Pith. sign in

REVIEW 3 major objections 5 minor 34 references

The electric field gradient tensor as a symmetry-adapted order parameter in Landau theory

T0 review · 3 major / 5 minor · reviewed 2026-07-30 · grok-4.5

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read The electric field gradient at a nuclear site is itself a Landau order-parameter realization whenever symmetry matches.

desk verdict Clean group-theory framework that finally treats the nuclear-site EFG as a Landau carrier; the tensor theorem is solid, the broad experimental validation is thinner than the abstract claims. read the letter →

arxiv 2607.26934 v1 pith:7CWOM6CJ submitted 2026-07-29 cond-mat.str-el cond-mat.mtrl-sci

L. Scalise , A. W. Carbonari This is my paper · ORCID
classification cond-mat.str-elcond-mat.mtrl-sci
keywords electricfieldgradientLandautheoryorderparameterNQRNMRhyperfinespectroscopyWyckofforbitnematictransition
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

Quadrupolar spectroscopies have long treated the electric field gradient (EFG) at a nucleus as a useful proxy for structural and electronic order parameters, without a general Landau role for the tensor itself. This paper supplies that role. The EFG is a pure rank-2 traceless tensor living at a crystallographic site; decomposing it under the site group and inducing over the Wyckoff orbit yields its irreducible content in the parent space group. When a zone-center transition’s representation appears in that content, symmetry forces the matching orbit-adapted EFG combination to vanish above the transition and grow linearly with the order parameter below it, inheriting exponent, sign, and domains. Orthogonal channels grow only quadratically, and forbidden channels stay zero—recovering classic empirical laws as theorems and giving a falsifiable primary/secondary/forbidden map from group theory alone. The claim is checked against decades of NQR/NMR data, all-electron quartz calculations that confirm the orbit-selection rule, and five concrete predictions for the arsenic site across the nematic transition in BaFe2As2, including a previously unstated null.

What carries the argument

Induced representation of the pure ℓ=2 EFG over the Wyckoff orbit: site-group subduction followed by induction into parent-group irreps, which fixes the linear/quadratic coupling dichotomy (matching channel p=1, orthogonal allowed channels p=2) and the primary/secondary/forbidden classification.

What would settle it

In BaFe2As2 below the nematic transition, the two 75As sublattices must acquire equal V_xy of the same sign; any genuine sublattice EFG inequivalence beyond twinning would falsify the framework’s B2g orbit assignment. Oriented-crystal satellites should read linear anisotropy while powder NQR reads quadratic.

Watch

Extended reading notes

Core claim

Whenever the induced EFG representation over a Wyckoff orbit contains the irreducible representation of a zone-center transition, the matching orbit-adapted EFG combination is a realization of the order parameter: it is identically zero in the parent phase, couples linearly to the microscopic order parameter, and inherits its critical exponent, sign, and domain structure. Complementary allowed channels grow quadratically; symmetry-orthogonal channels remain forbidden. The EFG realizes the order parameter; it does not drive the transition.

Load-bearing premise

The EFG channel itself stays non-critical and couples generically to the true instability, so it tracks the order parameter without driving the transition or accidentally decoupling from it.

Editorial extensions

If this is right

  • Historical powder NQR exponents can be reassigned as primary, masqueraded primary (transverse channel read quadratically), or secondary once site symmetry and one oriented-crystal measurement are combined.
  • Matching channels predict a Curie–Weiss divergence of the strain-induced EFG response above Tc (strain-NQR).
  • A complete set of null EFG channels becomes an exclusion statement for whole irreps in the induced representation.
  • Frozen-distortion DFT slopes are exactly the Landau couplings λ/κ, making hyperfine calculation and phenomenology mutually calibrating.
  • Non-identity EFG channels are background-free by symmetry, making them preferred local order-parameter observables for weak transitions.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The same subduction–induction logic applied to the hyperfine magnetic field would give the time-odd partner theorem for magnetic order parameters, which the paper only sketches.
  • A lookup table of induced EFG irreps per space group and Wyckoff position would make the classification a routine tool parallel to spontaneous-strain tables.
  • Systematic re-fitting of powder-only NQR critical exponents with the masquerade warning in mind could revise some claimed tricritical or secondary assignments.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. The manuscript constructs a Landau-theoretic framework in which the nuclear-site electric field gradient (EFG), a traceless symmetric rank-2 tensor, is decomposed under the site group and induced over the Wyckoff orbit to obtain its irreducible content in the parent space group. Whenever a zone-center transition irrep Γ_φ appears in that content, the matching orbit-adapted EFG combination is argued to be a realization of the order parameter: it vanishes above T_c by the orbit-level Neumann identity, couples bilinearly, and grows as v∝φ (Eqs. 10–12, Theorem of Sec. III), while symmetry-orthogonal channels are quadratic and others remain forbidden. The construction is checked structurally by all-electron frozen-mode calculations on α-quartz (orbit selection, |a+/a−|≈0.018) and confronted with historical NQR/NMR/TDPAC/Mössbauer data; a five-prediction case study for 75As in BaFe2As2, including a sublattice null, is proposed.

