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Observation of electromagnons in a monolayer multiferroic

T0 review · 4 major / 5 minor · reviewed 2026-08-04 · deepseek-v4-flash

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Pith's one-line read Inelastic tunneling maps reveal electromagnons in monolayer NiI2.

desk verdict First real-space IETS maps of purported electromagnons in monolayer NiI2 — promising, but the theoretical fingerprint depends on unspecified parameters. read the letter →

arxiv 2510.08253 v2 pith:SMI2VXCH submitted 2025-10-09 cond-mat.mtrl-sci cond-mat.mes-hall

Mohammad Amini , Tiago V. C. Antão , Liwei Jing , Ziying Wang , Antti Karjasilta , Robert Drost , Shawulienu Kezilebieke , Jose L. Lado
show 2 more authors
Adolfo O. Fumega Peter Liljeroth
This is my paper · ORCID
classification cond-mat.mtrl-scicond-mat.mes-hall PACS 75.85.+t68.37.Ef
keywords electromagnonsmultiferroicsNiI2scanningtunnelingmicroscopyinelasticspectroscopyspin-spiralordermagnetoelectriccouplingtwo-dimensionalmaterials
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 reports the first atomic-scale observation of electromagnons—collective excitations that oscillate in both spin and electric polarization—in a single layer of the multiferroic NiI2. Using low-temperature scanning tunneling microscopy, the authors find sharp inelastic tunneling features below 5 meV that appear only below the multiferroic transition temperature, and spatially resolved maps at those energies show a stripe modulation matching the spin-spiral periodicity. Comparing with spin-model and first-principles calculations, they identify these modes as electromagnons and argue that the stripe-modulated local spectral function is a distinctive real-space fingerprint of the coupled spin-polarization dynamics. If correct, this gives a general method to probe electromagnons at the atomic scale in two-dimensional multiferroics and connects directly to efforts toward electrically tunable, low-energy spintronics.

What carries the argument

The central object is the electromagnon, a collective mode of the spin-spiral multiferroic in which spin fluctuations are coupled to electric-polarization fluctuations through the inverse Dzyaloshinskii-Moriya interaction. The crucial theoretical step is adding a polarization-fluctuation energy cost, H_pol = sum_i P_i^2/(2 eps0 chi_e), to the J1-J3 Heisenberg spin Hamiltonian and decoupling it in a mean-field (Tyablikov-like) approximation. This term opens a gap in the magnon spectrum and produces a spatial modulation in the local spectral function with half the spin-spiral periodicity—the fingerprint the experiment targets. The calculations use linear spin-wave theory on a rotated Holstein-

What would settle it

Compute the low-energy spin-wave spectrum and spatial dI/dV maps for the same J1-J3 model with the polarization term omitted: if the stripe modulation and the magnon gap persist, they cannot be electromagnon fingerprints. Alternatively, measure the same IETS maps in a NiI2 monolayer on a substrate that strongly screens the electric polarization; a suppressed or shifted stripe modulation would confirm the magnetoelectric origin, while an unchanged stripe would refute it.

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Extended reading notes

Core claim

The paper's central claim is that the low-energy inelastic excitations observed in monolayer NiI2 by scanning tunneling microscopy are electromagnons, not ordinary magnons or phonons. The evidence is twofold: spectroscopically, the in-gap features below 5 meV appear and sharpen as the system is cooled through the multiferroic transition, and their energy positions match the inflection points of a calculated density of states that sums electromagnon and phonon contributions; spatially, dI/dV maps at electromagnon energies show a stripe modulation with the periodicity of the spin spiral, which the authors' theory says arises from the coupling between magnetic fluctuations and the emergent elec

Load-bearing premise

The load-bearing premise is that the predicted stripe-modulated spectral function follows from adding a polarization-fluctuation energy cost to the spin Hamiltonian and decoupling it in mean field, without independently fixing the strength of that term (the paper gives no numerical values for lambda or chi_e), so the fingerprint could in principle be an artifact of the model.

Editorial extensions

If this is right

  • Electromagnons can be detected and spatially resolved with STM-based inelastic tunneling spectroscopy, not only with terahertz optical probes.
  • The stripe-modulated local spectral function provides a real-space fingerprint for identifying electromagnons in other spin-spiral multiferroics.
  • The polarization-fluctuation energy term that produces the modulation also stabilizes long-range magnetic order in two dimensions, offering a concrete mechanism to evade the Mermin-Wagner restriction.
  • Atomic-scale access to electromagnon modes makes it possible to study their interaction with defects, domains, and heterostructure interfaces in a way bulk probes cannot.
  • The energy scale set by the multiferroic transition (Tc ~ 10.4 K) and the extracted exchange couplings tie the observed modes to the same physics that governs the static multiferroic order.

