Pith. sign in

REVIEW 2 major objections 4 minor 86 references

Topological switching in bilayer magnons via electrical control

T0 review · 2 major / 4 minor · reviewed 2026-08-05 · deepseek-v4-flash

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

Pith's one-line read A vertical electric field can switch magnon bands between Chern and trivial insulating states in bilayer ferromagnets, at predicted critical fields of ±0.05–±0.1 eV/Å.

desk verdict A credible, clean mechanism for E-field switching of magnon topology in bilayer CrXY; the predicted critical fields hinge on an unquantified assumption that DMI is Ez-independent. read the letter →

arxiv 2509.00815 v1 pith:PSV2DXOE submitted 2025-08-31 cond-mat.mes-hall cond-mat.mtrl-sci

Xueqing Wan , Quanchao Du , Jinlian Lu , Zhenlong Zhang , Jinyang Ni , Lei Zhang , Zhijun Jiang , Laurent Bellaiche This is my paper
classification cond-mat.mes-hallcond-mat.mtrl-sci PACS 75.30.Ds75.85.+t85.75.-d
keywords topologicalmagnonselectric-fieldcontrolspin-layercouplingbilayerferromagnetDzyaloshinskii–MoriyainteractionCherninsulatormagnonvalleypolarizationCrXYJanusmagnets
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

Magnons—the quantized spin waves of an ordered magnet—are charge-neutral, which has made their band topology hard to steer with voltages. This paper argues that a bilayer ferromagnet with strong spin-layer coupling breaks that rule: a vertical electric field pushes the two layers' electronic states in opposite directions, so the intralayer Heisenberg exchanges become unequal (J_a − J_b = −6E_z in CrSCl, per density-functional calculations). That exchange imbalance breaks inversion symmetry and opens a trivial gap at the magnon Dirac points, competing with the Dzyaloshinskii–Moriya interaction, an antisymmetric exchange that breaks the magnon analogue of time reversal and opens a topological Chern gap. The competition reduces to a simple phase boundary, ±(√3/2)(J_a − J_b) = D_z, so the field polarity decides whether magnon bands carry a nonzero Chern number (with chiral edge modes) or are topologically trivial; predicted switching fields are ±0.067 eV/Å (CrSCl) and ±0.033 eV/Å (CrSBr), within experimental reach. If correct, the mechanism gives a purely electric, nonvolatile switch for spin-wave transport—and, combined with a weak magnetic field of about 10 mT in the easy-plane materials, it cuts the field strength needed to manipulate magnon topology by two orders of magnitude.

What carries the argument

A two-band linear-spin-wave Hamiltonian (Holstein–Primakoff plus Fourier transformation) in which the two honeycomb sublattices are the two layers of the bilayer, with the interlayer bond playing the role of the nearest-neighbour bond. Band topology is decided by two competing terms of opposite Berry-curvature parity: the Dzyaloshinskii–Moriya interaction D_z breaks the magnon effective time-reversal symmetry T′ and gives a Chern gap, while the electric-field-induced exchange imbalance J_a − J_b breaks inversion symmetry P and gives a trivial gap. The carrying identity is the gap-closing condition at the Dirac points, ±(√3/2)(J_a − J_b) = D_z, combined with the DFT-computed linear response J

What would settle it

Measure the magnon dispersion of bilayer CrSCl under a gate voltage with inelastic neutron or electron scattering: the model predicts the gap at the Dirac points K and K′ closes at E_z = ±0.067 eV/Å and reopens across the transition with reversed Berry curvature, which would show up as a sign change in the thermal Hall conductivity. Extract D_z from the same spectra as a function of E_z—if the DMI shifts by a substantial fraction of the J_a − J_b response, the predicted boundary is wrong.

Watch

Extended reading notes

Core claim

An applied vertical electric field E_z can switch the topological phase of magnons in bilayer ferromagnets with strong spin-layer coupling: the field makes the two layers' Cr3+ crystal-field splittings unequal, so the intralayer Heisenberg exchanges become asymmetric (J_a − J_b = −6E_z for CrSCl). This inversion-breaking term opens a trivial gap at the magnon Dirac points, competing with the Dzyaloshinskii–Moriya interaction, which breaks the magnons' effective time reversal and opens a topological gap; the two Berry curvatures have opposite parity, so whichever term dominates sets the Chern number. The gap closes at the boundary ±(√3/2)(J_a − J_b) = D_z, giving critical fields ±0.067 eV/Å (

Load-bearing premise

The prediction assumes the Dzyaloshinskii–Moriya interaction (and the interlayer exchange and single-ion anisotropy) stay fixed while the electric field is applied—only the intralayer Heisenberg exchanges respond. The paper states this assumption explicitly and supports it with a single DFT panel; if the DMI also shifts with the field, the phase boundary and every quoted switching voltage move.

