Topological Magnons on the Ferromagnetic Zigzag Lattice

John W. Villanova; Lucas Lindsay; Randy S. Fishman; Skandan Subramanian; Tom Berlijn

Topological Magnons on the Ferromagnetic Zigzag Lattice

T0 review · 0 major / 7 minor · reviewed 2026-08-12 · deepseek-v4-flash

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

Pith's one-line read For a ferromagnet on the zigzag lattice, the magnon bands acquire Chern number ±1 exactly when two exchange-anisotropy ratios lie on opposite sides of 1, and they then host chiral edge magnons that survive strong defects.

desk verdict Clean analytic Chern-number conditions for the zigzag-lattice magnon model, with real but minor caveats; deserves a serious referee. read the letter →

arxiv 2411.18515 v1 pith:UVM2CG7P submitted 2024-11-27 cond-mat.mes-hall cond-mat.mtrl-sci

Skandan Subramanian , Tom Berlijn , Lucas Lindsay , Randy S. Fishman , John W. Villanova This is my paper · ORCID

classification cond-mat.mes-hallcond-mat.mtrl-sci

keywords topologicalmagnonszigzaglatticeCherninsulatorDzyaloshinskii-Moriyainteractionchiraledgestatesspin-wavetheoryanisotropicexchangestrain-tunabletopology

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 in ferromagnetic zigzag chain compounds are usually addressed through their dispersion, but this paper asks whether their band structure can be topologically nontrivial. It shows that in a model with anisotropic Heisenberg exchange and Dzyaloshinskii-Moriya interaction, the two magnon bands carry Chern numbers ±1 exactly when the exchange-anisotropy ratios α = |B/A| and β = |G/F| lie on opposite sides of 1, with D ≠ 0; at α = 1 or β = 1 the bands touch and the Chern number is undefined. This matters because a nonzero Chern number forces one chiral edge magnon per edge on a ribbon, and the paper demonstrates numerically that these edge states survive even strong local defects. The conditions are simple enough to be controlled by strain, so the result broadens the small family of materials that could realize magnon Chern insulators.

What carries the argument

The workhorse is the mapping of the $2\times2$ magnon Hamiltonian to a vector $\mathbf{h}(k)$ in a Pauli basis, so that the band topology reduces to the geometry of a two-dimensional surface traced by $\mathbf{h}(k)$ over the diamond Brillouin zone. Because the surface is closed, the Chern number of the lower band equals half the number of signed intersections of a line through the origin (the $h_z$-axis) with this surface, as in Eq. (16). Solving $\mathbf{h}(k)=0$ for the intersection points yields the closed-form conditions in Eqs. (20)–(21), and the natural coordinates for the phase diagram are $\alpha = |B/A|$ and $\beta = |G/F|$. This geometric device turns a Berry-curvature integral into an algebra problem, making the phase diagram exact and parameter-free.

What would settle it

Compute the same ribbon spectrum with a second DM interaction $D'$ of, say, $0.1D$ on the (1,1) diagonals included: if the predicted $|C_n|=1$ region for a CdVO$_3$-like set of exchange constants changes to $C_n=0$ or becomes gapless, then the phase diagram in Fig. 3 does not apply at that level of $D'$.

Watch

Extended reading notes

Core claim

The central discovery is that the topology of the two magnon bands of the ferromagnetic zigzag lattice is governed by two dimensionless ratios built from the exchange constants, not by the size of the DM interaction. Writing the Hamiltonian as $H(k) = \mathbf{h}(k)\cdot\boldsymbol{\sigma} + h_0 I$, the paper proves the Chern number of the lower band is nonzero if and only if the $\mathbf{h}$-surface encloses the origin, which is equivalent to the algebraic condition $(G/F)^2 \ge 1 \ge (B/A)^2$ or $(B/A)^2 \ge 1 \ge (G/F)^2$ with $D\neq 0$, where $A = J_{1x}-J_{2x}$, $B=J_{1y}-J_{2y}$, $F=-(J_{1x}+J_{2x})$, and $G=-(J_{1y}+J_{2y})$. In terms of $\alpha=|B/A|$ and $\beta=|G/F|$, this says $|C_n|=1$ when $\alpha$ and $\beta$ are on opposite sides of 1. At $\alpha=1$ or $\beta=1$ the spectrum is gapless and the Chern number is undefined; otherwise it is 0. The same condition predicts, via bulk-boundary correspondence, exactly one edge state per edge on a 45°-cut ribbon, and explicit supercell calculations show that an attractive defect in the ribbon center and even a defect on the edge do not remove this edge state.

