{"id":"0dabd56e-e423-47e0-ab1f-7692ac48ab27","arxiv_id":"2507.23232","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":7,"one_line_summary":"Certain 6H perovskite oxides are altermagnets with non-relativistic spin-split bands, and one candidate, Ba3NiRu2O9, shows a large piezomagnetic response when hole-doped and strained.","lead":"This paper identifies several 6H perovskite oxides as altermagnets, where a special arrangement of magnetic atoms and antiferromagnetic order splits electron bands by spin without net magnetization. Using symmetry analysis and density functional theory, the authors predict spin-split bands and a large strain-induced magnetization in two of these materials.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Altermagnetism claim is verified for only two of the four table entries; Ba3SrIr2O9 is classified from a DFT-predicted magnetic structure with no experimental TN, so the 'several compounds' claim is over-broad.","rationale":"I searched for a more internal weakness in the symmetry argument. The c-axis AFM arrangement in the centrosymmetric P63/mmc structures would naively give a PT-type operation; however, the relevant inversion at z=c/4 is non-symmorphic, and the explicit DFT spin-split bands in Figs. 2 and 5 demonstrate that the magnetic space group does not enforce full spin degeneracy. So I do not find an internal inconsistency in the central construction. The residual risk is empirical and matches the reader's weakest assumption. The paper itself flags the Ba3SrIr2O9 caveat in the Table I footnote, and no experimental ordering temperature is listed, so this is not a manufactured concern. I agree with the CONDITIONAL verdict: the two directly calculated compounds support the altermagnetic mechanism, but the breadth of the headline claim depends on a magnetic structure that has not been established. A single experimental determination would settle it. I do not change the reader's verdict; if the test fails, the paper should be revised to claim altermagnetism for the verified compounds only.","tokens_in":9787,"tokens_out":20596,"duration_ms":227858,"concrete_test":"Determine the magnetic ground state of Ba3SrIr2O9 by zero-field muSR or neutron diffraction (powder and, if available, single crystal) down to the temperature range where the DFT state would order; compare the observed propagation vector and moment orientation with the assumed collinear ac-plane configuration. If the measured magnetic structure differs, or no long-range order is found, remove Ba3SrIr2O9 from Table I and restrict the 'several' claim to the remaining compounds.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The broad claim 'several 6H perovskites are indeed altermagnets' is supported by explicit DFT for Ba3CoIr2O9 and Ba3NiRu2O9, but Table I extends the claim to Ba3SrIr2O9 and Ba3TbRu2O9 on the basis of symmetry analysis. The weakest link is Ba3SrIr2O9: its magnetic point group 2'/m' is not derived from any measured magnetic order. The table lists no TN and the footnote explicitly states that the collinear ac-plane state with a large ferromagnetic component was taken from previous DFT+U+SOC calculations. If that theoretical ground state is not realized (the compound may fail to order, or order with the 120-degree in-plane structure found in related 6H iridates, or with moments along c instead), the M-type altermagnetic classification and the predicted rho_xy/rho_yz response for this compound collapse. The abstract's 'indeed' and the 'several' wording implicitly weight all four Table I entries, so this unverified entry is load-bearing for the breadth of the central claim, even though the two directly computed compounds remain valid.