{"id":"4ccfdaa1-6edd-4bef-8fd1-22ca409b717f","arxiv_id":"2608.05528","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"In GdRu2Ge2, the local density of states on the Ru sites between nearest-neighbor Gd spins follows the Gd spin-spin alignment, producing multi-Q charge textures in every magnetic phase.","lead":"This paper uses scanning tunneling microscopy to image how electrons in GdRu2Ge2 rearrange in lockstep with five different magnetic textures, including two skyrmion crystal phases. It finds that the local electron density between neighboring magnetic atoms tracks whether those two magnetic moments are aligned, a direct view of spin and charge coupling in an itinerant magnet.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The 'tight correlation' between nearest-neighbor Gd spin dot products and Ru LDOS is not quantitatively established: the model produces unobserved QA+QB Fourier components (SI Sec. IX) and the Phase I spin structure is fitted ad hoc to the same STM data.","rationale":"The reader's stated weakest assumption is that the input spin structures are correct, especially the ad hoc revised Phase I. That is a real concern, but the deeper issue is that even granting the spin structures, the quantitative link between Eq. 2 and the measured L(r) is never established: the model's own admitted spurious Fourier components show the dot-product mapping is not faithful, and the paper explicitly concedes the approach may not capture the relevant physics. This is load-bearing because the central claim is phrased as a 'tight correlation', yet the only support is qualitative visual comparison and phase matching for selected components. The Phase I circularity compounds the problem, but the quantitative residual test would settle both: a good residual for Phases II-V would partly vindicate the relationship, while a poor residual for Phase II would show the model is incomplete independent of spin-structure uncertainties. The reader's rationale does mention the qualitative support and the QA+QB discrepancy, so the verdict is already CONDITIONAL; my concern reinforces that condition rather than changing it. Hence UNCHANGED, with the concrete test proposed as the natural acceptance criterion.","tokens_in":27142,"tokens_out":5005,"duration_ms":49940,"concrete_test":"For each phase, fit a complex scale a minimizing the squared residual sum over the 42 target wavevectors, |FQ[L] - a*FQ[W]|^2, and report the normalized residual R = ||FQ[L] - a*FQ[W]|| / ||FQ[L]||. Also report R restricted to the observed wavevector set and separately for the spurious QA+QB family. If R in Phase II is comparable to the signal, or if the spurious family dominates the residual, Eq. 2 is incomplete. Then repeat with an ablated model that includes only the wavevectors present in data, or with next-nearest-neighbor dot products or local chirality; if any alternative improves R substantially, the nearest-neighbor-only 'tight correlation' is not established.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim is that L(r) is tightly governed by P_{i,j,mu} (Eq. 1) through Eq. 2. The evidence for this is visual: Figs. 6(b/c) are said to reproduce 'broad qualitative features' and phases 'reasonably well'. The paper's own SI Sec. IX shows W(r) contains Fourier components at wavevectors such as QA+QB that are absent from the measured L(r) at V = -100 mV, and concludes that 'the spin-spin dot product approach does not capture the relevant physics determining the LDOS'. Because these components arise from the spin-interference (product) structure of P, their absence is not a benign kernel artifact: the kernel can only rotate phases, not create or destroy wavevectors (SI Sec. IX). Thus the observed LDOS is demonstrably not a linear rendering of nearest-neighbor dot products alone. In addition, the Phase I spin structure is modified by ad hoc trial-and-error to reproduce the same anomalous LDOS peaks it is then used to explain (SI Sec. VII B), so the Phase I comparison is partially circular. No quantitative residual, error bar, or alternative-descriptor test is reported, so the 'tightly correlates' phrasing exceeds the evidence.