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Spin-Splitting Magnetoresistance in Altermagnetic RuO2 Thin Films

T0 review · 4 major / 6 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read A phase-shifted magnetoresistance in (101)-RuO2/Co bilayers is claimed as spin-splitting magnetoresistance, placing the Néel vector near [001] and indicating altermagnetic order in epitaxial RuO2 thin films.

desk verdict Careful transport study proposing a new nonrelativistic MR effect, but the altermagnetic conclusion leans on DFT done inside the disputed magnetic state. read the letter →

arxiv 2412.18220 v2 pith:GHHTEZWK submitted 2024-12-24 cond-mat.mes-hall cond-mat.mtrl-scicond-mat.str-elcond-mat.supr-conphysics.app-ph

Hongyu Chen , Zian Wang , Peixin Qin , Ziang Meng , Xiaorong Zhou , Xiaoning Wang , Li Liu , Guojian Zhao
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Zhiyuan Duan Tianli Zhang Jinghua Liu Dingfu Shao Chengbao Jiang Zhiqi Liu
This is my paper · ORCID
classification cond-mat.mes-hallcond-mat.mtrl-scicond-mat.str-elcond-mat.supr-conphysics.app-ph
keywords altermagnetismspin-splittingmagnetoresistanceRuO2thinfilmsNéelvectorspinHallnonrelativisticcurrentspintronics
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

This paper claims that a nonrelativistic magnetoresistance effect, dubbed spin-splitting magnetoresistance (SSMR), appears in epitaxial (101)-RuO2/Co bilayers and can be separated from the conventional spin Hall magnetoresistance. The separation matters because RuO2 is one of the earliest candidate altermagnets, yet its magnetic order is hotly debated, especially in thin films. When current runs along RuO2[010], the longitudinal resistance as a function of magnetic-field angle is phase-shifted (minimum near $\beta^* \approx 55^\circ$), whereas along $[\bar{1}01]$ it follows the standard $\cos^2\beta$ form. Fitting the temperature dependence of this phase shift with a two-parameter formula yields a pure SSMR phase $\beta_0 \approx 33.6^\circ$, matching the ~35° tilting angle of a [001]-oriented Néel vector. If right, this is a simple electrical probe of the Néel vector in altermagnets and evidence that epitaxial RuO2 thin films sustain long-range altermagnetic order.

What carries the argument

The load-bearing object is the spin-splitting effect of a d-wave altermagnet—an antiferromagnet whose two opposite sublattices are connected by a crystal rotation, so its Fermi surface is spin-split even without spin-orbit coupling. In a (101)-oriented film, an electric field along [010] drives a nonrelativistic spin current along [100] with spin polarization $\mathbf{p}$ parallel to the Néel vector $\mathbf{n}$; at the altermagnet/ferromagnet interface this spin current is reflected with strength set by $(\mathbf{m}\cdot\mathbf{n})^2$, where $\mathbf{m}$ is the Co magnetization, producing a longitudinal resistance change. The key identity used to separate SSMR from conventional spin Hall magnetoresistance is Eq. 13: $\sin(\beta^*)\sqrt{\Delta R/R(0)}_{010} = \tan(\beta_0)\cos(\beta^*)\sqrt{\Delta R/R(0)}_{010} + \eta\sqrt{\Delta R/R(0)}_{\bar{1}01}$, where $\beta_0$ isolates the spin-splitting contribution (the Néel vector tilt) and $\eta$ absorbs the anisotropic spin Hall and spin-diffusion factors. Fitting temperature-dependent data to this formula yields $\beta_0 \approx 33.6^\circ$ with $\eta \approx 0.84$, and the calculated $\beta_0(T)$ stays close to 33.6° across the measured range.

What would settle it

A decisive test is to measure the same bilayers in relaxed, thicker RuO2 films where epitaxial strain is absent; if the phase-shifted magnetoresistance along [010] and the fitted $\beta_0 \approx 33.6^\circ$ persist unchanged, the altermagnetic SSMR explanation fails. A second decisive check is spin-torque ferromagnetic resonance on a single-domain film: the measured out-of-plane spin-polarization ratio $\sigma_z/\sigma_y$ should be close to $\tan(35^\circ)$ at low temperature if the DFT-based disentangling is correct.