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper argues that several 6H perovskites of the form A3BB'2O9 are altermagnets, based on magnetic point group symmetry analysis and density functional theory (DFT+U and DFT+U+SOC) calculations. For Ba3CoIr2O9 (M-type) and Ba3NiRu2O9 (S-type), the authors present band structures with non-relativistic spin splitting, Fermi-surface analyses, and, for Ba3CoIr2O9, a computed off-diagonal optical conductivity indicating magneto-optical activity. For Ba3NiRu2O9, they report a large hole-doping-induced magnetization under 1% tensile strain, which they label 'giant piezomagnetism.' The symmetry classification is extended in Table I to Ba3SrIr2O9 and Ba3TbRu2O9 on the basis of magnetic point group assignments, with the former relying on a theoretical magnetic structure from previous work.","tokens_in":10078,"tokens_out":5824,"duration_ms":66976,"significance":"If the central claims hold, the paper identifies a new family of altermagnets in layered hexagonal perovskites, which are attractive because single crystals can be grown and cleaved for surface-sensitive probes such as spin-resolved STM and ARPES. The direct DFT+U calculations for Ba3CoIr2O9 and Ba3NiRu2O9 are a strength, as they provide concrete band-structure evidence consistent with the symmetry analysis, and the stated Hubbard parameters and numerical settings make the calculations reproducible. However, the significance is tempered by two overreaching claims: the abstract's 'several 6H perovskites are indeed altermagnets' is only directly verified for two compounds, and the 'giant piezomagnetism' is a doped, strain-assisted response rather than an intrinsic piezomagnetic tensor of the stoichiometric material. These issues affect the breadth and headline impact of the paper but do not undermine the core altermagnetism evidence for the two directly computed compounds.","major_comments":[{"comment":"The abstract's claim that 'several 6H perovskites are indeed altermagnets' is over-broad relative to the evidence. Table I classifies Ba3SrIr2O9 as an M-type altermagnet using the footnote 'the theoretical magnetic ground state obtained in previous DFT+U+SOC calculations were used for analysis; moments are collinear in the ac plane with large ferromagnetic component.' This compound has no experimental TN and no measured magnetic structure. If the actual ground state differs (e.g., 120-degree in-plane order, or moments along c), the magnetic point group 2'/m' and the predicted rho_xy/rho_yz response would not apply. The two compounds computed in this work remain valid, but the 'several' wording implicitly weights all four entries. Please either provide additional verification of the assumed Ba3SrIr2O9 magnetic state or explicitly restrict the altermagnetism claim to the two compounds with direct computational evidence.","section":"Table I and Abstract"},{"comment":"The 'giant piezomagnetic effect' reported in the abstract and conclusions is not the intrinsic piezomagnetic response of stoichiometric Ba3NiRu2O9. In the text, direct DFT+U+SOC calculations for the unstrained or 1%-strained undoped compound yield a vanishingly small net magnetization of about 10^-3 µB/2 f.u. The large signal in Fig. 6(a) appears only after hole doping (e.g., δ = 0.1 in Ba3−δNiRu2O9), and Fig. 6(b) is computed at a fixed doping of 0.1 holes/u.c. while varying strain. Moreover, the Methods state that 'atomic positions were not relaxed' when strain was applied. The piezomagnetic tensor Λijk is defined for the undoped linear response, so what is calculated is a doping-enhanced strain-induced magnetization, not a conventional piezomagnetic coefficient. Please qualify the 'giant piezomagnetism' claim accordingly, report the undoped piezomagnetic tensor explicitly, and discuss the sensitivity of the magnitude to atomic relaxation.","section":"S-type altermagnet: Ba3NiRu2O9 and Methods"},{"comment":"The altermagnetic classification of Ba3NiRu2O9 and Ba3TbRu2O9 in Table I assumes the experimental moments are strictly along the c-axis. The paper does not discuss how robust the S-type classification is to small canting or to a spin reorientation (e.g., under strain or magnetic field). Since the piezomagnetic response is directly tied to the 6'/m'mm' magnetic point group, a quantitative statement about the allowable canting angles or a test with a canted configuration would strengthen the central claim. Without such analysis, the experimental relevance of the S-type classification for these two compounds is less certain than for the directly computed cases.","section":"Symmetry analysis and robustness of spin orientation"}],"minor_comments":[{"comment":"The DFT+U+SOC band structure in Fig. 2 plots both spin projections, but because SOC mixes spin states, the spin-resolved character is not evident in the main figure; the spin-weighted version in Fig. S2 should be included in the main