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper reports atomically resolved scanning tunneling microscopy (STM) measurements of the LDOS on the Ge-terminated surface of GdRu2Ge2 across five magnetic phases, including two skyrmion crystal phases. It introduces a model in which the LDOS at bond-centered Ru sites is expressed as the convolution of nearest-neighbor Gd spin-spin dot products P_{i,j,μ} (Eq. 1) with anisotropic kernel functions K_μ(r) (Eq. 2), and claims that this quantity 'tightly correlates' with the measured LDOS. The authors also propose a revised double-Q ground state for Phase I, motivated by the observation of modulations not expected for the previously proposed single-Q screw, and show that the model reproduces broad qualitative features of the measured patterns and their Fourier phases.","tokens_in":27444,"tokens_out":2197,"duration_ms":23280,"significance":"If the claimed relationship were quantitatively established, it would provide a concrete microscopic connection between multi-Q spin textures and intra-unit-cell charge patterns in an itinerant skyrmion magnet, with implications for understanding the electronic mechanisms behind centrosymmetric skyrmion stability. The paper's strengths include a well-described non-uniform DFT (NUDFT) phase-referencing procedure that correctly handles multiple incommensurate wavevectors, careful field- and energy-dependent measurements that show clear phase boundaries, and a transparent discussion of the model's limitations in the Supplemental Information. However, the central claim of a 'tight' correlation rests on qualitative visual comparison, and the paper's own Supplementary Information concedes that the dot-product model does not capture the relevant LDOS physics at certain wavevectors. Establishing the central claim will require quantitative residual analysis, tests against alternative descriptors, and independent support for the revised Phase I spin structure.","major_comments":[{"comment":"The model generates Fourier components at wavevectors such as Q_A+Q_B that are absent from the measured L(r) at V = -100 mV, as shown in SI Sec. IX and Fig. S9(i). The SI correctly notes that kernel functions cannot create or destroy wavevectors, so these spurious components cannot be dismissed as a kernel artifact; they indicate that nearest-neighbor spin dot products alone do not determine the LDOS at these wavevectors. The main text (Fig. 6) nevertheless summarizes the comparison as reproducing features 'reasonably well' and the abstract claims 'tightly correlates.' To support the central claim, the authors should provide a quantitative metric (e.g., normalized residuals per Fourier component, a correlation coefficient in real space, or a weighted phase/amplitude error) for each phase, and should explicitly test whether a linear spin model, a chirality-based descriptor, or higher-order spin correlations gives a better account of the data.","section":"§6, Eq. (2) and SI Sec. IX"},{"comment":"The revised Phase I spin structure is obtained by an ad hoc trial-and-error adjustment of the modulation amplitudes and phases to reproduce the 'anomalous' LDOS peaks that are then used to justify the revision. This is partially circular: the same data are used to fit the spin structure and to claim agreement between the model and the measurement. The authors should either verify the revised structure with an independent measurement (e.g., resonant x-ray scattering in the same field/phase regime, or neutron diffraction), or clearly demonstrate that the comparison is robust by showing that the key qualitative features of the measured L(r) and its Fourier phases are reproduced across a range of plausible parameter sets rather than a single fitted set.","section":"SI Sec. VII B and Fig. 6(a)"},{"comment":"The evidence for the claimed 'tight' correlation between P_{i,j,μ} and the measured LDOS is visual: Fig. 6(b/c) is stated to reproduce 'broad qualitative features' and phases 'reasonably well.' No quantitative figure of merit (e.g., Pearson correlation between W(r) and L(r), residual amplitude spectra, or phase error distributions) is reported for any of the five phases. The authors should quantify the agreement per phase and per wavevector, and specify what threshold they would take as support for the claim made in the abstract. Without such quantification, the central claim is not established at the level the paper asserts.","section":"Figs. 4 and 6; abstract"}],"minor_comments":[{"comment":"In the paragraph introducing the NUDFT, the phrase 'quan-\ntitatively' is broken across a line in the supplied text; this is a formatting issue, not a substantive one.","section":"Main text, Results section"},{"comment":"The DOI for reference [39] appears malformed ('10.1103/q853-plvr'); please verify and correct the identifier.","section":"Reference list, Ref. [39]"},{"comment":"The description of the NUDFT target set would benefit from a table or explicit list of all 84 