Load-bearing premise

The load-bearing premise is that the second DM interaction along the (1,1) diagonals, and all further-neighbor exchange couplings, are weak enough to omit from the model; the paper says they are 'generally weaker' but gives no quantitative bound.

Editorial extensions

If this is right

Any FM zigzag material whose exchange anisotropies satisfy $\alpha>1>\beta$ or $\beta>1>\alpha$, with any nonzero $D$, will have gapped magnon bands with Chern numbers $\pm1$ and one chiral edge mode per edge.
Because the condition involves only ratios, a strain that changes $J_{1x}/J_{1y}$ or $J_{2x}/J_{2y}$ can switch the system between $|C_n|=1$ and $C_n=0$; the paper gives a concrete example with $J_{1x}=1.9$ meV and $J_{1y}=2.1$ meV turning a previously isotropic material into a magnon Chern insulator.
The edge magnons remain intact in the presence of strong local defects, including an edge defect whose couplings are set to zero; the edge state negotiates the defect by moving into the second atomic layer.
The topological phase does not require a large DM interaction: any nonzero $D$ opens the gap once the exchange ratios straddle 1, and the easy-axis anisotropy $K$ keeps the spins ordered.

Reading between the lines

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

If the model holds in real zigzag magnets, a quantitative estimate of the second DM interaction $D'$ along the $(1,1)$ diagonals for CdVO$_3$, LaCrOS$_2$, or La$_3$MnAs$_5$ would be the decisive check; the paper only says $D'$ is 'generally weaker' without giving a number.
The same $\mathbf{h}$-surface intersection technique could be reused for other two-band magnon models with anisotropic exchange, producing analogous 'straddling' conditions without brute-force Berry-curvature integration.
Because the gap closes at $\alpha=1$ or $\beta=1$, a strain sweep across those lines should show a magnon gap collapse and reopening, a signature that inelastic neutron scattering could observe as the spin-wave gap going to zero.

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.

Desk Editor's Note

read the letter

Good — this is the paper that turns the zigzag-lattice magnon model from a numerical observation into an exact statement. The new content is the analytic Chern-number condition, Eqs. (20)-(21), and the phase diagram in Fig. 3. Those weren't in Ref. [30], which reported the same model numerically. The derivation is self-contained: write H = h·σ, reduce the Chern number to intersections of the h-surface with the hz-axis, solve hx=hy=0 exactly, and get conditions in terms of α and β. I checked the algebra and it works. The agreement with the earlier Berry-curvature integrals is a consistency check, not a fitted parameter. There are no free parameters.

The defect-robustness part is also new and useful: edge modes survive a strong attractive defect in the bulk and a site with zero couplings at the edge. The ribbon spectra look clean.

Soft spots, in order of real concern. First, the second DM interaction D' along [1,1] is dismissed as 'generally weaker than D' without a quantitative estimate. That is a real caveat for material applicability — if D' were comparable, the phase diagram would shift — but it doesn't undermine the claim for the model actually solved. Second, the step from hx=hy=0 to Eqs. (18)-(19) is stated without the intermediate algebra; the result is checkable but the paper would be easier to trust with a few more lines. Third, the numerical Berry curvature integrations are described but not shown, and no code is provided for the ribbon calculations. These are presentation gaps, not errors.

The paper knows what it does and doesn't prove. It doesn't claim material-specific predictions beyond noting that the exchange anisotropy in known zigzag compounds is unmeasured. I'd be comfortable citing the analytic conditions.

Verdict: this deserves a serious referee. It's a clean, incremental but real advance in topological magnonics, not a revolution. Send it out.

Referee Report

0 major / 7 minor

Summary. This paper analyzes magnon band topology in a two-dimensional ferromagnetic zigzag lattice with direction-dependent Heisenberg exchange couplings J1α, J2α (α = x, y) and a Dzyaloshinskii-Moriya interaction D on inversion-asymmetric bonds. Using the Holstein-Primakoff transformation and linear spin-wave theory, the Hamiltonian is reduced to a two-band model H(k) = h(k)·σ, and the authors apply the geometrical intersection method of Ref. [42] to derive exact Chern-number conditions. The main result is that for D ≠ 0 the Chern numbers are Cn = ±1 exactly when α = |J1y − J2y|/|J1x − J2x| and β = |J1y + J2y|/|J1x + J2x| satisfy α < 1 < β or β < 1 < α; both on the same side gives Cn = 0, and the lines α = 1 or β = 1 are gapless with undefined Chern numbers. The paper also presents ribbon calculations showing chiral edge modes and their persistence under strong defects, and discusses strain control and candidate materials.