text or described in the caption.","section":"Fig. 2"},{"comment":"The line 'PACS numbers:' is followed by no entries; either provide the PACS codes or remove the placeholder.","section":"Page 1"},{"comment":"The condition ε(k↑) = ε(k↓) is written without specifying the spin quantization axis; please define it (e.g., the z-axis) to avoid ambiguity.","section":"Symmetry analysis, Eq. for spin degeneracy"},{"comment":"The tensor components Λ112 = Λ211 = -2Λ and Λ222 = Λ are given without a sign convention or a definition of Λ; please specify the sign and the coordinate frame used in the DFT calculations.","section":"S-type altermagnet, piezomagnetic tensor"},{"comment":"The statement 'there are two antiferromagnetic sub-lattices (Ni and Ru)' is imprecise; the unit cell contains two Ni and four Ru ions, so clarify that each sublattice consists of symmetry-equivalent ions.","section":"Discussion"}],"recommendation":"major_revision","confidential_remarks":"The reliance on the authors' own classification scheme (ref. [30]) is not circular because the DFT calculations are independent, but the paper would benefit from acknowledging that the magnetic point group assignments inherit the assumptions of that scheme. The main concerns are the unverified Ba3SrIr2O9 entry and the overstatement of the piezomagnetic effect; both are fixable with rewording or by providing additional calculations (e.g., relaxed structures, undoped piezomagnetic tensor). The paper's length and presentation are appropriate for a letter-style journal, but the supplementary tables are not included in this arXiv version, which limits verification."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Papers like this are easy to underestimate: the headline is broad, the evidence uneven. My take: the altermagnetic classification for the two compounds with explicit DFT — Ba3CoIr2O9 and Ba3NiRu2O9 — is convincing. The symmetry argument is clean. 6H perovskites lack inversion between the magnetic B sites but have C2 axes at 1/4 and 3/4 of c, so AFM order between the two B' planes gives non-relativistic spin-split bands. The band structures show the expected splitting along L-Γ-V for the Co compound and M-A for the Ni compound, and the magneto-optical σxz follows directly from the 2/m magnetic point group. That core is solid.\n\nThe soft spots are real but not fatal. The 'giant piezomagnetism' headline is about hole-doped Ba3NiRu2O9; the undoped response under 1% strain is ~10^-3 µB, which the authors themselves call vanishingly small. The doped effect is there in the calculation, but the abstract and conclusions do not carry that caveat. Similarly, Ba3SrIr2O9 is classified from a previous DFT+U+SOC magnetic structure, not from any measured order; the table lists no TN. If that theoretical ground state is not realized, the M-type classification and the predicted ρxy/ρyz for that compound collapse. The paper does flag this in a footnote, so it is not hidden, but the plural 'several' in the abstract gives all four table entries equal weight.\n\nMinor points: the strain calculations used unrelaxed atomic positions, acceptable for a symmetry argument but weak for quantitative piezomagnetic coefficients. No code or data deposited; 'available upon reasonable request' is standard but a bit thin for a computational paper. The use of the authors' own classification scheme (ref 30) is not a problem; the DFT is independent.\n\nWho is this for? People working on altermagnet candidates, hexagonal perovskites, and magneto-optical responses. It deserves a serious referee. I would send it to review with a request to revise the abstract so it separates the two DFT-verified compounds from the symmetry-only candidates, and to state plainly that the piezomagnetic effect is doping-activated. The core physics for Ba3CoIr2O9 and Ba3NiRu2O9 is sound.","headline":"Clear symmetry case for two 6H altermagnets; 'giant piezomagnetism' and the Ba3SrIr2O9 entry need qualification.","tokens_in":10640,"tokens_out":4224,"would_cite":true,"duration_ms":41080,"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":"This paper identifies a family of layered oxides, 6H perovskites with formula A$_3$BB'$_2$O$_9$, as altermagnets: their collinear antiferromagnetic order splits spin-up and spin-down bands without spin-orbit coupling, and