagnetic spin splitting character in rutile oxide RuO 2.Phys. Rev. Lett.133, 176401 (2024)

    2024

  23. [23]

    Wenzel, M.et al.Fermi-liquid behavior of nonaltermag- netic RuO2.Phys. Rev. B111, L041115 (2025)

    2025

  24. [24]

    Kiefer, L.et al.Crystal structure and absence of mag- netic order in single-crystalline RuO2.J. Phys. Condens. Matter.37, 135801 (2025)

    2025

  25. [25]

    G.et al.Altermagnetic polar metallic phase in ultra-thin epitaxially-strained RuO2 films.arXiv preprint arXiv:2405.05838(2024)

    Jeong, S. G.et al.Altermagnetic polar metallic phase in ultra-thin epitaxially-strained RuO2 films.arXiv preprint arXiv:2405.05838(2024)

    Pith/arXiv arXiv 2024

  26. [26]

    G.et al.Metallicity and anomalous Hall effect in epitaxially strained, atomically thin RuO2 films.Proc

    Jeong, S. G.et al.Metallicity and anomalous Hall effect in epitaxially strained, atomically thin RuO2 films.Proc. Natl. Acad. Sci. USA.122, e2500831122 (2025)

    2025

  27. [27]

    Bai, H.et al.Efficient spin-to-charge conversion via alter- magnetic spin splitting effect in antiferromagnet RuO 2. Phys. Rev. Lett.130, 216701 (2023)

    2023

  28. [28]

    Sci.11, 2400967 (2024)

    Guo, Y.et al.Direct and inverse spin splitting effects in altermagnetic RuO2.Adv. Sci.11, 2400967 (2024)

    2024

  29. [29]

    Liao, C.-T., Wang, Y.-C., Tien, Y.-C., Huang, S.-Y. & Qu, D. Separation of Inverse altermagnetic spin-splitting effect from inverse spin Hall effect in RuO 2.Phys. Rev. Lett.133, 056701 (2024)

    2024

  30. [30]

    Li, Z.et al.Fully Field-Free Spin-Orbit Torque Switching Induced by Spin Splitting Effect in Altermagnetic RuO2. Adv. Mater.37, 2416712 (2025)

    2025

  31. [31]

    Jung, H.et al.Reversible Spin Splitting Effect in Alter- magnetic RuO2 Thin Films.Nano Lett.25, 16985–16991 (2025)

    2025

  32. [32]

    Wang, Z.et al.Inverse Spin Hall Effect Dominated Spin- Charge Conversion in (101) and (110)-Oriented RuO 2 Films.Phys. Rev. Lett.133, 046701 (2024)

    2024

  33. [33]

    Wang, Y.-C.et al.Robust Anisotropic Spin Hall Effect in Rutile RuO2.arXiv preprint arXiv:2503.07985(2025)

    arXiv 2025

  34. [34]

    See supplemental material

  35. [35]

    & Wang, J.-P

    Ji, N., Lauter, V., Zhang, X., Ambaye, H. & Wang, J.-P. Strain induced giant magnetism in epitaxial Fe 16N2 thin film.Appl. Phys. Lett.102(2013)

    2013

  36. [36]

    com- mun.9, 2058 (2018)

    Quarterman, P.et al.Demonstration of Ru as the 4th ferromagnetic element at room temperature.Nat. com- mun.9, 2058 (2018)

    2058

  37. [37]

    & Mokrousov, Y

    Freimuth, F., Bl¨ ugel, S. & Mokrousov, Y. Spin-orbit torques in Co/Pt(111) and Mn/W(001) magnetic bilayers from first principles.Phys. Rev. B90, 174423 (2014)

    2014

  38. [38]

    & Yan, B

    ˇZelezn´ y, J., Zhang, Y., Felser, C. & Yan, B. Spin- polarized current in noncollinear antiferromagnets.Phys. Rev. Lett.119, 187204 (2017)

    2017

  39. [39]

    ˇZelezn` y, J.et al.Spin-orbit torques in locally and glob- ally noncentrosymmetric crystals: Antiferromagnets and ferromagnets.Phys. Rev. B95, 014403 (2017)