Reading between the lines

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

  • Editorial inference: the same technique should work in other van der Waals multiferroics and in twisted bilayers, where the spin-spiral periodicity can be tuned; the stripe period in the IETS maps should track the magnetic q-vector if the electromagnon assignment is correct.
  • Editorial inference: because the modulation is attributed to the polarization-fluctuation term, changing the dielectric environment (e.g., by substrate choice or capping layers) should shift the gap and modulation amplitude—a controlled experiment that would test the mechanism independently.
  • Editorial inference: if the electromagnon fingerprint is robust, then the strong visibility of the stripe at biases above the electromagnon energy range implies a large electron-electromagnon coupling relative to electron-phonon coupling; quantifying that coupling would be a natural next step.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 5 minor

Summary. The manuscript reports low-temperature STM/IETS measurements on monolayer NiI2 grown on HOPG, combined with DFT, Monte Carlo, and spin-wave calculations. The authors identify low-energy in-gap IETS features as electromagnons and claim that spatially resolved dI/dV maps at these energies reveal a stripe-like modulation that matches theoretical predictions for the electromagnon local spectral function. Temperature-dependent STM imaging is used to locate the multiferroic transition at Tc≈10.4 K and to estimate the exchange parameters J1=-1.25 meV and J3=0.42 meV. The central claim is that this constitutes 'unambiguous evidence of the internal structure of electromagnons.'

Significance. If the identification holds, this would be the first atomic-scale real-space visualization of electromagnons and would establish a potentially general STM-based methodology for probing magnetoelectric collective modes in van der Waals multiferroics. The paper combines a substantial experimental dataset (temperature-dependent imaging, spectroscopic mapping, IETS histograms) with a multi-level theoretical framework (DFT phonons, spin model, Monte Carlo, HPBdG spin waves). The experimental observations themselves are interesting and likely reproducible. However, the strength of the claim depends on the theoretical fingerprint being derived from independently fixed physics, and this is currently not fully established.

major comments (4)
  1. [Methods, Eqs. (6)–(8)] The spatial modulation that constitutes the paper's central electromagnon fingerprint is generated by the polarization-fluctuation term H_pol = Σ P_i^2/(2ε0χ_e), treated by the mean-field decoupling of Eq. (6). The coupling λ and the susceptibility χ_e are never assigned numerical values anywhere in the text or Methods. The paper explicitly states that this term has a negligible effect on the ground-state spin configuration, so it is not constrained by the measured q-vector or Tc. Consequently, the amplitude and even the existence of the modulation in the HPBdG spectrum depend on parameters that could in principle be tuned to match the observed stripe contrast. The λ→0 limit is not shown, and no independent DFT estimate of λ or χ_e is provided. The authors should specify these parameters (or their ratio), show how the predicted spectral-function modulation depends on them, and demonstrat
  2. [Fig. 3(e,f) and 'Observation of electromagnon excitations'] The theoretical maps predict a phonon-related stripe modulation at ~12 mV with half the spin-spiral periodicity, but the experiment shows no visible phonon modulation. The text explains this post hoc by a stronger electron-electromagnon coupling relative to electron-phonon coupling, without specifying these couplings or providing any estimate. Moreover, the I_TDOS used to assign the IETS peaks in Fig. 3(c,d) is computed with equal weights for electromagnon and phonon contributions, an arbitrary choice that the authors acknowledge. Since the peak assignment and the real-space fingerprint are validated by matching to this theory, the discrepancy at 12 mV and the arbitrary weighting need to be addressed quantitatively (e.g., via matrix-element estimates, selection rules, or a parameter scan) rather than explained post hoc.
  3. [Fig. 2(g,h) and 'Temperature-dependent observation of multiferroicity'] The exchange parameters J1=-1.25 meV and J3=0.42 meV, as well as Tc≈10.4 K, are extracted by fitting data from the same sample: the stripe periodicity gives J3/J1≈-0.3 and the thermal evolution is fitted with 1/σ=A(Tc-T)^{1/4}. No error bars or uncertainties are reported for these quantities. Because these parameters set the energy scale of the computed electromagnon modes that are then compared with the IETS peaks, the lack of uncertainty propagation is a gap in the central argument. Independent determination (e.g., DFT or literature values) or a propagation-of-errors analysis is needed to avoid circularity.
  4. [Methods, Eq. (6) and following semiclassical interpretation] The mean-field decoupling of the quartic P_i^2 term replaces one spin operator by its ground-state expectation value, resulting in a static renormalization of the exchange and anisotropy tensors. The eigenmodes are thus magnons of an effective static spin Hamiltonian; their interpretation as electromagnons relies on the semiclassical identification p_i = λ/6a Σ m_i × r_ij × (m_j - m_i). The paper does not demonstrate that this captures the coupled spin-polarization dynamics that define an electromagnon, nor that dynamical polarization fluctuations are negligible. A benchmark against a full coupled spin-polarization or spin-lattice calculation, or at least a discussion of the regime of validity of the mean-field decoupling, would strengthen the claim that the observed modulation is a fingerprint of electromagnons rather than of the static mean-field magnons.
minor comments (5)
  1. [Fig. 2(g,h)] The fit 1/σ=A(Tc-T)^{1/4} is described but no fit residuals, goodness-of-fit, or confidence interval for Tc is provided; adding these would help the reader judge the robustness of Tc≈10.4 K.
  2. [Fig. 3(b) and Methods] The Methods state a peak-to-peak bias modulation of 0.25 mV for 'short-range spectra' and 10 mV for 'long-range spectra'. The distinction is not defined in the main text; please clarify which spectra are shown in Figs. 3(a,b) and how the modulation amplitude affects the IETS peak resolution.
  3. [Methods, Eq. (6)] The notation for the polarization term is inconsistent: the main text writes P_i^2/(2ε0χ_e), while Eq. (6) uses λ² multiplied by the spin-spin cross terms. Please define the relationship between λ, χ_e, and the prefactor explicitly.
  4. [Methods, HPBdG section] The definition of the unitary matrix U_i^(jk) is unclear; 'the two indices in parenthesis (jk) to the spatial indices of the matrix' is difficult to parse. Please write out the transformation explicitly or reference a standard notation.
  5. [Conclusions] The phrase 'unambiguous evidence of the internal structure of electromagnons' is stronger than the presented comparison supports, given the theoretical caveats above. A more cautious wording would better match the current evidence.