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Extended reading notes

Core claim

The central claim is that the unusual anisotropic magnetoresistance of (101)-RuO2/Co bilayers contains a genuine spin-splitting magnetoresistance caused by the altermagnetic spin-splitting effect, not just the relativistic spin Hall effect. For current along [010], the spin-splitting effect generates an out-of-plane spin current whose polarization is collinear with the Néel vector; reflection of that current at the Co interface modulates the resistance with a phase minimum at the Néel vector's out-of-plane tilt angle. The authors disentangle this SSMR from the coexisting spin Hall magnetoresistance using Eq. 13, which combines the measured phase $\beta^*$ and amplitudes $\sqrt{\Delta R/R(0)}$ along [010] and $[\bar{1}01]$ with two parameters, $\beta_0$ and $\eta$. The best fit gives $\beta_0 \approx 33.6^\circ$ and $\eta \approx 0.84$, and $\beta_0$ matches the ~35° tilting angle of a [001]-oriented Néel vector reported by resonant x-ray scattering. They therefore conclude that the SSMR is a nonrelativistic magnetoresistance effect, that the Néel vector of their RuO2 films lies near [001], and that these thin films exhibit long-range altermagnetic order.

Load-bearing premise

The load-bearing assumption, stated in supplemental Note 6, is that the out-of-plane spin polarization seen for current along [010] comes almost entirely from the altermagnetic spin-splitting effect rather than the conventional spin-orbit mechanism; if that balance were reversed, the phase-shifted magnetoresistance could be explained without altermagnetism.

Editorial extensions

If this is right

  • Long-range altermagnetic order in epitaxial (101)-RuO2 thin films follows if the SSMR interpretation is right, with the Néel vector lying close to [001].
  • The SSMR provides a simple all-electrical way to read the Néel vector direction of an altermagnet, without magnetic tunnel junctions or lock-in detection.
  • Because the spin-splitting effect lives at the Fermi surface, the SSMR is strongly suppressed by electron scattering at high temperature, so low-temperature transport is the natural regime for detecting altermagnetic signatures.
  • In any altermagnet/ferromagnet bilayer, SSMR and spin Hall magnetoresistance coexist, so separating them requires comparing angular phase and temperature dependence, not just the size of the magnetoresistance.
  • The same phase-shifted mechanism should appear in other unconventional antiferromagnets with momentum-dependent spin splitting, making SSMR a general probe of that material class.

Reading between the lines

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

  • Inference: If the RuO2 layer could be prepared as a single antiferromagnetic domain, the measured phase $\beta^*$ should approach $\beta_0 \approx 33.6^\circ$ without any subtraction; the larger observed $\beta^*$ reflects partially compensated domains with opposite Néel vectors.
  • Inference: A direct spin-torque ferromagnetic resonance measurement on the same films could test the predicted polarization ratio $\sigma_z/\sigma_y = \tan(35^\circ)$ of the generated spin current, connecting the transport phase to the band-structure calculation.
  • Inference: The fitting method as written assumes a dominant and strongly anisotropic spin-splitting effect; applying it to altermagnets with weak or nearly isotropic spin splitting would need extra parameters, a limitation the paper itself flags.
  • Inference: The paper's picture predicts a sharp strain dependence: fully strained ultrathin films should show the SSMR phase shift, while relaxed thick films should revert to the conventional spin Hall magnetoresistance form, which is a testable boundary between the altermagnetic and nonmagnetic scenarios.
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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

4 major / 6 minor

Summary. The manuscript proposes a nonrelativistic magnetoresistance effect, termed spin-splitting magnetoresistance (SSMR), that is driven by the altermagnetic spin-splitting effect (SSE), and reports its observation in epitaxial (101)-RuO2/Co bilayers. The central experimental observation is a phase-shifted angular dependence of the longitudinal magnetoresistance for current along RuO2[010], with a minimum at β* ≈ 55° before AMR subtraction and ≈69° after subtraction, in contrast to the ≈90° minimum found for current along [1-01]. The authors interpret this as coexistence of SSMR and conventional spin Hall magnetoresistance (SMR), and fit their Eq. (13) to extract a pure SSMR phase shift β0 ≈ 33.6° and an anisotropy parameter η ≈ 0.84. They argue that β0 matches the ≈35° out-of-plane tilting angle of a [001]-oriented Néel vector, and combine this with exchange-bias observations on thicker films to conclude that the thin films are altermagnetic with long-range magnetic order.

