{"id":"ef1e8ec4-dc3d-42ad-ba5a-5baee3a8a705","arxiv_id":"2608.04638","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":7.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"A first-principles comparison of IPA, RPA, TD-ALDA, and BSE for the frequency-dependent spin magnetoelectric tensor of Cr2O3 finds BSE reproduces excitonic resonances and TDDFT reproduces the magnonic static limit.","lead":"This paper computes, from first principles, how the spin part of a material's magnetoelectric response changes with frequency, using Cr2O3 as a test case. It shows different theoretical methods capture different physics: electron-hole interactions reproduce high-energy resonances, while time-dependent DFT captures the low-energy magnon and the static limit.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The lowest BSE ME-active pole is labeled a magnon on three indirect signatures that a spin-flip d-d exciton would also satisfy; the Goldstone-violation explanation for the missing BSE static limit therefore lacks decisive support.","rationale":"Good-faith summary: The paper is a careful, transparent computational study with convergence tests, a clear formal framework, and explicit acknowledgment of limitations. Its main numerical results (IPA/RPA/TD-ALDA/BSE spectra) are plausibly converged and reproducible. However, the central physical conclusion depends on a single unverified identification: that the low-energy BSE ME-active pole is a magnon. The reader's weakest assumption pointed to exactly this, and I agree. The three suggested indicators do not distinguish a collective magnon from a single-particle spin-flip d-d exciton; both are spin-flip, optically dark, and can produce near-degenerate multiplets. The energy mismatch with experiment (~1.9 eV vs ~0.68 meV) is enormous, and no dispersion is provided. The paper's own proposed resolution, that GW-BSE violates the Goldstone theorem and places the magnon at eV energies, is a hypothesis cited from other systems (CrI3, Refs. [45-47]) and is not tested here for Cr2O3. The concrete test I propose, a finite-q BSE dispersion calculation, would settle the matter: an acoustic magnon must disperse to zero at q=0, whereas a local exciton will not. If the test confirms the magnon identification, the paper's conditional acceptance is justified; if not, the central dichotomy must be reframed. I therefore recommend keeping the reader's CONDITIONAL verdict unchanged (UNCHANGED), with the condition that the magnon interpretation be supported by a dispersion calculation or explicitly presented as a conjecture.","tokens_in":19782,"tokens_out":7196,"duration_ms":82466,"concrete_test":"Compute the transverse spin-flip BSE spectrum of Cr2O3 at finite momentum q (e.g., along Gamma-Z and Gamma-K) using the same spinorial BSE and double-grid method (Sec. III B), and extract omega(q) for the lowest ME-active spin-flip mode. If this is the acoustic magnon, omega(q) must approach the measured ~0.68 meV (or zero) as q -> 0 in the thermodynamic limit, confirming that the 1.9 eV q=0 energy is a Goldstone-violation gap. If the mode is dispersionless or remains of order eV for all q, it is a local d-d exciton and the magnon classification, and the Goldstone-violation explanation for the missing BSE static limit, is falsified. An orthogonal, cheaper check: derive exchange parameters from the same LDA/GGA ground state via the magnetic force theorem and compute zone-center spin-wave energies; a spin-wave mode near 1.9 eV would be needed to support the assignment.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's central assertion is that the dynamical ME response separates into a magnon-driven low-frequency regime and an exciton-driven optical regime, with BSE failing in the static limit because of the 'well-known Goldstone rule violation in GW-BSE approaches to magnons' (p. 7, Sec. IV C). The linchpin of this argument is the identification of the lowest BSE ME-active pole (1.947/1.960 eV for LDA, 1.728/1.739 eV for GGA; Fig. 4, Table I) as a magnonic excitation. The evidence is circumstantial: (i) it coincides with a pole of the transverse spin susceptibility Im chi+-; (ii) it is optically dark yet ME-active; (iii) it forms a nearly degenerate quartet, 'naturally associated with the separately degenerate acoustic and optical modes at zero magnon momentum.' Every one of these features is also satisfied by a spin-flip Cr d->d crystal-field exciton: such a transition is chi+- active, is optically dark by spin selection rules and acquires ME activity through SOC, and the low-symmetry crystal field splits the Cr3+ d-electron multiplets into near-degenerate groups. The assignment is made without any magnon dispersion or spin-wave calculation, and the pole at ~1.9 eV is more than three orders of magnitude above the measured antiferromagnetic resonance at 0.682 meV [6]. If this state is instead a local spin-flip exciton, the Goldstone-violation narrative collapses, and the conclusion that 'collective spin excitations are required to recover the static limit' (abstract) loses its BSE-based support. The paper would then demonstrate only that BSE and TD-ALDA place spin-flip resonances at different energies, without establishing which, if either, is the collective magnon.