Polarization switching in sliding ferroelectrics: the roles of fluctuation and domain wall

Shuai Dong; Ziwen Wang

REVIEW 3 major objections 4 minor 37 references

Polarization switching in sliding ferroelectrics: the roles of fluctuation and domain wall

T0 review · 3 major / 4 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read Sliding ferroelectricity in bilayer h-BN switches by avalanche rather than by climbing a fixed intrinsic energy barrier, because off-diagonal Born effective charges couple a vertical electric field to horizontal ionic motion.

desk verdict A solid ab initio case that off-diagonal Born effective charges and C3 symmetry make h-BN sliding switching avalanche-like, with quantitative coercive fields that are static estimates rather than dynamical predictions. read the letter →

arxiv 2505.09084 v1 pith:LBK4ZZGJ submitted 2025-05-14 cond-mat.mtrl-sci cond-mat.mes-hall

Ziwen Wang , Shuai Dong This is my paper · ORCID

classification cond-mat.mtrl-scicond-mat.mes-hall

keywords slidingferroelectricityhexagonalboronnitridebilayerBorneffectivechargecoercivefieldavalancheswitchingdomainwalldensityfunctionaltheoryabinitiomoleculardynamics

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 paper seeks to explain how an out-of-plane electric field can switch the in-plane interlayer sliding that creates ferroelectric polarization in bilayer hexagonal boron nitride. Its central claim is that the switching is driven by off-diagonal Born effective charges—tensors that map a vertical field into horizontal forces on ions—so the required electric field is not an intrinsic constant but drops monotonically as sliding proceeds, giving avalanche-like reversal. The paper argues that any perturbation breaking the in-plane C3 symmetry, including thermal fluctuation, wrinkling, interlayer gap changes, or domain walls, sets the starting point and therefore controls the effective coercive field. If this holds, sliding ferroelectrics differ fundamentally from conventional ferroelectrics like BaTiO3, and their low switching fields are a consequence of symmetry, not just low energy barriers.

What carries the argument

The central object is the Born effective charge tensor $Z^*_{\kappa,ij}$, defined as the change of polarization of ion $\kappa$ along direction $i$ due to a unit displacement along $j$ (equivalently the force on the ion from an electric field). In h-BN, its off-diagonal element $Z^*_{xz}$ vanishes in the AB/BA ferroelectric states by C3 symmetry, becomes finite and peaks sharply at the P=0 saddle-point state, and its layer sum governs the perpendicular field-to-sliding coupling. The paper uses this tensor together with the intrinsic resistance force $f^r$ from the energy barrier to estimate the required critical field $E^r_z = f^r/Z^*_{xz}$ along the switching path. That ratio is the mechanism that converts a symmetric barrier into an avalanche: the denominator grows at intermediate sliding, so the field needed to continue sliding falls even as the resistance force rises.

What would settle it

Measure polarization reversal in an ultraclean, strain-free, atomically flat h-BN bilayer at low temperature under a perfectly homogeneous vertical electric field; the paper predicts zero or near-zero probability of switching unless a symmetry-breaking perturbation nucleates sliding, so observing low-field uniform switching would falsify the avalanche picture.

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Extended reading notes

Core claim

For bilayer h-BN, the paper's key finding is that the off-diagonal Born effective charge tensor element $Z^*_{xz}$, which is exactly zero in the high-symmetry AB/BA ferroelectric states due to in-plane C3 symmetry, becomes nonzero as soon as the layers slide. Because the electrostatic force on an ion is $f_i = E_j Z^*_{ij}$, this nonzero $Z^*_{xz}$ provides the perpendicular coupling that lets an out-of-plane field drive in-plane motion. The resistance force from the energy barrier rises then falls, but the required critical field $E^r_z = f^r/Z^*_{xz}$ monotonically decreases with sliding, starting from an arbitrarily high value at the symmetric state and reaching a minimum near P=0, then rising as $Z^*_{xz}$ vanishes again. This avalanche-like behavior means the measured coercive field is set by the initial symmetry-breaking perturbation, not by an intrinsic maximum. The authors also show that the large $Z^*_{xz}$ near the P=0 intermediate state makes the center of a domain wall move faster than its flanks, producing a wriggling motion that may explain the high switching speeds reported experimentally.

Load-bearing premise

The load-bearing premise is that the quasistatic force-balance estimate $E^r_z = f^r/Z^*_{xz}$, evaluated at frozen intermediate configurations starting from an arbitrary tiny sliding of 0.045 Å, represents the real switching trajectory; if inertia, dissipation, or field-dependent deformation changes that path, the monotonic decrease and coercive values would not hold.