Significance. The central result is a clean, parameter-free classification: the Chern numbers are determined solely by two ratios of exchange parameters, with no fitted inputs, and the derivation is self-contained from the Hamiltonian in Eq. (5) and the Chern formula in Eq. (16). The paper explicitly verifies the bulk-boundary correspondence through numerical ribbon diagonalization and tests edge-state robustness against two strong local defects. If correct, this substantially generalizes the zigzag-lattice magnon platform and provides falsifiable predictions for strain-controlled switching between trivial, gapless, and Chern phases. The main caveat, the neglect of the second DM interaction D′ on the (1,1) diagonals, is acknowledged but not quantified; this concerns material applicability rather than the exact statement for the model actually solved.

minor comments (7)

[Section III.A, Eqs. (18)–(19)] The derivation of the arctangent solutions is not shown; please include the algebra or an appendix, and state the branch choices for the arctangent and the simultaneous upper/lower sign convention, so that the radicand (G² − F²)/(A² − B²) and the conditions (20)–(21) can be followed step by step.
[Section III.A, after Eq. (16)] The statement that the Chern number is undefined if either nz(k) = 0 or hz(k) = 0 should specify that this condition applies at the intersection points in the set D, since hz vanishes on curves in the Brillouin zone without affecting Eq. (16).
[Section III.A, Eqs. (22)–(23)] The numerical Chern-number verification is only described in words; please include a figure or table comparing the numerically integrated Berry curvature with the analytic phase diagram.
[Section II, Hamiltonian] The neglect of D′ along [1,1] is justified only by the qualitative phrase 'generally weaker than D'; please provide a quantitative estimate or a symmetry/geometry argument for the specific candidate materials, because this is the assumption that controls the applicability of the phase diagram.
[Section IV] The claim that the topological effects are independent of the size of the DM interaction should explicitly state D ≠ 0, since Eq. (15) and the gap condition require a nonzero D.
[Section I] The word 'Toplogical' in the introduction should be corrected to 'Topological'.
[Section III.A, paragraph after Eq. (15)] The statement that h0(k) must be 'small enough not to close the gap' is misleading, because h0 is a constant shift in this model and cannot close the gap; the sentence could simply say that the topology is independent of h0.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the analytic Chern-number phase diagram is derived self-contained from the model Hamiltonian, with self-citations used only as consistency checks.

full rationale

The central claim is an exact statement about the two-band magnon Hamiltonian in Eq. (5). The paper writes H(k) = h(k)\u00b7\u03c3, computes hx, hy, hz in Eqs. (13)-(15), solves hx = hy = 0 to obtain the momentum solutions in Eqs. (18)-(19), and derives the nontrivial-Chern conditions (20)-(21) from the reality of those solutions. The topological classification then follows from the standard intersection formula Eq. (16), attributed to the external reference [42] (Fruchart and Carpentier), not to the authors' own prior work. The prior paper [30] is cited for the excitation frequencies in Eqs. (9)-(10) and for numerical Berry-curvature Chern numbers, but both are presented as independent checks: the frequencies follow directly from the Hamiltonian within linear spin-wave theory, and the numerical agreement in Section III.A is described as corroboration, not as an input fitted to produce the phase diagram. The ribbon edge-mode calculations in Section III.B are independent numerical solutions of the same model and verify the bulk-boundary correspondence; no parameter is fitted to the predicted edge states. The stated neglect of the second DM interaction D' along the [1,1] diagonals is a material-modeling caveat concerning applicability to specific compounds, not a circular step in the derivation of the Chern conditions for the Hamiltonian actually solved. Overall, the derivation chain is self-contained and internally consistent, and the self-citations are not load-bearing.