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper presents first-principles calculations of the frequency-dependent spin contribution to the magnetoelectric tensor of Cr2O3, comparing independent-particle (IPA), random-phase (RPA), time-dependent density-functional (TD-ALDA), and Bethe-Salpeter (BSE) approaches. The central claim is that the dynamical spin ME response separates into a low-frequency regime governed by collective spin excitations (magnons), which is required for the static limit, and an optical regime dominated by excitonic electron-hole correlations. The authors report that IPA and RPA yield no static spin ME response, TD-ALDA converges to about 0.2 ps/m through a low-energy mode, and BSE produces excitonic resonances with a lowest ME-active pole at about 1.9 eV (LDA) or 1.7 eV (GGA), which they interpret as a magnonic mode misplaced by the Goldstone-rule violation of GW-BSE. They compare BSE rotation and ellipticity spectra with experimental reflectance data and find qualitative agreement after energy shifts and amplitude scaling.","tokens_in":20133,"tokens_out":14138,"duration_ms":178578,"significance":"If the main claim is correct, this is a useful contribution to the relatively underdeveloped field of dynamical first-principles magnetoelectric response. The systematic comparison of four levels of theory, the inclusion of spin-orbit coupling in a spinorial formulation, the convergence tests over k-meshes and bands, and the additional DFT+U and LDA/GGA checks are all genuine strengths. The paper also makes a falsifiable statement about the static limit requiring collective spin excitations, which is interesting even if the magnon identification remains under-supported. However, the significance is moderated by the fact that the central decomposition relies on the classification of the lowest BSE pole as a magnon, and that classification is not directly established by the presented evidence.","major_comments":[{"comment":"The identification of the lowest BSE ME-active pole as a magnon is not established. The three indicators listed (coincidence with the transverse spin-susceptibility pole, optical darkness, and the near-degenerate quartet) are equally consistent with a local spin-flip Cr d-to-d crystal-field exciton. In fact, Table I reports W_d->d = 0.71 for this pole and energies of 1.947/1.960 eV (LDA), which is precisely the known d-d exciton region, while the measured antiferromagnetic resonance is at 0.682 meV (Ref. [6]). No magnon dispersion, spin-wave calculation, or non-Tamm-Dancoff BSE test is provided to support the Goldstone-violation interpretation. Because this assignment is the basis for the claim that BSE misses the static limit due to the Goldstone rule violation (Sec. V), that load-bearing conclusion is currently unsupported. Please either provide direct evidence of collective spin-wave character (for example, a momentum-resolved spin-spin correlation function or a comparison with a converged TDDFT magnon dispersion) or explicitly reframe the conclusions so that the BSE low-energy pole is treated as a spin-flip d-d exciton.","section":"IV C, Table I, Fig. 4"},{"comment":"The claim that TD-ALDA recovers the finite static spin ME response through a low-energy magnonic mode is central, but the numerical support is incomplete. The text states that the low-frequency peak at 250 meV converges slowly with the number of bands and that the static limit converges to approximately 0.2 ps/m, yet no table or plot gives the static value as a function of bands (v25c25 to v40c40), k-mesh (2x2x2 to 6x6x6), and broadening (0.1 eV vs 0.01 eV), nor an uncertainty estimate. Furthermore, 250 meV is still more than two orders of magnitude above the 0.682 meV AFMR, so the statement that this is 'closer to the expected low-energy magnonic regime' requires a quantitative comparison with a converged magnon calculation for Cr2O3, such as the TDDFT results of Ref. [43]. Without this, the mechanism linking the low-energy peak to the static limit is asserted rather than demonstrated.","section":"IV B, Sec. III B, Fig. S7"},{"comment":"The comparison with the