Significance. If the classification holds, the paper supplies a missing, falsifiable assignment rule that turns routine quadrupolar observables from empirical proxies into symmetry-labeled primary, secondary, or forbidden channels, with concrete payoffs (background-free onset, domain-sign resolution, strain-NQR Curie–Weiss response, null-result exclusion logic). Strengths that should be credited include: standard but carefully executed subduction/induction and vanishing theorem; an explicit linear/quadratic dichotomy derived from invariant minimization rather than assumed; honest scope boundaries (A4–A6, realization not driver); reproducible-style quartz DFT with reported slopes, R², and suppression ratio; and five stated, including one previously unstated, predictions for BaFe2As2. The contribution is conceptual and methodological rather than a new microscopic mechanism, but it is of clear use to the hyperfine and structural-transition communities.

major comments (3)
  1. [Abstract; Sec. V C; Sec. VI A; Table III] Abstract and Sec. VI framing overstate what is demonstrated versus proposed. The abstract asserts first-principles calculations “satisfying the predicted parity and zero theorems,” yet Sec. V explicitly states that single-site parity and identically vanishing forbidden channels “are not isolable from the present dataset” and are left to a pure-mode refinement (SM Sec. S9); only the orbit-selection contrast is cleanly confirmed. Likewise, “validated against five decades… reproducing critical exponents” sits uneasily with Table III, where most entries are tier I/B and the clean channel-resolved case AgNa(NO2)2 is proposed for reanalysis (Sec. VI A 3), not executed. Please align abstract, highlights, and Sec. VI claims with the epistemic levels already distinguished in Sec. V C (demonstrated / theoretical consequence / prospective).
  2. [Sec. III; Sec. VI A 1; Eq. (17)–(18), (22); Fig. 6; Table III] The theorem (Sec. III, Eqs. 10–12) correctly establishes exponent inheritance for the orbit-adapted EFG tensor combination v under irrep match. Sec. VI A 1’s own masquerade warning, however, shows that a primary transverse channel enters powder NQR/Mössbauer frequencies as ∼φ², so the measured exponent is 2β unless oriented-crystal satellites (linear in Vz′z′) are used. Several places (abstract; “inherits its critical exponent” language; Fig. 6 powder examples treated as supporting β) blur tensor realization with routine spectroscopic scalars. Please state systematically, for each evidence row and for the BaFe2As2 dictionary (Eq. 22), whether the reported map is linear in v or quadratic through (VZZ, η), so that “inherits β” is claimed only where the observable map is linear.
  3. [Sec. III (A5–A6, Eq. 11–12); Sec. VI C (free energy, Prediction table, First principles)] Assumption A5/A6 (κ_α>0, generic λ≠0) is load-bearing for calling a channel “primary” in experiment: if λ is accidentally small, the irrep match still holds but the realization is faint (honest boundary, Sec. III). The manuscript does not give a practical criterion or DFT protocol bound for “generic” beyond the quartz slope. For the BaFe2As2 centerpiece, a short frozen-B2g Vxy(δ) scan (proposed but not performed at the end of Sec. VI C) would convert Λ into a number and test that the primary channel is not accidentally weak; without it, Prediction table items that assume a usable linear satellite anisotropy remain conditional. Either supply that calculation or flag the five signatures as contingent on non-small λ/κ.
minor comments (5)
  1. [Throughout; Sec. VI heading] Typographical inconsistencies: “Ressonance” in the opening paragraph; “COMP ARISON”, “LITERA TURE”, “VERIFICA TION”, “THEOR Y” spacing artifacts in headings; “BaF e2As2” in the Sec. VI C heading.
  2. [Fig. 3] Fig. 3 caption: “α tr2γ2/9β4” appears to omit “=” (should match Eq. after the cubic-invariant solution).
  3. [Table I; Sec. V] Table I lists a 2×2×1 k-mesh and no relaxation at each δ; a one-sentence sensitivity note (or SM pointer) on whether the activated/suppressed ratio is stable under denser k-meshes would help readers who reimplement the protocol.
  4. [Sec. VI C] Convention warning on B1g↔B2g (1-Fe vs 2-Fe cell) in Sec. VI C is important; consider a short explicit character or basis note so that non-pnictide readers do not mis-assign Vxy.
  5. [End matter; Refs.] Declaration of generative AI is present; ensure journal policy on wording is met and that no AI-generated citations remain unchecked (e.g. completeness of the ferroelastic/strain and nematic Landau citations).

