{"id":"4926f09f-b2af-424c-b844-bff573dd8d00","arxiv_id":"2501.05219","paper_version":3,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"Internal electric fields in ferroelectric/non-ferroelectric bilayers renormalize the Landau coefficients so that both layers acquire nearly equal remanent polarization and coercive fields, enabling 'proximity switching'.","lead":"A new thermodynamic model explains how a 'frozen' polar material like AlN can switch ferroelectric polarization when stacked with a switchable ferroelectric like AlScN. The mechanism is a self-consistent internal electric field that reshapes the energy barrier, and the theory predicts when the entire stack switches or stays suppressed.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The internal-field barrier-renormalization mechanism is internally consistent, but its quantitative connection to experiment rests on defect parameters fitted to the same data and on an extrapolation from 20 nm to 200 nm, so the central claim is not yet independently validated.","rationale":"The paper develops a coherent Landau-Ginzburg theory in which the internal depolarization field couples the layers, renormalizes their Landau coefficients, and equalizes their effective coercive fields. The algebra in Appendix A is internally consistent, and the predicted qualitative regimes of proximity switching and suppression follow from standard electrostatics. The main risk is not in the analytical derivation but in its quantitative application to the experimental systems. The reader identified the single-domain assumption and the fitted defect parameters as the weakest point; I agree. The paper is honest about these limitations, explicitly stating that the analytical conclusion fails when domain kinetics are considered and that the defect parameters are convenient fitting parameters. Nevertheless, because the experimentally observed switching in thick layers is reproduced only with defect parameters fitted to the same data and with FEM extrapolated from thin cells, the central claim that the internal-field mechanism is the operative cause of proximity ferroelectricity is not yet independently confirmed. An out-of-sample prediction with fixed defect parameters would directly settle whether the quantitative model has predictive power. Since the reader already recommended a conditional verdict and my analysis does not call for a different outcome, the verdict remains unchanged.","tokens_in":34813,"tokens_out":12244,"duration_ms":121283,"concrete_test":"Using the defect parameters fitted in Fig. 5 (n_d = 7.8–8.2 × 10^25 m^-3, q_d ≈ 2.3 e, l_d ≈ 1.5 nm, with the 5.1% asymmetry between layers), predict without further fitting the coercive field and remanent polarization of (i) a bilayer with thickness ratio h2/h1 = 3 or 0.33 and (ii) a symmetric 100 nm AlBN / 500 nm AlN / 100 nm AlBN trilayer, then measure these quantities in the same experimental system. If the predicted Ec deviates from experiment by more than about 20%, the defect model is overfit and the internal-field mechanism alone is not validated as the quantitative explanation of proximity ferroelectricity.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central mechanism of proximity ferroelectricity is the self-consistent internal field of Eq. (5) renormalizing the double-well potential via Eq. (6), leading to equal effective coercive fields in both layers. This derivation assumes homogeneous single-domain polarization with natural boundary conditions, uniform background permittivity, and perfect electrodes with no free-carrier screening. For the experimental 200 nm layers, however, the paper itself states in Section 4 that the single-domain conclusion 'becomes invalid in the case when the domain kinetics is considered,' and the FEM calculations that reproduce the observed switching require randomly distributed bulk charges whose density, charge, and separation are fitted to the same experiment (Fig. 5). The FEM curves for h2 > 20 nm are extrapolations from computationally feasible cells of 50–100 nm at most. Thus the quantitative claim that proximity switching is caused by the internal-field barrier renormalization is not independently established: the observed low coercive fields could be dominated by the fitted defect-induced nucleation, with the internal-field mechanism contributing little in thick, multi-domain samples. The qualitative phase diagrams are plausible and self-consistent, but the load-bearing connection between the mechanism and the experimental demonstrations remains conditional on validating the defect model and the thick-layer extrapolation.