Circularity Check

1 steps flagged · score 4.0 of 10

Predicted stripe periodicity in the electromagnon spectral maps recycles the experimentally fitted spin-spiral wavevector; the P^2-term strength is unspecified.

  1. fitted input called prediction [Fig. 3e-f caption; main text 'Temperature-dependent observation of multiferroicity'; Methods Eqs. 6-8]
    "Corresponding theoretical dI/dV maps computed from the integrated total local spectral function from electromagnon and phonons at the same bias as the experimental ones. At low bias, where the electromagnon excitations are dominant, a stripe modulation (direction is indicated with a red arrow in panele) with the periodicity of the spin spiral can be identified."

    The spin-spiral wavevector q was measured from the same sample's STM stripe modulation (Fig. 2c) and used to constrain J3/J1 ≈ −0.3. The spin model is solved on that spiral ground state, and the mean-field P^2 correction (Methods Eqs. 6-8) makes the local spectral function inherit the same q. Thus the theoretical map's stripe periodicity at electromagnon energies is not an independent prediction: it is the input q returned as output. The energy range and the appearance of the modulation in the inelastic channel retain predictive content, but the claimed 'matching theoretical predictions' of the stripe periodicity is partly circular. Additionally, the P^2-term parameters (λ, χ_e) are not quantified, so the modulation amplitude is not independently fixed.

full rationale

Most of the paper's derivation chain is not circular: the spin model is standard, the inverse-DMI polarization mechanism is independently established, and the experimental IETS energies are not used to fit the exchange parameters. The J1 and J3 values are derived from the measured transition temperature and stripe periodicity, and the subsequent comparison to the inelastic peak positions is a consistency check rather than a fitted prediction. However, the central real-space fingerprint—the stripe modulation in the theoretical dI/dV maps—has its periodicity set by the very same spin-spiral q that was measured and used to fix J3/J1. The theoretical model therefore cannot be said to independently predict that periodicity. The existence of a modulation at electromagnon energies is a genuine additional prediction, but its amplitude depends on the polarization-energy term P^2/(2ε0χ_e), whose parameters are not given numerically. This weakens the evidential force of the 'unambiguous evidence' claim but does not make the entire identification circular. No load-bearing self-citation chain or imported uniqueness theorem is present, so the appropriate score is moderate, not high.

Assumptions & free parameters 6 free parameters · 5 assumptions · 0 invented entities

No new physical entities are invented; electromagnons are established quasiparticles. The load-bearing assumptions are the fitted spin-model parameters, the unspecified strength of the P^2 polarization-fluctuation term, and the equal-weight approximation for the inelastic spectral function. These choices control the predicted spectra and spatial maps used to identify the experimental modes.