Editorial extensions

If this is right

  • Bilayer CrSCl and CrSBr become electrically switchable magnonic Chern insulators: reversing the voltage polarity selects between chiral edge transport (nonzero Chern number) and a trivial insulator, at critical fields ±0.067 and ±0.033 eV/Å that lie within reach of current gate stacks.
  • Because valley polarization changes sign with field direction and reaches ~3.5 meV at 0.2 eV/Å, the electric field is a control knob for nonreciprocal magnon transport—an energy scale that would otherwise require roughly 30 T.
  • The magnon thermal Hall and orbital Hall conductivities respond to E_z, so heat and orbital currents carried by spin waves can be modulated electrically rather than magnetically.
  • In the easy-plane members, rotating the magnetization with a ~10 mT field cuts the switching voltage about fourfold (from ~±0.08 to ~±0.02 eV/Å)—cooperative magnetoelectric control that the paper notes lowers the needed magnetic field by two orders of magnitude relative to earlier proposals.

Reading between the lines

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

  • If the linear exchange-field response (J_a − J_b = −6E_z) holds in real devices, the mechanism is effectively a voltage-controlled topological phase transition—a natural building block for magnon switches, diodes, and directional logic that need no magnetic field at all.
  • Because the asymmetry originates in electric-field-driven crystal-field shifts at the Cr sites, the switching field should depend on the dielectric environment and substrate strain; strain gradients or high-κ gates are testable tuning knobs that the paper does not explore.
  • The parity argument is generic: any time-reversal-breaking bond term, not only DMI, would compete with the field-induced exchange imbalance, so doping- or strain-tuned DMI could shift the phase boundary in materials where the intrinsic DMI is small.
  • The same layer-stacked honeycomb symmetry appears in other charge-neutral bosonic systems (phonons, exciton–polaritons in bilayers), so a vertical field creating a sublattice potential imbalance could switch their topology by the same mechanism.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 4 minor

Summary. The paper proposes a mechanism for electrically controlling topological magnons in AB-stacked bilayer Janus magnets CrXY (X = S, Se; Y = Cl, Br). The central idea is that a vertical electric field Ez creates an interlayer potential imbalance, which modifies the intralayer Heisenberg exchanges Ja and Jb, while the Dzyaloshinskii-Moriya interaction (DMI) remains essentially unchanged. Using a two-band effective magnon Hamiltonian, the authors derive a phase boundary ±(√3/2)(Ja−Jb) = D_z, and with DFT-computed linear relations Ja−Jb = −6E_z (CrSCl) and −7E_z (CrSeBr), they predict switching between Chern and trivial magnon insulators at ±0.067 eV/Å and ±0.033 eV/Å, respectively. They also discuss easy-plane CrSeBr, where an in-plane magnetic field of order 10 mT can synergistically tune the topology, and they report electrically tunable valley polarization and thermal/orbital Hall conductivities.

Significance. If the underlying assumptions are quantitatively validated, the paper offers a general and falsifiable strategy for electric-field control of magnon topology, a topic of current interest for magnonic devices. The model analysis (Eqs. 2–5) is internally consistent, and the phase boundary follows from the Hamiltonian rather than being fitted to the target result. The explicit predictions for the critical fields are specific and testable, and the connection to DFT parameters in a concrete material family is a strength. However, the central quantitative predictions rest on two assumptions that are not yet rigorously supported: the constancy of D_z under Ez, and the accuracy of the linear relations Ja−Jb = cE_z. These issues limit the current certainty in the predicted switching fields.

major comments (2)
  1. [Spin-layer coupling / Easy axis bilayer, Eq. (5) and Fig. 2(b)] The predicted critical fields (±0.067 eV/Å and ±0.033 eV/Å) rely on treating D_z as independent of E_z. The sentence after Eq. (2) asserts this from a 'weak response', but Fig. 2(b) provides no numerical slope, error bars, or convergence tests for D_z^a and D_z^b versus E_z. Since E_z breaks inversion symmetry, there is no symmetry protecting D_z from a linear field dependence; a slope |dD_z/dE_z| of only ~0.6 meV per eV/Å (about 10% of d(Ja−Jb)/dE_z) would shift the CrSCl critical field by ~10%. Given the DFT DMI magnitude (~0.35 meV) and typical numerical uncertainties of tens of μeV, the plotted flatness could mask a field response comparable to the effect being exploited. The authors should report D_z(E_z) with error bars and convergence checks, and estimate the resulting uncertainty in the switching fields.
  2. [Spin-layer coupling, Fig. 2(b), and Eq. (5)] The phase boundary and switching fields are directly proportional to the empirical slopes Ja−Jb = −6E_z (CrSCl) and −7E_z (CrSeBr). However, the text reports only a single data point at E_z = 0.1 eV/Å and states linearity; no raw data, number of E_z points, fitting procedure, or uncertainties are provided. Because the critical fields are linear in these slopes, the absence of error bars leaves the quantitative predictions underdetermined. The authors should include the full data set, the fit residuals, and the uncertainty in the fitted coefficients.
minor comments (4)
  1. [Magnetic anisotropy dependence] In the text, 'the critical Ez for bilayer CrSeCl is ±0.08 eV/Å' appears to be a typo for CrSeBr. Table I gives D_x = 0.15 meV for CrSeCl, which would imply a critical field of about ±0.025 eV/Å, while 0.08 eV/Å corresponds to CrSeBr with D_x = 0.49 meV. Also, citing Eq. (5) for the easy-plane case is misleading; the correct formula is Eq. (6) with χ = 0.
  2. [Abstract] The phrase 'nonvolatile control' applied to an electric field is ambiguous, since electric fields are generally volatile. Please clarify whether 'nonvolatile' refers to the magnetic state persisting after the field is removed or to some other sense.
  3. [Fig. 2(b)] The figure would be more informative with error bars, numerical values on the axes, and an explicit caption distinguishing D_z^a and D_z^b. Without these, the claimed invariance of D_z is difficult to assess.
  4. [Data availability] The statement 'All data are available from the authors upon reasonable request' is not ideal for a computational paper. Consider depositing the DFT input/output files and fitting scripts in a public repository to enable reproducibility.