Significance. If the central claim holds, the paper would provide a new electrical probe of the Néel vector in altermagnets and would contribute important evidence on the disputed magnetic ground state of RuO2 thin films. The manuscript has clear strengths: the control experiments are extensive (Pt substitution, Cu insertion, AMR subtraction, magnetic-field and rotation-polarity checks, magnon-excitation exclusion), the exchange-bias data independently support antiferromagnetic order in thicker films, and the first-principles calculations are documented with explicit parameters. The main weakness is that the identification of SSMR rests on a DFT-based assignment of the out-of-plane spin polarization to the T-odd SSE rather than to the T-even spin Hall effect, and the T-even comparison is not computed for the nonmagnetic state of the same film. Because the phase-shift feature is the load-bearing evidence for altermagnetism, this missing calculation is a substantive gap.

major comments (4)
  1. [Note 6 / Table S1 / Eq. (13)] The disentangling procedure sets σz010 = σSSE,z010 (Eq. 7) and attributes the phase shift to the T-odd SSE on the basis of Table S1, where the T-even SHE z-component is -33 (Ω cm)^-1 against a T-odd value of 1728.6. This comparison is computed for the altermagnetic band structure, not for a nonmagnetic (101)-RuO2 film. As Note 6 itself states, the low symmetry of the (101) film permits an out-of-plane z-polarized spin current for E along [010] even in the nonmagnetic state. If the nonmagnetic T-even σz is of order 10^2-10^3 (Ω cm)^-1, the observed phase-shifted magnetoresistance could be a conventional SMR of low-symmetry nonmagnetic RuO2, and the inference of altermagnetism would not follow. Please compute the T-even spin conductivity for the nonmagnetic state of the same (101) film and same Ueff, and report the resulting bound on σz; the IrO2 control is a different material and does not close this gap.
  2. [Note 2 / Figure S2 / main text Fig. 2] The exchange-bias evidence for antiferromagnetic order is obtained on RuO2(5 nm)/Co(5 nm), RuO2(10 nm)/Co(5 nm), and RuO2(20 nm)/Co(5 nm) films, whereas the SSMR analysis is performed on RuO2(3 nm)/Co(2.5 nm) devices. Since the magnetic state of RuO2 is argued to be sensitive to strain, thickness, and interface effects, the AFM order of the 3-nm film is not directly established. Please provide a control on the same 3-nm/2.5-nm stack used in the transport measurements, or state explicitly that the transport conclusions assume transfer of the magnetic state across thicknesses.
  3. [Eqs. (8), (13), (14) / Figure 4(c)] β0 is defined in Eq. (8) as tan^-1(σSSE^y/σSSE^z), and the DFT values in Table S1 (1237.7 and 1728.6) already give about 35.6°, so the agreement between the fitted β0 ≈ 33.6° and the ≈35° x-ray tilt is partly a consistency check on the DFT input rather than an independent measurement of the Néel-vector orientation. The temperature-independence check in Eq. (14) also reuses the globally fitted η, so it does not provide an independent validation of the model. Please quantify how much the fitted β0 would change if the DFT input were varied within the uncertainty of Ueff and Γ (for example, using the Γ = 50 meV row of Table S1).
  4. [Eq. (13) and Note 7] The extraction of β* assumes that the total angular-dependent MR after AMR subtraction follows a single sin^2(β - β*) form, but a coexisting SSMR and SMR would in general sum two sin^2 terms with different phases and amplitudes. The fitted β* of the total curve is then not simply related to the ratio of the total σy and σz by Eqs. (4)-(5). Please test the sensitivity of β0 and η to fitting the raw ΔR(β) with the two-component line shape directly, rather than first compressing each curve into a single β*.
minor comments (6)
  1. [Throughout] There are several typographical errors: 'qualitaively' (Section 2), 'interpretated' (Section 2), 'matetials' (Introduction), and 'Agular' (Note 3(1)).
  2. [Figure 4 caption] The caption states that data were 'measured at 50 K', but panels (a) and (b) show temperature-dependent behavior; the caption should read 'as a function of temperature' or specify the temperature range.
  3. [Note 2, paragraph 2] The text refers to 'Figure 2(e) in the main text' for the 20-nm-thick RuO2 exchange-bias loop, but the relevant panel appears to be Figure 2(c) in the main text.
  4. [Figure 4(c) caption] The caption attributes the ~35° tilting angle to 'a previous x-ray scattering study[26]', but the cited x-ray scattering work is reference [28] (Zhu et al.).
  5. [Eq. (2) and surrounding text] The definitions of σy and σz are given twice (in the paragraph after Eq. (1) and again after Eq. (2)); please consolidate to avoid redundancy.
  6. [Note 7] The fitting is described as 'ternary-variable', but Eq. (13) has only two unknown parameters, β0 and η; please clarify whether the third variable refers to the three experimental inputs (β*, ΔR010, ΔR1-01).

