Dipolar-exchange spin waves in thin bilayers

Artem V. Bondarenko; Elena V. Tartakovskaya; Gerrit E. W. Bauer; Ritesh Das; Rob den Teuling; Yaroslav M. Blanter

arxiv: 2504.00631 · v2 · submitted 2025-04-01 · ❄️ cond-mat.mes-hall

Dipolar-exchange spin waves in thin bilayers

Rob den Teuling , Ritesh Das , Artem V. Bondarenko , Elena V. Tartakovskaya , Gerrit E. W. Bauer , Yaroslav M. Blanter This is my paper

Pith reviewed 2026-05-22 22:04 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall

keywords spin wavesferromagnetic bilayersdipolar interactionsnonreciprocitystray fieldssynthetic antiferromagnetsvan der Waals bilayersmagnetometry

0 comments

The pith

Nonreciprocity of stray magnetic fields from spin waves in thin bilayers depends on the relative orientation of layer magnetizations.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper investigates the spectrum of dipolar-exchange spin waves in thin ferromagnetic bilayers that have in-plane magnetization. It includes the effects of interlayer exchange coupling along with intra- and interlayer dipolar interactions. Using the continuum approximation, the analysis focuses on how the nonreciprocity of the propagating magnetic stray fields emitted by these spin waves changes with the relative orientation of the magnetizations in the two layers. This nonreciprocity is presented as observable through magnetometry in synthetic antiferromagnets or weakly coupled type-A van der Waals antiferromagnetic bilayers, and it varies with an applied magnetic field. A reader would care because it links the alignment of magnetizations to directional properties of spin wave emissions that could be measured experimentally.

Core claim

In the continuum approximation the dipolar-exchange spin wave spectrum in thin bilayers produces nonreciprocal propagating magnetic stray fields whose degree of nonreciprocity is determined by the relative orientation of the layer magnetizations. This orientation dependence is observable by magnetometry of synthetic antiferromagnets or weakly coupled type-A van der Waals antiferromagnetic bilayers as a function of an applied magnetic field.

What carries the argument

The continuum approximation of the dipolar-exchange spin wave spectrum that incorporates interlayer exchange coupling and intra- and interlayer dipolar interactions.

If this is right

The nonreciprocity of the stray fields can be controlled by adjusting the relative orientation of the layer magnetizations through an external magnetic field.
Magnetometry provides a direct method to observe the orientation-dependent nonreciprocity in these bilayer systems.
Synthetic antiferromagnets exhibit tunable nonreciprocal spin wave emission based on layer alignment.
Weakly coupled van der Waals bilayers display similar field-dependent nonreciprocity in their stray fields.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

Such nonreciprocity could be used to design directional spin wave channels in magnetic devices.
Applying this to other multilayer magnetic structures might uncover analogous orientation effects.
The results suggest that magnetization configuration acts as a control knob for spin wave propagation symmetry.

Load-bearing premise

The continuum approximation remains valid for these thin bilayers, permitting smooth magnetization profiles without needing to account for atomic-scale discreteness.

What would settle it

An experiment measuring the directionality of stray fields from spin waves in a bilayer with fixed but varying relative magnetization orientations that finds the nonreciprocity to be independent of the angle between the magnetizations.

Figures

Figures reproduced from arXiv: 2504.00631 by Artem V. Bondarenko, Elena V. Tartakovskaya, Gerrit E. W. Bauer, Ritesh Das, Rob den Teuling, Yaroslav M. Blanter.

**Figure 1.** Figure 1: sketches a ferromagnetic layer of thickness a in the (y, z)-plane. The magnetization M0 and the external magnetic field H⃗ both lie along the z-axis. For weak excitations M⃗ = M⃗ 0 + ⃗m(y, z)e iΩt = [mx(y, z)e iΩt , my(y, z)e iΩt , M0] T (1) FIG. 1: Ferromagnetic layer with external magnetic field along the in-plane magnetization. The linearized Landau-Lifshitz (LL) equation takes the arXiv:2504.00631v2 [c… 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: shows the dispersion relation of the bilayer with the parameters for permalloy/Ru/permalloy. We see that the splitting of the bands along (0, 0, kz) is larger than along (0, 0, −kz) due to sign(kz) in Nnr. FIG. 3: Dispersion relation of the bilayer for φ = π 4 , a = 7 nm, L = 10 nm, J = 0.02, D = 32.48 nm2 and M0 = 7 · 105 A/m [33]. The blue and orange curves are the acoustic and optical branches, respecti… view at source ↗