reflectance data of Ref. [5] is made after a rigid downward shift of 0.82 eV (LDA) or 0.40 eV (GGA) and after multiplying the experimental rotation and ellipticity by a factor of four. These adjustments are calibrated to the first absorption feature and to the amplitude, so the resulting agreement in peak ordering and relative signs is a consistency check rather than a quantitative prediction. To make the qualitative-validity claim meaningful, please state which features survive independent of the shift and scaling choices and report how the comparison changes when the shift is varied within, say, ±0.2 eV.","section":"IV D, Fig. 6"}],"minor_comments":[{"comment":"The terminology is inconsistent: the abstract speaks of a 'magnon-like peak' while Sec. V refers to a 'low-energy magnonic pole'; please align the wording to avoid overclaiming in one place and underclaiming in another.","section":"Abstract and Sec. V"},{"comment":"Please specify the convention for the sign of Im alpha in the figures and state the Kramers-Kronig relation used for the static limit; currently the sign of the imaginary part is not defined in the text.","section":"II C, Eq. (7)"},{"comment":"The description of the double-grid BSE method (6x6x6 coarse and 16x16x16 fine) should state explicitly which grid enters the screening and which enters the exciton Hamiltonian; this is standard but should be written out for reproducibility.","section":"III B"},{"comment":"The BSE band-convergence test compares only v12c28 and v18c28; given the paper's emphasis on low-energy convergence, a test with more valence or conduction bands would strengthen the claim that the low-frequency structure is converged.","section":"Fig. S7"},{"comment":"The atomic magnetic moments are reported with six decimals; this is overprecise and should be rounded to a physically meaningful precision.","section":"III A, Table S1"}],"recommendation":"major_revision","confidential_remarks":"The paper is technically solid in its implementation and convergence tests, and the idea that the dynamical spin ME tensor requires a low-energy collective mode to recover the static limit is worth publishing if the magnon identification is either properly supported or explicitly downgraded. The weakest point is the classification of the lowest BSE pole as a magnon; if the authors cannot provide a direct spin-wave or non-TDA test, they should reframe the conclusions and remove the Goldstone-violation explanation. I would not recommend rejection because the methodology and the TD-ALDA static-limit result have independent value."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Read this paper. It is the first systematic comparison of IPA, RPA, TD-ALDA, and BSE for the frequency-dependent spin magnetoelectric tensor of Cr2O3. The work is careful, the convergence tests are real, and the authors are unusually transparent about the limitations, including the BSE static-limit failure, the scissor shift, and the ad hoc experimental shifts. The SOC phase-locking decomposition in Figure 5 is a genuinely nice piece of analysis. If you work on magnetoelectric response or on excitonic/magnonic spectra from many-body perturbation theory, this is a reference to know.\n\nThe soft spot is exactly where the stress-test note lands. The lowest BSE ME-active pole (~1.9 eV LDA, ~1.7 eV GGA) is called magnon-like on three indirect signatures: coincidence with the transverse spin susceptibility, optical darkness, and a near-degenerate quartet. A spin-flip Cr d-to-d crystal-field exciton would also satisfy all three. The paper contains no magnon dispersion or spin-wave calculation, and the pole sits about three orders of magnitude above the measured 0.682 meV antiferromagnetic resonance. The authors do say the absolute energy is misplaced by the Goldstone rule violation, and they are careful with the word \"magnon-like,\" but the central conclusion that collective spin excitations are required for the static limit leans heavily on this assignment. If that pole is actually a local spin-flip exciton, the BSE static-limit failure is just a different failure, and the magnon claim rests mostly on the TD-ALDA result, which itself shows a low-energy peak at 250 meV that creeps down with bands but never reaches the meV scale.\n\nThat said, the paper does not overclaim. The experimental comparison is honestly qualitative, with the shifts and the factor of four made explicit, and the sensitivity to the starting point is flagged. The linear response machinery is standard and has no circularity. The TD-ALDA static limit of about 0.2 ps/m, consistent with the prior ~0.3 ps/m value, gives independent support for a low-energy spin contribution.