Circularity Check

0 steps flagged · score 2.0 of 10

No circular derivation; the phase boundary and critical fields are consequences of the DFT-parameterized Hamiltonian. Only minor non-load-bearing self-citations appear.

full rationale

The central derivation is self-contained. Eq. (2) is the linear spin-wave Hamiltonian built from DFT-computed parameters (Table I, Fig. 2). The switching condition Eq. (5) follows by diagonalizing h(k) and requiring the K/K' gap to close; it directly gives ±(√3/2)(Ja−Jb)=Dz. The linear response Ja−Jb=−6Ez is extracted from DFT exchange calculations, not fitted to a target topology, and the critical fields ±0.067 eV/Å (CrSCl) and ±0.033 eV/Å (CrSBr) are then arithmetic consequences of substituting that response and the computed Dz into the phase boundary. No Berry curvature or Chern number is used to adjust the parameters. The paper does assume after Eq. (2) that Jab, SIA, and DMI are Ez-invariant, supported by Fig. 2(b). That is a quantitative accuracy assumption, not a circular input: if D_z(E_z) is nonzero, Eq. (5) remains the correct gap-closure condition and the predicted fields shift—an uncertainty, not a reduction to the conclusion. Refs. 37 and 67 involve overlapping authors, but the facts they support (magnon effective time reversal T′, spin-layer coupling, topology of DMI-induced gaps) are standard and also cited to external works (e.g., Refs. 16, 19, 48–50) or re-derived here from DFT. The central claim does not rely on a self-citation chain. Score 2 reflects only the presence of minor self-citations; no circular step was identified.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

The central predictions rely on a small set of DFT-derived exchange parameters and the explicit assumption that only Ja and Jb respond significantly to Ez. These parameters are fitted or assumed, not derived from a closed-form theory. No new physical entities are introduced.

free parameters (4)
  • Ez-coupling coefficient c in Ja - Jb = c Ez = -6 meV/(eV/angstrom) for CrSCl; -7 meV/(eV/angstrom) for CrSeBr
    Linear fit to DFT-computed exchange differences at several Ez values (Fig. 2b and text); central to the predicted critical fields.
  • DMI magnitude Dz = CrSCl +-0.35, CrSBr +-0.17, CrSeCl +-0.14, CrSeBr +-0.07 meV (Table I)
    DFT-computed; sets the phase boundary in Eq. 5 and the critical Ez values.
  • In-plane anisotropy difference between x and y axes in CrSeBr = 0.005 meV
    DFT-computed; the basis for the claim that a 10 mT magnetic field can rotate the spin and lower the critical Ez.
  • SIA Kz and interlayer exchange Jab = Kz values in Table I; Jab not given numerically
    DFT-computed; assumed invariant under Ez, but if they vary the phase diagram shifts.
assumptions (5)
  • standard math Linear spin-wave theory via Holstein-Primakoff transformation is valid for the FM ground state
    Used to derive the magnon Hamiltonian in k-space (Easy axis bilayer section).
  • domain assumption The bilayer magnetic lattice maps to a honeycomb lattice with interlayer exchange as NN and intralayer exchange as 2NN
    Stated in the Spin-layer coupling section and used to identify the DMI chirality and phase boundary.
  • domain assumption Second-order perturbation theory with U >> Delta_cf and fixed t gives Eex proportional to 1/Delta_cf
    Derivation in Spin-layer coupling section, Eq. 1; used to explain the linear Ja - Jb response to Ez.
  • ad hoc to paper Jab, SIA, and Dz remain invariant under the applied electric field
    Explicitly assumed in Easy axis bilayer section after Eq. 2; load-bearing for the phase boundary calculation.
  • standard math Berry curvature and Chern number computed from the effective two-band Hamiltonian
    Eq. 4 and the parity argument for the topological vs trivial gap.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Topological switching in bilayer magnons via electrical control." pith.science (2026). https://pith.science/paper/PSV2DXOE