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: irrep classification and linear/quadratic dichotomy follow from standard representation theory plus Landau minimization, tested against external DFT and literature rather than fitted to themselves.

full rationale

The load-bearing chain is: (i) EFG is a pure ℓ=2 traceless symmetric tensor at a site; (ii) subduction to the site group plus induction over the Wyckoff orbit yields parent-group irrep content; (iii) Neumann’s principle forces non-identity channels to vanish in the parent phase; (iv) the lowest allowed coupling is linear iff the EFG channel irrep matches Γφ, else quadratic (Eq. 10); (v) minimization then gives v∝φ with inherited β under A4–A6 (Eqs. 11–12). None of these steps defines the output in terms of the measured exponents or DFT slopes. Coupling constants λ/κ are computed outputs of frozen-distortion scans, not knobs tuned to recover β. Quartz DFT (Sec. V) tests the structural half (orbit selection, odd-in-δ activated channel, |a+/a−|≈0.018) at T=0 against a controlled amplitude δ, independent of the thermodynamic claim. Historical NQR/NMR/TDPAC results and the BaFe2As2 five-signature proposal are external benchmarks or prospective falsifiers, not inputs that force the theorem. Classic ∆νQ∝φ² phenomenology is recovered as a corollary, not smuggled in as the premise. No self-citation uniqueness theorem, no fitted-then-predicted loop, and no definitional equivalence of claim to input.

Assumptions & free parameters 2 free parameters · 7 assumptions · 1 invented entities

The central classification is almost entirely representation theory plus standard Landau analyticity. Load-bearing domain assumptions are zone-center scope, non-critical EFG channels with generic λ≠0, static thermally averaged potential, and mean-field free energies. No new physical entities; material couplings are computed or left as DFT outputs rather than global fitted constants driving the claim.