\n\nThe paper deserves a serious referee. The right referee will push for a sharper magnon diagnostic: a finite-q spin-wave calculation, a spin-wave-model comparison, or at least an explicit argument for why a local d-d exciton is ruled out. I would send it to review with expectation of major revision or conditional acceptance. It is a useful contribution even if the magnon identification turns out to be wrong, and I would cite it if I were working in this area.","headline":"A careful, honest first-principles study of the dynamical spin ME tensor; the magnon identification is the main thing to push on in review.","tokens_in":20703,"tokens_out":2898,"would_cite":true,"duration_ms":36240,"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":"This paper claims that the dynamical magnetoelectric response of Cr2O3 separates into a magnon-governed static regime and an exciton-governed optical regime, each captured by a different level of theory.","keywords":["magnetoelectric response","chromia Cr2O3","magnon","exciton","Bethe-Salpeter equation","time-dependent density functional theory","spin-orbit coupling","frequency-dependent response"],"falsifier":"A direct check would be to compute the zone-center acoustic and optical magnon energies of Cr2O3 from a spin-wave Hamiltonian fitted to the DFT exchange parameters, or from a converged TDDFT magnon calculation, and compare them with the pole of the transverse spin susceptibility that underlies the claimed magnonic ME peak in both TD-ALDA and BSE; if that pole does not coincide with a spin-wave magnon (or with the experimentally reported 0.68 meV spin resonance) while remaining dark in optical absorption, the magnon identification and the explanation of the static-limit failure would collapse.","tokens_in":19582,"feed_emoji":"🧲","tokens_out":16394,"duration_ms":159676,"temperature":0.7,"pith_summary":"The paper sets out to establish what microscopic excitations control the frequency-dependent spin contribution to the magnetoelectric (ME) tensor of the prototype magnetoelectric Cr2O3. It implements four levels of theory — the independent-particle approximation (IPA), the random-phase approximation (RPA), time-dependent density functional theory in the adiabatic local-density form (TD-ALDA), and the Bethe–Salpeter equation (BSE) — and finds that they capture complementary physics. The core claim is that the static and low-frequency ME response is carried by collective spin excitations (magnons), while the optical response near 1.7–2.0 eV is dominated by electron–hole (excitonic) correlations. BSE reproduces the excitonic resonances seen in reflectance spectroscopy but places the magnonic pole at about 1.7–1.9 eV because of the known Goldstone-rule violation for magnons in this framework, whereas TD-ALDA puts the spin-dominated mode at 250 meV and recovers a static limit near 0.2 ps/m. The result matters because a correct frequency-dependent ME tensor is the prerequisite for quantitative use of electric-field control of magnetism and of magnetoelectric spectroscopy.","feed_headline":"Magnons set the static magnetoelectric response; excitons the optical","feed_subtitle":"Bethe–Salpeter and TDDFT each capture one half of Cr2O3's magnetoelectric response.","key_machinery":"The central object is the frequency-dependent spin magnetoelectric tensor, computed in the length gauge with the magnetic dipole operator $\\mathbf{m} = -\\mu_B \\boldsymbol{\\sigma}$, so that a Zeeman-like coupling $\\mathbf{E}(\\omega)\\cdot(-e\\mathbf{r})$ produces a spin magnetization response. In its spectral representation, each excitation contributes a pole at energy $\\omega_\\lambda$ with residue $R^\\lambda_{\\mu\\nu}$, which is the product of the magnetic and electric dipole matrix elements $\\langle 0|m_\\nu|\\lambda\\rangle$ and $\\langle 0|(-er_\\mu)|\\lambda\\rangle$ of the excited state $\\lambda$. The paper's machinery is the systematic comparison of these poles across IPA, RPA, TD-ALDA and BSE, supplemented by the transverse spin susceptibility $\\chi_{\\pm}(\\omega)$ to distinguish spin-dominated (optically dark) from charge-dominated excitations, and by a decomposition of the BSE residues into amplitude and phase to show that spin–orbit coupling locks the relative phase of the two matrix elements and thereby sets the sign of each ME contribution. The static limit is then controlled by the Kramers–Kronig-weighted spectral sum $\\alpha^{\\mathrm{spin}}_{\\perp}(0)\\propto\\int d\\omega\\,\\mathrm{Im}\\,\\alpha^{\\mathrm{spin}}_{\\perp}(\\omega)/\\omega$, which is why an eV-scale magnonic pole cannot build up a finite static response.","core_discovery":"Within the spin-only, clamped-ion approximation, the dynamical