Exploring magneto-electric coupling through lattice distortions: insights from a pantograph model

Daniel C. Cabra; Gerardo L. Rossini

REVIEW 4 major objections 6 minor 151 references

Exploring magneto-electric coupling through lattice distortions: insights from a pantograph model

T0 review · 4 major / 6 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read The paper claims that lattice distortions alone can drive the defining behaviors of collinear type II multiferroics, including a complete magnetic-field switch-off of electric polarization.

desk verdict A competent self-review of the pantograph mechanism, with a clean topological-soliton picture and one unproven load-bearing assumption: fixed Ising dipoles above the critical field. read the letter →

arxiv 2505.16611 v1 pith:KEUBHGGE submitted 2025-05-22 cond-mat.str-el

Daniel C. Cabra , Gerardo L. Rossini This is my paper · ORCID

classification cond-mat.str-el PACS 75.85.+t75.10.Jm75.10.Pq

keywords multiferroicstypeIIimproperpantographmodelmagneto-electriccouplinglatticedistortionsmagnetizationplateautopologicalsolitonsspin-Peierlsinstability

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

This review paper argues that a single microscopic mechanism—lattice distortions that simultaneously change magnetic exchange couplings and the magnitudes of electric dipoles—can account for the ubiquitous phenomenology of collinear type II multiferroics. The mechanism, called a pantograph model, predicts a spontaneous ferrielectric polarization at zero magnetic field, a complete switch-off of that polarization once a magnetic field exceeds a threshold, and converse electric-field-driven magnetization jumps. The paper reaches this conclusion by revisiting a coherent set of numerical and analytical studies on one-dimensional spin-dipole chains, extensions with frustration and easy-axis anisotropy, higher-spin chains, and a two-dimensional Ising version. If the picture is right, it provides a concrete microscopic route for designing materials where magnetic fields control electric polarization and electric fields control magnetization.

What carries the argument

The load-bearing object is the pantograph relation $p_i(\sigma_i,\delta_i)=p_0(1-\beta\delta_i)\,2\sigma_i$, which ties each electric dipole's magnitude to the local bond-length change $\delta_i$, together with the spin-Peierls modulation $J_1(\delta_i)=J_1(1-\alpha\delta_i)$ of the magnetic exchange. These feed self-consistent distortion equations, for example $K\delta_i = \alpha J_1\langle S_i\cdot S_{i+1}\rangle - \beta\varepsilon\sigma_i + J_e(\beta+\tfrac{3}{2a})(\sigma_{i-1}\sigma_i+\sigma_i\sigma_{i+1})$ in the minimal model, so that distortions minimize the total energy while spins and dipoles adjust to the distorted lattice. The same distortions act as the communication channel between magnetic and electric order, and the topological solitons that carry the first magnetic excitations separate domains of opposite local polarization, which is what makes the total polarization vanish above $h_{c1}$.

What would settle it

Measure the electric polarization across the magnetization onset in a quasi-one-dimensional collinear type II multiferroic such as LiCuVO4: a smooth or partial polarization drop instead of a sharp switch-off to zero would refute the model's central claim. Alternatively, treat the dipoles as dynamical quantum variables in the self-consistent calculation and check whether $P^{\rm z}_{\rm total}(h>h_{c1})$ remains exactly zero.

Watch

Extended reading notes

Core claim

The paper's central claim is that a pantograph mechanism—where lattice distortions simultaneously modulate magnetic exchange couplings and the magnitudes of electric dipoles—provides a successful microscopic description of ubiquitous phenomena in type II improper multiferroics. In the model, the zero-field magnetic order is a gapped state accompanied by alternating (dimerized) lattice distortions; because each dipole's strength is $p_i=p_0(1-\beta\delta_i)2\sigma_i$, the alternating distortions turn an antiferroelectric dipole pattern into a ferrielectric one with a spontaneous bulk polarization. The first magnetic excitations are not single magnons but pairs of topological solitons that separate domains with opposite local polarization; as solitons proliferate above the critical field $h_{c1}$, the domain polarizations cancel and the total polarization drops identically to zero. The same shared-distortion coupling lets an electric field, by reorganizing dipoles and distortions, open or close magnetization plateaus and thereby produce electrically driven magnetization jumps. The paper reports that these features persist in extended models with next-nearest-neighbor frustration and easy-axis anisotropy, where the experimentally common $\uparrow\uparrow\downarrow\downarrow$ order emerges, and in higher-spin and two-dimensional versions.