free parameters (6)
  • J1 (first-neighbor exchange) = -1.25 meV
    Fitted to the observed stripe periodicity and the MC-determined transition temperature; sets the energy scale of the electromagnons.
  • J3 (third-neighbor exchange) = 0.42 meV
    Fitted together with J1; antiferromagnetic J3 drives the spin-spiral ground state.
  • Az (single-ion anisotropy) = not quoted
    Included in Eq. 1 to stabilize the spiral plane, but no numerical value is given in the text.
  • lambda (inverse DMI coupling) = not quoted
    Controls the emergent polarization P_i and therefore the P^2 polarization-fluctuation term; no numerical value provided.
  • chi_e (electric susceptibility) = not quoted
    Appears in H_pol = P^2/(2 eps0 chi_e); sets the energy cost of polarization fluctuations and the gap; no numerical value provided.
  • Relative electron-electromagnon vs electron-phonon coupling weights = not quoted
    Theoretical ITDOS uses equal weights, while the observed maps and peak intensities are explained post hoc by an assumed stronger electron-electromagnon coupling.
assumptions (5)
  • domain assumption A J1-J3 Heisenberg model with easy-plane single-ion anisotropy captures the magnetic ground state of monolayer NiI2.
    Used throughout; the spin-spiral ground state and electromagnon spectrum are computed from Eq. 1, with parameters fitted from STM and MC.
  • domain assumption Inverse DMI gives emergent polarization P_i = lambda S_i x (nabla x S_i).
    Standard mechanism for type-II multiferroics, invoked to connect spin order to electric polarization.
  • ad hoc to paper The P_i^2/(2 eps0 chi_e) energy cost with the mean-field decoupling of Eq. 6 describes polarization fluctuations and produces the spatial modulation.
    This is the central modeling assumption behind the claimed fingerprint. It is not derived from a microscopic Hamiltonian, and lambda and chi_e are not specified.
  • ad hoc to paper Tunneling conductance is proportional to the integrated total local spectral function from electromagnons and phonons with equal weights.
    The paper states that relative weights depend on unknown electron-magnon and electron-phonon coupling constants and selection rules; the inflection-point comparison is weight-independent, but the map comparison is not.
  • domain assumption GGA-PBE DFT with SOC in Elk, plus phonopy harmonic phonons, correctly describe the phonon spectrum in the Cm multiferroic phase.
    Used to compute phonon DOS and local spectral functions; standard first-principles methodology with stated convergence parameters.

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Pith. "Pith review of Observation of electromagnons in a monolayer multiferroic." pith.science (2026). https://pith.science/paper/SMI2VXCH

@misc{pith2026251008253,
  author       = {Pith},
  title        = {Pith review of: Observation of electromagnons in a monolayer multiferroic},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/SMI2VXCH}},
  note         = {Machine review of arXiv:2510.08253}
}
abstract

Van der Waals multiferroics have emerged as a promising platform to explore novel magnetoelectric phenomena. Recently, it has been shown that monolayer NiI$_2$ hosts robust type-II multiferroicity down to the two-dimensional limit, a giant dynamical magnetoelectric coupling at terahertz frequencies, and an electrically switchable spin polarization. These developments present the possibility of engineering ultrafast, low-energy-consumption, and electrically-tunable spintronic devices based on the collective excitations of the multiferroic order, electromagnons. However, the direct visualization of these bosonic modes in real space and within the monolayer limit remains elusive. Here, we report the atomic-scale observation of electromagnons in monolayer NiI$_2$ using low-temperature scanning tunneling microscopy. By tracking the thermal evolution of the multiferroic phase, we establish the energy scale and resolve coherent in-gap excitations of the symmetry-broken multiferroic state. Comparison with first-principles and spin-model calculations reveals that the low-energy modes originate from electromagnon excitations. Spatially resolved inelastic tunneling spectroscopy maps show a stripe-like modulation of the local spectral function at electromagnon energies, matching theoretical predictions. These results provide direct evidence of the internal structure of electromagnons and establish a methodology to probe these modes at the atomic scale, opening avenues for electrically tunable spintronics.

Figures

Figures reproduced from arXiv: 2510.08253 by the authors.

Figure 1
Figure 1. FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

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  1. Dimensional crossover and local strain induced deflection of the spin spiral state in multiferroic NiI2

    cond-mat.mes-hall 2026-08 conditional novelty 8.0 of 10

    In few-layer NiI2, increasing thickness rotates and lengthens the spin spiral wavevector, while wrinkles deflect it locally, establishing thickness and strain as tuning knobs for this 2D multiferroic.

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Works this paper leans on

52 extracted references · 24 canonical work pages · cited by 1 Pith paper

  1. [1]

    author author Yunye \ Gao , author Mingyuan \ Gao , \ and\ author Yuerui \ Lu ,\ title title Two-dimensional multiferroics , \ 10.1039/d1nr06598j journal journal Nanoscale \ volume 13 ,\ pages 19324--19340 ( year 2021 ) NoStop

    work page doi:10.1039/d1nr06598j 2021

  2. [2]

    author author Ping \ Man , author Lingli \ Huang , author Jiong \ Zhao , \ and\ author Thuc Hue \ Ly ,\ title title Ferroic phases in two-dimensional materials , \ 10.1021/acs.chemrev.3c00170 journal journal Chemical Reviews \ volume 123 ,\ pages 10990–11046 ( year 2023 ) NoStop

    work page doi:10.1021/acs.chemrev.3c00170 2023

  3. [3]