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper develops a Landau-Ginzburg-Devonshire theory of multilayer stacks containing ferroelectric, paraelectric, dielectric, and non-switchable polar layers, with emphasis on bilayers. The central result is that the self-consistent internal depolarization field (Eq. 5) renormalizes the single-layer double-well potentials (Eq. 6) so that the effective coercive fields in both layers become equal, producing collective 'proximity switching' or collective 'proximity suppression' depending on layer thicknesses and LGD parameters. The authors present dimensionless phase diagrams, identify regimes for FE/PE, FE/W-FE, FE/H-FE, and FE/N-FE stacks, and apply the theory to AlScN/AlN and ZnMgO/ZnO bilayers. Charged defects are introduced in FEM calculations as nucleation centers to further reduce coercive fields to experimentally observed values.","tokens_in":35108,"tokens_out":4837,"duration_ms":51717,"significance":"If the central mechanism is correct, the paper offers a useful general framework for proximity ferroelectricity and makes falsifiable predictions, including induced ferroelectricity in paraelectric and dielectric layers. The analytical derivation is explicit and internally consistent within the stated single-domain approximation, and the paper is commendably candid about several limitations. The dimensionless phase diagrams and the identification of the internal-field barrier-renormalization mechanism are valuable. However, the quantitative connection to experiment is not yet independently established: the charged-defect parameters are fitted to the same experimental data they are used to explain, and the finite-element thickness dependence is extrapolated from roughly 20 nm cells to the 200-500 nm experimental layers.","major_comments":[{"comment":"The quantitative agreement with experiment is not an independent validation. The single-domain bilayer coercive field in Fig. 4(c) is about 15 MV/cm, well above the breakdown field, and the experimentally observed value of about 6.5 MV/cm is obtained only after introducing charged-defect parameters (n_d, q_d, l_d) that the text states are varied 'in trying to match experiment results [13]' and later calls 'convenient fitting parameters.' Fitting the same data and then comparing with those data demonstrates consistency, not predictive validation; the paper should either validate the defect model on independent data or explicitly temper the claim that the theory quantitatively describes the experiments.","section":"Section 4, Figs. 4(c) and 5(b)"},{"comment":"The thickness dependence used to explain the experimental coercive fields and remanent polarization in Ref. [13] is an uncontrolled extrapolation. The text says FEM for computational cells thicker than 50-100 nm was not possible and that the curves for h2 > 20 nm are extrapolations based on the assumption that behavior depends only on the h1/h2 ratio. The experimental layers are 200-500 nm thick, so the predicted critical thickness h_cr and the comparison with the 500-nm-layer data in Ref. [13] rest on this unverified scaling assumption. A scaling argument, larger-cell computations, or an explicit sensitivity check is needed for this load-bearing comparison.","section":"Section 4, Figs. 5(c) and 5(d)"},{"comment":"The paper states that the single-domain conclusion 'becomes invalid in the case when the domain kinetics is considered.' Yet the experimental switching is described and simulated as defect-nucleated domain formation and intergrowth (Fig. 6). This means the central claim that the internal-field barrier renormalization is the cause of the observed low coercive fields is not isolated: in thick multi-domain samples the measured coercivity could be dominated by defect-induced nucleation, with the renormalized-barrier mechanism contributing only marginally. The authors should quantify the relative contributions, for example by comparing defect-only simulations with simulations combining defects and the internal-field renormalization.","section":"Section 4, paragraph beginning 'To summarize the section'"},{"comment":"The LGD parameter extraction involves assumptions that materially affect the quantitative coercive-field values used in the paper: identical beta and gamma are assumed for Al0.73Sc0.27N and AlN, gamma is set to zero for ZnO, and the ZnMgO parameters are fitted only near zero field. These assumptions are disclosed, but the paper does not provide a sensitivity analysis. Since the quantitative claims about threefold coercive-field reduction rely on the resulting thermodynamic coercive fields (e.g., about 26 MV/cm for AlN and 25 MV/cm for ZnO), the robustness of these magnitudes to the parameter-extraction assumptions should be examined.","section":"Appendix C and Appendix D; Tables II and III"}],"minor_comments":[{"comment":"The notation 'Alx-1ScxN' appears in the abstract, title context, and several places in the text; this should be 'Al1-xScxN'.","section":"Throughout"},{"comment":"The composition label 'Al0.83Sc0.27N' appears in the text and figure captions, which