Circularity Check

1 steps flagged · score 2.0 of 10

Core SSMR/Néel-vector result is a model-based fit with independent external anchors; only the internal β0(T) consistency check round-trips its own fit parameters.

  1. fitted input called prediction [Section 2 (Results and Discussions), after Eq. 14, Figure 4(c)]
    "The best fitting gives β0 ~33.6° and η ~0.84. Note that the calculated β0 values at different temperatures with the obtained η according to Equation 14 are all close to 33.6° [Figure 4(c)], confirming the reliability of the fitting."

    Equation 14 is just Equation 13 solved for tan(β0) at fixed η. Since η and β0 are the two global fit parameters of Equation 13, inserting the fitted η together with the same measured sin(β*)√ΔR/R010, cos(β*)√ΔR/R010, and √ΔR/R1̅01 into Equation 14 at each temperature is an algebraic rearrangement of the fitted relation, not an independent prediction. A good fit will by construction return β0 values clustered around the fitted 33.6°, so the 'confirming the reliability' statement round-trips the fit output. This does not affect the central Néel-vector identification, which is anchored to the external ~35° x-ray value and exchange bias, but the temperature-independence check is not independent evidence.

full rationale

The central claim is not circular in the strong sense. The SSE spin-current polarization direction is obtained from parameter-free DFT (Table S1: T-odd σz/σy giving cot-1(σz/σy) ≈ 35°), conditional on the altermagnetic state; the experimental fit then yields β0 ≈ 33.6°, and the agreement with this DFT angle and with the external x-ray tilting angle (~35°) is a genuine consistency check. Exchange bias provides independent evidence of antiferromagnetic order. The key disentangling assumption σ010_z = σSSE,010_z (Eq. 7) is justified by the T-even calculation in Note 6/Table S1 rather than fitted to the magnetoresistance data. That T-even calculation is performed for the altermagnetic band structure, so if nonmagnetic (101)-RuO2 had a substantially larger T-even σz, the phase-shifted MR could be reinterpreted as ordinary low-symmetry SMR; this is a real falsifiability/correctness risk, but it is not a reduction of the result to its own inputs by construction. The one identifiable circular element is the Eq. 14 temperature check, which reuses the globally fitted η and therefore cannot independently confirm the fit. Weighing the independent DFT prediction, the external x-ray anchor, and the exchange-bias evidence, the paper's central derivation is substantially self-contained; the circularity score is therefore low.

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

The central claim rests on four classes of inputs: (1) the SMR formula of refs 49-51 assumed to hold quantitatively; (2) the DFT-computed spin conductivity tensors, which presuppose the collinear altermagnetic state and depend on chosen Ueff and broadening; (3) an ad hoc multidomain compensation assumption invoked to reconcile the observed β* with the expected 35°; (4) the benchmark Néel-vector orientation from a prior x-ray study. No new physical entities are introduced; the proposed SSMR is a transport effect assembled from existing spin-current physics.