two of the four…","keywords":["altermagnetism","6H perovskites","non-relativistic spin splitting","magneto-optical Kerr effect","piezomagnetism","Ba3CoIr2O9","Ba3NiRu2O9","density functional theory"],"falsifier":"A decisive test is spin-resolved photoemission or tunneling spectroscopy on a cleaved surface below the Neel temperature: if Ba$_3$CoIr$_2$O$_9$ or Ba$_3$NiRu$_2$O$_9$ does not show non-relativistic spin-split bands along the predicted $k$-path (L-$\\Gamma$-V for the cobalt compound, M-A for the nickel-ruthenium compound) that disappear above the ordering temperature, the altermagnetic assignment fails. For the piezomagnetic claim, an experiment applying about 1% tensile strain along $y$ to hole-doped Ba$_3$NiRu$_2$O$_9$ should find a magnetization along $y$ with the magnitude and doping dependence shown in the paper; absence of that response would falsify the quantitative prediction.","tokens_in":9578,"feed_emoji":"🧲","tokens_out":9135,"duration_ms":97449,"temperature":0.7,"pith_summary":"Altermagnets are magnetic materials in which a collinear antiferromagnetic arrangement splits spin-up and spin-down electron bands even without spin-orbit coupling. This paper argues that 6H perovskites, a family of layered oxides with formula A$_3$BB'$_2$O$_9$, form a natural altermagnet platform: centrosymmetric in structure, yet lacking inversion between the magnetic B sites while possessing C$_2$ axes that connect the two magnetic planes. Symmetry analysis of fifteen known antiferromagnetic 6H perovskites yields four altermagnets, and density-functional calculations on representatives confirm non-relativistic spin splitting, magneto-optical activity in the M-type members, and a large piezomagnetic response in Ba$_3$NiRu$_2$O$_9$. Because these compounds can be grown as cleavable single crystals, the claim opens a practical route to imaging altermagnetic spin textures with surface-sensitive probes.","feed_headline":"Four 6H perovskite compounds are altermagnets","feed_subtitle":"Layered oxides gain non-relativistic spin-split bands, with predicted magneto-optics and giant piezomagnetism.","key_machinery":"The load-bearing object is the set of C$_2$ rotation axes perpendicular to the $c$-axis in the 6H perovskite space groups P63/mmc, Cmcm, and C2/c. These axes lie at 1/4 and 3/4 of the $c$-axis, and also at 0 and 1/2 in the hexagonal space group, and they map a magnetic B site in the plane at $z=0$ onto a B site in the plane at $z=c/2$. Because there is no inversion center connecting those sites, the combined operation of the C$_2$ rotation with time reversal changes the spin and the momentum of an electron in a way that makes the spin degeneracy at general $k$ points fail, while special mirror-plane points remain degenerate. The companion mechanism is the exchange pattern: ferromagnetic B-B' superexchange through nearly 180$^\\circ$ B-O-B' bonds involving empty $e_g$ orbitals, together with antiferromagnetic intradimer B'-B' exchange, selects the required antiferromagnetic stacking of the two ferromagnetic B' planes. This combination of local orbital physics and crystal symmetry is what turns an otherwise conventional antiferromagnet into an altermagnet.","core_discovery":"The central claim is that a centrosymmetric crystal structure combined with collinear antiferromagnetism can still produce altermagnetism. In the 6H perovskite structure there is no inversion center connecting the magnetic B sites, but there are C$_2$ rotation axes perpendicular to the $c$-axis that exchange the two $ab$ planes of B ions. When those two planes order antiferromagnetically with spins mostly along $c$, the C$_2$ operation flips spin and momentum in a way that forces spin-up and spin-down bands to split in momentum space even without spin-orbit coupling. Applying magnetic point group classification to the fifteen known antiferromagnetic 6H perovskites, the paper finds four altermagnets: Ba$_3$CoIr$_2$O$_9$ and Ba$_3$SrIr$_2$O$_9$ are M-type, with broken time-reversal symmetry, weak ferromagnetism, and magneto-optical response, while Ba$_3$NiRu$_2$O$_9$ and Ba$_3$TbRu$_2$O$_9$ are S-type, with pure spin splitting and piezomagnetism. DFT+U calculations for Ba$_3$CoIr$_2$O$_9$ show non-relativistic spin splitting along L-$\\Gamma$-V; adding spin-orbit coupling opens