Load-bearing premise

The load-bearing premise is that the electric dipoles stay locked in their antiferroelectric up-down pattern while the spins and lattice relax; if those dipoles can flip or fluctuate in a real material, the predicted complete switch-off of polarization could be weakened or lost.

Editorial extensions

If this is right

A magnetic field above the spin gap $h_{c1}$ produces a complete switch-off of the spontaneous electric polarization, $P^{\rm z}_{\rm total}(h>h_{c1})=0$, in both the minimal and the extended one-dimensional models.
An electric field that drives the dipoles into a period-four quadrumerized phase opens a magnetization plateau at $M=1/2$, so crossing the electro-elastic transition at fixed magnetic field yields an electrically driven magnetization jump.
With next-nearest-neighbor frustration and easy-axis anisotropy, the model stabilizes the experimentally common $\uparrow\uparrow\downarrow\downarrow$ spin order while keeping the polarization switch-off, connecting the mechanism to materials such as AgCrS2 and related chain compounds.
Long-range dipole-dipole interactions create a period-three $\Uparrow\Uparrow\Downarrow$ dipolar phase; at simultaneous polarization and magnetization equal to one third of saturation, the distortions favor a quantum dimer plateau in some parameter ranges and a classical $\uparrow\uparrow\downarrow$ plateau in others.
For $S=3/2$ magneto-elastic chains, a first-order structural transition opens a spin gap and magnetization plateaus; coupling those distortions to dipoles would again produce a zero-field ferrielectric polarization that switches off under field.

Reading between the lines

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

Beyond the paper: the sharpness of the predicted polarization switch-off depends on soliton pairs being equally spaced; quenched disorder or inter-chain couplings that pin domain walls would leave a residual polarization, so the cleanest test should be in highly uniform quasi-one-dimensional compounds.
Beyond the paper: the Z2-degenerate polarization together with magnetic erasure and poling-field rewrite suggests a concrete memory cycle; strain-engineered heterostructures, where lattice mismatch controls the effective electro-elastic coupling, offer a way to tune the switch-off field experimentally.
Beyond the paper: because the S=3/2 transition is first order in the spin-phonon coupling, applying hydrostatic pressure should produce a steeply varying magnetization and polarization, a testable prediction that goes beyond the fields the paper considers.
Beyond the paper: in two dimensions the model selects zig-zag stripe order when dipolar coupling is strong, implying a material trend—compounds with larger dipole-dipole interactions should favor E-type $\uparrow\uparrow\downarrow\downarrow$ order over checkerboard order—that could be checked across manganite families.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Dear colleague,

This is a self-review of the authors' pantograph mechanism for type-II multiferroics. Honest bottom line: no new results, but a useful package. If you work on collinear multiferroics, the core idea—lattice distortions modulate both exchange couplings and dipole strengths, producing ferrielectric polarization from an antiferroelectric background—is worth having in one place.

The strongest part is the topological-soliton explanation for why polarization cancels above hc1: magnetic excitations fractionalize into solitons, the dimerization domains become equal length, and the opposite ferrielectric contributions cancel. That argument is clean and consistent across the minimal and extended 1D models, and the S=3/2 and 2D extensions are sketched with the right caveats.

The soft spot I care about most is the fixed-Ising-dipole assumption. The paper says they checked that no dipole flips are energetically convenient, but that check is documented for the zero-field, zero-magnetization state. Above hc1, where soliton domain walls form, the dipole energy depends on the local distortion pattern through the terms in Eq. (15); nothing in the text proves that a dipole-flip pattern following the short/long bond domains would not lower the energy or break the exact +P/-P domain balance. The abstract's P_total = 0 is exact, while the body sometimes says 'drops nearly to zero.' That discrepancy matters. If dipoles can relax or fluctuate in the magnetized regime, the complete switch-off likely becomes a small but nonzero polarization. This is the load-bearing claim for the device narrative, so a referee should ask the authors to supply the dipole-flip check above hc1, or soften the claim to strong suppression.