members of Q (or the 42 unique wavevectors), rather than relying on ellipses in the text, to allow the reader to reproduce the analysis.","section":"Supplementary Information, Sec. III B"},{"comment":"The term 'Na¨ıvely' in the main text is spelled with a nonstandard ligature and should be written as 'Naively' or 'Naïvely.'","section":"Fig. 3 caption and SI Fig. S1"}],"recommendation":"major_revision","confidential_remarks":"The core measurement appears sound and the NUDFT phase-referencing is a methodological contribution worth publishing. The main risk is that the authors overstate the strength of the spin-dot-product/LDOS relationship while the SI concedes the model is incomplete. I also note that the Phase I structural revision draws on the same STM data used for validation, and the spin structures for Phases II–V are imported from the authors' prior work without independent verification. These issues are fixable with quantitative reanalysis and clearer framing, so I recommend major revision rather than rejection."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Bottom line: a valuable, carefully executed STM study of GdRu2Ge2 with a well-described phase-resolved NUDFT methodology, but the headline claim of a tight spin–charge correlation goes beyond what the data and the model actually show. The paper deserves serious refereeing, with the expectation that the authors will need to either dial back the claim or add real quantitative support.\n\nWhat is genuinely new: atomically resolved LDOS motifs for five magnetic phases, the phase-resolved NUDFT analysis (methodologically solid and clearly explained), the basketweave pattern in Phase II, and a revised double-Q ground state proposal for Phase I. Credit where it is due: the paper is unusually open about the model's failures. The SI (Sec. IX) explicitly states that the spin-spin dot product approach 'does not capture the relevant physics determining the LDOS.' That is not a buried caveat; it is central to evaluating the claim.\n\nThe soft spots are real and central. The abstract says the nearest-neighbor Gd spin alignment 'tightly correlates' with the Ru LDOS, but the evidence is visual. Figures 6(b/c) reproduce 'broad qualitative features' and phases 'reasonably well,' with no quantitative residuals, no error bars, and no alternative-descriptor test. More seriously, the model generates Fourier components at QA+QB that are absent from the measured L(r) at -100 mV. As the SI notes, the kernels can only rotate phases, not create or destroy wavevectors, so this discrepancy is structural: the observed LDOS cannot be a linear rendering of nearest-neighbor dot products alone.\n\nThe Phase I revised spin structure is also fitted ad hoc to the same anomalous peaks it is then used to explain (SI Sec. VII B). The paper admits this is trial-and-error. That is a reasonable hypothesis-generating step, but it should be clearly labeled as unverified, and preferably backed by neutron or resonant x-ray scattering. The spin structures for Phases II–V are taken from prior work by the same group (Yoshimochi et al.), which is fine as a starting point but means the inferred relationship is only as good as those inputs.\n\nIf I were refereeing, I would ask for: (1) quantitative agreement measures between W(r) and L(r); (2) explicit treatment of the QA+QB discrepancy, ideally by testing a different descriptor or adding a term; (3) independent evidence for the revised Phase I structure or a clear label as a proposal; and (4) a more calibrated description—'is consistent with' rather than 'tightly correlates.'\n\nWho gets value from this? STM practitioners and anyone working on itinerant skyrmion materials. The dataset is a useful resource and the NUDFT phase-referencing approach is worth knowing. It deserves a serious referee, not a desk reject, but the authors have work to do on the claim.","headline":"Valuable STM dataset and a solid NUDFT methodology, but the central claim of a tight spin–charge correlation is not quantitatively supported, and the model's own acknowledged failures are the key issue.","tokens_in":27955,"tokens_out":3540,"would_cite":false,"duration_ms":31146,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"In GdRu2Ge2, the atomically resolved charge texture at the Ge surface is set by nearest-neighbor Gd spin alignment, so each multi-Q magnetic phase carries a corresponding multi-Q Ru 4d charge pattern.","keywords":["skyrmion","multi-Q magnetism","spin-charge coupling","scanning tunneling microscopy","GdRu2Ge2","RKKY interaction","local density of