{"id":"5cf2cc39-3467-42be-bb38-27452e232ac8","arxiv_id":"2506.18978","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"In a model of multipolar magnets, ferro-octupolar order splits the Eg phonon doublet into pseudo-chiral modes with a gap near 1 meV, which Raman spectroscopy can resolve, while quadrupolar order leaves no resolvable splitting.","lead":"This paper predicts that a hidden magnetic order called ferro-octupolar order splits the two degenerate vibration modes of certain crystals into 'pseudo-chiral' modes with a detectable energy gap. The result gives Raman spectroscopy a new way to see octupolar order that is invisible to ordinary magnetic probes.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The predicted ~1 meV pseudo-chiral phonon splitting scales as λ² with λ≈5 meV inferred from self-cited DFT; if λ is overestimated by even a factor ~1.7, the splitting falls below the assumed phonon linewidth and the proposed Raman diagnostic loses its quantitative basis.","rationale":"The reader's weakest assumption identifies exactly the parameter that controls the headline quantitative claim: λ ≈ 5 meV, inferred from the authors' own prior DFT work, enters the FO splitting as λ². The linewidth assumed in the paper is about 0.9 meV, so the predicted 1 meV splitting is already marginal; any reduction in λ by a factor of 1.5–2 makes the splitting unresolvable. This is a genuine, load-bearing soft spot, and it is externally testable. I found no independent internal contradiction in the model: the static-background approximation is well justified by Ω0 >> J0, and the off-diagonal γr term in Eq. 17 does produce an antisymmetric imaginary contribution after analytic continuation, consistent with pseudo-chiral eigenmodes. The SM contains minor typographical slips (e.g., the printed Szx2 expression repeats Sxz2), but these do not appear to change the main-text result. Since the paper's own text flags the FO/AFQ ground-state uncertainty and the λ inference is clearly conditional, the appropriate status is CONDITIONAL, matching the reader's verdict. Therefore the verdict should remain unchanged.","tokens_in":19831,"tokens_out":37172,"duration_ms":361122,"concrete_test":"Perform an independent first-principles calculation of the quadrupole-phonon coupling λ for Ba2CaOsO6: compute the splitting of the Γ3 non-Kramers doublet under each Eg strain mode using DFT+U or DFT+DMFT, extract λ from the strain derivative, then recompute ΔΩ ≈ 4λ²/Ω0 and compare with the assumed damping 2πη/Ω0 ≈ 0.07. If the independently obtained λ is below about 3 meV, the predicted FO phonon splitting is below the linewidth and the central detectability claim needs to be revised; if λ ≈ 5 meV is confirmed, the concern is resolved.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim that ferro-octupolar (FO) order yields a detectable splitting of the Eg phonon doublet rests on the magnitude ΔΩ ≈ 4λ²/Ω0, which follows from the γr off-diagonal term in Eq. 17. The paper fixes λ ≈ 5 meV by citing the authors' earlier DFT work (Refs. [44,79]) on the strain splitting of the non-Kramers doublet; λ is not recomputed or independently benchmarked here. Because ΔΩ ∝ λ², the observability is strongly sensitive to this single parameter. With the assumed damping 2πη/Ω0 ≈ 0.07 and Ω0 ≈ 80 meV, the phonon linewidth is about 0.9 meV. If the true λ were 3 meV, ΔΩ would drop to roughly 0.36 meV—below the linewidth and experimentally unresolved. If λ were 2 meV, ΔΩ would be about 0.16 meV, completely masked. The paper's headline 'detectable energy splitting' and its proposed use of Raman spectroscopy to diagnose FO order are therefore calibrated to a self-cited coupling constant at the upper end of plausible values. The competing AFQ splitting is also proportional to λ², so the qualitative FO-versus-AFQ contrast is less sensitive, but the central detectability claim is not. The paper itself acknowledges that the FO versus AFQ ground state of the candidate materials is not experimentally established, but that is a condition for applying the probe rather than an internal flaw. The single most load-bearing uncertainty is the value of λ.