free parameters (4)
  • β0 (Néel-vector tilting angle from SSMR fit) = ~33.6°
    Fitted in Eq. 13 to the temperature dependence of sin(β*)√ΔR/R and √ΔR/R; identified with the out-of-plane tilting angle of the SSE spin polarization and then with the Néel vector direction. The prior x-ray value of ~35° (ref 28) is an external benchmark, but the extracted value is a fit parameter of this paper's model.
  • η (anisotropy ratio of SHE and spin diffusion) = ~0.84
    Fitted in Eq. 13 as a constant describing the ratio σ_SHE,010^y SF_010 / σ_SHE,1̅01^y SF_1̅01. It absorbs unknown anisotropy and is used to recalculate β0(T); the temperature-independence check therefore depends on this fitted parameter.
  • Ueff (Hubbard U on Ru 4d) = 2 eV
    DFT input chosen by hand (GGA+U); the computed T-odd and T-even spin conductivities in Table S1, which underpin the claim that SSE dominates σ_z, depend on this choice.
  • Γ (broadening for T-odd spin conductivity) = 25 meV and 50 meV
    Chosen by hand to mimic electron scattering when computing SSE conductivities; the claimed dominance of SSE over SHE is evaluated at these values.
assumptions (4)
  • domain assumption Equation 1 (SMR theory from refs 49-51) applies quantitatively to the RuO2/Co bilayer with a transparent interface
    The decomposition of measured magnetoresistance into SSMR and SMR uses Eq. 1 as the backbone; interface transparency and spin-mixing conductance details are not independently measured.
  • domain assumption The RuO2 thin films are in the assumed collinear altermagnetic state with Néel vector along [001] or [001̄] for the DFT calculations
    Table S1 T-odd spin conductivities (the basis for attributing σ_z to SSE) are computed for this ground state. The magnetic order itself is the disputed question the paper aims to settle.
  • ad hoc to paper SSE contributions from domains with antiparallel Néel vectors partially cancel, reducing the net SSE relative to single-domain calculations
    Introduced in Note 6 to explain why the measured β* (~69° after AMR subtraction) differs from the ~35° expected from a pure SSE scenario.
  • domain assumption The reference value of ~35° for the Néel-vector tilting angle from the x-ray scattering study (ref 28) is correct and applicable to these films
    Used as the benchmark to validate the fitted β0 ≈ 33.6° and to assign the [001] orientation; the paper's own exchange-bias anisotropy provides partial but weaker support.

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Pith. "Pith review of Spin-Splitting Magnetoresistance in Altermagnetic RuO2 Thin Films." pith.science (2026). https://pith.science/paper/GHHTEZWK

@misc{pith2026241218220,
  author       = {Pith},
  title        = {Pith review of: Spin-Splitting Magnetoresistance in Altermagnetic RuO2 Thin Films},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/GHHTEZWK}},
  note         = {Machine review of arXiv:2412.18220}
}
read the original abstract

The recently discovered altermagnets, featured by the exotic correlation of magnetic exchange interaction and alternating crystal environments, have offered exciting cutting-edge opportunities for spintronics. Nevertheless, the altermagnetism of RuO2, one of the earliest-discovered altermagnets, is currently under intense debate. Here we try to resolve this controversy by demonstrating an altermagnetic spin-splitting magnetoresistance (SSMR) effect that is driven by a spin current associated with the giant nonrelativistic spin splitting of an altermagnet. Compared to the spin Hall magnetoresistance induced by a conventional relativistic spin current, the SSMR is characterized by unusual angular dependence with a phase-shift feature underpinned by the Neel-vector orientation and pronounced temperature dependence caused by its susceptibility to electron scattering. Through systematical investigations on the magnetoresistance of (101)-RuO2/Co bilayers, we disentangle a sizable SSMR and hence unveil a Neel vector along [001] direction. Our work not only demonstrates a simple electric avenue to probing the Neel vector of altermagnets, but also indicates long-range magnetic order in thin films of RuO2.

Figures

Figures reproduced from arXiv: 2412.18220 by the authors.

Figure 3
Figure 3. (a, b) ΔR(β)/R(0) measured at 50 K along RuO2[010] and RuO2[1̅01] in different magnetic fields a (101)-RuO2(3 nm)/Pt(3 nm) bilayer. (c) ΔR(β)/R(0) measured at 50 K in different magnetic fields of a Cu(1 nm)/Co(2.5 nm) bilayer [PITH_FULL_IMAGE:figures/full_fig_p021_3.png] view at source ↗

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Works this paper leans on

12 extracted references · 10 canonical work pages · cited by 1 Pith paper

  1. [1]

    Kresse, D

    [S1] G. Kresse, D. Joubert, From Ultrasoft Pseudopotentials to the Projector Augmented - Wave Method, Phys. Rev. B 1999, 59,

    work page 1999

  2. [59]

    Laukhin, V

    [S18] V . Laukhin, V . Skumryev, X. Martí, D. Hrabovsky, F. Sánchez, M. V . García-Cuenca, C. Ferrater, M. Varela, U. Lüders, J. F. Bobo, J. Fontcuberta, Electric-Field Control of Exchange Bias in Multiferroic Epitaxial Heterostructures, Phys. Rev. Lett. 2006, 97, 227201. [S19] Y . Cui, Z. Li, H. Chen, Y . Wu, Y . Chen, K. Pei, T. Wu, N. Xie, R. Che, X. Q...