Other soft spots are minor: several figures are schematic or reprinted, there is an unresolved 'Fig.??' and a placeholder '[REFERENCES]' in the S>1/2 section, and the experimental comparison is qualitative. The self-citation load is inherent to a review; the cited papers are the actual source of the results, so I would not penalize that.

Bottom line: the synthesis is competent, the mechanism is plausible, but the exact switch-off rests on an assumption not fully proven. I would send it to peer review with a request to address the dipole-relaxation point and tighten the editorial gaps. A reader working on multiferroics gets a compact account; a skeptical reader will find the fixed-dipole question unresolved.

Referee Report

4 major / 6 minor

Summary. The manuscript is a review of a series of the authors' own prior works (Refs. [20,22,24,29,30]) on a 'pantograph' model of magneto-electric coupling mediated by lattice distortions in low-dimensional multiferroics. The model couples spin-1/2 (and higher-spin) magnetic moments, classical Ising electric dipoles, and elastic bond distortions, with both spin-exchange and dipole strengths depending on the distortions. The central claims are that (i) at zero magnetic field the magneto-elastic instability produces alternating lattice distortions that turn an antiferroelectric dipole configuration into a ferrielectric state with spontaneous polarization, and (ii) above a critical magnetic field the lowest magnetic excitations are pairs of topological solitons separating domains of opposite ferrielectric polarization, leading to 'a complete switch-off of electrical polarization, P_total(h > hc1) = 0' (Section IIIC). The review also discusses magnetization plateaus at M = 1/2 and M = 1/3, electric-field-driven magnetization jumps, extensions to S > 1/2 chains with a first-order spin-phonon transition, and a two-dimensional Ising version with zig-zag stripe order.

Significance. If the claims are correct, the pantograph mechanism provides a concrete and falsifiable microscopic route to collinear type II multiferroic behavior, with a solitonic domain-wall mechanism that explains (and predicts) the polarization switch-off at the magnetization onset. The manuscript collects a substantial body of numerical results (DMRG with truncation errors below 10^-12, Monte Carlo for the 2D case) and makes specific predictions: equidistant repelling solitons, ferrielectric domains of equal length, and a first-order spin-phonon transition for S = 3/2 at lambda_c ~ 0.1355. These are strengths. However, the paper is essentially a self-review: the evidence for the central claims comes from the authors' own previous computations, with no independent replication and no quantitative comparison to experimental measurements. The exact zero-polarization statement rests on a frozen-dipole assumption whose stability is not demonstrated in the magnetized regime, and the text wavers between 'vanishes identically' and 'drops nearly to zero'.

major comments (4)

[Section IIIB3 and Section IIIC] The exact statement 'P_total(h > hc1) = 0' (Section IIIC) rests on the assumption that the electric dipoles remain fixed in the antiferroelectric Ising configuration throughout the self-consistent iteration. Section IIIB3 justifies this with the sentence 'Proving different dipolar configurations we have concluded that no dipole flips are energetically convenient,' but no proof or numerical check is presented, and this justification is only framed for the zero-field, zero-magnetization state. In the magnetized regime, the self-consistent distortions develop soliton domain walls (Figs. 9, 18, 19), and the dipole energy in Eq. (15) contains couplings to the local distortion pattern; a dipole-flip pattern following the short/long bond domains could break the exact cancellation between opposite ferrielectric domains. The authors should either provide a quantitative test of dipole-flip stability for the Sz_total = 1 and higher excited states, or explicitly state that the exact zero is a property of the frozen-dipole approximation and that the physically expected value is near-zero but not identically zero.
[Abstract, Section IIIC, Section IVC1, Section VII] The manuscript is internally inconsistent about the sharpness of the polarization switch-off. The abstract and Section IIIC claim a 'complete switch-off' with 'P_total(h > hc1) = 0' and 'vanishes identically,' while Section IVC1 states that the polarization 'drops nearly to zero,' and Section VII acknowledges that with a poling electric field 'the polarization of the magnetized states [is] not to be completely turned off.' These are materially different claims. Since the exact zero is central to the abstract's technological narrative (erase/rewrite polarization), the authors must reconcile these statements and make clear under which conditions (poling field, frozen dipoles) the polarization is exactly zero versus merely small.
[Abstract and Section VII] The claim that the model 'successfully describes ubiquitous phenomena in type II improper multiferroics' is not substantiated in this manuscript by any quantitative comparison to experimental data for a specific material. The evidence consists of the authors' prior numerical studies (Refs. [20,22,24,29,30]); the many experimental materials mentioned (AgCrS2, Ca3CoMnO6, HoMnO3, etc.) are discussed only qualitatively. For a review that makes a success claim, a table comparing computed polarization, magnetization-plateau fields, and distortion amplitudes with measured values for at least one material would be needed. Without that, the 'successful description' claim is stronger than the evidence presented.
[Section VIA2] The first-order spin-phonon transition for S = 3/2, with critical coupling lambda_c ~ 0.1355, is presented as a robust finding ('the value of lambda_c is not sensitive to the chain length'), but the manuscript gives no finite-size scaling analysis, chain-length dependence plot, or error estimate to support this claim. Because this transition is a new feature presented in this review (not in the earlier spin-1/2 works), the numerical evidence should be shown rather than only stated.