@misc{pith2026250900815,
  author       = {Pith},
  title        = {Pith review of: Topological switching in bilayer magnons via electrical control},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/PSV2DXOE}},
  note         = {Machine review of arXiv:2509.00815}
}
read the original abstract

Topological magnons, quantized spin waves featuring nontrivial boundary modes, present a promising route toward lossless information processing. Realizing practical devices typically requires magnons excited in a controlled manner to enable precise manipulation of their topological phases and transport behaviors. However, their inherent charge neutrality and a high frequency nature pose a significant challenge for nonvolatile control, especially via electric means. Herein, we propose a general strategy for electrical control of topological magnons in bilayer ferromagnetic insulators. With strong spin-layer coupling, an applied vertical electric field induces an interlayer potential imbalance that modifies intralayer Heisenberg exchanges between adjacent layers. This electric-field-driven modulation competes with the bilayer's intrinsic Dzyaloshinskii-Moriya interaction, enabling the accurate tuning of the band topology and nonreciprocal dynamics of magnons. More importantly, such an electric control mechanism exhibits strong coupling with external magnetic fields, unveiling new perspectives on magnetoelectric coupling in charge-neutral quasiparticles

Figures

Figures reproduced from arXiv: 2509.00815 by the authors.

Figure 1
Figure 1. FIG. 1. (a) Side view of AB-stacking Janus bilayer Cr [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. The spin exchanges of bilayer CrSCl under [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. The magnon nonreciprocity and phase diagram. (a) [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: FIG. 4. The magnon phase diagram (a) and the valley polar [PITH_FULL_IMAGE:figures/full_fig_p005_4.png]

Discussion (0). Sign in to comment.

Reference graph

Works this paper leans on

86 extracted references · 65 canonical work pages

  1. [1]

    D. J. Thouless, M. Kohmoto, M. P. Nightingale, and M. den Nijs, Quantized Hall conductance in a two- dimensional periodic potential, Phys. Rev. Lett. 49, 405 (1982)

    1982

  2. [2]

    F. D. M. Haldane, Model for a quantum Hall effect with- out Landau levels: Condensed-matter realization of the ”Parity Anomaly”, Phys. Rev. Lett. 61, 2015 (1988)

    2015

  3. [3]

    C. L. Kane and E. J. Mele, z2 topological order and the quantum spin Hall effect, Phys. Rev. Lett. 95, 146802 (2005)

    2005

  4. [4]

    B. A. Bernevig, T. L. Hughes, and S. C. Zhang, Quantum spin Hall effect and topological phase transition in HgTe quantum wells, Science 314, 1757 (2006)

    2006

  5. [5]

    M. Z. Hasan and C. L. Kane, Colloquium: Topological insulators, Rev. Mod. Phys. 82, 3045 (2010)

    2010

  6. [6]

    R. Yu, W. Zhang, H. J. Zhang, S. C. Zhang, X. Dai, and Z. Fang, Quantized anomalous Hall effect in magnetic topological insulators, Science 329, 61 (2010)

    2010

  7. [7]

    C. Z. Chang, J. Zhang, X. Feng, J. Shen, Z. Zhang, 6 M. Guo, K. Li, Y. Ou, P. Wei, L. L. Wang, Z. Q. Ji, Y. Feng, S. Ji, X. Chen, J. Jia, X. Dai, Z. Fang, S. C. Zhang, K. He, Y. Wang, L. Lu, X. C. Ma, and Q. K. Xue, Experimental observation of the quantum anoma- lous Hall effect in a magnetic topological insulator, Sci- ence 340, 167 (2013)

    work page 2013

  8. [8]

    Bansil, H

    A. Bansil, H. Lin, and T. Das, Colloquium: Topological band theory, Rev. Mod. Phys. 88, 021004 (2016)

    2016

Show all 86 references
  1. [9]

    Senthil, Symmetry-protected topological phases of quantum matter, Annu

    T. Senthil, Symmetry-protected topological phases of quantum matter, Annu. Rev. Condens. Matter Phys. 6, 299 (2015)

    2015

  2. [10]

    ˇSmejkal, Y

    L. ˇSmejkal, Y. Mokrousov, B. Yan, and A. H. Mac- Donald, Topological antiferromagnetic spintronics, Nat. Phys. 14, 242 (2018)

    2018

  3. [11]

    Y. Xu, M. Vergniory, D. S. Ma, J. L. Ma˜ nes, Z. D. Song, B. A. Bernevig, N. Regnault, and L. Elcoro, Catalog of topological phonon materials, Science 384, eadf8458 (2024)