    work page 2006

  3. [203]

    Karube, T

    [S12] S. Karube, T. Tanaka, D. Sugawara, N. Kadoguchi, M. Kohda, J. Nitta, Observation of Spin-Splitter Torque in Collinear Antiferromagnetic RuO2, Phys. Rev. Lett. 2022, 129, 137201. [S13] X. Feng, H. Bai, X. Fan, M. Guo, Z. Zhang, G. Chai, T. Wang, D. Xue, C. Song, X. Fan, Incommensurate Spin Density Wave in Antiferromagnetic RuO 2 Evinced by Abnormal S...

    arXiv 2022

  4. [267]

    Patton, D

    [S24] M. Patton, D. A. Pharis, G. Gurung, X. Huang, G. Noh, E. Y . Tsymbal, S.-Y . Choi, D. C. Ralph, M. S. Rzchowski, C.-B. Eom, Crystallographic Spin Torque Conductivity Tensor of Epitaxial IrO2 Thin Films for Oxide Spintronics, Adv. Mater. 2025, 37, 2414267. [S25] R. González-Hernández, L. Šmejkal, K. Výborný, Y . Yahagi, J. Sinova, T. Jungwirth, J. Že...

    work page 2025

  5. [943]

    [S5] S. L. Dudarev, G. A. Botton, S. Y . Savrasov, C. J. Humphreys, A. P. Sutton, Electron- Energy-Loss Spectra and the Structural Stability of Nickel Oxide: An LSDA+U Study, Phys. Rev. B 1998, 57,

    work page 1998

  6. [1213]

    [S10] J. R. Yates, X. Wang, D. Vanderbilt, I. Souza, Spectral and Fermi surface properties from Wannier interpolation, Phys. Rev. B 2007, 75, 195121. [S11] J. Nogués, I. K. Schuller, Exchange Bias, J. Magn. Magn. Mater. 1999, 192,

    work page 2007

  7. [1419]

    [S7] A. A. Mostofi, J. R. Yates, G. Pizzi, Y .-S. Lee, I. Souza, D. Vanderbilt, N. Marzari, An Updated Version of Wannier90: A Tool for Obtaining Maximally-Localised Wannier Functions, Comput. Phys. Commun. 2014, 185,

    work page 2014

  8. [1505]

    Marzari, A

    [S6] N. Marzari, A. A. Mostofi, J. R. Yates, I. Souza, D. Vanderbilt, Maximally Localized Wannier Functions: Theory and Applications, Rev. Mod. Phys. 2012, 84,

    work page 2012

Show all 12 references
  1. [1758]

    Kresse, J

    [S2] G. Kresse, J. Furthmüller, Efficient Iterative Schemes for ab Initio Total -Energy Calculations Using a Plane-Wave Basis Set, Phys. Rev. B 1996, 54, 11169. [S3] J. P. Perdew, K. Burke, M. Ernzerhof, Generalized Gradient Approximation Made Simple, Phys. Rev. Lett. 1996, 77,

    1996

  2. [2309]

    Železn ý, Y

    [S8] J. Železn ý, Y . Zhang, C. Felser, B. Yan, Spin -Polarized Current in Noncollinear Antiferromagnets, Phys. Rev. Lett. 2017, 119, 187204. [S9] J. Sinova, S. O. Valenzuela, J. Wunderlich, C. H. Back, T. Jungwirth, Spin Hall Effects, Rev. Mod. Phys. 2015, 87,

    2017

  3. [2362]

    [S20] D. A. Reiss, T. Kampfrath, P. W. Brouwer, Theory of Spin -Hall Magnetoresistance in the ac Terahertz Regime, Phys. Rev. B 2021, 104, 024415. [S21] J. Kim, P. Sheng, S. Takahashi, S. Mitani, M. Hayashi, Spin Hall Magnetoresistance in 40 Metallic Bilayers, Phys. Rev. Lett....

    2021 arXiv

  4. [3865]

    [S4] V . I. Anisimov, J. Zaanen, O. K. Andersen, Band Theory and Mott Insulators: Hubbard U Instead of Stoner I, Phys. Rev. B 1991, 44,

    1991

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