free parameters (2)
  • Material-specific couplings λ_α, κ_α, μ (and Λ composite) = Quartz activated slope a=−4.81×10^−2 a.u./(Å√amu); general materials left symbolic or for future DFT
    Enter the free energy and set the slope v=(λ/κ)φ; they are not fitted to prove the symmetry class, but amplitudes and strain-NQR Curie–Weiss scale depend on them. Quartz reports a numerical slope a=−4.81e-2 a.u./(Å√amu) as the microscopic λ/κ.
  • Landau coefficients a0, b, γ, β4 (and strain C66)
    Standard thermodynamic expansion coefficients controlling Tc, β, and first-order jumps; borrowed universality, not derived. Needed for temperature shapes, not for the primary/secondary assignment.
assumptions (7)
  • domain assumption Landau criterion: a continuous transition is described by a single irrep of the parent group with an analytic free energy and generic non-multicritical quadratic coefficient sign change (A3, A8, A9).
    Foundation of Sec. II–IV; standard but excludes fluctuation-driven and intrinsically non-Landau cases.
  • ad hoc to paper Scope limited to zone-center (k=0, translationengleiche) transitions so space-group irreps reduce to point-group irreps (A4).
    Stated explicitly; incommensurate/zone-boundary cases deferred though partly illustrated with Rb2ZnBr4.
  • domain assumption EFG channels are non-critical (κα>0) and only realize, not drive, the instability (A5); generic λ≠0 (A6).
    Sec. III theorem and free-energy elimination; fails if EFG is accidentally soft or decoupled.
  • domain assumption Static Born–Oppenheimer averaged potential; traceless EFG defined by decoupling of the trace from the quadrupole Hamiltonian, not by Laplace’s equation in charge-free space (A1, A2).
    Sec. II A; standard for static hyperfine splittings, excludes dynamic fluctuation observables.
  • standard math Neumann’s principle: equilibrium tensor equals its projection onto the identity irrep of the site (or parent) group.
    Used for vanishing of non-A1 channels and cubic-site theorem (Eq. 7–8).
  • standard math Frobenius reciprocity / induction: parent irrep content of the EFG is Ind_{Gq}^{G0}(D^(ℓ=2)↓Gq) over the Wyckoff orbit.
    Sec. II B bridge from site to parent; core mathematical engine.
  • domain assumption Mean-field exponents and first-order cubic-invariant solutions are used; true universality classes are borrowed, not derived.
    Sec. VII C limitations; temperature comparisons assume Landau or stated β.
invented entities (1)
  • Primary/secondary/forbidden EFG channel classification (and strain-NQR response) independent evidence
    purpose: Taxonomy assigning each orbit-adapted EFG combination a Landau role and proposing Curie–Weiss strain-induced EFG above Tc.
    Not a new particle or field; a named organizational scheme plus an experimental protocol proposal built from standard invariants. independent_evidence is supported by quartz orbit contrast and existing nematic NMR phenomenology, but strain-NQR itself is untested here.

how reviews work

0 comments
Cite this review

Pith. "Pith review of The electric field gradient tensor as a symmetry-adapted order parameter in Landau theory." pith.science (2026). https://pith.science/paper/7CWOM6CJ

@misc{pith2026260726934,
  author       = {Pith},
  title        = {Pith review of: The electric field gradient tensor as a symmetry-adapted order parameter in Landau theory},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/7CWOM6CJ}},
  note         = {Machine review of arXiv:2607.26934}
}
abstract

Quadrupolar hyperfine spectroscopies, including Nuclear Quadrupole Resonance (NQR), Nuclear Magnetic Resonance (NMR), Time-Differential Perturbed Angular Correlations (TDPAC), and M\"ossbauer spectroscopy, have long used the electric field gradient (EFG) at a nuclear site as an empirical proxy for order parameters in structural and electronic phase transitions, yet the EFG has never been systematically incorporated into Landau theory. Here we provide that framework. The EFG is an exactly traceless, symmetric rank-2 tensor defined at a crystallographic site. Decomposing it under the site-symmetry group and inducing over the Wyckoff orbit determines its irreducible representation content in the parent space group. Whenever the representation of a zone-center transition is present, symmetry requires the corresponding EFG combination to vanish above the transition and grow linearly with the order parameter below it, inheriting its critical exponent, sign, and domain structure. Symmetry-orthogonal channels are quadratic, recovering the classic empirical relations. This yields a falsifiable classification of primary, secondary, and forbidden EFG responses. The framework is validated against five decades of quadrupolar experiments, reproducing critical exponents, first-order discontinuities, and a null result, and by first-principles calculations satisfying the predicted parity and zero theorems. All-electron calculations for $\alpha$-quartz confirm the orbit-selection rule: only the EFG combination transforming as the soft-mode irreducible representation varies linearly with distortion amplitude, while the orthogonal combination remains suppressed by two orders of magnitude. A proposed study of the $^{75}$As site across the nematic transition in BaFe$_2$As$_2$ provides five falsifiable predictions, including a previously unstated null result.

Figures

Figures reproduced from arXiv: 2607.26934 by the authors.