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

The paper adds no new entities or fitted constants. It solves a fixed model Hamiltonian with parameters taken as inputs, and the central derivation rests on standard spin-wave theory and the two-band Chern formula. The main modeling choices are the neglect of D' and the assumption of sufficient easy-axis anisotropy.

assumptions (4)

domain assumption Linear spin-wave theory: the Holstein-Primakoff expansion truncated at quadratic order gives the correct noninteracting magnon Hamiltonian for the FM zigzag model.
Section II maps spin operators to bosons and retains quadratic terms; magnon-magnon interactions are neglected, and the topological analysis is performed on this quadratic Hamiltonian.
ad hoc to paper The DM interaction D' along (1,1) diagonals and further-neighbor exchange couplings are negligible.
Section II states D' is generally weaker than D and drops it without a quantitative estimate; the phase diagram depends on the Hamiltonian without D'.
standard math The Chern number formula Eq. (16) from Ref. [42] applies to the two-band spin-wave Hamiltonian, and bulk-boundary correspondence holds for the ribbon edge modes.
Used in Section III.A to compute Chern numbers and in Section III.B to interpret edge states; these are standard results for two-band topological insulators.
domain assumption The easy-axis anisotropy K is large enough that the lower magnon branch ω1(k) = JtS(1 - μ_k + κ) is positive across the BZ, so the FM state is stable.
Invoked implicitly via the claim that K can always stabilize the FM state for any D; if violated, the spin-wave vacuum is unstable and the Chern numbers are not physically meaningful.

how reviews work

0 comments

Cite this review

Pith. "Pith review of Topological Magnons on the Ferromagnetic Zigzag Lattice." pith.science (2026). https://pith.science/paper/UVM2CG7P

@misc{pith2026241118515,
  author       = {Pith},
  title        = {Pith review of: Topological Magnons on the Ferromagnetic Zigzag Lattice},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/UVM2CG7P}},
  note         = {Machine review of arXiv:2411.18515}
}

read the original abstract

Motivated by the experimental identification of magnetic compounds consisting of zigzag chains, we analyze the band structure topology of magnons in ferromagnets on a zigzag lattice. We account for the general lattice geometry by including spatially anisotropic Heisenberg exchange interactions and by Dzyaloshinskii-Moriya interaction on inversion asymmetric bonds. Within the linear spin-wave theory, we find two magnon branches, whose band structure topology (i.e., Chern numbers) we map out in a comprehensive phase diagram. Notably, besides topologically trivial and gapless phases, we identify topologically nontrivial phases that support chiral edge magnons. We show that these edge states are robust against elastic defect scattering.

Figures

Figures reproduced from arXiv: 2411.18515 by the authors.

**Figure 2.** FIG. 2. Topology of the Hamiltonian and band structure. (a) Side and (b) top views of the [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 4.** FIG. 4. A ribbon of zigzag width 8 constructed from the FM [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗

Figures from the paper (3 more)

**Figure 5.** Figure 5: FIG. 5. (a) Magnon bands for a ribbon of width [PITH_FULL_IMAGE:figures/full_fig_p005_5.png]

**Figure 6.** Figure 6: FIG. 6. (a) Magnon bands for a ribbon of size [PITH_FULL_IMAGE:figures/full_fig_p006_6.png]

**Figure 7.** Figure 7: FIG. 7. (a) Magnon bands for a ribbon of size [PITH_FULL_IMAGE:figures/full_fig_p007_7.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

45 extracted references · 30 canonical work pages

[30]

R. S. Fishman, T. Berlijn, J. Villanova, and L. Lind- say, Magnon orbital angular momentum of ferromagnetic honeycomb and zigzag lattice models, Phys. Rev. B 108, 214402 (2023)

work page 2023
[42]

Fruchart and D

M. Fruchart and D. Carpentier, An introduction to topo- logical insulators, Comptes Rendus. Physique 14, 779 (2013)

work page 2013
[1]

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

2010
[2]

Qi and S.-C

X.-L. Qi and S.-C. Zhang, Topological insulators and su- perconductors, Rev. Mod. Phys. 83, 1057 (2011)

2011
[3]

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

2022
[4]

P. A. Pantale´ on and Y. Xian, Edge states in a ferro- magnetic honeycomb lattice with armchair boundaries, Physica B: Condens. Matter 530, 191 (2018)

work page 2018
[5]

F. Mei, G. Chen, N. Goldman, L. Xiao, and S. Jia, Topological magnon insulator and quantized pumps from strongly-interacting bosons in optical superlattices, New J. Phys. 21, 095002 (2019)

work page 2019
[6]