read the original abstract

We investigate the dipolar-exchange spin wave spectrum in thin ferromagnetic bilayers with inplane magnetization, incorporating interlayer exchange coupling and intra- and interlayer dipolar interactions. In the continuum approximation we analyze the nonreciprocity of propagating magnetic stray fields emitted by spin waves as a function of the relative orientation of the layer magnetizations that are observable by magnetometry of synthetic antiferromagnets or weakly coupled type-A van der Waals antiferromagnetic bilayers as a function of an applied magnetic field.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper computes orientation-dependent nonreciprocity of stray fields from dipolar-exchange spin waves in bilayers under the continuum limit, but that limit is the exposed assumption for atomically thin vdW cases.

read the letter

The paper works out the dipolar-exchange spin-wave spectrum for thin in-plane magnetized bilayers, folds in interlayer exchange plus intra- and interlayer dipolar terms, and then tracks how the nonreciprocity of the emitted stray fields changes with the relative angle between the two layer magnetizations. The target is synthetic antiferromagnets and weakly coupled type-A van der Waals bilayers, where an external field can set the configuration and magnetometry can read the stray-field signature. That orientation dependence is the concrete new piece they add to existing models. The calculation stays inside the standard continuum framework, which keeps the algebra manageable and produces explicit predictions for the field patterns. Within those assumptions the technical steps appear consistent and the connection to an observable is direct. The main vulnerability is the continuum approximation itself when the bilayers are only a few atomic layers thick. Discrete lattice effects can alter the dipolar tensor and the allowed wave-vector structure, and the work does not show a cross-check against a discrete bilayer model. That is the step that could shift the predicted nonreciprocity. The paper is aimed at specialists already working on magnonics in layered magnets or on synthetic antiferromagnets. A reader who needs a ready calculation for interpreting stray-field measurements in these systems will get usable results. It is not broad enough to reset the field but it addresses a specific experimental need. I would bring it to a reading group focused on spin waves or vdW magnets. I would not cite it in my own work unless I needed that exact nonreciprocity curve. It deserves peer review because the calculation is grounded in a standard model and the observable is relevant, even though the thin-layer justification will need strengthening.

Referee Report

1 major / 0 minor

Summary. The manuscript investigates the dipolar-exchange spin wave spectrum in thin ferromagnetic bilayers with in-plane magnetization, incorporating interlayer exchange coupling along with intra- and interlayer dipolar interactions. In the continuum approximation, it analyzes the nonreciprocity of propagating magnetic stray fields emitted by spin waves as a function of the relative orientation of the layer magnetizations. These effects are proposed to be observable via magnetometry in synthetic antiferromagnets or weakly coupled type-A van der Waals antiferromagnetic bilayers under an applied magnetic field.

Significance. If the central derivations are sound, the work could offer a useful theoretical description of field-orientation-dependent nonreciprocity in bilayer stray fields, with potential relevance to magnonics experiments on synthetic AFMs and vdW systems. However, the significance is tempered by the absence of any explicit validation of the continuum limit or comparison to discrete-lattice calculations, which directly impacts the reliability of the predicted nonreciprocity for atomically thin layers.

major comments (1)

[Abstract] Abstract: the analysis is performed entirely within the continuum approximation, yet the central claim concerns nonreciprocity observable in type-A vdW antiferromagnetic bilayers whose thickness is only a few atomic layers. No section provides an explicit check of the continuum limit against a discrete bilayer model (e.g., via comparison of dipolar tensors or allowed wave-vector quantization), leaving the load-bearing assumption that smooth magnetization profiles remain valid untested.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their thoughtful review. The primary concern is the lack of validation for the continuum approximation in the context of atomically thin van der Waals bilayers. We provide our response below.

read point-by-point responses

Referee: [Abstract] Abstract: the analysis is performed entirely within the continuum approximation, yet the central claim concerns nonreciprocity observable in type-A vdW antiferromagnetic bilayers whose thickness is only a few atomic layers. No section provides an explicit check of the continuum limit against a discrete bilayer model (e.g., via comparison of dipolar tensors or allowed wave-vector quantization), leaving the load-bearing assumption that smooth magnetization profiles remain valid untested.