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript studies the effect of multipolar order on the Raman-active E_g phonon doublet of non-Kramers Γ₃ doublet systems, motivated by the osmate double perovskites Ba₂CaOsO₆ and Ba₂MgOsO₆ and by PrV₂Al₂₀. The authors introduce a symmetry-allowed linear coupling λ between the local quadrupolar pseudospin components (τ_x, τ_z) and the E_g phonon coordinates (Q_x, Q_z), treat the pseudospins as a static background for the fast Einstein phonons, integrate out transverse spin fluctuations in a second-order cumulant expansion, and average the local phonon spectral function over Monte Carlo Weiss-field configurations. The central claim is that both ferro-octupolar (FO) and antiferro-quadrupolar (AFQ) order lift the phonon degeneracy, but only the FO phase produces pseudo-chiral eigenmodes Q_± = Q_x ± iQ_z with a sizable splitting ΔΩ ≈ 4λ²/Ω₀ ≈ 1 meV, while the AFQ splitting (≈0.2 meV) is masked by realistic phonon damping. The paper proposes the splitting, its anomalous temperature dependence, and pump-probe beat dynamics as diagnostics of hidden octupolar order. The derivation in Eqs. (9)–(18) is internally consistent, and the FO/AFQ contrast follows from the structure of the phonon self-energy rather than from any fitting to the target observable.","tokens_in":20178,"tokens_out":23023,"duration_ms":222460,"significance":"If the quantitative prediction holds, this is a genuinely new and experimentally actionable probe of hidden T-odd multipolar order: it requires no applied field, no net magnetization, and no circular atomic motion, and it introduces pseudo-chiral (rotationless but pseudo-angular-momentum-carrying) phonon eigenmodes as a diagnostic concept. Credit is due for several concrete strengths: the phonon self-energy is derived in closed form rather than parametrized (Eqs. 16–18), the FO versus AFQ contrast is a structural consequence of the antisymmetric γ_r term, Fig. 4 makes the falsifiable statement that the splitting tracks the octupolar order parameter only qualitatively, and the pump-probe extension gives an independent experimental handle. The main fragility, identified below, is that the headline 'detectable' splitting inherits its entire magnitude from the magnetoelastic coupling λ, which is taken from same-group DFT work without an uncertainty estimate; the qualitative diagnostic contrast is more robust than the quantitative detectability claim.","major_comments":[{"comment":"The central quantitative claim — that FO order produces a detectable pseudo-chiral splitting ΔΩ ≈ 4λ²/Ω₀ ≈ 1 meV — is controlled by a single input, λ ≈ 5 meV, which is inferred from the 'DFT splitting of the non-Kramers doublet under a strain field' in Refs. [44, 79]. Both references involve the present group, and no uncertainty, spread, or independent benchmark for λ is given. Because the splitting scales as λ², and because the realistic damping adopted in Figs. 2(b,d) and 3(b) (2πη/Ω₀ ≈ 0.07, i.e., η ≈ 0.9 meV at Ω₀ = 80 meV) is already comparable to the quoted splitting, a reduction of λ from 5 to 3 meV would lower ΔΩ to about 0.4 meV, putting the two peaks below the linewidth and invalidating the Raman-detectability proposal while leaving the qualitative FO-versus-AFQ contrast intact. I request: (i) a statement of the estimated accuracy of λ from the strain-DFT calculation, ideally with an independent corroboration; (ii) a plot of the FO peak separation versus λ with the damping-limited resolution threshold marked; and (iii) a reformulated detectability claim that explicitly states the λ range over which it holds.","section":"Main text, after Eq. (3) and in the discussion of Fig. 2(a,b)"},{"comment":"The spin sector is treated in a Holstein-Primakoff expansion truncated at quadratic order, and the effective phonon action keeps only the second-order cumulant built from noninteracting spin-wave Green functions (SM Eqs. (11)–(22)). For a pseudospin-1/2 Γ₃ doublet, the dropped 1/S and anharmonic terms are a priori of order one, and the Weiss fields h_r entering Eqs. (16)–(18) are extracted from classical Monte Carlo configurations of the same S = 1/2 Hamiltonian, so the quantitative value of ΔΩ and the quoted phase boundaries (T_FO ≈ 3.2 J₀) carry an unquantified semiclassical error. The effect itself is plausibly robust, because the FO splitting originates in the antisymmetric, commutator-type part of the transverse spin correlation, which survives at zero temperature and does not depend on spin-wave occupation; nevertheless, the manuscript should