minor comments (6)

[Section I] There are several typographical errors, for example 'an that the low temperature magnetic order is still protected by a spin gap an that' should read 'and that,' and 'to to higher dimensional lattices' in the outline should read 'to higher dimensional lattices.'
[Section IVB2b] The text contains an unresolved cross-reference 'cf. Fig.??' which should be replaced with the actual figure number.
[Section VIA1] The placeholder '[REFERENCES]' appears in the sentence about single ion anisotropy and should be replaced with actual citations.
[Section IVA1] The parenthetical instruction '(revise units in fig and text)' is left in the main text and should be removed.
[Figure 6 caption] The caption contains a typo: 'doble arrows' should be 'double arrows.'
[Section IVC1] There is a bracket mismatch in 'as it also occurs in the magneto-elastic case,47]' where the bracket should be closed as '47].'

Circularity Check

1 steps flagged · score 4.0 of 10

Central validation rests on the authors' own prior papers, but the equation-level derivation is self-contained and not circular.

self citation load bearing [Abstract; Section IIIC (Fig. 8 caption); Section IVC1]
"The model successfully describes ubiquitous phenomena in type II improper multiferroics. ... The numerical results shown in Fig. 8 express the polarization switch-off mechanism ... Original data in Ref. [20]. ... the spontaneous electric polarization observed at zero magnetization is switched off by means of the applied magnetic field.20"

The abstract's central claim that the pantograph model 'successfully describes ubiquitous phenomena' is supported in this manuscript only by the authors' own prior numerical studies (Refs. [20,22,24,29,30]), all co-authored by the present authors or their immediate collaborators. The key quantitative outputs — the polarization switch-off, the magnetization plateaus, and the soliton-domain cancellation — are explicitly labeled as 'Original data in Ref. [20]' or 'reprinted from Ref. [22]' rather than independently recomputed or tested against external quantitative benchmarks. The paper itself only says the results 'could help in fitting actual parameters,' acknowledging that no quantitative experimental fit is provided.

full rationale

The internal derivation chain in the manuscript is not circular: Eq. (12) defines the minimal pantograph Hamiltonian; Eq. (15) is obtained by minimizing that Hamiltonian with respect to the elastic distortions; and the polarization switch-off P_total(h>hc1)=0 follows from the soliton-domain distortion pattern combined with the fixed antiferroelectric dipole background. That is a model computation, not an identity smuggled in as a prediction. The h=0 ferrielectric polarization also follows directly from Eq. (4)-(5) once the spin-Peierls dimerization is solved. The main caveat is the fixed-dipole assumption in Section IIIB3 ('In practice they are kept fixed during the iterations'); this is a genuine modeling constraint and a correctness risk for the magnetized regime, but it is an unvalidated assumption rather than a circular reduction, so it does not by itself raise the circularity score. The reason the score is not zero is that the manuscript is essentially a self-review: the abstract's 'successfully describes ubiquitous phenomena' claim and the specific numerical predictions are imported from the authors' own earlier papers without independent verification. That is a load-bearing self-citation chain, giving a moderate circularity score of 4 rather than a fully independent derivation.