Figure 1
Figure 1. FIG. 1. Geometric content of the EFG tensor. (a) Represen [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Channel decomposition of the EFG at a tetragonal site and its rearrangement at a symmetry-lowering transition. [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Landau free energy in EFG variables (Sec. IV). [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figures from the paper (6 more)
Figure 4
Figure 4. Figure 4: FIG. 4. First-principles verification of the induced-representation theorem on [PITH_FULL_IMAGE:figures/full_fig_p009_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. The frequency-map masquerade (Sec. VI A 1). A [PITH_FULL_IMAGE:figures/full_fig_p010_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6. The exponent dichotomy in the experimental record (data digitized from Refs. [12, 13, 24]). (a) Second-order, [PITH_FULL_IMAGE:figures/full_fig_p011_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7. The complete argument on one material (Sec. VI C). Left to right: the [PITH_FULL_IMAGE:figures/full_fig_p012_7.png]
Figure 8
Figure 8. Figure 8: FIG. 8. Residuals of the linear model for the Si [PITH_FULL_IMAGE:figures/full_fig_p022_8.png]
Figure 9
Figure 9. Figure 9: FIG. 9. Log-scale comparison of the activated and suppressed Si [PITH_FULL_IMAGE:figures/full_fig_p023_9.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

34 extracted references

  1. [1]

    S8) yields the single frequency νQ = eQVZZ 2h r 1 + η2 3 .(17) The masquerade warning.If the critical channel changes VZZ linearly, ∆νQ ∝φandβis inherited

    The observable dictionary, and a warning (a) Pure NQR,I= 3/2.Diagonalizing the quadrupole Hamiltonian (SM, Sec. S8) yields the single frequency νQ = eQVZZ 2h r 1 + η2 3 .(17) The masquerade warning.If the critical channel changes VZZ linearly, ∆νQ ∝φandβis inherited. But if the crit- ical channel istransverse—appearing whereη (0) = 0— thenν Q ∝1 +η 2/6 +....

  2. [2]

    Observable map

    The record, organized by evidence quality Clean validations (oriented-crystal satellites; masquerade-free).AgNa(NO 2)2: the 23Na EFGtensor through theF ddd→F d2dferroelectric transition, read from first-order satellites [22], gives a channel-resolved test in which the linear (p= 1) and quadratic (p= 2) components are separately resolved without the pow- d...

  3. [3]

    Reanalysis target: AgNa(NO 2)2 The ferroelectric transitionF ddd→F d2dis zone- center, and the two required ingredients exist sepa- rately: the 23Na EFGtensorwas determined from first-order satellites through the transition [22]—a no- table exception to the two-scalar practice noted in the Introduction— while independent Landau analysis of the polarizatio...

    1978

  4. [4]

    Elastic anomalies in minerals due to structural phase transitions

    Michael A Carpenter and Ekhard KH Salje. Elastic anomalies in minerals due to structural phase transitions. European Journal of Mineralogy, pages 693–812, 1998

    1998

  5. [5]

    A.W.C. acknowledges the Conselho Nacional de De- senvolvimento Cient ´ ıfico e Tecnol´ ogico (CNPq) for fi- nancial support through grant numbers 307322/2021- 1, 408139/2022-6, 404949/2024-0, and 445223/2024-3. Additionally, this work was supported by the Coor- dena¸ c˜ ao de Aperfei¸ coamento de Pessoal de N ´ ıvel Superior (CAPES) through a scholarship....

    2021

  6. [6]

    Elsevier, 2013

    Lev Davidovich Landau and Evgenii Mikhailovich Lif- shitz.Statistical physics: volume 5, volume 5. Elsevier, 2013

    2013

  7. [7]

    World Scientific Publishing Company, 1987

    Pierre Toledano and Jean-claude Toledano.Landau the- ory of phase transitions, the: application to structural, incommensurate, magnetic and liquid crystal systems, volume 3. World Scientific Publishing Company, 1987

    1987

  8. [8]

    Phase transitions in ferroelastic and co- elastic crystals.Ferroelectrics, 104(1):111–120, 1990

    Ekhard Salje. Phase transitions in ferroelastic and co- elastic crystals.Ferroelectrics, 104(1):111–120, 1990

    1990

Show all 34 references
  1. [9]

    First-principles calculation of the electric-field gradient in hcp metals

    P Blaha, K Schwarz, and PH Dederichs. First-principles calculation of the electric-field gradient in hcp metals. Physical Review B, 37(6):2792, 1988

    1988

  2. [10]