Editorial extensions

If this is right

The coercive field of sliding ferroelectrics is not a material constant; it can be engineered by strain, wrinkles, interlayer spacing, temperature, and domain-wall density.
Any C3-breaking perturbation, including thermal fluctuations, twist, edges, or defects, can nucleate switching, so nominally identical samples may show very different switching fields depending on preparation.
The avalanche mechanism should appear in other C3-symmetric sliding ferroelectrics, including 3R-MoS2 bilayers and MoS2/WS2 heterobilayers, not just h-BN.
The leading role of the domain-wall center means switching speed is governed by the large off-diagonal Born effective charge near P=0, which could account for the observed ultrafast polarization reversal.

Reading between the lines

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

If the avalanche picture is right, measurements of switching statistics on nominally identical h-BN devices should show a distribution of coercive fields, with the tail controlled by the largest thermal fluctuation or local wrinkle; this is a testable corollary the paper does not pursue.
The C3 symmetry-selection rule suggests that a perfectly homogeneous vertical field cannot switch a defect-free, unstrained, zero-temperature h-BN bilayer at any field strength, so the paper's switching mechanism implicitly relies on a fluctuating or inhomogeneous environment.
One could extend the calculation to the dynamics of a single domain wall under an electric-field pulse to obtain a predicted wall velocity, connecting the quasistatic estimates to the experimentally measured switching times.

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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

Here's my read.

The paper deserves a serious referee. The central mechanism—nonzero off-diagonal Born effective charges couple an out-of-plane field to in-plane sliding, and C3 symmetry at the AB/BA stacks forces Z*_xz to vanish there, so switching requires a symmetry-breaking perturbation and then proceeds avalanche-like—is clearly argued and supported by the DFPT data. The comparison with BaTiO3 is nicely done: it makes the distinction between climbing-like and avalanche-like coercive behavior concrete. The AIMD result that 0.2 V/Å switches the polarization at 250 K but not at 10 K gives real qualitative support for the thermal-fluctuation picture, and the wrinkle/gap trends are a sensible first look. The authors also honestly acknowledge the two concurrent preprints, and their added value—the symmetry argument, the finite-temperature trend, and the domain-wall local Z* analysis—is real.

Now the soft spots, which are mostly about the quantitative claims. The coercive-field numbers come from f^r/Z*_xz evaluated on zero-field relaxed geometries with an arbitrarily chosen initial sliding s=0.045 Å. That is a static force balance, not a switching threshold. The monotonic decrease of E^r_z along the path is necessary for avalanche-like switching but not sufficient: inertia, damping, thermal nucleation, and field-induced changes to the path can all alter the outcome. The wrinkle reduction to about one quarter is also not self-consistent—the Z* and f^r are computed at a fixed \bar h=0.01 Å structure, but the field that actually produces that wrinkle is not the same field at which the balance is evaluated. That is a real fixed-point gap, and the stress-test note has it right. The domain-wall 'wriggling' is plausible and the static local Z* profiles support it qualitatively, but no time-dependent domain-wall velocity is computed; the authors themselves say it warrants further investigation. So the physics is likely right, but the paper's strongest quantitative form—E_c values and avalanche claim—is inferred, not demonstrated dynamically.

Citation pattern is clean: the comparison with experiment is honest (their static estimate is two orders above the measured coercive field, which is exactly the puzzle), and they don't fit parameters to experiment. Self-citations are to their own prior method papers, which is appropriate.

Who benefits: people working on sliding ferroelectrics, 2D memory, and domain-wall dynamics. I'd send it to referee with a request to separate demonstrated static coupling from inferred dynamics, ideally with a direct finite-field MD or at least a self-consistent wrinkle treatment.

Referee Report

3 major / 4 minor

Summary. This Letter uses DFPT and AIMD to study polarization switching in bilayer h-BN as a model sliding ferroelectric. The authors compute off-diagonal Born effective charges Z*_xz along the AB→SP→BA sliding path (Path II) and show that an out-of-plane electric field exerts an in-plane force proportional to Z*_xz. They find that the quasistatic balance field E^r_z = f^r/Z*_xz decreases monotonically with sliding, in contrast to conventional ferroelectrics such as BaTiO3 where it peaks mid-path. They further analyze how a field-induced layer wrinkle, the interlayer gap, temperature, and the presence of domain walls modify Z*_xz, f^r, and hence E^r_z, concluding that any perturbation breaking the in-plane C3 symmetry assists an avalanche-like switching process. The paper reports AIMD showing polarization switching at 250 K under E_z = 0.2 V/Å and static estimates predicting a much larger zero-temperature coercive field. Domain-wall calculations show enhanced off-diagonal Z* near the wall center, which the authors propose leads to a wriggling motion of domain walls.