estimate the leading 1/S or anharmonic correction to the prefactor of ΔΩ, or otherwise justify confidence in the numerical factor in Eqs. (16)–(18) at the level implied by the ≈1 meV claim.","section":"Main text Eqs. (5)–(7) and SM §II"}],"minor_comments":[{"comment":"Please fix typographical errors: 'T j T_FO' should be 'T ≪ T_FO' (two occurrences), '∼ 105' should be '∼10⁵', 'Matusbara' should be 'Matsubara', 'pesudogap' should be 'pseudogap', and '1MeV' should be '1 meV'.","section":"Throughout, including SM §II and §III"},{"comment":"The definitions of the four three-fold axes contain a duplication: n̂₂ and n̂₃ are both given as (x̂+ŷ−ẑ)/√3. The third axis should presumably be (x̂−ŷ+ẑ)/√3, and the C₃ eigenvalue assignments for n̂₂–n̂₄ in Eq. (6) should be rechecked once the axis is corrected.","section":"SM §I, around Eq. (4)"},{"comment":"Please clarify the relation between the quoted ΔΩ ≈ 4λ²/Ω₀ ≈ 1 meV and the actual peak separation obtained from Eqs. (16)–(18). Solving the 2×2 pole condition for a uniform FO configuration with Ω₀ = 80 meV, λ = 5 meV, and h_r ≈ 12 meV gives an off-diagonal self-energy magnitude ≈1.4 meV at the phonon frequency and a peak-to-peak separation closer to 2.7 meV, roughly twice the quoted value; either ΔΩ denotes the half-splitting, or the exact expression used for Fig. 4 should be stated explicitly.","section":"Main text, discussion of Fig. 2"},{"comment":"The damping convention is under-specified: the text states that damping is implemented by Ω₀ → Ω₀ + iη with 2πη/Ω₀ ≈ 0.07, but the resulting peak FWHM is never given. With that convention the FWHM is approximately 1.8 meV at Ω₀ = 80 meV, which makes the quoted 1 meV splitting only marginally resolvable; stating the FWHM in meV alongside the peak separation would materially help the reader assess the detectability claim.","section":"Main text, 'Phonon spectral function' paragraph"},{"comment":"The criterion defining the pseudogap regime ('spectral weight 10% more than at ω = 0' in the main text; 'differ in spectral weight by more than 10% from the spectral weight at Ω₀' in the SM) is stated differently in the two places, and the precise way in which the weight difference is computed is not defined; please make the definition unambiguous and consistent.","section":"SM §III and Fig. S2"}],"recommendation":"major_revision","confidential_remarks":"The manuscript is well suited to a letters-type venue in strongly correlated electron physics, and I believe the qualitative physics is sound. My main concern, beyond the two major comments, is the citation pattern for the crucial parameter λ: Refs. [44] and [79] are both from the same group, with three of the four authors of the present paper appearing on Ref. [44]. That is not improper, but because the entire detectability claim scales as λ², an independent determination or an explicit error estimate would materially harden the paper. I would also gently note that the paper's own statement that the FO versus AFQ ground state is not yet experimentally established should be carried into the abstract and conclusion as a boundary condition on the proposed diagnostic, rather than presented as a side remark."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Bottom line: this is a worthwhile theory paper that makes a genuinely new prediction — that ferro-octupolar (FO) order should split the Eg phonon doublet in non-Kramers doublet systems into pseudo-chiral modes with a measurable splitting, while antiferro-quadrupolar (AFQ) order should not. The contrast is derived cleanly from symmetry and the structure of the phonon self-energy, and it is not something you’ll find in the earlier chiral-phonon literature. If the splitting is real, it gives Raman spectroscopy a way to attack a long-standing hidden-order problem in Ba2CaOsO6 and PrV2Al20.\n\nWhat they do well: the cumulant expansion to second order in spin-phonon coupling is worked out carefully, and the static-background averaging over Monte Carlo spin configurations is a sensible way to get temperature dependence. They also correctly point out that these modes are 'pseudo-chiral' — they carry quantized pseudo-angular momentum but no circular motion, which distinguishes them from the dipolar chiral phonon work. The FO versus AFQ contrast is a genuinely useful fingerprint: in the FO state the splitting scales as 4λ²/Ω0, while in the AFQ state it is further suppressed by an extra factor of hr/Ω0, so the qualitative distinction should survive even if the overall scale is off.