    2024

  4. [12]

    Stenull and T

    O. Stenull and T. C. Lubensky, Signatures of topological phonons in superisostatic lattices, Phys. Rev. Lett. 122, 248002 (2019)

    2019

  5. [13]

    Zhang, J

    L. Zhang, J. Ren, J. S. Wang, and B. Li, Topological nature of the phonon Hall effect, Phys. Rev. Lett. 105, 225901 (2010)

    2010

  6. [14]

    P. A. McClarty, Topological magnons: A review, Annu. Rev. Condens. Matter Phys. 13, 171 (2022)

    2022

  7. [15]

    L. Chen, J. H. Chung, B. Gao, T. Chen, M. B. Stone, A. I. Kolesnikov, Q. Huang, and P. Dai, Topological spin excitations in honeycomb ferromagnet CrI 3, Phys. Rev. X 8, 041028 (2018)

    2018

  8. [16]

    A. Mook, K. Plekhanov, J. Klinovaja, and D. Loss, Interaction-stabilized topological magnon insulator in ferromagnets, Phys. Rev. X 11, 021061 (2021)

    2021

  9. [17]

    R¨ uckriegel, A

    A. R¨ uckriegel, A. Brataas, and R. A. Duine, Bulk and edge spin transport in topological magnon insulators, Phys. Rev. B 97, 081106 (2018)

    2018

  10. [18]

    Plekhanov, G

    K. Plekhanov, G. Roux, and K. Le Hur, Floquet engi- neering of Haldane Chern insulators and chiral bosonic phase transitions, Phys. Rev. B 95, 045102 (2017)

    2017

  11. [19]

    F. Zhu, L. Zhang, X. Wang, F. J. Dos Santos, J. Song, T. Mueller, K. Schmalzl, W. F. Schmidt, A. Ivanov, J. T. Park, S. Lounis, S. Bl¨ ugel, Y. Mokrousov, Y. Su, and T. Br¨ uckel, Topological magnon insulators in two- dimensional van der Waals ferromagnets CrSiTe 3 and CrGeTe3...

    2021

  12. [20]

    X. T. Zhang, Y. H. Gao, and G. Chen, Thermal Hall effects in quantum magnets, Phys. Rep. 1070, 1 (2024)

    2024

  13. [21]

    Onose, T

    Y. Onose, T. Ideue, H. Katsura, Y. Shiomi, N. Nagaosa, and Y. Tokura, Observation of the magnon Hall effect, Science 329, 297 (2010)

    2010

  14. [22]

    Katsura, N

    H. Katsura, N. Nagaosa, and P. A. Lee, Theory of the thermal Hall effect in quantum magnets, Phys. Rev. Lett. 104, 066403 (2010)

    2010

  15. [23]

    Zhang, C

    H. Zhang, C. Xu, C. Carnahan, M. Sretenovic, N. Suri, D. Xiao, and X. Ke, Anomalous thermal Hall effect in an insulating van der Waals magnet, Phys. Rev. Lett. 127, 247202 (2021)

    2021

  16. [24]

    A. Mook, J. Henk, and I. Mertig, Magnon Hall effect and topology in kagome lattices: A theoretical investigation, Phys. Rev. B 89, 134409 (2014)

    2014

  17. [25]

    A. V. Chumak, V. I. Vasyuchka, A. A. Serga, and B. Hillebrands, Magnon spintronics, Nat. Phys. 11, 453 (2015)

    2015

  18. [26]

    B. Lenk, H. Ulrichs, F. Garbs, and M. M¨ unzenberg, The building blocks of magnonics, Phys. Rep. 507, 107 (2011)

    2011

  19. [27]

    Prabhakar and D

    A. Prabhakar and D. D. Stancil, Spin waves: Theory and applications, Vol. 5 (Springer, 2009)

    2009

  20. [28]

    Pirro, V

    P. Pirro, V. I. Vasyuchka, A. A. Serga, and B. Hille- brands, Advances in coherent magnonics, Nat. Rev. Mater. 6, 1114 (2021)

    2021

  21. [29]

    A. V. Chumak, A. A. Serga, and B. Hillebrands, Magnon transistor for all-magnon data processing, Nat. Commun. 5, 4700 (2014)

    2014

  22. [30]

    Arakawa, Controlling stability of Bose-Einstein con- densation of interacting magnons in an antiferromagnet by an external magnetic field, Phys

    N. Arakawa, Controlling stability of Bose-Einstein con- densation of interacting magnons in an antiferromagnet by an external magnetic field, Phys. Rev. B 99, 014405 (2019)

    2019

  23. [31]

    Shen, Electrical and magnetic control of spin-lattice configuration and magnon-ferron hybridization in a two- dimensional multiferroic model, Phys