a 40 meV gap with a net moment of 1.4 $\\mu_B$ per formula unit and a single nonzero off-diagonal optical conductivity component. For Ba$_3$NiRu$_2$O$_9$, collinear calculations show spin splitting along M-A, and calculations with 1% tensile strain plus hole doping give a magnetization along $y$ whose piezomagnetic coefficient is an order of magnitude larger than earlier estimates.","pith_inferences":["A follow-up calculation could relax atomic positions under strain, since the paper fixed the crystal structure when computing the piezomagnetic response; relaxation might shift the size of the induced magnetization, and that shift is not yet quantified.","Because altermagnetism here depends on the B' dimers being magnetically active and isolated, varying the 3d/4d/5d occupancy in the B' site is a natural chemical lever for tuning the spin splitting and the piezomagnetic coefficient, which the paper only sketches.","The quasialtermagnet idea for 120-degree and spin-liquid systems suggests a continuum in which materials without a simple doubled magnetic cell may still show field-dependent magneto-optical and piezomagnetic effects; Ba$_3$CoSb$_2$O$_9$ and similar compounds could be tested for this weaker response.","If surface cleavage preserves the magnetic space group, spin-resolved STM on Ba$_3$NiRu$_2$O$_9$ could spatially resolve the spin-split dimer states; the paper proposes ARPES and STM experiments but does not estimate surface reconstruction effects."],"forward_implications":["Spin-resolved ARPES or STM on cleaved 6H perovskite surfaces should see spin-up and spin-down band splitting appear below the Neel temperature along the specified $k$-paths, providing a direct test of the altermagnetic state.","For Ba$_3$CoIr$_2$O$_9$, the M-type symmetry implies a measurable magneto-optical Kerr response: the paper lists eight nonzero components of the $q_{ijk}$ tensor and finds a single nonzero off-diagonal optical conductivity $\\sigma_{xz}(\\omega)$, so optical experiments can fingerprint the altermagnetic ordering.","For Ba$_3$NiRu$_2$O$_9$, stress along $x$ or $y$ with modest hole doping should generate transverse magnetization along $y$; the computed piezomagnetic coefficient is an order of magnitude larger than earlier estimates, making it a candidate for strain-controlled magnetization.","The same symmetry logic extends to other mixed perovskites with 4H, 9R, and different layer sequences, which may contain additional altermagnets.","When non-magnetic ions occupy the dimer sites, the in-plane order becomes antiferromagnetic and the compounds are not formal altermagnets; the paper calls these quasialtermagnets with a ferromagnetic point group and weaker magneto-optical or piezomagnetic effects."],"supporting_citations":[{"why":"Supplies the magnetic point group classification used to label M-type and S-type altermagnets and to predict which Hall and piezomagnetic components are allowed.","marker":"[30]"},{"why":"Provides the experimental structure, magnetic structure, and electronic properties of Ba$_3$CoIr$_2$O$_9$ used in the DFT+U+SOC calculations and the spin-orbit-assisted insulating gap.","marker":"[24]"},{"why":"Provides the experimental crystal and magnetic structure of Ba$_3$NiRu$_2$O$_9$ used for the collinear DFT+U calculations and the strain-dependent piezomagnetic study.","marker":"[26]"},{"why":"Provides the theoretical DFT+U+SOC magnetic ground state used to classify Ba$_3$SrIr$_2$O$_9$ as an M-type altermagnet.","marker":"[25]"},{"why":"A large-scale ab initio study of spin-split collinear antiferromagnets that supplies context and prior Hall-effect reference data for identifying new altermagnet candidates.","marker":"[14]"},{"why":"Establishes the crystal structure and magnetic properties of Ba$_3$TbRu$_2$O$_9$, supporting its S-type altermagnetic classification.","marker":"[28]"},{"why":"Reports magnetic and calorimetric data for Ba$_3$TbRu$_2$O$_9$ that fix its ordering temperature and ground state used in the classification table.","marker":"[29]"},{"why":"Defines altermagnetism and the expected anomalous transport and magneto-optical phenomena that the paper extends to 6H perovskites.","marker":"[13]"},{"why":"Gives the earlier estimate of piezomagnetism in antiferromagnetic materials that the paper's predicted response in