    author author Zikun \ Tang , author Yi Hu , author Lukas \ Rogée , author Duanzijing \ Liu , \ and\ author Shu Ping \ Lau ,\ title title Towards multiferroicity in two-dimensional van der Waals materials: Challenges and opportunities , \ 10.1021/acs.chemmater.5c01047 journal journal Chemistry of Materials \ volume 37 ,\ pages 4925–4934 ( year 2025 ) NoStop

    work page doi:10.1021/acs.chemmater.5c01047 2025

  4. [4]

    author author Hwiin \ Ju , author Youjin \ Lee , author Kwang-Tak \ Kim , author In Hyeok \ Choi , author Chang Jae \ Roh , author Suhan \ Son , author Pyeongjae \ Park , author Jae Ha \ Kim , author Taek Sun \ Jung , author Jae Hoon \ Kim , author Kee Hoon \ Kim , author Je-Geun \ Park , \ and\ author Jong Seok \ Lee ,\ title title Possible persistence o...

    doi:10.1021/acs.nanolett.1c01095 2021

  5. [5]

    author author Qian \ Song , author Connor A. \ Occhialini , author Emre \ Erge c en , author Batyr \ Ilyas , author Danila \ Amoroso , author Paolo \ Barone , author Jesse \ Kapeghian , author Kenji \ Watanabe , author Takashi \ Taniguchi , author Antia S. \ Botana , author Silvia \ Picozzi , author Nuh \ Gedik , \ and\ author Riccardo \ Comin ,\ title ti...

    doi:10.1038/s41586-021-04337-x 2022

  6. [6]

    author author Adolfo O \ Fumega \ and\ author J L \ Lado ,\ title title Microscopic origin of multiferroic order in monolayer NiI _2 , \ 10.1088/2053-1583/ac4e9d journal journal 2D Materials \ volume 9 ,\ pages 025010 ( year 2022 ) NoStop

    doi:10.1088/2053-1583/ac4e9d

  7. [7]

    \ Fumega , author Héctor \ González‐Herrero , author Viliam \ Vaňo , author Shawulienu \ Kezilebieke , author Jose L

    author author Mohammad \ Amini , author Adolfo O. \ Fumega , author Héctor \ González‐Herrero , author Viliam \ Vaňo , author Shawulienu \ Kezilebieke , author Jose L. \ Lado , \ and\ author Peter \ Liljeroth ,\ title title Atomic‐scale visualization of multiferroicity in monolayer NiI _2 , \ 10.1002/adma.202311342 journal journal Advanced Materials \ vol...

    doi:10.1002/adma.202311342 2024

  8. [8]

    \ Gao , author Xinyue \ Peng , author Xinle \ Cheng , author Emil \ Viñas Bostr\" o m , author Dong Seob \ Kim , author Ravish K

    author author Frank Y. \ Gao , author Xinyue \ Peng , author Xinle \ Cheng , author Emil \ Viñas Bostr\" o m , author Dong Seob \ Kim , author Ravish K. \ Jain , author Deepak \ Vishnu , author Kalaivanan \ Raju , author Raman \ Sankar , author Shang-Fan \ Lee , author Michael A. \ Sentef , author Takashi \ Kurumaji , author Xiaoqin \ Li , author Peizhe \...

    2024

Show all 52 references
  1. [9]

    \ Antonenko , author J\" o rn W

    author author Qian \ Song , author Srdjan \ Stavrić , author Paolo \ Barone , author Andrea \ Droghetti , author Daniil S. \ Antonenko , author J\" o rn W. F. \ Venderbos , author Connor A. \ Occhialini , author Batyr \ Ilyas , author Emre \ Erge c en , author Nuh \ Gedik , au...

    2025 doi

  2. [10]

    author author Youtarou \ Takahashi , author Ryo \ Shimano , author Yoshio \ Kaneko , author Hiroshi \ Murakawa , \ and\ author Yoshinori \ Tokura ,\ title title Magnetoelectric resonance with electromagnons in a perovskite helimagnet , \ 10.1038/nphys2161 journal journal Natur...

    2011 doi

  3. [11]

    Takahashi , author Y

    author author Y. Takahashi , author Y. Yamasaki , \ and\ author Y. Tokura ,\ title title Terahertz magnetoelectric resonance enhanced by mutual coupling of electromagnons , \ 10.1103/PhysRevLett.111.037204 journal journal Phys. Rev. Lett. \ volume 111 ,\ pages 037204 ( year 20...

    2013 doi

  4. [12]

    author author Masakazu \ Matsubara , author Sebastian \ Manz , author Masahito \ Mochizuki , author Teresa \ Kubacka , author Ayato \ Iyama , author Nadir \ Aliouane , author Tsuyoshi \ Kimura , author Steven L. \ Johnson , author Dennis \ Meier , \ and\ author Manfred \ Fiebi...