\n\nSoft spots: the quantitative detectability is hostage to λ. The paper takes λ ≈ 5 meV from the authors' own earlier DFT-based strain calculations; the splitting scales as λ², and with the assumed linewidth 2πη/Ω0 ≈ 0.07, a λ of 3 meV drops the splitting to roughly 0.45 meV, which is hidden under the ~0.9 meV linewidth. That is not a fatal flaw — the FO/AFQ contrast remains — but the headline 'detectable splitting' is conditional on λ being at the upper end of plausible values. A referee should ask for either an independent estimate of λ or an explicit sensitivity analysis. The spin-wave treatment at S=1/2 is also uncontrolled, though it is a standard approximation and probably not the dominant uncertainty. And, as the authors acknowledge, the candidate materials have not yet been shown to actually realize FO order; that is a scope condition rather than an internal error.\n\nWho it's for: anyone working on multipolar order, chiral phonons, or Raman probes of hidden order. The proposed probe is concrete and falsifiable — a Raman experiment on Ba2CaOsO6 could confirm or kill the idea. It deserves a serious referee. My recommendation: send it to review. The quantitative worry is real but addressable; the core mechanism is solid and the prediction is new.","headline":"A new, plausibly correct proposal for a Raman probe of hidden octupolar order; the FO/AFQ contrast is solid, but the headline 1 meV splitting rests on a self-cited coupling constant and may be optimistic.","tokens_in":20775,"tokens_out":3156,"would_cite":true,"duration_ms":30617,"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":"Hidden octupolar order splits phonon doublets by about 1 meV.","keywords":["pseudo-chiral phonons","octupolar order","multipolar magnets","phonon splitting","Raman spectroscopy","non-Kramers doublet","Ba2CaOsO6","PrV2Al20"],"falsifier":"Measure helicity- and polarization-resolved Raman spectra of the $E_g$ phonon doublet across the ordering transition in a Ba$_2$CaOsO$_6$ single crystal whose octupolar order is independently confirmed by resonant X-ray or NMR. If no two-peak structure with splitting near 1 meV and opposite pseudo-angular-momentum selection rules appears below $T_{\\mathrm{FO}}$, the prediction is falsified. Alternatively, a first-principles calculation of $\\lambda$ from strain-induced splitting that yields a value well below 5 meV would falsify the quantitative claim.","tokens_in":19588,"feed_emoji":"⚛️","tokens_out":7559,"duration_ms":68454,"temperature":0.7,"pith_summary":"This paper claims that hidden ferro-octupolar order in certain magnets can be detected through the lattice vibrations it leaves behind. The authors study non-Kramers $\\Gamma_3$ doublets whose quadrupolar moments couple linearly to the doubly degenerate $E_g$ phonon doublet, and show that ferro-octupolar order splits that doublet into two pseudo-chiral modes separated by about 1 meV, while competing antiferro-quadrupolar order produces only a small redshift that realistic damping hides. The calculation treats fast phonons as living in a static, slowly varying background of pseudospins, and Monte Carlo averages the resulting spectral functions over spin configurations. If correct, Raman spectroscopy of phonons becomes an optical probe of octupolar order in materials such as Ba$_2$CaOsO$_6$ and PrV$_2$Al$_{20}$, whose octupolar order is otherwise difficult to see.","feed_headline":"Hidden octupolar order splits phonon doublets by about 1 meV","feed_subtitle":"Raman phonon spectra could reveal ferro-octupolar order hidden from other probes.","key_machinery":"The mathematical engine is a second-order cumulant expansion of the spin-phonon action, which yields a $2\\times2$ local inverse phonon Green function $G^{-1}(r,i\\nu_n)$ for the $(Q_x,Q_z)$ doublet at each site. The off-diagonal $G^{-1}_{zx}$ term containing $\\gamma_r = 2i\\sin\\theta_r\\sin\\phi_r$ is what breaks time reversal and generates the large pseudo-chiral splitting in ferro-octupolar order; because it depends on the direction of the local Weiss field rather than its magnitude, the mode splitting tracks but is not proportional to the octupolar order parameter. The static background of 