{"id":"876a47fd-c0a4-4787-8baf-4d82e41dd816","arxiv_id":"2412.18220","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":7.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"A phase-shifted magnetoresistance in (101)-RuO2/Co bilayers is attributed to spin-splitting magnetoresistance, indicating altermagnetism with a Néel vector near [001] in epitaxial RuO2 thin films.","lead":"The authors report a new type of magnetoresistance in RuO2/Co bilayers, called spin-splitting magnetoresistance, and use it to infer the magnetic order direction in the RuO2 film. The result offers a simple electrical probe for altermagnets, a disputed class of magnetic materials.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"SSMR identification rests on a T-odd vs T-even spin-conductivity ratio computed inside the disputed altermagnetic state; if nonmagnetic RuO2 has a larger T-even sigma_z, the phase-shifted MR could be ordinary low-symmetry SMR, and the Néel-vector claim loses its foundation.","rationale":"The reader's weakest assumption is precisely the most load-bearing point: the separation of SSMR from SMR hinges on the relative T-odd/T-even spin conductivities, and the T-odd value is computed in the disputed order. My concern does not move the verdict because the paper already warrants a conditional reading: the experimental controls are substantial (Pt substitution, Cu insertion, AMR subtraction, field and rotation-polarity checks, exchange-bias evidence), but the decisive interpretive link depends on an unverified nonmagnetic baseline. A nonmagnetic DFT calculation or a nonmagnetic rutile control would settle this cleanly. I therefore agree with the reader's conditional verdict and identify no additional independent objection.","tokens_in":27273,"tokens_out":13146,"duration_ms":111281,"concrete_test":"Compute the T-even spin Hall conductivity tensor of nonmagnetic (paramagnetic) RuO2 with the same VASP/Wannier setup (PAW, PBE+U with U = 2 eV, SOC) and the same (101)-film geometry, and evaluate sigma_zxz for E//[010] at the experimental Fermi level. If this nonmagnetic T-even sigma_z is <10% of the T-odd 1728.6 value, the disentangling premise survives; if it is larger, the phase-shifted MR can be explained without altermagnetism. As a complementary experimental check, measure the same beta-dependent MR on a (101)-oriented nonmagnetic rutile control (e.g., IrO2 or intentionally nonmagnetic RuO2) and look for a phase-shifted minimum along [010].","verdict_should_be":"UNCHANGED","load_bearing_attack":"The load-bearing step is in Note 6/Table S1: for E//[010], the out-of-plane spin polarization is assigned almost entirely to the T-odd SSE (sigma_z = 1728.6 at Gamma = 25 meV), with the T-even SHE negligible (sigma_z = -33). This assignment is used in Eqs. 4-13 to set sigma_z = sigma_SSE_z and then to extract beta0 = 33.6 deg as the Néel-vector tilt. The problem is that the T-odd conductivity is computed for the collinear altermagnetic state with U = 2 eV, which is precisely the disputed ground state. Recent DFT (Ref 30) and experiments (Refs 31-39) question this order, especially in bulk. For a nonmagnetic (101)-RuO2 film, the T-odd tensor is identically zero by symmetry; the phase-shifted magnetoresistance would then have to arise from the T-even SHE of the low-symmetry rutile structure. The authors have not computed the T-even spin conductivity in the nonmagnetic state; their -33 value is for the magnetic band structure. The IrO2 control (Ref S24) is a different material, and the measured temperature dependence of beta* is indirect. If the nonmagnetic T-even sigma_z is comparable to or larger than the T-odd value, the disentangling fails and the conclusion of altermagnetism does not follow from the data.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","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.","tokens_in":27637,"tokens_out":7199,"duration_ms":64819,"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":[{"comment":"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.","section":"Note 6 / Table S1 / Eq. (13)"},{"comment":"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.","section":"Note 2 / Figure S2 / main text Fig. 2"},{"comment":"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).","section":"Eqs. (8), (13), (14) / Figure 4(c)"},{"comment":"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*.","section":"Eq. (13) and Note 7"}],"minor_comments":[{"comment":"There are several typographical errors: 'qualitaively' (Section 2), 'interpretated' (Section 2), 'matetials' (Introduction), and 'Agular' (Note 3(1)).","section":"Throughout"},{"comment":"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.","section":"Figure 4 caption"},{"comment":"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.","section":"Note 2, paragraph 2"},{"comment":"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.).","section":"Figure 4(c) caption"},{"comment":"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.","section":"Eq. (2) and surrounding text"},{"comment":"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).","section":"Note 7"}],"recommendation":"major_revision","confidential_remarks":"The experimental work is careful and the controls are extensive, but the central claim depends on a missing calculation: the T-even spin conductivity of nonmagnetic (101)-RuO2. I believe this is fixable within a revision, and I would be willing to review a revised version. The paper is potentially suitable for a high-impact venue once that gap is addressed."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The paper is worth a serious look. The new piece is the SSMR concept—a spin-splitting analog of SMR with a phase-shifted angular dependence tied to the Néel vector—and the authors back it with a lot of careful transport work. The control experiments are genuinely thorough: Pt substitution, Cu insertion, AMR subtraction, field/rotation checks, and the magnon exclusion are all sensible, and the exchange-bias data independently support antiferromagnetic order in thicker films. I also give them credit for citing the skeptical literature on bulk RuO2 and for putting a limitation statement in Note 7, admitting the method is not universal.