Assumptions & free parameters 7 free parameters · 5 assumptions · 0 invented entities

The model introduces no new particles, mediators, or fields. The pantograph coupling is a modeling assumption about how dipole magnitudes depend on bond distortions, captured in the axioms above. The numerical values of parameters are chosen by hand, not fitted to experiments.

free parameters (7)

J1 (exchange energy) = 0.5 (energy scale)
Sets the magnetic energy scale; K=1 and a=1 define units in Section IVA3.
J2/J1 frustration ratio = 0.8 (also 0.2, 0.5)
Chosen by hand in Section IVA3 to access the frustrated regime where the up-up-down-down magnetic order is stable.
gamma (XXZ anisotropy) = 1 to 1/8 (also 1/4)
Varied to interpolate between isotropic Heisenberg and Ising-like easy-axis limits, Eq. (20).
alpha (magneto-elastic coupling) = 0.2 (minimal model also uses 1.0)
Controls the linear modulation of J1 by bond distortions, Eq. (9); sets the spin-Peierls energy scale.
beta (dipole-elastic or pantograph coupling) = 0.2
Controls the change of dipole magnitude with bond distortion, Eq. (4).
Je (effective dipolar exchange) = 0.2 or 0.5
Effective electrostatic coupling between dipoles, chosen below the magnetic exchanges, Eq. (11).
lambda_c (critical spin-phonon coupling for S=3/2) = 0.1355 (S=1: 0.192)
Numerically determined first-order transition point in the S=3/2 magneto-elastic chain, Section VIA2.

assumptions (5)

domain assumption The lattice can be treated adiabatically and as a mean-field order parameter; phonon frequencies are much smaller than magnetic energy scales.
Invoked in Section IIA and IIIB3 to justify the elastic energy and the self-consistent equations.
ad hoc to paper Dipolar variables are classical Ising degrees of freedom and remain in the antiferroelectric configuration; dipole flips are not energetically favorable.
Section IIIB3 states dipoles are kept fixed during iterations; the polarization switch-off argument depends on this.
domain assumption Only the nearest-neighbor exchange J1 depends on distortions; J2 is distortion independent.
Section IVA2 justifies this by the fact that alternating distortions do not change second-neighbor distances.
domain assumption Dipolar interactions can be truncated at second neighbors with linear expansion in distortions.
Section IIB and IVA1; screening arguments justify truncation, and small distortions justify linearization.
domain assumption The global constraint sum_i delta_i = 0 fixes the lattice constant.
Eq. 2 introduced in Section IIA; used throughout the self-consistent minimization.

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Cite this review

Pith. "Pith review of Exploring magneto-electric coupling through lattice distortions: insights from a pantograph model." pith.science (2026). https://pith.science/paper/KEUBHGGE

@misc{pith2026250516611,
  author       = {Pith},
  title        = {Pith review of: Exploring magneto-electric coupling through lattice distortions: insights from a pantograph model},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/KEUBHGGE}},
  note         = {Machine review of arXiv:2505.16611}
}

read the original abstract

Multiferroic materials exhibit the coexistence of magnetic and electric order. They are at the forefront of modern condensed matter physics due to their potential applications in next-generation technologies such as data storage, sensors, and actuators. Despite significant progress, understanding and optimizing the coupling mechanisms between electric polarization and magnetism remain active areas of research. We review here a series of papers presenting a comprehensive numerical and theoretical exploration of a pantograph mechanism modeling magneto-electric coupling through lattice distortions in low dimensional multiferroic systems. These works introduce and elaborate a microscopic model where elastic lattice distortions mediate interactions between spin 1/2 magnetic moments and electric dipoles, uncovering novel physics and functionalities. The model successfully describes ubiquitous phenomena in type II improper multiferroics, particularly when dominant Ising spin components are introduced through XXZ-type rotational symmetry breaking spin interactions. We also study more realistic extensions relevant for materials with higher spin magnetic ions and to materials where magnetic couplings draw higher dimensional lattices.

Figures

Figures reproduced from arXiv: 2505.16611 by the authors.