    K. Shen, Electrical and magnetic control of spin-lattice configuration and magnon-ferron hybridization in a two- dimensional multiferroic model, Phys. Rev. B 108, 094413 (2023)

    2023

  24. [32]

    Venema, B

    L. Venema, B. Verberck, I. Georgescu, G. Prando, E. Couderc, S. Milana, M. Maragkou, L. Persechini, G. Pacchioni, and L. Fleet, The quasiparticle zoo, Nat. Phys. 12, 1085 (2016)

    2016

  25. [33]

    A. M. Kuzmenko, D. Szaller, T. Kain, V. Dziom, L. Wey- mann, A. Shuvaev, A. Pimenov, A. A. Mukhin, V. Y. Ivanov, I. A. Gudim, L. N. Bezmaternykh, and A. Pi- menov, Switching of magnons by electric and magnetic fields in multiferroic borates, Phys. Rev. Lett. 120, 027203 (2018)

    2018

  26. [34]

    Vidal Silva, E

    N. Vidal Silva, E. Aguilera, A. Rold´ an Molina, R. A. Duine, and A. S. Nunez, Magnon polarons induced by a magnetic field gradient, Phys. Rev. B102, 104411 (2020)

    2020

  27. [35]

    F. Y. Li, Y. D. Li, Y. B. Kim, L. Balents, Y. Yu, and G. Chen, Weyl magnons in breathing pyrochlore antifer- romagnets, Nat. Commun. 7, 12691 (2016)

    2016

  28. [36]

    G. Go, D. An, H. W. Lee, and S. K. Kim, Magnon or- bital Nernst effect in honeycomb antiferromagnets with- out spin–orbit coupling, Nano Lett. 24, 5968 (2024)

    2024

  29. [37]

    J. Ni, Y. Jin, Q. Du, and G. Chang, Magnon nonlinear Hall effect in two-dimensional antiferromagnetic insula- tors, Phys. Rev. B 112, 054424 (2025)

    2025

  30. [38]

    Mukherjee, S

    R. Mukherjee, S. Verma, and A. Kundu, Nonlinear magnon transport in bilayer van der Waals antiferromag- nets, Phys. Rev. B 107, 245426 (2023)

    2023

  31. [39]

    Kondo and Y

    H. Kondo and Y. Akagi, Nonlinear magnon spin Nernst effect in antiferromagnets and strain-tunable pure spin current, Phys. Rev. Res. 4, 013186 (2022)

    2022

  32. [40]

    Shrestha, M

    S. Shrestha, M. Souri, C. J. Dietl, E. M. P¨ arschke, M. Krautloher, G. A. Calderon Ortiz, M. Minola, X. Shi, A. V. Boris, J. Hwang, G. Khaliullin, G. Cao, B. Keimer, J.-W. Kim, J. Kim, and A. Seo, Tunable magnons of an antiferromagnetic Mott insulator via interfacial metal- i...

    2025

  33. [41]

    A. V. Sadovnikov, A. A. Grachev, S. E. Sheshukova, Y. P. Sharaevskii, A. A. Serdobintsev, D. M. Mitin, and S. A. Nikitov, Magnon straintronics: Reconfigurable spin-wave routing in strain-controlled bilateral magnetic stripes, Phys. Rev. Lett. 120, 257203 (2018)

    2018

  34. [42]

    Y. H. Li and R. Cheng, Magnonic Su-Schrieffer-Heeger model in honeycomb ferromagnets, Phys. Rev. B 103, 014407 (2021)

    2021

  35. [43]

    Vidal-Silva and R

    N. Vidal-Silva and R. E. Troncoso, Time-dependent strain-tuned topological magnon phase transition, Phys. Rev. B 106, 224401 (2022). 7

    2022

  36. [44]

    Soenen and M

    M. Soenen and M. V. Miloˇ sevi´ c, Tunable magnon topol- ogy in monolayer CrI3 under external stimuli, Phys. Rev. Mater. 7, 084402 (2023)

    2023

  37. [45]

    F. Zhuo, H. Li, and A. Manchon, Topological phase tran- sition and thermal Hall effect in kagome ferromagnets, Phys. Rev. B 104, 144422 (2021)

    2021

  38. [46]

    S. D. Bader and S. S. P. Parkin, Spintronics, Annu. Rev. Condens. Matter Phys. 1, 71 (2010)

    2010

  39. [47]

    Kim and S

    H. Kim and S. K. Kim, Topological phase transition in magnon bands in a honeycomb ferromagnet driven by sublattice symmetry breaking, Phys. Rev. B 106, 104430 (2022)

    2022

  40. [48]

    R. W. Zhang, C. Cui, R. Li, J. Duan, L. Li, Z. M. Yu, and Y. Yao, Predictable gate-field control of spin in alter- magnets with spin-layer coupling, Phys. Rev. Lett. 133, 056401 (2024)