    2015 doi

  5. [13]

    author author Jae Ha \ Kim , author Taek Sun \ Jung , author Youjin \ Lee , author Chaebin \ Kim , author Je-Geun \ Park , \ and\ author Jae Hoon \ Kim ,\ title title Terahertz evidence of electromagnon excitations in the multiferroic van der Waals insulator NiI _ 2 , \ 10.110...

    2023 doi

  6. [14]

    author author Liesbeth \ Venema , author Bart \ Verberck , author Iulia \ Georgescu , author Giacomo \ Prando , author Elsa \ Couderc , author Silvia \ Milana , author Maria \ Maragkou , author Lina \ Persechini , author Giulia \ Pacchioni , \ and\ author Luke \ Fleet ,\ title...

    2016 doi

  7. [15]

    author author Martin \ Maldovan ,\ title title Sound and heat revolutions in phononics , \ 10.1038/nature12608 journal journal Nature \ volume 503 ,\ pages 209–217 ( year 2013 ) NoStop

    2013 doi

  8. [16]

    author author A. V. \ Chumak , author V. I. \ Vasyuchka , author A. A. \ Serga , \ and\ author B. Hillebrands ,\ title title Magnon spintronics , \ 10.1038/nphys3347 journal journal Nature Physics \ volume 11 ,\ pages 453–461 ( year 2015 ) NoStop

    2015 doi

  9. [17]

    \ Vasyuchka , author Alexander A

    author author Philipp \ Pirro , author Vitaliy I. \ Vasyuchka , author Alexander A. \ Serga , \ and\ author Burkard \ Hillebrands ,\ title title Advances in coherent magnonics , \ 10.1038/s41578-021-00332-w journal journal Nature Reviews Materials \ volume 6 ,\ pages 1114–1135...

    2021 doi

  10. [18]

    author author Manfred \ Fiebig , author Thomas \ Lottermoser , author Dennis \ Meier , \ and\ author Morgan \ Trassin ,\ title title The evolution of multiferroics , \ 10.1038/natrevmats.2016.46 journal journal Nature Reviews Materials \ volume 1 ,\ pages 16046 ( year 2016 ) NoStop

    2016 doi

  11. [19]

    author author N. A. \ Spaldin \ and\ author R. Ramesh ,\ title title Advances in magnetoelectric multiferroics , \ 10.1038/s41563-018-0275-2 journal journal Nature Materials \ volume 18 ,\ pages 203--212 ( year 2019 ) NoStop

    2019 doi

  12. [20]

    Kubacka , author J

    author author T. Kubacka , author J. A. \ Johnson , author M. C. \ Hoffmann , author C. Vicario , author S. de Jong , author P. Beaud , author S. Gr\" u bel , author S.-W. \ Huang , author L. Huber , author L. Patthey , author Y.-D. \ Chuang , author J. J. \ Turner , author G....

    2014

  13. [21]

    author author Ryoji \ Masuda , author Yoshio \ Kaneko , author Yoshinori \ Tokura , \ and\ author Youtarou \ Takahashi ,\ title title Electric field control of natural optical activity in a multiferroic helimagnet , \ 10.1126/science.aaz4312 journal journal Science \ volume 37...

    2021 doi

  14. [22]

    author author Makiko \ Ogino , author Yoshihiro \ Okamura , author Kosuke \ Fujiwara , author Takahiro \ Morimoto , author Naoto \ Nagaosa , author Yoshio \ Kaneko , author Yoshinori \ Tokura , \ and\ author Youtarou \ Takahashi ,\ title title Terahertz photon to dc current co...

    2024 doi

  15. [23]

    author author A. K. \ Geim \ and\ author I. V. \ Grigorieva ,\ title title Van der Waals heterostructures , \ 10.1038/nature12385 journal journal Nature \ volume 499 ,\ pages 419–425 ( year 2013 ) NoStop

    2013 doi

  16. [24]

    \ Andrei , author Dmitri K

    author author Eva Y. \ Andrei , author Dmitri K. \ Efetov , author Pablo \ Jarillo-Herrero , author Allan H. \ MacDonald , author Kin Fai \ Mak , author T. Senthil , author Emanuel \ Tutuc , author Ali \ Yazdani , \ and\ author Andrea F. \ Young ,\ title title The marvels of m...

    2021 doi

  17. [25]

    o hr , author Di Xiao , author Ting \ Cao , author J\

    author author Tiancheng \ Song , author Qi-Chao \ Sun , author Eric \ Anderson , author Chong \ Wang , author Jimin \ Qian , author Takashi \ Taniguchi , author Kenji \ Watanabe , author Michael A. \ McGuire , author Rainer \ St\" o hr , author Di Xiao , author Ting \ Cao , au...

    2021 doi

  18. [26]

    \ Goldberger , author Kenji \ Watanabe , author Takashi \ Taniguchi , author David A

    author author Yang \ Xu , author Ariana \ Ray , author Yu-Tsun \ Shao , author Shengwei \ Jiang , author Kihong \ Lee , author Daniel \ Weber , author Joshua E. \ Goldberger , author Kenji \ Watanabe , author Takashi \ Taniguchi , author David A. \ Muller , author Kin Fai \ Ma...