    2017

  40. [40]

    Roy, A., Guimar˜ aes, M. H. & S lawi´ nska, J. Unconven- tional spin hall effects in nonmagnetic solids.Phys. Rev. Mater.6, 045004 (2022)

    2022

  41. [41]

    & Kwon, Y.-K

    Jeong, D., Kang, S.-H. & Kwon, Y.-K. Magnetic and crystal symmetry effects on spin hall conductivity in al- termagnets.arXiv preprint arXiv:2508.07639(2025)

    Pith/arXiv arXiv 2025

  42. [42]

    Phys.13, 300–305 (2017)

    MacNeill, D.et al.Control of spin–orbit torques through crystal symmetry in WTe 2/ferromagnet bilayers.Nat. Phys.13, 300–305 (2017)

    2017

  43. [43]

    Liu, L.et al.Symmetry-dependent field-free switching of perpendicular magnetization.Nature Nanotechnology 16, 277–282 (2021)

    2021

  44. [44]

    Mater.95, 2416763 (2025)

    Yang, Y.et al.Large Spin-Orbit Torque with Multi- Directional Spin Components in Ni 4W.Adv. Mater.95, 2416763 (2025)

    2025

  45. [45]

    Forte, J. D. S.et al.Strain Engineering of Altermagnetic Symmetry in Epitaxial RuO 2 Films (2025). 2510.26581

    Pith/arXiv arXiv 2025

  46. [46]

    G.et al.Anisotropic strain relaxation-induced directional ultrafast carrier dynamics in RuO2 films.Sci

    Jeong, S. G.et al.Anisotropic strain relaxation-induced directional ultrafast carrier dynamics in RuO2 films.Sci. Adv.11, eadw7125 (2025)

    2025

  47. [47]

    Zhang, Y.et al.Observation of mirror-odd and mirror- even spin texture in ultra-thin epitaxially-strained RuO 2 films.arXiv preprint arXiv:2509.16361(2025)

    arXiv 2025

  48. [48]

    & Yan, B

    Sun, Y., Zhang, Y., Liu, C.-X., Felser, C. & Yan, B. Dirac nodal lines and induced spin hall effect in metallic rutile oxides.Phys. Rev. B95, 235104 (2017)

    2017

  49. [49]

    & Sartain, C

    Ryden, W., Lawson, A. & Sartain, C. C. Electrical Trans- port Properties of IrO 2 and RuO2.Phys. Rev. B1, 1494 (1970)

    1970

  50. [50]

    & Nagaosa, N

    Guo, G.-Y., Murakami, S., Chen, T.-W. & Nagaosa, N. Intrinsic spin hall effect in platinum: First-principles cal- culations.Phys. Rev. Lett.100, 096401 (2008)

    2008

  51. [51]

    Liu, L., Moriyama, T., Ralph, D. C. & Buhrman, R. A. Spin-torque ferromagnetic resonance induced by the spin hall effect.Phys. Rev. Lett.106, 036601 (2011)

    2011

  52. [52]

    Liu, L.et al.Spin-torque switching with the giant spin hall effect of tantalum.Science336, 555–558 (2012)

    2012

  53. [53]

    Noh, S.et al.Tunneling Magnetoresistance in Alter- magnetic RuO2-Based Magnetic Tunnel Junctions.Phys. Rev. Lett.134, 246703 (2025)

    2025

  54. [54]

    Q., To, D

    Ho, D. Q., To, D. Q., Hu, R., Bryant, G. W. & Janotti, A. Symmetry-breaking induced surface magnetization in nonmagnetic RuO2.Phys. Rev. Mater.9, 094406 (2025)

    2025

  55. [55]

    Akashdeep, A.et al.Surface-Localized Magnetic Or- der in RuO 2 Thin Films Revealed by Low-Energy Muon Probes.arXiv preprint arXiv:2510.08064(2025)

    arXiv 2025

This paper was first reviewed by deepseek-v4-flash on August 3, 2026.