'slow' pseudospins is described by Holstein-Primakoff bosons rotated into a local frame, and the final spectral functions $A(\\omega)$ and pump-probe $A_{\\mathrm{pp}}(\\omega)$ are obtained by averaging the site-resolved Green functions over Monte Carlo spin configurations.","core_discovery":"The central claim is that the pseudospin-phonon coupling, though linear only in the time-reversal-even quadrupole components, carries a time-reversal-odd imprint once the pseudospins order: in the ferro-octupolar phase the effective inverse phonon Green function develops an off-diagonal term proportional to $\\gamma_r = 2i\\sin\\theta_r\\sin\\phi_r$, which mixes $Q_x$ and $Q_z$ and produces eigenmodes $Q_\\pm = Q_x \\pm i Q_z$ with frequencies split by $\\Delta\\Omega \\approx 4\\lambda^2/\\Omega_0 \\approx 1$ meV. The paper shows these modes are pseudo-chiral rather than truly chiral: the oxygen displacements remain linear and carry no circular motion or ordinary angular momentum, but the modes acquire opposite quantized pseudo-angular momentum under threefold rotations about the cubic [111] axes. It further finds that the competing antiferro-quadrupolar ordering splits the doublet by an order of magnitude less, with one mode redshifted by $\\approx 0.2$ meV, so the splitting is washed out by realistic phonon damping $2\\pi\\eta/\\Omega_0 \\sim 0.07$. The result is proposed as a means to distinguish ferro-octupolar from quadrupolar order and to detect hidden octupolar order in candidate materials.","pith_inferences":["If the 1 meV splitting is confirmed, the same symmetry argument should transfer to any material with a $\\Gamma_3$ non-Kramers doublet and Raman-active $E_g$ phonons, making phonon spectroscopy a generic screen for hidden octupolar order beyond the two named families.","The undamped spectral functions show a 'pseudogap' of split peaks persisting above $T_{\\mathrm{FO}}$ to about $1.2T_{\\mathrm{FO}}$, suggesting that short-range octupolar correlations or domain walls may leave phonon signatures even without long-range order; this regime deserves a targeted search with low-damping samples or pump-probe setups.","Because the splitting mechanism requires only time-reversal symmetry breaking in a pseudospin background and not circular ionic motion, it may apply to other rotationless phonons in time-reversal-broken phases, such as altermagnets or the pseudogap regime of cuprates, as the paper itself hints; that extension is speculative until a concrete model is built."],"forward_implications":["A Raman experiment below $T_{\\mathrm{FO}}$ in Ba$_2$CaOsO$_6$ should show two resolvable $E_g$ peaks split by roughly 1 meV even with realistic damping, whereas the competing AFQ phase would show a single broadened peak; phonon spectra can therefore discriminate the two orders.","The split modes $Q_\\pm = Q_x \\pm iQ_z$ carry opposite pseudo-angular momentum along the cubic body diagonals, which imposes distinguishable selection rules in helicity- or polarization-resolved Raman scattering.","The temperature dependence of the splitting tracks the octupolar order parameter qualitatively but is not proportional to it, because the splitting comes from local Weiss-field directions; this offers an explanation for similar order-parameter-versus-splitting discrepancies seen in dipolar magnets.","An optical pump exciting one $E_g$ component in the ferro-octupolar phase should transfer energy into the other component on the timescale $2\\pi/\\Delta\\Omega$, a beat signature that disappears above $T_{\\mathrm{FO}}$.","In the antiferro-quadrupolar phase the prediction is a redshifted second mode of order 0.2 meV, which realistic damping masks; observation of such a weak shift would not be evidence for octupolar order."],"supporting_citations":[{"why":"Supplies the spin-phonon Hamiltonian and previous phonon-driven multipolar dynamics, and together with [79] the DFT estimate $\\lambda \\approx 5$ meV from strain splitting of the doublet.","marker":"[44]"},{"why":"Establishes the pseudospin model and the competing FO/AFQ tendencies for osmium double perovskites, giving the Hamiltonian in Eq. (1).","marker":"[75]"},{"why":"Provides the first-principles case for ferro-octupolar order in $d^2$ double perovskites and the exchange parameters $J_0$, $J_1$, $\\gamma$ used in the Monte Carlo.","marker":"[78]"},{"why":"Supplies