states"],"falsifier":"A neutron or resonant x-ray measurement of the GdRu2Ge2 ground state that finds a pure single-Q spin screw, with no perpendicular modulation, would falsify the revised Phase I model and therefore the claimed correspondence between nearest-neighbor Gd spin alignment and the LDOS in that phase.","tokens_in":26948,"feed_emoji":"🧲","tokens_out":6657,"duration_ms":50982,"temperature":0.7,"pith_summary":"The paper tries to establish that in GdRu2Ge2, a centrosymmetric magnet hosting atomic-scale skyrmions, the charge density seen by a scanning tunneling microscope is not an independent electronic pattern but a direct image of nearest-neighbor Gd spin alignments. Using atomically resolved conductance maps in five magnetic phases, the authors show that the local density of states on the two Ru bond-centered sublattices of the Gd square net follows the nearest-neighbor spin-spin dot products $P_{i,j,\\mu}$ of Eq. (1). A simple convolution model built from those dot products reproduces each phase's distinctive LDOS motif, including the 'basketweave' pattern of the elliptical skyrmion phase. If correct, this gives a concrete microscopic spin-charge relationship in an itinerant skyrmion magnet and implies that multi-$Q$ magnetism and multi-$Q$ charge textures are two sides of the same electronic reconstruction.","feed_headline":"Gd spins dictate the atomic-scale charge pattern in a skyrmion magnet","feed_subtitle":"STM images across five magnetic phases tie Ru 4d charge modulations directly to Gd-Gd spin alignment.","key_machinery":"The load-bearing object is the bond-centered spin-spin dot product $P_{i,j,\\mu}=(1-\\mu)(\\mathbf S_{i,j}\\cdot \\mathbf S_{i+1,j})+\\mu(\\mathbf S_{i,j}\\cdot \\mathbf S_{i,j+1})$ defined on the two inequivalent bonds of the Gd square net (Eq. 1), together with the weight image $W(\\mathbf r)=\\sum_{i,j,\\mu}[P_{i,j,\\mu}K_\\mu(\\mathbf r)]*\\delta(\\mathbf r-\\mathbf r_{i,j,\\mu})$ (Eq. 2). The kernels $K_\\mu(\\mathbf r)$ are negative-valued and elongated along the bond axis, chosen to match the observed 'trenches' of low LDOS along Gd-Ru-Gd bonds. This construction turns the spin structure of each magnetic phase into a predicted real-space charge texture whose Fourier amplitudes and phases can be compared directly with STM conductance maps; the comparison is what carries the argument that spin alignment controls the LDOS.","core_discovery":"The central claim is that the relationship between magnetism and charge in GdRu2Ge2 is local and quantitative: the normalized tunneling conductance $L(\\mathbf r, V)$ at the Ge surface is governed by the nearest-neighbor Gd spin-spin dot product $P_{i,j,\\mu}$ evaluated on the two bond-centered sublattices of the Gd square net. The weight image $W(\\mathbf r)$ obtained by placing those dot products on bond-centered delta functions and convolving with anisotropic, negative-valued kernels $K_\\mu(\\mathbf r)$ reproduces, phase by phase, the measured LDOS motifs: bond-order-like stripes in Phase I, the basketweave in Phase II, checkerboard-like patterns in Phases III and IV, and a crossed-stripe sum in Phase V. The same construction reproduces the Fourier phases of the measured patterns, in particular the satellite phases that encode the basketweave. Because the kernels resemble the in-plane projections of Ru $d_{xz}$ and $d_{yz}$ orbitals and are centered at Ru sites, the paper concludes that the Ru $4d$ itinerant states that mediate the magnetic interactions also carry the observable charge modulations.","pith_inferences":["The same dot-product construction could be applied to other centrosymmetric skyrmion hosts such as GdRu2Si2 or EuAl4 to test whether bond-centered spin alignment universally governs the STM-visible charge texture.","If the correspondence is quantitative rather than qualitative, measured LDOS maps could be inverted: atomically resolved conductance images might be used to reconstruct the underlying spin structure with unit-cell resolution.","The energy-dependent 90-degree rotation of the basketweave bond-order pattern near -150 meV hints at an electronic nematic instability coupled to the magnetic order, which goes beyond the paper's static dot-product model.","A systematic iterative scheme that refines spin structures against predicted LDOS images could replace the ad hoc trial-and-error revision of Phase I, turning the method into a general spin-structure refinement tool."],"forward_implications":["The five magnetic phases of GdRu2Ge2 each reconstruct the Ru 4d bands near the Fermi level, producing distinct multi-Q