    2021 doi

  19. [27]

    author author Tiago V. C. \ Antão , author Jose L. \ Lado , \ and\ author Adolfo O. \ Fumega ,\ title title Electric field control of moiré skyrmion phases in twisted multiferroic NiI _2 bilayers , \ 10.1021/acs.nanolett.4c04582 journal journal Nano Letters \ volume 24 ,\ page...

    2024 doi

  20. [28]

    Billerey , author C

    author author D. Billerey , author C. Terrier , author N. Ciret , \ and\ author J. Kleinclauss ,\ title title Neutron diffraction study and specific heat of antiferromagnetic NiI _2 , \ 10.1016/0375-9601(77)90863-5 journal journal Physics Letters A \ volume 61 ,\ pages 138–140...

    1977 doi

  21. [29]

    \ Kuindersma , author J.P

    author author S.R. \ Kuindersma , author J.P. \ Sanchez , \ and\ author C. Haas ,\ title title Magnetic and structural investigations on NiI _2 and CoI _2 , \ 10.1016/0378-4363(81)90100-5 journal journal Physica B+C \ volume 111 ,\ pages 231–248 ( year 1981 ) NoStop

    1981 doi

  22. [30]

    Kurumaji , author S

    author author T. Kurumaji , author S. Seki , author S. Ishiwata , author H. Murakawa , author Y. Kaneko , \ and\ author Y. Tokura ,\ title title Magnetoelectric responses induced by domain rearrangement and spin structural change in triangular-lattice helimagnets NiI _ 2 and C...

    2013 doi

  23. [31]

    \ Balatsky ,\ title title Spin current and magnetoelectric effect in noncollinear magnets , \ 10.1103/PhysRevLett.95.057205 journal journal Phys

    author author Hosho \ Katsura , author Naoto \ Nagaosa , \ and\ author Alexander V. \ Balatsky ,\ title title Spin current and magnetoelectric effect in noncollinear magnets , \ 10.1103/PhysRevLett.95.057205 journal journal Phys. Rev. Lett. \ volume 95 ,\ pages 057205 ( year 2...

    2005 doi

  24. [32]

    author author Maxim \ Mostovoy ,\ title title Ferroelectricity in spiral magnets , \ 10.1103/PhysRevLett.96.067601 journal journal Phys. Rev. Lett. \ volume 96 ,\ pages 067601 ( year 2006 ) NoStop

    2006 doi

  25. [33]

    author author Jiangping \ Hu ,\ title title Microscopic origin of magnetoelectric coupling in noncollinear multiferroics , \ 10.1103/PhysRevLett.100.077202 journal journal Phys. Rev. Lett. \ volume 100 ,\ pages 077202 ( year 2008 ) NoStop

    2008 doi

  26. [34]

    author author Yi Tseng , author Connor A. \ Occhialini , author Qian \ Song , author Paolo \ Barone , author Sahaj \ Patel , author Meghna \ Shankar , author Raul \ Acevedo‐Esteves , author Jiarui \ Li , author Christie \ Nelson , author Silvia \ Picozzi , author Ronny \ Sutar...

    2025 doi

  27. [35]

    author author Danila \ Amoroso , author Paolo \ Barone , \ and\ author Silvia \ Picozzi ,\ title title Spontaneous skyrmionic lattice from anisotropic symmetric exchange in a Ni -halide monolayer , \ 10.1038/s41467-020-19535-w journal journal Nature Communications \ volume 11 ...

    2020 doi

  28. [38]

    author author Suhan \ Son , author Youjin \ Lee , author Jae Ha \ Kim , author Beom Hyun \ Kim , author Chaebin \ Kim , author Woongki \ Na , author Hwiin \ Ju , author Sudong \ Park , author Abhishek \ Nag , author Ke‐Jin \ Zhou , author Young‐Woo \ Son , author Hyeongdo \ Ki...

    2022

  29. [39]

    author author Yangliu \ Wu , author Zhaozhuo \ Zeng , author Haipeng \ Lu , author Xiaocang \ Han , author Chendi \ Yang , author Nanshu \ Liu , author Xiaoxu \ Zhao , author Liang \ Qiao , author Wei \ Ji , author Renchao \ Che , author Longjiang \ Deng , author Peng \ Yan , ...