Ba$_3$NiRu$_2$O$_9$ exceeds by an order of magnitude.","marker":"[35]"}],"fun_headline_variants":["Four 6H perovskites are altermagnets","Altermagnetism emerges in layered 6H perovskites","Broken PT symmetry yields altermagnetism in 6H perovskites","Nonrelativistic spin splitting in 6H perovskites","6H perovskites: new altermagnet family"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The classification assumes the magnetic point group assigned to each compound is the true one, specifically that the two B-plane sublattices are antiferromagnetically stacked with spins along or near the $c$-axis; for Ba$_3$SrIr$_2$O$_9$ this rests on a theoretical ground state rather than a fully determined experimental magnetic structure, so an error in that assignment would remove the predicted spin splitting.","fun_headline_variants_meta":{"raw":{"variants":["Four 6H perovskites are altermagnets","Altermagnetism emerges in layered 6H perovskites","Broken PT symmetry yields altermagnetism in 6H perovskites","Nonrelativistic spin splitting in 6H perovskites","6H perovskites: new altermagnet family"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000968,"raw_usage":{"total_tokens":4198,"prompt_tokens":1107,"completion_tokens":3091,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":723,"completion_tokens_details":{"reasoning_tokens":3007}},"tokens_in":723,"tokens_out":3091,"duration_ms":25767,"temperature":1.0,"reasoning_tokens":3007,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-06T10:55:13.654104+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A decisive test is spin-resolved photoemission or tunneling spectroscopy on a cleaved surface below the Neel temperature: if Ba$_3$CoIr$_2$O$_9$ or Ba$_3$NiRu$_2$O$_9$ does not show non-relativistic spin-split bands along the predicted $k$-path (L-$\\Gamma$-V for the cobalt compound, M-A for the nickel-ruthenium compound) that disappear above the ordering temperature, the altermagnetic assignment fails. For the piezomagnetic claim, an experiment applying about 1% tensile strain along $y$ to hole-doped Ba$_3$NiRu$_2$O$_9$ should find a magnetization along $y$ with the magnitude and doping dependence shown in the paper; absence of that response would falsify the quantitative prediction.","supporting_citations":[{"cited_title":"& author Huang, F.-T","cited_arxiv_id":null,"evidence_quote":"Supplies the magnetic point group classification used to label M-type and S-type altermagnets and to predict which Hall and piezomagnetic components are allowed."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the experimental structure, magnetic structure, and electronic properties of Ba$_3$CoIr$_2$O$_9$ used in the DFT+U+SOC calculations and the spin-orbit-assisted insulating gap."},{"cited_title":"& author Battle, P","cited_arxiv_id":null,"evidence_quote":"Provides the experimental crystal and magnetic structure of Ba$_3$NiRu$_2$O$_9$ used for the collinear DFT+U calculations and the strain-dependent piezomagnetic study."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the theoretical DFT+U+SOC magnetic ground state used to classify Ba$_3$SrIr$_2$O$_9$ as an M-type altermagnet."},{"cited_title":"Spin-split collinear antiferromagnets: a large-scale ab-initio study","cited_arxiv_id":"2207.07592","evidence_quote":"A large-scale ab initio study of spin-split collinear antiferromagnets that supplies context and prior Hall-effect reference data for identifying new altermagnet candidates."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Establishes the crystal structure and magnetic properties of Ba$_3$TbRu$_2$O$_9$, supporting its S-type altermagnetic classification."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Reports magnetic and calorimetric data for Ba$_3$TbRu$_2$O$_9$ that fix its ordering temperature and ground state used in the classification table."},{"cited_title":", author Sinova, J","cited_arxiv_id":null,"evidence_quote":"Defines altermagnetism and the expected anomalous transport and magneto-optical phenomena that the paper extends to 6H perovskites."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Gives the earlier estimate of piezomagnetism in antiferromagnetic materials that the paper's predicted response in Ba$_3$NiRu$_2$O$_9$ exceeds by an order of magnitude."}],"review_version":1}