    P. G. de Gennes and J. Prost.The Physics of Liquid Crystals. Clarendon Press, Oxford, 2nd edition, 1993

    1993

  3. [11]

    Schatz and A

    G. Schatz and A. Weidinger.Nuclear Condensed Matter Physics: Nuclear Methods and Applications. John Wiley, Chichester, 1996

    1996

  4. [12]

    Magnetic resonance of phase transitions.ed

    F Borsa and A Rigamonti. Magnetic resonance of phase transitions.ed. FJ Owens et al, page 79, 1979

    1979

  5. [13]

    Nmr-nqr studies of structural phase tran- sitions.Advances in Physics, 33(2):115–191, 1984

    A Rigamonti. Nmr-nqr studies of structural phase tran- sitions.Advances in Physics, 33(2):115–191, 1984

    1984

  6. [14]

    Origin of the tetragonal-to-orthorhombic phase transition in fese: A combined thermodynamic and nmr study of nematicity

    AE B¨ ohmer, T Arai, F Hardy, T Hattori, T Iye, T Wolf, H v L¨ ohneysen, K Ishida, and C Meingast. Origin of the tetragonal-to-orthorhombic phase transition in fese: A combined thermodynamic and nmr study of nematicity. Physical review letters, 114(2):027001, 2015

    2015

  7. [15]

    The Elk Code.http://elk.sourceforge.net/

  8. [16]

    wien2k.An aug- mented plane wave+ local orbitals program for calculating crystal properties, 60(1):155–169, 2001

    Peter Blaha, Karlheinz Schwarz, Georg KH Madsen, Di- eter Kvasnicka, Joachim Luitz, et al. wien2k.An aug- mented plane wave+ local orbitals program for calculating crystal properties, 60(1):155–169, 2001

    2001

  9. [17]

    Cl 35 nqr study of the structural order-disorder transition in (c h 3 n h 3) 2 mn cl 4.Phys- ical Review B, 13(1):45, 1976

    R Kind and J Roos. Cl 35 nqr study of the structural order-disorder transition in (c h 3 n h 3) 2 mn cl 4.Phys- ical Review B, 13(1):45, 1976

    1976

  10. [18]

    Observation of87rb nmr satellite transitions in the commensurate and incommen- surate phases of rb2zncl4.Zeitschrift f¨ ur Physik B Con- densed Matter, 46(2):169–175, 1982

    E Schneider and J Petersson. Observation of87rb nmr satellite transitions in the commensurate and incommen- surate phases of rb2zncl4.Zeitschrift f¨ ur Physik B Con- densed Matter, 46(2):169–175, 1982

    1982

  11. [19]

    The mathematical theory of symmetry in solids oxford, uk: Oxford univ, 1972

    CJ Bradley and AP Cracknell. The mathematical theory of symmetry in solids oxford, uk: Oxford univ, 1972

    1972

  12. [20]

    Competing magnetic fluctuations in iron pnictide superconductors: role of ferromagnetic spin correlations revealed by nmr.Physical Review Letters, 115(13):137001, 2015

    P Wiecki, B Roy, DC Johnston, SL Bud’ko, PC Canfield, and Yuji Furukawa. Competing magnetic fluctuations in iron pnictide superconductors: role of ferromagnetic spin correlations revealed by nmr.Physical Review Letters, 115(13):137001, 2015

    2015

  13. [21]

    secondary

    (a +10% GGA overestimate at exploratory set- tings), confirming the calculation is on scale before any symmetry-resolved claim. B. The orbit-resolved prediction and what the data show Site descent and orbit combinations.Along theA 1 co- ordinate the Si site descendsD2 →C 2. Th...