    2024

  41. [49]

    J. Tian, J. Li, H. Liu, Y. Li, Z. Liu, L. Li, J. Li, G. Liu, and J. Shi, Spin-layer coupling in an altermagnetic mul- tilayer: A design principle for spintronics, Phys. Rev. B 111, 035437 (2025)

    2025

  42. [50]

    Y. H. Shen, Y. Liu, and M. Luo, Electrical reversal of the magnon thermal Hall coefficient in a van der Waals bi- layer antiferromagnet, Phys. Rev. B 110, 045423 (2024)

    2024

  43. [51]

    Fiebig, Revival of the magnetoelectric effect, J

    M. Fiebig, Revival of the magnetoelectric effect, J. Phys. D: Appl. Phys. 38, R123 (2005)

    2005

  44. [52]

    for more details about 1

    See Supplemental Material at ... for more details about 1. Additional computational results of bilayer CrXY and 2. Topological properties and magnon transport of bilayer CrXY

  45. [53]

    Winkler, Spin-orbit coupling effects in two dimen- sional electron and hole systems

    R. Winkler, Spin-orbit coupling effects in two dimen- sional electron and hole systems . (Springer Science & Business Media, Springer Berlin, Heidelberg, 2003)

    2003

  46. [54]

    D. Wang, R. Wu, and A. J. Freeman, First-principles theory of surface magnetocrystalline anisotropy and the diatomic-pair model, Phys. Rev. B 47, 14932 (1993)

    1993

  47. [55]

    Huang, J

    C. Huang, J. Feng, F. Wu, D. Ahmed, B. Huang, H. Xi- ang, K. Deng, and E. Kan, Toward intrinsic room- temperature ferromagnetism in two-dimensional semi- conductors, J. Am. Chem. Soc. 140, 11519 (2018)

    2018

  48. [56]

    P. E. Bl¨ ochl, Projector augmented-wave method, Phys. Rev. B 50, 17953 (1994)

    1994

  49. [57]

    J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev, Lett. 77, 3865 (1996)

    1996

  50. [58]

    A. Togo, L. Chaput, T. Tadano, and I. Tanaka, Imple- mentation strategies in phonopy and phono3py, J. Phys. Condens. Matter 35, 353001 (2023)

    2023

  51. [59]

    Togo, First-principles phonon calculations with phonopy and phono3py, J

    A. Togo, First-principles phonon calculations with phonopy and phono3py, J. Phys. Soc. Jpn. 92, 012001 (2023)

    2023

  52. [60]

    Liechtenstein, V

    A. Liechtenstein, V. I. Anisimov, and J. Zaanen, Density- functional theory and strong interactions: Orbital order- ing in Mott-Hubbard insulators, Phys. Rev. B 52, R5467 (1995)

    1995

  53. [61]

    Kresse and J

    G. Kresse and J. Furthm¨ uller, Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set, Comput. Mater. Sci. 6, 15 (1996)

    1996

  54. [62]

    Xiang, E

    H. Xiang, E. Kan, S. H. Wei, M. H. Whangbo, and X. Gong, Predicting the spin-lattice order of frustrated systems from first principles, Phys. Rev. B 84, 224429 (2011)

    2011

  55. [63]

    Grimme, J

    S. Grimme, J. Antony, S. Ehrlich, and H. Krieg, A con- sistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 ele- ments H-Pu, J. Chem. Phys. 132, 154104 (2010)

    2010

  56. [64]

    Xiang, C

    H. Xiang, C. Lee, H. J. Koo, X. Gong, and M. H. Whangbo, Magnetic properties and energy-mapping analysis, Dalton T. 42, 823 (2013)

    2013

  57. [65]

    M. C. Chang and Q. Niu, Berry phase, hyperorbits, and the Hofstadter spectrum: Semiclassical dynamics in mag- netic Bloch bands, Phys. Rev. B 53, 7010 (1996)

    1996

  58. [66]

    D. Xiao, M. C. Chang, and Q. Niu, Berry phase effects on electronic properties, Rev. Mod. Phys. 82, 1959 (2010)

    1959

  59. [67]

    J. Ni, Z. Zhang, J. Lu, Q. Du, Z. Jiang, and L. Bel- laiche, Nonvolatile magnonics in bilayer magnetic insula- tors, Nano Lett. 25, 1207 (2025)

    2025

  60. [68]

    Bhowal and G

    S. Bhowal and G. Vignale, Orbital Hall effect as an al- ternative to valley Hall effect in gapped graphene, Phys. Rev. B 103, 195309 (2021)

    2021

  61. [69]

    Zhang, Q

    X. Zhang, Q. Lu, W. Liu, W. Niu, J. Sun, J. Cook, M. Vaninger, P. F. Miceli, D. J. Singh, and S. W. Lian, Room-temperature intrinsic ferromagnetism in epitaxial CrTe2 ultrathin films, Nat. Commun. 12, 2492 (2021)