the strain-field DFT estimate of the quadrupole-phonon coupling strength $\\lambda \\approx 5$ meV and discusses hidden octupolar order probes.","marker":"[79]"},{"why":"Underlies the nearest-neighbor pseudospin interactions and octupolar order physics on the fcc lattice.","marker":"[80]"},{"why":"Is the dipolar-magnet chiral-phonon experiment whose $\\sim 1$ meV splitting and Raman detection this work compares against.","marker":"[28]"},{"why":"Provides the ferrimagnetic chiral-phonon data whose splitting-versus-order-parameter discrepancy the paper explains through local Weiss-field directions.","marker":"[31]"},{"why":"Documents the field-induced quadrupolar quantum criticality in PrV$_2$Al$_{20}$, one of the candidate materials with $\\Gamma_3$ doublets.","marker":"[64]"}],"fun_headline_variants":["Pseudo-chiral phonon splitting exposes hidden octupolar order","Ferro-octupolar order gives phonons a pseudo-chiral split","Raman scattering can reveal pseudo-chiral phonon splitting","Octupolar order leaves pseudo-chiral imprint on phonon modes","Hidden octupolar order detected via phonon doublet splitting"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The predicted observable splitting scales as $\\lambda^2/\\Omega_0$ with the linear quadrupole-phonon coupling $\\lambda \\approx 5$ meV; if the true coupling is smaller, or if the candidate material orders antiferro-quadrupolar rather than ferro-octupolar, the splitting shrinks below the phonon linewidth and the proposed probe goes silent.","fun_headline_variants_meta":{"raw":{"variants":["Pseudo-chiral phonon splitting exposes hidden octupolar order","Ferro-octupolar order gives phonons a pseudo-chiral split","Raman scattering can reveal pseudo-chiral phonon splitting","Octupolar order leaves pseudo-chiral imprint on phonon modes","Hidden octupolar order detected via phonon doublet splitting"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000901,"raw_usage":{"total_tokens":3939,"prompt_tokens":1069,"completion_tokens":2870,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":685,"completion_tokens_details":{"reasoning_tokens":2780}},"tokens_in":685,"tokens_out":2870,"duration_ms":20402,"temperature":1.0,"reasoning_tokens":2780,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T18:41:39.743312+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure helicity- and polarization-resolved Raman spectra of the $E_g$ phonon doublet across the ordering transition in a Ba$_2$CaOsO$_6$ single crystal whose octupolar order is independently confirmed by resonant X-ray or NMR. If no two-peak structure with splitting near 1 meV and opposite pseudo-angular-momentum selection rules appears below $T_{\\mathrm{FO}}$, the prediction is falsified. Alternatively, a first-principles calculation of $\\lambda$ from strain-induced splitting that yields a value well below 5 meV would falsify the quantitative claim.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the spin-phonon Hamiltonian and previous phonon-driven multipolar dynamics, and together with [79] the DFT estimate $\\lambda \\approx 5$ meV from strain splitting of the doublet."},{"cited_title":"Voleti, A","cited_arxiv_id":null,"evidence_quote":"Establishes the pseudospin model and the competing FO/AFQ tendencies for osmium double perovskites, giving the Hamiltonian in Eq. (1)."},{"cited_title":"Churchill and H.-Y","cited_arxiv_id":null,"evidence_quote":"Provides the first-principles case for ferro-octupolar order in $d^2$ double perovskites and the exchange parameters $J_0$, $J_1$, $\\gamma$ used in the Monte Carlo."},{"cited_title":"Voleti, K","cited_arxiv_id":null,"evidence_quote":"Supplies the strain-field DFT estimate of the quadrupole-phonon coupling strength $\\lambda \\approx 5$ meV and discusses hidden octupolar order probes."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Underlies the nearest-neighbor pseudospin interactions and octupolar order physics on the fcc lattice."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Is the dipolar-magnet chiral-phonon experiment whose $\\sim 1$ meV splitting and Raman detection this work compares against."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the ferrimagnetic chiral-phonon data whose splitting-versus-order-parameter discrepancy the paper explains through local Weiss-field directions."}],"review_version":1}