magnetoelectric tensor $\\alpha^{\\mathrm{spin}}_{\\mu\\nu}(\\omega)=\\delta M_\\nu(\\omega)/\\delta E_\\mu(\\omega)$ of antiferromagnetic Cr2O3 is shaped by three kinds of excitation. Independent interband transitions (IPA and RPA) produce no static or low-frequency response, so they cannot reproduce the established finite static spin ME response of roughly 0.3 ps/m. The BSE introduces bound exciton states, of dominant Cr-(d)-to-Cr-(d) character, whose spectrum reproduces the qualitative sign and shape of the experimental rotation and ellipticity on reflection; its lowest ME-active pole, at 1.9 eV (LDA starting point) or 1.7 eV (GGA), lies at a pole of the transverse spin susceptibility, is dark in optical absorption, and splits into two nearly degenerate pairs separated by about 10 meV, a quartet the paper identifies as the acoustic and optical magnons of the four-sublattice antiferromagnet, misplaced to eV energies by the Goldstone-rule violation of GW–BSE. TD-ALDA places the same spin-dominated mode at 250 meV and, once enough bands are included, yields a finite static limit of about 0.2 ps/m, consistent with earlier first-principles values. The paper's conclusion is that the dynamical ME response separates into regimes: low-energy collective spin excitations set the static limit, and electron–hole interactions set the optical excitonic response, and no single one of the four approximations captures both.","pith_inferences":["A natural test the paper leaves implicit: if the BSE magnon pole were corrected downward to meV energies (for example by restoring the Goldstone mode through a spin-wave-informed correction of the kernel), the Kramers–Kronig integral should bring the BSE static limit up toward the TD-ALDA value of about 0.2 ps/m; the paper does not perform this correction.","The 250 meV TD-ALDA peak is still roughly two orders of magnitude above the measured 0.68 meV spin resonance, so the claim that TD-ALDA places the mode closer to the expected regime leaves substantial room; an exchange-correlation kernel with nonlocal or frequency dependence might be needed to close the gap.","The regime separation suggests a practical division of labour for future calculations on other magnetoelectrics: TDDFT-type kernels for the low-frequency and static tensor, BSE for the optical spectrum, with the two joined at intermediate frequencies where both magnon and exciton poles contribute.","Because the paper treats only the spin channel with clamped ions, its quantitative values apply to the electronic spin part; including orbital and lattice contributions would modify absolute magnitudes but, if the separation is robust, not the qualitative picture that different excitation classes dominate different frequency windows."],"forward_implications":["First-principles calculations of the finite-frequency spin ME response of magnetic insulators cannot stop at IPA or RPA: both miss the low-energy spectral weight that the static limit requires.","BSE-based predictions of the dynamical ME tensor will systematically underestimate the static limit whenever the magnon pole sits at eV rather than meV energies, because the static value is an integral weighted by $1/\\omega$ over the absorption spectrum.","The BSE approach does capture the excitonic ME resonances: the calculated non-reciprocal rotation and ellipticity reproduce the signs and peak ordering of the measured spectra across the 1.6–2.4 eV region, after a rigid shift of the energy axis.","A magnetoelectrically active magnon mode, excitable by both electric and magnetic terahertz fields, is the physical counterpart of the low-energy pole that carries the static ME response; the paper connects this to a recent pump–probe experiment at 0.165 THz.","TD-ALDA, despite lacking bound excitons, is a practical route to the static spin ME response in this material once the band and k-point content of the kernel is converged."],"supporting_citations":[{"why":"Supplies the established first-principles static spin ME value (about 0.3 ps/m) that the TD-ALDA result is benchmarked against.","marker":"[8]"},{"why":"Provides the other reference static spin contribution to the ME response of Cr2O3, used to frame the electronic spin part.","marker":"[17]"},{"why":"The localized-electron perturbative theory attributing the optical ME response to Cr3+ d–d transitions, which the BSE analysis corroborates.","marker":"[19]"},{"why":"The reflectance spectroscopy data (rotation and ellipticity) that the BSE spectra are compared with after shifting the energy axis.","marker":"[5]"},{"why":"The terahertz experiment showing a magnetoelectrically active magnon at 0.165 THz, used as experimental evidence for the low-energy