is inconsistent with 'Al0.73Sc0.27N' used elsewhere; please check the stoichiometry labeling throughout.","section":"Section 4 and Fig. 5"},{"comment":"The phrase 'back-envelope consideration' should read 'back-of-the-envelope consideration.'","section":"Appendix A"},{"comment":"The sentence 'we choice it equal to 7 MV/cm' contains a typo and should read 'we choose it equal to 7 MV/cm.'","section":"Section 4"},{"comment":"The reference list contains several duplicated entries in slightly different formats (e.g., Refs. 28/43, 29/44, 32/46, 39/49); these should be consolidated.","section":"References"},{"comment":"The fraction for the external field contribution would be clearer with explicit parentheses: U divided by [epsilon_b^{(i)} sum_k (h_k / epsilon_b^{(k)})], rather than the current typeset form.","section":"Eq. (5a)"}],"recommendation":"major_revision","confidential_remarks":"The paper is unusually candid about its own limitations, and the analytical mechanism is internally consistent. The main risk is overclaiming quantitative experimental validation when the defect parameters are fitted to the same data and the thick-layer behavior is extrapolated. I would support publication after the authors either strengthen the independent validation or explicitly moderate the quantitative claims to consistency checks rather than confirmation."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Dear X,\n\nThe paper gives a general Landau-Ginzburg treatment of proximity ferroelectricity: the internal depolarization field that couples layers is shown to renormalize the LGD coefficients so the effective coercive fields of the layers equalize. That mechanism is derived from the free energy, not assumed, and it leads to clean analytical expressions (Eq. 6) and phase diagrams. The qualitative predictions—collective switching or suppression depending on thickness ratio, and induced ferroelectricity in paraelectric/dielectric layers—are plausible and follow directly from the electrostatic coupling. This is a useful contribution to the phenomenology of wurtzite ferroelectric heterostructures.\n\nThe main soft spot is the quantitative link to experiment. The single-domain theory gives coercive fields (15 MV/cm for AlScN/AlN) still above breakdown; the match to the observed ~6.5 MV/cm comes from adding charged defects with parameters (density, charge, separation) fitted to the same experiment. The paper says so explicitly, and the FEM is only practical for 20 nm cells, so the 200 nm curves are extrapolations. In thick, multi-domain samples the observed switching may be dominated by defect-assisted nucleation rather than by the internal-field barrier renormalization. So the central qualitative claim is sound, but the quantitative demonstration is not independent.\n\nA couple of minor points: the LGD parameters for AlScN and AlN are inferred using the same beta and gamma for both compounds, a rough approximation, and the paper assumes uniform background permittivity. These are acceptable for a first theory but worth flagging.\n\nOverall, this is a serious phenomenological theory that deserves referee time. I'd send it to review, but I'd ask the authors to state more carefully the limits of the quantitative comparison and to separate the derived mechanism from the fitted defect contribution. The qualitative predictions for FE/PE and FE/dielectric stacks are likely right and should motivate experiments.","headline":"A useful LGD framework for proximity ferroelectricity, but the quantitative match to experiments rests on fitted defect parameters and a thick-layer extrapolation.","tokens_in":35639,"tokens_out":2854,"would_cite":true,"duration_ms":28538,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Proximity ferroelectricity works by an internal field that equalizes the effective coercive fields of the layers in a stack, so that layers switch together or stay frozen together.","keywords":["proximity ferroelectricity","Landau-Ginzburg-Devonshire theory","coercive field reduction","depolarization field","ferroelectric multilayers","AlScN/AlN","ZnMgO/ZnO","charged defect nucleation"],"falsifier":"Grow an atomically abrupt AlN/Al$_{0.73}$Sc$_{0.27}$N bilayer with independently measurable layer polarizations and measure whether the AlN layer switches below the breakdown field; if the two layers do not show nearly equal effective coercive fields, the renormalization identity fails. A more direct test of the unique prediction is to place a high-permittivity paraelectric layer such as SrTiO$_3$ thinner than a ferroelectric layer and check whether the paraelectric layer develops a ferroelectric hysteresis loop for thickness ratio $h_2/h_1 < 1$.","tokens_in":48,"feed_emoji":"⚡","tokens_out":5122,"duration_ms":111856,"temperature":0.7,"pith_summary":"The paper claims that proximity ferroelectricity—switching a normally