LDOS superstructures.","The basketweave motif in Phase II is generated by specific phase relations among Bragg and satellite Fourier components, not by amplitudes alone, and the same phase relations are reproduced by the dot-product model.","The ground state of GdRu2Ge2 is a double-Q structure, a spin screw plus a perpendicular in-plane sinusoid, with topological charge stripes but zero net skyrmion number.","Electronic band reconstructions accompanying each magnetic phase feed back into the interactions that stabilize the magnetism, forming a coupled spin-charge problem.","Because the kernels resemble Ru $d_{xz}$ and $d_{yz}$ orbital projections, the Ru sites are the active mediators: the charge texture is carried by the same Ru 4d states that mediate the magnetic interactions."],"supporting_citations":[{"why":"supplies the experimentally inferred spin structures and magnetic phase diagram for Phases I–V that the modeling uses as input.","marker":"[30]"},{"why":"established the STM imaging of itinerant-electron coupling to local moments in the sister compound GdRu2Si2 and the charge-density-wave modeling approach this paper extends.","marker":"[22]"},{"why":"provides the catalog of multiple-Q spin textures in centrosymmetric tetragonal magnets that motivates treating the observed textures as multi-Q states.","marker":"[12]"},{"why":"reports a double-Q ground state with topological charge stripes in GdRu2Si2, used to motivate the revised Phase I structure for GdRu2Ge2.","marker":"[38]"},{"why":"defines the non-collinear magnetoresistance mechanism in which the LDOS depends on nearest-neighbor spin alignment, the premise adopted for the dot-product model.","marker":"[36]"},{"why":"identifies Ru 4d-derived electronic states as the mediators of the helical Q structure in Gd-based skyrmion materials, supporting the bond-centered Ru interpretation.","marker":"[17]"}],"fun_headline_variants":["STM shows Gd spin alignment drives charge patterns in skyrmion magnet","Gd spins write atomic charge textures in GdRu2Ge2","Charge and spin intertwine atomically in skyrmion magnet","Local spin alignment dictates charge modulation in skyrmion crystal","Skyrmion magnet: spin alignment governs atomic-scale charge"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the input spin structures are correct: Phases II–V come from prior resonant x-ray analysis, while the revised Phase I structure is adjusted by ad hoc trial-and-error to reproduce the anomalous LDOS peaks, so if any of these spin structures is wrong the inferred spin-charge relationship fails.","fun_headline_variants_meta":{"raw":{"variants":["STM shows Gd spin alignment drives charge patterns in skyrmion magnet","Gd spins write atomic charge textures in GdRu2Ge2","Charge and spin intertwine atomically in skyrmion magnet","Local spin alignment dictates charge modulation in skyrmion crystal","Skyrmion magnet: spin alignment governs atomic-scale charge"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000214,"raw_usage":{"total_tokens":1448,"prompt_tokens":990,"completion_tokens":458,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":606,"completion_tokens_details":{"reasoning_tokens":372}},"tokens_in":606,"tokens_out":458,"duration_ms":5337,"temperature":1.0,"reasoning_tokens":372,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-08T11:25:07.015933+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A neutron or resonant x-ray measurement of the GdRu2Ge2 ground state that finds a pure single-Q spin screw, with no perpendicular modulation, would falsify the revised Phase I model and therefore the claimed correspondence between nearest-neighbor Gd spin alignment and the LDOS in that phase.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"supplies the experimentally inferred spin structures and magnetic phase diagram for Phases I–V that the modeling uses as input."},{"cited_title":"Ozawa, S","cited_arxiv_id":null,"evidence_quote":"established the STM imaging of itinerant-electron coupling to local moments in the sister compound GdRu2Si2 and the charge-density-wave modeling approach this paper extends."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"provides the catalog of multiple-Q spin textures in centrosymmetric tetragonal magnets that motivates treating the observed textures as multi-Q states."},{"cited_title":"Gould, C","cited_arxiv_id":null,"evidence_quote":"defines the non-collinear magnetoresistance mechanism in which the LDOS depends on nearest-neighbor spin alignment, the premise adopted for the dot-product model."}],"review_version":1}