ME pole.","marker":"[6]"},{"why":"Establishes the spinorial GW–BSE formulation, including spin–orbit coupling, on which the BSE and TD-ALDA ME calculations are built.","marker":"[23]"},{"why":"Provides the transverse spin susceptibility framework used to classify the lowest ME pole as spin-dominated, and earlier TDDFT magnon work on Cr2O3.","marker":"[43]"},{"why":"Documents the Goldstone-rule violation for BSE magnons that is invoked to explain the eV-scale placement of the magnonic pole.","marker":"[45]"},{"why":"Shows a unified treatment of magnons and excitons in many-body perturbation theory that underlies the magnon/exciton separation.","marker":"[46]"},{"why":"Analyzes the acoustic-magnon Goldstone violation in the long-wavelength limit, the known limitation that the paper relies on.","marker":"[47]"}],"fun_headline_variants":["Magnons set static ME; excitons set optical","Cr2O3 ME: magnons for static, excitons for optical","Spin excitations fix static ME; electron-hole fix optical","IPA/RPA miss static ME; BSE/TDDFT each get half"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the lowest optically dark BSE pole, which matches the transverse spin susceptibility and forms a near-degenerate quartet, really is the magnon misplaced to eV energies, a conclusion drawn from indirect indicators with no spin-wave or magnon-dispersion calculation to confirm it.","fun_headline_variants_meta":{"raw":{"variants":["Magnons set static ME; excitons set optical","Cr2O3 ME: magnons for static, excitons for optical","Spin excitations fix static ME; electron-hole fix optical","IPA/RPA miss static ME; BSE/TDDFT each get half"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001075,"raw_usage":{"total_tokens":4600,"prompt_tokens":1144,"completion_tokens":3456,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":760,"completion_tokens_details":{"reasoning_tokens":3393}},"tokens_in":760,"tokens_out":3456,"duration_ms":28504,"temperature":1.0,"reasoning_tokens":3393,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-06T20:05:14.582608+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A direct check would be to compute the zone-center acoustic and optical magnon energies of Cr2O3 from a spin-wave Hamiltonian fitted to the DFT exchange parameters, or from a converged TDDFT magnon calculation, and compare them with the pole of the transverse spin susceptibility that underlies the claimed magnonic ME peak in both TD-ALDA and BSE; if that pole does not coincide with a spin-wave magnon (or with the experimentally reported 0.68 meV spin resonance) while remaining dark in optical absorption, the magnon identification and the explanation of the static-limit failure would collapse.","supporting_citations":[{"cited_title":"Malashevich, S","cited_arxiv_id":null,"evidence_quote":"Supplies the established first-principles static spin ME value (about 0.3 ps/m) that the TD-ALDA result is benchmarked against."},{"cited_title":"Bousquet, N","cited_arxiv_id":null,"evidence_quote":"Provides the other reference static spin contribution to the ME response of Cr2O3, used to frame the electronic spin part."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"The localized-electron perturbative theory attributing the optical ME response to Cr3+ d–d transitions, which the BSE analysis corroborates."},{"cited_title":"Krichevtsov, V","cited_arxiv_id":null,"evidence_quote":"The reflectance spectroscopy data (rotation and ellipticity) that the BSE spectra are compared with after shifting the energy axis."},{"cited_title":"Marsili, A","cited_arxiv_id":null,"evidence_quote":"Establishes the spinorial GW–BSE formulation, including spin–orbit coupling, on which the BSE and TD-ALDA ME calculations are built."},{"cited_title":"Skovhus and T","cited_arxiv_id":null,"evidence_quote":"Provides the transverse spin susceptibility framework used to classify the lowest ME pole as spin-dominated, and earlier TDDFT magnon work on Cr2O3."},{"cited_title":"Esquembre-Kuˇ cukali´ c, K","cited_arxiv_id":null,"evidence_quote":"Documents the Goldstone-rule violation for BSE magnons that is invoked to explain the eV-scale placement of the magnonic pole."},{"cited_title":"Olsen, Unified treatment of magnons and excitons in monolayer CrI3 from many-body perturbation theory, Physical Review Letters127, 166402 (2021)","cited_arxiv_id":null,"evidence_quote":"Shows a unified treatment of magnons and excitons in many-body perturbation theory that underlies the magnon/exciton separation."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Analyzes the acoustic-magnon Goldstone violation in the long-wavelength limit, the known limitation that the paper relies on."}],"review_version":1}