  14. [22]

    Electric field gradient in accurate quantum chemical calculations

    Andrei Derevianko, UC Perera, Marek Kro´ snicki, Kamil Nalikowski, HWT Morgan, and Valera Veryazov. Electric field gradient in accurate quantum chemical calculations. arXiv preprint arXiv:2601.07098, 2026. 15

    2026

  15. [23]

    What drives nematic order in iron-based su- perconductors?Nature physics, 10(2):97–104, 2014

    Rafael M Fernandes, Andrey V Chubukov, and J¨ org Schmalian. What drives nematic order in iron-based su- perconductors?Nature physics, 10(2):97–104, 2014

    2014

  16. [24]

    Scalise and A

    L. Scalise and A. W. Carbonari. Supplemental material for: The electric field gradient tensor as a symmetry- adapted order parameter in landau theory. 2026

    2026

  17. [25]

    Princeton university press, 1946

    Hermann Weyl.The classical groups: their invariants and representations, volume 1. Princeton university press, 1946

    1946

  18. [26]

    Quartz: structural and thermodynamic analyses across theα↔βtransition with origin of neg- ative thermal expansion (nte) inβquartz and calcite

    Sytle M Antao. Quartz: structural and thermodynamic analyses across theα↔βtransition with origin of neg- ative thermal expansion (nte) inβquartz and calcite. Structural Science, 72(2):249–262, 2016

    2016

  19. [27]

    J Grossmann, D M¨ uller, J Petersson, and E Schneider. Study of the23na efg tensor as determined from first or- der nmr satellite lines near the ferroelectric phase transi- tion of agna (no2) 2.Zeitschrift f¨ ur Physik B Condensed Matter, 31(2):187–193, 1978

    1978

  20. [28]

    Back to the struc- tural and dynamical properties of neutral-ionic phase transitions.Crystals, 7(10):285, 2017

    Marylise Buron-Le Cointe, Eric Collet, Bertrand Toudic, Piotr Czarnecki, and Herv´ e Cailleau. Back to the struc- tural and dynamical properties of neutral-ionic phase transitions.Crystals, 7(10):285, 2017

    2017

  21. [29]

    Nmr lineshape and phase soliton effects in incommensurate rb2zncl4.Journal of Physics C: Solid State Physics, 15(3):547–563, 1982

    R Blinc, IP Aleksandrova, AS Chaves, F Milia, V Rutar, J Seliger, and S Zumer. Nmr lineshape and phase soliton effects in incommensurate rb2zncl4.Journal of Physics C: Solid State Physics, 15(3):547–563, 1982

    1982

  22. [30]

    H Yurtseven and O Tari. Analysis of the spontaneous polarization, susceptibility and the specific heat for the ferroelectric agna (no2) 2 using the landau mean field model.Journal of Advanced Dielectrics, page 2650011, 2026

    2026

  23. [31]

    Effect of uniaxial strain on the structural and magnetic phase transitions in bafe 2 as 2.Physical review letters, 108(8):087001, 2012

    Chetan Dhital, Z Yamani, Wei Tian, J Zeretsky, AS Se- fat, Ziqiang Wang, RJ Birgeneau, and Stephen D Wilson. Effect of uniaxial strain on the structural and magnetic phase transitions in bafe 2 as 2.Physical review letters, 108(8):087001, 2012

    2012

  24. [32]

    Commensu- rate itinerant antiferromagnetism in bafe2as2: 75as-nmr studies on a self-flux grown single crystal.Journal of the Physical Society of Japan, 77(11):114709–114709, 2008

    Kentaro Kitagawa, Naoyuki Katayama, Kenya Ohgushi, Makoto Yoshida, and Masashi Takigawa. Commensu- rate itinerant antiferromagnetism in bafe2as2: 75as-nmr studies on a self-flux grown single crystal.Journal of the Physical Society of Japan, 77(11):114709–114709, 2008

    2008

  25. [33]

    Isosubgroup: an internet tool for generating isotropy sub- groups of crystallographic space groups.Applied Crystal- lography, 49(5):1849–1853, 2016

    Harold T Stokes, S van Orden, and Branton J Campbell. Isosubgroup: an internet tool for generating isotropy sub- groups of crystallographic space groups.Applied Crystal- lography, 49(5):1849–1853, 2016

    2016

  26. [34]

    masquerade

    Danel Orobengoa, Cesar Capillas, Mois I Aroyo, and J Manuel Perez-Mato. Amplimodes: symmetry-mode analysis on the bilbao crystallographic server.Applied Crystallography, 42(5):820–833, 2009. 16 SUPPLEMENT AR Y MA TERIALS This Supplemental Material collects the derivations, tab...

    2009

Pith tools

Reviewed July 30, 2026 · model on record in the stance chip above.