Significance. If the avalanche-like switching picture is correct, it would explain why experimental coercive fields in sliding ferroelectrics are far below the naive barrier-derived estimates and why switching can be ultrafast. The identification of off-diagonal Born effective charges as the coupling mechanism is a valuable step and is supported by independent DFPT calculations. The paper's strengths include a clean benchmark against BaTiO3, explicit consideration of wrinkle and gap dependences, AIMD support for room-temperature switching at low fields, and an open disclosure of two overlapping preprints. However, the dynamical conclusions (avalanche and domain-wall wriggling) are inferred from static calculations and require either additional simulation or more careful wording.

major comments (3)

[Eq. (2) and Fig. 1(f)] The coercive field curve E^r_z = f^r/Z*_xz is a quasistatic force balance evaluated at zero-field relaxed geometries along Path II, starting from an arbitrarily chosen initial sliding s = 0.045 Å. This calculation demonstrates that the static balance field decreases with sliding, but it does not by itself demonstrate avalanche-like switching dynamics, which requires a time-dependent or finite-field instability. The paper contains no simulation of the switching trajectory under a sustained field; the AIMD in Fig. 3(b) shows switching at 250 K with E_z = 0.2 V/Å but is not analyzed in terms of the force-balance curve. Please either add a self-consistent finite-field calculation or a direct time-dependent simulation (e.g., AIMD with the field on from the start) to support the avalanche claim, or revise the wording throughout (abstract, Fig. 1(f)) to 'the static critical field decreases monotonically with sliding' rather than 'avalanche-like switching dynamics.'
[Fig. 2(c)-(d)] The wrinkle reduction of E^r_z is not self-consistent. The wrinkle amplitude \bar h is the equilibrium response to E_z (Fig. 2c, linear growth), but the reported E^r_z = 0.61 V/Å at \bar h = 0.01 Å is obtained by inserting the \bar h = 0.01 Å structure into the zero-field formula E^r_z = f^r/Z*_xz with s = 0.045 Å fixed. The paper does not verify that E_z = 0.61 V/Å actually produces \bar h = 0.01 Å in the staggered geometry, nor that the finite field leaves Z*_xz and f^r unchanged. If the field needed for \bar h = 0.01 Å differs from 0.61 V/Å, the claimed reduction to about one quarter is not a fixed point of the coupled problem. Please perform a self-consistent calculation (relax under a fixed E_z and recompute Z* and f^r at that geometry) or explicitly state the E_z value corresponding to \bar h = 0.01 Å and check the consistency.
[Paragraph beginning 'Finally, it is worth to investigate...' and Fig. 4] The 'wriggling motion' of domain walls is inferred from the static spatial profile of Z*_xz and Z*_yz in a relaxed domain-wall supercell. No dynamical simulation of the domain wall under E_z is reported, and the text itself states this 'warranting further investigation.' As written, the abstract and concluding sentence present the wriggling as a result ('results in a wriggling motion of domain walls'), which overstates the evidence. Please either add a minimal time-dependent simulation (e.g., MD of the DW under a field) or label the wriggling explicitly as a qualitative prediction, and adjust the abstract accordingly.

minor comments (4)

[Reference [28]] The Supplemental Material reference [28] contains a corrupted citation string 'including Refs. [13, 24? ? ? ? ? ? ? ? ?]'; this must be repaired before publication.
[Fig. 1(f) and text near 'Beginning from a staggered stacking mode'] The choice of initial sliding s = 0.045 Å is arbitrary; please justify it from the thermal fluctuation amplitude at 250 K or provide a short sensitivity study over s to show that the monotonic decrease of E^r_z is robust.
[Fig. 3(c)] Fig. 3(c) reports a temperature-dependent coercive field estimated from AIMD, but the main text does not describe the AIMD protocol (e.g., how E_z is ramped, what polarization threshold defines switching). Please specify the protocol in the main text or refer the reader to a detailed SM section.
[Fig. 2(d) and text] The quantity \bar h is used in Fig. 2(d) but defined only in the caption; please define it in the body text before the discussion of the wrinkle effect.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the switching mechanism follows from independently computed Born effective charges and energy barriers, not from fitted or self-cited inputs.

full rationale

I find no circular step. The central relation E^r_z = f^r / Z*_xz is an algebraic definition of the field needed to balance the computed intrinsic resistance, but the physical content is the ab initio evaluation of Z*_xz and f^r along the switching path. The off-diagonal Born effective charges are obtained by DFPT at frozen intermediate geometries, not imposed to produce the conclusion. The monotonically decreasing E^r_z profile and the 'avalanche-like' interpretation follow from those computed numbers. The initial sliding s = 0.045 Å and the wrinkle amplitude bar h = 0.01 Å are hand-set structural inputs that affect quantitative values, but they are not fitted to the experimental coercive field; the comparison with the measured ~0.03 V/Å is presented as a physical discrepancy motivating wrinkle, gap, and temperature effects rather than as a fitting target. The d- and bar-h-dependent scans and the AIMD simulations are additional first-principles calculations. The two recent preprints acknowledged in the Note are not used to justify the present derivation, and the domain-wall 'wriggling' is explicitly left as 'warranting further investigation'. The self-citations are background or previously established structural statements and are not load-bearing. The static force-balance assumption and the non-self-consistent treatment of field-induced wrinkling are modeling limitations, but they are not circular reductions of the result to its inputs.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The central switching mechanism rests on the standard Born effective charge formalism and on a quasistatic force-balance estimate, not on fitted input. The quantitative coercive fields depend on three hand-set structural parameters (initial sliding s, wrinkle amplitude hbar, interlayer gap d) listed as free parameters. No new particles, forces, or conserved quantities are introduced.