D. Malz, J. Knolle, and A. Nunnenkamp, Topological magnon amplification, Nature Commun. 10, 3937 (2019)

work page 2019

Show all 45 references

[7]

Zhang, D

L.-c. Zhang, D. Go, J.-P. Hanke, P. M. Buhl, S. Gryt- siuk, S. Bl¨ ugel, F. R. Lux, and Y. Mokrousov, Imprinting and driving electronic orbital magnetism using magnons, Commun. Phys. 3, 227 (2020)

2020
[8]

Fujimoto, Hall Effect of Spin Waves in Frustrated Mag- nets, Phys

S. Fujimoto, Hall Effect of Spin Waves in Frustrated Mag- nets, Phys. Rev. Lett. 103, 047203 (2009)

2009
[9]

X. Cao, K. Chen, and D. He, Magnon Hall effect on the Lieb lattice, J. Phys.: Condens. Matter 27, 166003 (2015)

2015
[10]

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

2021
[11]

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
[12]

Ideue, Y

T. Ideue, Y. Onose, H. Katsura, Y. Shiomi, S. Ishiwata, N. Nagaosa, and Y. Tokura, Effect of lattice geometry on magnon Hall effect in ferromagnetic insulators, Phys. Rev. B 85, 134411 (2012)

2012
[13]

Hirschberger, J

M. Hirschberger, J. W. Krizan, R. J. Cava, and N. P. Ong, Large thermal Hall conductivity of neutral spin ex- citations in a frustrated quantum magnet, Science 348, 106 (2015). 8

2015
[14]

Hirschberger, R

M. Hirschberger, R. Chisnell, Y. S. Lee, and N. P. Ong, Thermal Hall effect of spin excitations in a Kagome mag- net, Phys. Rev. Lett. 115, 106603 (2015)

2015
[15]

Murakami and A

S. Murakami and A. Okamoto, Thermal Hall effect of magnons, J. Phys. Soc. Jpn 86, 011010 (2017)

2017
[16]

R. R. Neumann, A. Mook, J. Henk, and I. Mertig, Ther- mal Hall effect of magnons in collinear antiferromagnetic insulators: Signatures of magnetic and topological phase transitions, Phys. Rev. Lett. 128, 117201 (2022)

2022
[17]

Uchida, H

K.-i. Uchida, H. Adachi, T. Ota, H. Nakayama, S. Maekawa, and E. Saitoh, Observation of longitudinal spin-Seebeck effect in magnetic insulators, Appl. Phys. Lett. 97, 172505 (2010)

2010
[18]

S. M. Wu, W. Zhang, A. KC, P. Borisov, J. E. Pearson, J. S. Jiang, D. Lederman, A. Hoffmann, and A. Bhat- tacharya, Antiferromagnetic spin Seebeck effect, Phys. Rev. Lett. 116, 097204 (2016)

2016
[19]

Chang and Q

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
[20]

Sundaram and Q

G. Sundaram and Q. Niu, Wave-packet dynamics in slowly perturbed crystals: Gradient corrections and Berry-phase effects, Phys. Rev. B 59, 14915 (1999)

1999
[21]

Xiao, M.-C

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

2010
[22]

M. A. McGuire, H. Dixit, V. R. Cooper, and B. C. Sales, Coupling of crystal structure and magnetism in the lay- ered, ferromagnetic insulator CrI 3, Chemistry of Materi- als 27, 612 (2015)

2015
[23]

Chen, J.-H

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
[24]

D. G. Joshi, Topological excitations in the ferromag- netic Kitaev-Heisenberg model, Phys. Rev. B 98, 060405 (2018)

2018
[25]

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
[26]

Owerre, Topological magnon bands in ferromagnetic star lattice, J

S. Owerre, Topological magnon bands in ferromagnetic star lattice, J. Phys.: Condens. Matter 29, 185801 (2017)

2017
[27]

Cheng, S

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

2016
[28]

Owerre, Topological honeycomb magnon Hall effect: A calculation of thermal Hall conductivity of magnetic spin excitations, J

S. Owerre, Topological honeycomb magnon Hall effect: A calculation of thermal Hall conductivity of magnetic spin excitations, J. Appl. Phys. 120, 043903 (2016)

2016
[29]