    2021

  62. [70]

    L. Meng, Z. Zhou, M. Xu, S. Yang, K. Si, L. Liu, X. Wang, H. Jiang, B. Li, and P. Qin, Anomalous thick- ness dependence of Curie temperature in air-stable two- dimensional ferromagnetic 1T-CrTe 2 grown by chemical vapor deposition, Nat. Commun. 12, 809 (2021)

    2021

  63. [71]

    J. J. Xian, C. Wang, J. H. Nie, R. Li, M. Han, J. Lin, W. H. Zhang, Z. Y. Liu, Z. M. Zhang, and M. P. Miao, Spin mapping of intralayer antiferromagnetism and field-induced spin reorientation in monolayer CrTe2, Nat. Commun. 13, 257 (2022)

    2022

  64. [72]

    Y. Hou, F. Xue, L. Qiu, Z. Wang, and R. Wu, Multi- functional two-dimensional van der Waals janus magnet Cr-based dichalcogenide halides, npj Comput. Mater. 8, 120 (2022)

    2022

  65. [73]

    W. Z. Xiao, L. Xu, G. Xiao, L. L. Wang, and X. Y. Dai, Two-dimensional hexagonal chromium chalco-halides with large vertical piezoelectricity, high-temperature ferromagnetism, and high magnetic anisotropy, Phys. Chem. Chem. Phys. 22, 14503 (2020)

    2020

  66. [74]

    Holstein and H

    T. Holstein and H. Primakoff, Field dependence of the intrinsic domain magnetization of a ferromagnet, Phys. Rev. 58, 1098 (1940)

    1940

  67. [75]

    Cheng, S

    R. Cheng, S. Okamoto, and D. Xiao, Spin Nernst effect of magnons in collinear antiferromagnets, Phys. Rev. Lett. 117, 217202 (2016)

    2016

  68. [76]

    V. A. Zyuzin and A. A. Kovalev, Magnon spin Nernst effect in antiferromagnets, Phys. Rev. Lett. 117, 217203 (2016)

    2016

  69. [77]

    Y. Bai, L. Zhang, N. Mao, R. Li, Z. Chen, Y. Dai, B. Huang, and C. Niu, Coupled electronic and magnonic topological states in two-dimensional ferromagnets, ACS Nano 18, 13377 (2024)

    2024

  70. [78]

    Y. Bai, X. Zou, Z. Chen, R. Li, B. Yuan, Y. Dai, B. Huang, and C. Niu, Dual chern insulators with elec- tronic and magnonic edge states in two-dimensional fer- romagnets, ACS Nano 19, 9265 (2025)

    2025

  71. [79]

    Owerre, A first theoretical realization of honeycomb topological magnon insulator, J

    S. Owerre, A first theoretical realization of honeycomb topological magnon insulator, J. Phys. Condens. Matter 28, 386001 (2016)

    2016

  72. [80]

    Matsumoto and S

    T. Matsumoto and S. Hayami, Nonreciprocal magnons due to symmetric anisotropic exchange interaction in honeycomb antiferromagnets, Phys. Rev. B 101, 224419 (2020)

    2020

  73. [81]

    Wildes, S

    A. Wildes, S. Okamoto, and D. Xiao, Search for nonre- ciprocal magnons in MnPS 3, Phys. Rev. B 103, 024424 8 (2021)

    2021

  74. [82]

    Hayami and T

    S. Hayami and T. Matsumoto, Essential model param- eters for nonreciprocal magnons in multisublattice sys- tems, Phys. Rev. B 105, 014404 (2022)

    2022

  75. [83]

    W. Y. Tong, S. J. Gong, X. Wan, and C. G. Duan, Con- cepts of ferrovalley material and anomalous valley Hall effect, Nat. Commun. 7, 13612 (2016)

    2016

  76. [84]

    N. D. Mermin and H. Wagner, Absence of ferromag- netism or antiferromagnetism in one- or two-dimensional isotropic Heisenberg models, Phys. Rev. Lett. 17, 1133 (1966)

    1966

  77. [85]

    Gitgeatpong, Y

    G. Gitgeatpong, Y. Zhao, P. Piyawongwatthana, Y. Qiu, L. W. Harriger, N. P. Butch, T. Sato, and K. Matan, Non- reciprocal magnons and symmetry-breaking in the non- centrosymmetric antiferromagnet, Phys. Rev. Lett. 119, 047201 (2017)

    2017

  78. [86]

    Iguchi, S

    Y. Iguchi, S. Uemura, K. Ueno, and Y. Onose, Nonre- ciprocal magnon propagation in a noncentrosymmetric ferromagnet LiFe5O8, Phys. Rev. B 92, 184419 (2015)

    2015

Pith tools

Reviewed August 5, 2026 · model on record in the stance chip above.