unswitchable polar material by stacking it against a switchable ferroelectric—has a purely electrostatic mechanism: an internal field set by the layer polarizations and their thickness ratio renormalizes each layer's double-well potential so that their effective coercive fields become equal. When this works, both layers switch together, which the authors call proximity switching; when the non-ferroelectric layer is too thick or too polar, both layers are suppressed, which they call proximity suppression. The theory is applied to AlScN/AlN and ZnMgO/ZnO bilayers, explaining how AlN and ZnO, whose intrinsic coercive fields exceed their dielectric breakdown fields, can be switched with practical fields. The paper further predicts that paraelectric and dielectric layers can be made ferroelectric by proximity, opening a large class of switchable ferroelectrics made from pristine, undoped materials.","feed_headline":"A self-consistent internal field thaws frozen ferroelectrics","feed_subtitle":"AlN and ZnO, unswitchable alone, switch together with a ferroelectric neighbor as theory matches experiments.","key_machinery":"The engine is the self-consistent internal field expression Eq. (5), $$$E_z^{{(i)}}$ = -\\frac{$P_z^{{(i)}}$-\\bar{D}}{\\varepsilon_0\\$varepsilon_b^{{(i)}}$} + \\frac{U}{\\$varepsilon_b^{{(i)}}$\\sum_k h_k/\\$varepsilon_b^{{(k)}}$},$$ which combines a depolarization contribution with the splitting of the applied field, where $\\bar{D}$ is the thickness-averaged displacement. Substituting this field into the Landau-Ginzburg-Devonshire equations renormalizes the coefficients $\\alpha_i, \\beta_i, \\gamma_i$ into $\\alpha_i^{(R)}, \\beta_i^{(R)}, \\gamma_i^{(R)}$ through depolarization factors $\\aleph_1$ and $\\aleph_2$ defined in Eq. (7). The load-bearing identity is that, for $|\\alpha_i|/\\aleph_i \\ll 1$, the ratios of renormalized coefficients satisfy $\\alpha_1^{(R)}/\\alpha_2^{(R)} \\approx \\beta_1^{(R)}/\\beta_2^{(R)} \\approx \\gamma_1^{(R)}/\\gamma_2^{(R)} \\approx \\aleph_2/\\aleph_1 \\approx h_1/h_2$, which makes the effective coercive fields $E_{ca}^{(i)} = E_c^{(i)}/\\eta_i^{(R)}$ equal across the layers, so the stack switches collectively.","core_discovery":"The central claim is that proximity ferroelectricity is driven by a self-consistent internal electric field, not by chemical doping or short-range interface bonding. The depolarization field arising from the polarization mismatch between layers, combined with the splitting of the applied field, renormalizes the Landau-Ginzburg-Devonshire coefficients of each layer, effectively lowering the switching barrier of the hard layer. For common material parameters the renormalized coefficients satisfy ratio identities that force the effective coercive fields of the two layers to be approximately equal, $E_{ca}^{(1)} \\approx E_{ca}^{(2)}$, and the remanent polarizations to be nearly identical. Consequently, either both layers undergo simultaneous ferroelectric switching with the same coercive field and similar loops, or both remain non-switchable. Applying the theory to Al$_{0.73}$Sc$_{0.27}$N/AlN and Zn$_{0.66}$Mg$_{0.34}$O/ZnO bilayers, the authors show that the thermodynamic coercive field of the hard layer is reduced, and that including random charged defects as nucleation centers further lowers the coercive field to values below the breakdown field, matching the experimentally observed proximity switching.","pith_inferences":["A direct testable extension is that a high-permittivity paraelectric like SrTiO$_3$ or rutile TiO$_2$ stacked on a thicker ferroelectric should show induced ferroelectric hysteresis for $h_2/h_1 < 1$; absence of such a loop would challenge the mechanism.","The paper's own caveat that domain kinetics dominate in thick layers suggests that the quantitative single-domain coercive fields are upper bounds, and quantitative predictions for thick experimental stacks rely on defect parameters.","The equal-effective-coercive-field identity, if general, implies that proximity engineering could tune coercive fields continuously by choosing thickness ratios, potentially replacing chemical doping as a doping-free design route for Si-compatible ferroelectric memories.","The same thermodynamic mechanism should apply to other ferroelectric/paraelectric and ferroelectric/dielectric material families beyond wurtzites, including fluorite-based stacks such as ZrO$_2$/HfZrO$_2$, where the depolarization-field coupling would collectively switch nominally non-ferroelectric layers."],"forward_implications":["Multilayers pairing a switchable ferroelectric with a non-switchable polar material such as AlN or ZnO can switch below the dielectric breakdown field, effectively thawing frozen ferroelectrics without bulk doping.","Paraelectric and dielectric layers thinner than or comparable to the ferroelectric layer can be