\n\nThe soft spot is exactly where the stress-test note lands. The disentangling procedure hinges on assigning the out-of-plane spin polarization almost entirely to the T-odd SSE (σ_z ≈ 1728 vs -33 in Table S1), and that calculation assumes the collinear altermagnetic state with Ueff = 2 eV—the very order under dispute. The T-even SHC for nonmagnetic RuO2 is not computed, and the IrO2 control is a different material. So the phase-shifted MR could conceivably be a low-symmetry SHE effect in nonmagnetic RuO2. That is a real hole, not a manufactured one.\n\nTwo smaller issues. First, β0 is a fit parameter, and the temperature-independence check reuses the globally fitted η; it is not an independent validation. The agreement with the x-ray ~35° value is suggestive but the confidence interval is wide. Second, the multidomain compensation argument that rescues the small net SSE is reasonable but ad hoc; there is no direct domain imaging or field-history study to back it.\n\nEven with these reservations, the paper is not confused. The experimental evidence for a phase-shifted, temperature-sensitive MR in (101)-RuO2/Co is solid, and the proposal of SSMR as a distinct mechanism stands on its own. The altermagnetism conclusion is conditional, but the authors have framed a testable hypothesis.\n\nWho gets value: spintronics and altermagnet experimentalists, plus theorists who can check the nonmagnetic T-even SHC. I would send this to a good referee rather than desk reject. The referee should ask for a calculation of the T-even SHC in nonmagnetic RuO2, or at least a bound showing it cannot reproduce the observed phase shift. That is the load-bearing missing piece.","headline":"Careful transport study proposing a new nonrelativistic MR effect, but the altermagnetic conclusion leans on DFT done inside the disputed magnetic state.","tokens_in":28225,"tokens_out":921,"would_cite":true,"duration_ms":11366,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"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.","keywords":["altermagnetism","spin-splitting magnetoresistance","RuO2 thin films","Néel vector","spin Hall magnetoresistance","nonrelativistic spin current","spintronics"],"falsifier":"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.","tokens_in":27051,"feed_emoji":"🧲","tokens_out":13257,"duration_ms":105993,"temperature":0.7,"pith_summary":"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.","feed_headline":"Phase-shifted magnetoresistance reveals altermagnetic RuO2","feed_subtitle":"The phase shift traces to a Néel vector near [001], giving a simple electric probe of altermagnetism","key_machinery":"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.","core_discovery":"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.","pith_inferences":["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."],"forward_implications":["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."],"supporting_citations":[{"why":"Supplies the spin-splitting effect: an electric current along [010] in RuO2 generates a nonrelativistic spin current with polarization collinear to the Néel vector, the core mechanism of SSMR.","marker":"[11]"},{"why":"Resonant x-ray scattering study reporting the RuO2 Néel vector near [001], giving the ~35° tilt angle used to calibrate β0.","marker":"[28]"},{"why":"Introduces spin Hall magnetoresistance, the relativistic counterpart whose angular form the SSMR is compared against and distinguished from.","marker":"[49]"},{"why":"Provides the SMR theory used to write Eq. 1 and the disentangling formula for the bilayer magnetoresistance.","marker":"[50]"},{"why":"Quantitative SMR baseline that supplies the expected magnitude and angular dependence for separating SSMR from SMR.","marker":"[51]"},{"why":"Recent calculation questioning bulk RuO2 magnetism, motivating the thin-film epitaxial context in which the altermagnetic claim is made.","marker":"[30]"},{"why":"Earlier evidence of itinerant antiferromagnetism in RuO2, supporting the collinear magnetic ground state assumed in the DFT calculations.","marker":"[27]"},{"why":"Experimental report of a tilted spin current from collinear antiferromagnetic RuO2, supporting the out-of-plane spin polarization used in the SSMR scenario.","marker":"[15]"}],"fun_headline_variants":["Spin-splitting magnetoresistance pins down RuO2 altermagnetism","Unusual magnetoresistance reveals Néel vector in RuO2 thin films","Nonrelativistic spin current puts RuO2's altermagnetism on solid ground","Phase shift in RuO2/Co bilayers traces altermagnetic order","Altermagnetic spin-splitting magnetoresistance solves RuO2 debate"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"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.","fun_headline_variants_meta":{"raw":{"variants":["Spin-splitting magnetoresistance pins down RuO2 altermagnetism","Unusual magnetoresistance reveals Néel vector in RuO2 thin films","Nonrelativistic spin current puts RuO2's altermagnetism on solid ground","Phase shift in RuO2/Co bilayers traces altermagnetic order","Altermagnetic spin-splitting magnetoresistance solves RuO2 debate"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001047,"raw_usage":{"total_tokens":4448,"prompt_tokens":1038,"completion_tokens":3410,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":654,"completion_tokens_details":{"reasoning_tokens":3307}},"tokens_in":654,"tokens_out":3410,"duration_ms":24941,"temperature":1.0,"reasoning_tokens":3307,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-11T04:55:25.555928+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"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.","supporting_citations":[],"review_version":1}