R. S. Fishman, Gauge-invariant measure of the magnon orbital angular momentum, Phys. Rev. B 107, 214434 (2023)

2023
[31]

Onoda and N

M. Onoda and N. Nishiguchi, S=1/2 zigzag-chain struc- ture and ferromagnetism of CdVO 3, Journal of Physics: Condensed Matter 11, 749 (1999)

1999
[32]

A. A. Tsirlin, O. Janson, and H. Rosner, Unusual fer- romagnetic superexchange in CdVO 3: The role of Cd, Phys. Rev. B 84, 144429 (2011)

2011
[33]

Takano, T

Y. Takano, T. Tsubaki, C. Itoi, K. Takase, and K. Sek- izawa, Magnetization and specific heat of a ferromagnetic zigzag spin chain compound LaCrOS 2, Solid State Com- mun. 122, 661 (2002)

2002
[34]

L. Duan, X. C. Wang, J. Zhang, Z. Hu, J. F. Zhao, Y. G. Feng, H. L. Zhang, H.-J. Lin, C. T. Chen, W. Wu, Z. Li, R. Wang, J. F. Zhang, T. Xiang, and C. Q. Jin, Synthesis, structure, and magnetism in the ferromagnet La3MnAs5: Well-separated spin chains coupled via itin- erant el...

2022
[35]

Matsumoto and S

R. Matsumoto and S. Murakami, Theoretical prediction of a rotating magnon wave packet in ferromagnets, Phys. Rev. Lett. 106, 197202 (2011)

2011
[36]

Matsumoto and S

R. Matsumoto and S. Murakami, Rotational motion of magnons and the thermal Hall effect, Phys. Rev. B 84, 184406 (2011)

2011
[37]

R. S. K. Mong and V. Shivamoggi, Edge states and the bulk-boundary correspondence in Dirac Hamiltoni- ans, Phys. Rev. B 83, 125109 (2011)

2011
[38]

Zhang, J

L. Zhang, J. Ren, J.-S. Wang, and B. Li, Topological magnon insulator in insulating ferromagnet, Phys. Rev. B 87, 144101 (2013)

2013
[39]

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
[40]

Pizzi et al., Wannier90 as a community code: new features and applications, J

G. Pizzi et al., Wannier90 as a community code: new features and applications, J. Phys.: Condens. Matter 32, 165902 (2020)

2020
[41]

Coh and D

S. Coh and D. Vanderbilt, Python Tight Binding (PythTB), Zenodo 10.5281/zenodo.12721315 (2022)

2022 doi
[43]

Parity Anomaly

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)

1988
[44]

Shindou, R

R. Shindou, R. Matsumoto, S. Murakami, and J.-i. Ohe, Topological chiral magnonic edge mode in a magnonic crystal, Phys. Rev. B 87, 174427 (2013)

2013
[45]

R. S. Fishman, J. Fernandez-Baca, and T. R˜ o˜ om,Spin- Wave Theory and its Applications to Neutron Scattering and THz Spectroscopy(Morgan and Claypool Publishers, San Rafael, 2018)

2018

Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.

[1] [30]

R. S. Fishman, T. Berlijn, J. Villanova, and L. Lind- say, Magnon orbital angular momentum of ferromagnetic honeycomb and zigzag lattice models, Phys. Rev. B 108, 214402 (2023)

work page 2023

[2] [42]

Fruchart and D

M. Fruchart and D. Carpentier, An introduction to topo- logical insulators, Comptes Rendus. Physique 14, 779 (2013)

work page 2013

[3] [1]

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

2010

[4] [2]

Qi and S.-C

X.-L. Qi and S.-C. Zhang, Topological insulators and su- perconductors, Rev. Mod. Phys. 83, 1057 (2011)

2011

[5] [3]

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

2022

[6] [4]

P. A. Pantale´ on and Y. Xian, Edge states in a ferro- magnetic honeycomb lattice with armchair boundaries, Physica B: Condens. Matter 530, 191 (2018)

work page 2018

[7] [5]

F. Mei, G. Chen, N. Goldman, L. Xiao, and S. Jia, Topological magnon insulator and quantized pumps from strongly-interacting bosons in optical superlattices, New J. Phys. 21, 095002 (2019)

work page 2019

[8] [6]

D. Malz, J. Knolle, and A. Nunnenkamp, Topological magnon amplification, Nature Commun. 10, 3937 (2019)

work page 2019