    2024 doi

  30. [40]

    author author Joachim \ Sødequist \ and\ author Thomas \ Olsen ,\ title title Type II multiferroic order in two-dimensional transition metal halides from first principles spin-spiral calculations , \ 10.1088/2053-1583/acd4d0 journal journal 2D Materials \ volume 10 ,\ pages 03...

    doi

  31. [41]

    author author Markus \ Ternes ,\ title title Spin excitations and correlations in scanning tunneling spectroscopy , \ 10.1088/1367-2630/17/6/063016 journal journal New Journal of Physics \ volume 17 ,\ pages 063016 ( year 2015 ) NoStop

    2015 doi

  32. [42]

    Spinelli , author B

    author author A. Spinelli , author B. Bryant , author F. Delgado , author J. Fernández-Rossier , \ and\ author A. F. \ Otte ,\ title title Imaging of spin waves in atomically designed nanomagnets , \ 10.1038/nmat4018 journal journal Nature Materials \ volume 13 ,\ pages 782–78...

    2014 doi

  33. [43]

    Bellaiche , \ and\ author Hongjun \ Xiang ,\ title title Realistic spin model for multiferroic NiI _ 2 , \ 10.1103/PhysRevLett.131.036701 journal journal Phys

    author author Xuanyi \ Li , author Changsong \ Xu , author Boyu \ Liu , author Xueyang \ Li , author L. Bellaiche , \ and\ author Hongjun \ Xiang ,\ title title Realistic spin model for multiferroic NiI _ 2 , \ 10.1103/PhysRevLett.131.036701 journal journal Phys. Rev. Lett. \ ...

    2023 doi

  34. [44]

    author author Kira \ Riedl , author Danila \ Amoroso , author Steffen \ Backes , author Aleksandar \ Razpopov , author Thi Phuong Thao \ Nguyen , author Kunihiko \ Yamauchi , author Paolo \ Barone , author Stephen M. \ Winter , author Silvia \ Picozzi , \ and\ author Roser \ V...

    2022 doi

  35. [45]

    author author R. M. \ White , author M. Sparks , \ and\ author I. Ortenburger ,\ title title Diagonalization of the antiferromagnetic magnon-phonon interaction , \ 10.1103/PhysRev.139.A450 journal journal Phys. Rev. \ volume 139 ,\ pages A450--A454 ( year 1965 ) NoStop

    1965 doi

  36. [46]

    author author S Toth \ and\ author B Lake ,\ title title Linear spin wave theory for single-q incommensurate magnetic structures , \ 10.1088/0953-8984/27/16/166002 journal journal Journal of Physics: Condensed Matter \ volume 27 ,\ pages 166002 ( year 2015 ) NoStop

    2015 doi

  37. [47]

    author author Andi \ Cong \ and\ author Ka Shen ,\ title title Soft magnons in van der Waals multiferroic NiI _ 2 , \ 10.1103/PhysRevB.109.224419 journal journal Phys. Rev. B \ volume 109 ,\ pages 224419 ( year 2024 ) NoStop

    2024 doi

  38. [48]

    author author R. A. \ Tahir-Kheli \ and\ author D. ter Haar ,\ title title Use of Green functions in the theory of ferromagnetism. I . general discussion of the spin- S case , \ 10.1103/PhysRev.127.88 journal journal Phys. Rev. \ volume 127 ,\ pages 88--94 ( year 1962 ) NoStop

    1962 doi

  39. [49]

    author author S. H. \ Liu \ and\ author D. B. \ Siano ,\ title title Interpolation theory of ferromagnetic Heisenberg model , \ 10.1103/PhysRev.164.697 journal journal Phys. Rev. \ volume 164 ,\ pages 697--705 ( year 1967 ) NoStop

    1967 doi

  40. [50]

    Hohenberg \ and\ author W

    author author P. Hohenberg \ and\ author W. Kohn ,\ title title Inhomogeneous electron gas , \ 10.1103/PhysRev.136.B864 journal journal Phys. Rev. \ volume 136 ,\ pages B864--B871 ( year 1964 ) NoStop

    1964 doi

  41. [51]

    Kohn \ and\ author L

    author author W. Kohn \ and\ author L. J. \ Sham ,\ title title Self-consistent equations including exchange and correlation effects , \ 10.1103/PhysRev.140.A1133 journal journal Phys. Rev. \ volume 140 ,\ pages A1133--A1138 ( year 1965 ) NoStop

    1965 doi

  42. [52]

    @noop title Elk code , \ howpublished http://elk.sourceforge.net/ NoStop

  43. [53]

    author author John P. \ Perdew , author Kieron \ Burke , \ and\ author Matthias \ Ernzerhof ,\ title title Generalized gradient approximation made simple , \ 10.1103/PhysRevLett.77.3865 journal journal Phys. Rev. Lett. \ volume 77 ,\ pages 3865--3868 ( year 1996 ) NoStop

    1996 doi

  44. [54]

    author author Atsushi \ Togo ,\ title title First-principles phonon calculations with phonopy and phono3py , \ 10.7566/jpsj.92.012001 journal journal Journal of the Physical Society of Japan \ volume 92 ,\ pages 012001 ( year 2023 ) NoStop

    2023 doi

Pith tools

Reviewed August 4, 2026 · model on record in the stance chip above.