free parameters (3)

initial sliding displacement s = 0.045 Å
The AB state has exact C3 symmetry and Z*_xz=0, so the switching field is undefined without a perturbation. The chosen value is arbitrary; the resulting coercive field depends on it.
wrinkle amplitude hbar = 0.01 Å
Selected from the scan in Fig. 2(d) as the amplitude at which Z*_xz peaks and E^r_z is minimized (0.61 V/Å). No self-consistency check is given that the applied E_z generating this wrinkle is below the quoted E^r_z.
interlayer gap d = 3.62 Å
Optimal value from the scan in Fig. 2(e), about 0.13 Å above the equilibrium gap, giving the minimum E^r_z of 1.90 V/Å.

assumptions (4)

domain assumption The force on an ion in a periodic insulator under an electric field is f^E_κ,i = Σ_j E_j Z*_κ,ij (Eq. 2), with Z* from DFPT.
Standard Born effective charge formalism; the paper uses it to convert computed Z* and resistance force into a required electric field.
domain assumption Switching occurs quasistatically when the electrostatic force overcomes the intrinsic resistance f^r = -∂H/∂u; dynamics are not integrated for the single-domain coercive field.
The E^r_z curves in Fig. 1(f) are derived from force balance, treating each intermediate geometry as a fixed configuration; no kinetic or thermal activation term is included in the single-domain estimate.
standard math The vertical electric field preserves the in-plane C3 symmetry, so Z*_xz=0 exactly at the AB and BA stacks.
Symmetry argument in the text: a field along z does not select among the three equivalent sliding directions.
domain assumption DFT/DFPT/AIMD with the chosen functional, vdW correction, and supercell sizes describe h-BN polarization and switching.
Numerical reliability depends on methods details deferred to the Supplemental Material, which was not available for review.

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Pith. "Pith review of Polarization switching in sliding ferroelectrics: the roles of fluctuation and domain wall." pith.science (2026). https://pith.science/paper/LBK4ZZGJ

@misc{pith2026250509084,
  author       = {Pith},
  title        = {Pith review of: Polarization switching in sliding ferroelectrics: the roles of fluctuation and domain wall},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/LBK4ZZGJ}},
  note         = {Machine review of arXiv:2505.09084}
}

abstract

Sliding ferroelectricity is highly attractive for its low energy barriers and fatigue resistance. As the origin of these exotic properties, its unconventional switching dynamics remains poorly understood: how an electric field drives a perpendicular sliding? Taking $h$-BN bilayer as a model system, its switching dynamics is studied using \textit{ab initio} calculations. The off-diagonal Born effective charge leads to the perpendicular relationship between the electric field and ionic movements. Interestingly, the rules of intrinsic coercive field are distinct between $h$-BN bilayer and conventional ferroelectrics. For $h$-BN bilayer, any perturbation breaking the in-plane symmetry plays a key role to assist the avalanche-like switching dynamics. Moreover, the exotic large off-diagonal Born effective charge near the $P=0$ intermediate state results in a wriggling motion of domain walls in $h$-BN bilayer. Our results reveal the key factors in the ferroelectric switching of sliding ferroelectrics at room temperature.

Figures

Figures reproduced from arXiv: 2505.09084 by the authors.

**Figure 2.** FIG. 2. (a) Top view of the tiny sliding [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

**Figure 3.** (a), at 10 K without external fields, the AB stacking mode is stable, with a ferroelectric Pz ∼ 0.82 pC/m. By increasing temperature to 250 K, the thermal fluctuation is enhanced while an average Pz ∼ 0.78 pC/m is maintained. When an out-of-plane electric field Ez = 0.2 V/˚A is applied at 250 K, the polarization can be easily switched within a short time, as shown in [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

Figures from the paper (1 more)

**Figure 4.** Figure 4: FIG. 4. (a) Sketch of domain walls between two ferroelectric [PITH_FULL_IMAGE:figures/full_fig_p005_4.png]

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Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.

[1] [1]

J. F. Scott, Applications of modern ferroelectrics, Science 315, 954 (2007)

2007

[2] [2]

K. Rabe, C. H. Ahn, and J.-M. Triscone, eds.,Physics of Ferroelectrics: A Modern Perspective(Springer, 2007)

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