**Figure 4.** Schematic picture of a frustrated J1 − J2 antiferromagnetic chain. Large enough J2 favors antiferromagnetic correlations every two sites, forcing half of the first neighbors bonds to bear ferromagnetic correlations instead of the energetically convenient antiferromagnetic ones. Spins are drawn arbitrarily, suggesting a tendency to ↑↑↓↓ order. antiferromagnetic couplings J2 and easy-axis coupling anisotropy22. The … view at source ↗

**Figure 3.** Schematic picture of a magnetic response to the [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗

Figures from the paper (22 more)

**Figure 5.** Figure 5: Generic change ∆P in the electric polarization, occurring when the magnetic field h drives the magnetic sector through a magnetization plateau. A detailed example is discussed in Section V C. top of the magnetic frustration (arising from competing magnetic orders), a…

**Figure 6.** Figure 6: Dipolar phases and electro-elastic distortions under [PITH_FULL_IMAGE:figures/full_fig_p007_6.png]

**Figure 8.** Figure 8: Magnetization curve (relative to saturation) and [PITH_FULL_IMAGE:figures/full_fig_p009_8.png]

**Figure 9.** Figure 9: Topological character of the magnetic excitations [PITH_FULL_IMAGE:figures/full_fig_p010_9.png]

**Figure 10.** Figure 10: Magnetization curves for E ̸= 0 (sketch from actual data in Ref. [20] setting Jm = 1, Je = 0.5, α = 1 and β = 0.2). A plateau at M = 0 is always present; for E < Ec1 this is the only plateau. When E > Ec1 drives the dipolar system into a quadrumerized phase a second …

**Figure 11.** Figure 11: Electro-elastic phase diagram (scale corresponds [PITH_FULL_IMAGE:figures/full_fig_p012_11.png]

**Figure 12.** Figure 12: Schematic ground state diagram for the spin [PITH_FULL_IMAGE:figures/full_fig_p013_12.png]

**Figure 13.** Figure 13: Schematic magnetization curves obtained for the [PITH_FULL_IMAGE:figures/full_fig_p015_13.png]

**Figure 15.** Figure 15: Numerical results for the M = 0 plateau configuration in a chain of 84 sites with periodic boundary conditions (J1 = 0.5. J2 = 0.4, Je = 0.2, α = β = 0.2, in the presence of an antiferroelectric dipolar background; reprinted from Ref. [22]). Upper panels: local profi…

**Figure 16.** Figure 16: Schematic picture for the quantum plateau state at [PITH_FULL_IMAGE:figures/full_fig_p016_16.png]

**Figure 17.** Figure 17: Schematic picture for the classical ↑↑↓↓ plateau state at M = 0. The collinear spin configuration represented by black arrows gains magnetic energy by enlarging the exchange coupling of anti-parallel nearest neighbors, shortening their distance. These distortions pro…

**Figure 18.** Figure 18: Qualitative picture of a magnetic soliton connect [PITH_FULL_IMAGE:figures/full_fig_p018_18.png]

**Figure 21.** Figure 21: A magnetic field pulse, in any orientation and [PITH_FULL_IMAGE:figures/full_fig_p019_21.png]

**Figure 20.** Figure 20: Polarization curves (red solid lines, scale in the [PITH_FULL_IMAGE:figures/full_fig_p019_20.png]

**Figure 22.** Figure 22: Qualitative pictures of: (A) a classical [PITH_FULL_IMAGE:figures/full_fig_p021_22.png]

**Figure 23.** Figure 23: Schematic phase diagram in the frustration ra [PITH_FULL_IMAGE:figures/full_fig_p022_23.png]

**Figure 25.** Figure 25: Schematic description of the change in polarization [PITH_FULL_IMAGE:figures/full_fig_p022_25.png]

**Figure 26.** Figure 26: Left: total energy computed for alternating dis [PITH_FULL_IMAGE:figures/full_fig_p024_26.png]

**Figure 27.** Figure 27: Amplitude of alternating displacements (top) and [PITH_FULL_IMAGE:figures/full_fig_p024_27.png]

**Figure 28.** Figure 28: Magnetization curves of the magneto-elastic [PITH_FULL_IMAGE:figures/full_fig_p025_28.png]

**Figure 29.** Figure 29: Elementary magnetic excitation of the S = 3/2 magneto-elastic chain. Arrows here represent S z i = 3/2 spin states and ellipses represent S = 3/2 dimer singlets. Letters S, L emphasize the alternation of short, long bonds disrupted by a domain wall. From the distortio…

**Figure 30.** Figure 30: Zig-zag stripe configuration, found to be the [PITH_FULL_IMAGE:figures/full_fig_p027_30.png]

Discussion (0). Continue with ORCID to comment.

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