induced to switch ferroeletrically, with the entire stack undergoing collective polarization reversal.","Thick paraelectric or hard polar layers can suppress ferroelectric switching in the thinner ferroelectric layer, defining a proximity suppression regime that must be avoided in device design.","Random charged defects in the bulk act as nucleation centers that reduce the coercive field further, with the model reproducing the observed AlN/AlScN switching when defect parameters are fitted to experiment.","Because the effective coercive fields of the layers are equalized, the individual layer hysteresis loops have the same coercive field and nearly equal remanent polarizations regardless of the thickness ratio."],"supporting_citations":[{"why":"Supplies the experimental observation of proximity ferroelectricity in wurtzite heterostructures that this theory is built to explain and quantitatively match.","marker":"[13]"},{"why":"Provides the Landau-Ginzburg-Devonshire energy density for ferroelectric wurtzite Al$_{1-x}$Sc$_x$N used as the starting free-energy form.","marker":"[14]"},{"why":"Provides the measured spontaneous polarization of Al$_{0.73}$Sc$_{0.27}$N used to determine the LGD coefficients in Appendix C.","marker":"[28]"},{"why":"Provides the measured dielectric permittivity of AlScN used to fix the LGD parameters of the switchable layer.","marker":"[30]"},{"why":"Describes the procedure for determining LGD coefficients of AlScN from experimental polarization and permittivity, which the paper follows for AlN and AlScN.","marker":"[31]"},{"why":"Provides the experimental hysteresis loops of Zn$_{1-x}$Mg$_x$O used to fit the LGD coefficients for the ZnMgO/ZnO bilayer calculations.","marker":"[49]"},{"why":"Supplies the expression for the average displacement of a multilayer that enters the internal-field formula Eq. (5b).","marker":"[20]"},{"why":"Establishes the depolarization-field formalism used in the internal electric field expression that drives the renormalization.","marker":"[21]"}],"fun_headline_variants":["Proximity ferroelectricity: internal field unlocks frozen materials","How a neighboring ferroelectric makes AlN switchable","Self-consistent field explains proximity ferroelectricity","Frozen ferroelectrics thaw via internal field","Proximity switching: theory matches experiments"],"cache_read_input_tokens":37760,"weakest_assumption_plain":"The analytical theory assumes each layer is a homogeneous single domain with natural boundary conditions and uses the simplified uniform-background-permittivity field expression of Eq. (5), and the paper itself notes this description breaks down when domain kinetics dominate, with quantitative agreement for AlScN/AlN achieved only by fitting defect parameters to the same experiment.","fun_headline_variants_meta":{"raw":{"variants":["Proximity ferroelectricity: internal field unlocks frozen materials","How a neighboring ferroelectric makes AlN switchable","Self-consistent field explains proximity ferroelectricity","Frozen ferroelectrics thaw via internal field","Proximity switching: theory matches experiments"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001099,"raw_usage":{"total_tokens":4686,"prompt_tokens":1146,"completion_tokens":3540,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":762,"completion_tokens_details":{"reasoning_tokens":3463}},"tokens_in":762,"tokens_out":3540,"duration_ms":22633,"temperature":1.0,"reasoning_tokens":3463,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-10T21:13:58.839877+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Grow an atomically abrupt AlN/Al$_{0.73}$Sc$_{0.27}$N bilayer with independently measurable layer polarizations and measure whether the AlN layer switches below the breakdown field; if the two layers do not show nearly equal effective coercive fields, the renormalization identity fails. A more direct test of the unique prediction is to place a high-permittivity paraelectric layer such as SrTiO$_3$ thinner than a ferroelectric layer and check whether the paraelectric layer develops a ferroelectric hysteresis loop for thickness ratio $h_2/h_1 < 1$.","supporting_citations":[{"cited_title":"Ferri, S","cited_arxiv_id":null,"evidence_quote":"Provides the experimental hysteresis loops of Zn$_{1-x}$Mg$_x$O used to fit the LGD coefficients for the ZnMgO/ZnO bilayer calculations."},{"cited_title":"Polar Properties and Hysteresis Loops in Multilayered Thin Films Ferroelectric/Virtual Ferroelectric","cited_arxiv_id":"1406.7548","evidence_quote":"Supplies the expression for the average displacement of a multilayer that enters the internal-field formula Eq. (5b)."},{"cited_title":"Kretschmer and K","cited_arxiv_id":null,"evidence_quote":"Establishes the depolarization-field formalism used in the internal electric field expression that drives the renormalization."}],"review_version":1}