Authors: While we acknowledge that a direct comparison to a discrete model would be valuable, the continuum approximation is justified for the long-wavelength limit relevant to the spin waves considered here. In thin bilayers, each layer is treated as having a uniform magnetization profile across its thickness, which is appropriate for atomically thin systems where the exchange length is larger than the layer thickness. The nonreciprocity in stray fields is a consequence of the dipolar interactions between the layers and does not rely on sub-layer resolution. We have added a paragraph in the discussion section to elaborate on the applicability of the continuum model to vdW bilayers. revision: partial

Circularity Check

0 steps flagged

No circularity: derivation is self-contained in continuum model

full rationale

The paper derives the dipolar-exchange spin-wave spectrum and stray-field nonreciprocity for thin bilayers using the continuum approximation, interlayer exchange, and dipolar interactions. No equations or steps reduce by construction to fitted inputs, self-definitions, or load-bearing self-citations; the central analysis of nonreciprocity versus magnetization orientation follows directly from the stated micromagnetic framework without renaming known results or smuggling ansatzes. The continuum limit is an explicit modeling choice whose validity is an external assumption rather than a tautology. This is the normal case for a first-principles theoretical derivation in the field.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract provides insufficient detail to enumerate free parameters, axioms, or invented entities; typical assumptions in such models (e.g., continuum limit, specific forms of dipolar tensor) cannot be audited.

pith-pipeline@v0.9.0 · 5624 in / 1136 out tokens · 25275 ms · 2026-05-22T22:04:24.839504+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

36 extracted references · 36 canonical work pages · 1 internal anchor

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S. V. Maleev, V. G. Bar’yakhtar, and R. A. Suris, The scattering of slow neutrons by complex magnetic struc- tures, Soviet Phys.-Solid State (English Transl.)4 (1963)

work page 1963

[2] [2]

S. V. Maleev, Polarized neutron scattering in magnets, Physics-Uspekhi 45, 569 (2002)

work page 2002

[3] [3]

A. T. D. Gr¨ unwald, A. R. Wildes, W. Schmidt, E. V. Tar- takovskaya, G. Nowak, K. Theis-Br¨ ohl, and A. Schreyer, Neutron scattering measurements of magnetic excitations in gd/y superlattices, Applied Physics Letters 96, 192505 (2010)

work page 2010

[4] [4]

A. T. D. Gr¨ unwald, A. R. Wildes, W. Schmidt, E. V. Tartakovskaya, J. Kwo, C. Majkrzak, R. C. C. Ward, and A. Schreyer, Magnetic excitations in dy/y superlattices as seen via inelastic neutron scattering, Phys. Rev. B 82, 014426 (2010)

work page 2010

[5] [5]

A. J. Grutter, K. L. Krycka, E. V. Tartakovskaya, J. A. Borchers, K. S. M. Reddy, E. Ortega, A. Ponce, and B. J. H. Stadler, Complex three-dimensional magnetic ordering in segmented nanowire arrays, ACS Nano 11, 8311 (2017)

work page 2017

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Pardavi-Horvath and E

M. Pardavi-Horvath and E. V. Tartakovskaya, Spin waves and electromagnetic waves in magnetic nanowires, in Spin Waves: Theory and Applications (Elsevier, 2019) p. 219

work page 2019

[7] [7]

D. Lott, J. Fenske, A. Schreyer, P. Mani, G. Mankey, F. Klose, E. Schmidt, K. Schmalzl, and E. Tatakovskaya, Antiferromagnetism in a Fe 50Pt40Rh10 thin film investi- gated using neutron diffraction, Physical Review B 78, 174413 (2008)

work page 2008

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Fenske, D

J. Fenske, D. Lott, E. V. Tartakovskaya, H. Lee, P. R. LeClair, G. J. Mankey, W. Schmidt, K. Schmalzl, F. Klose, and A. Schreyer, Magnetic order and phase transitions in Fe 50Pt50−xRhx, J. Appl. Cryst. 48, 1142 (2015)

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V. G. Bar’yakhtar, B. A. Ivanov, and M. V. Chetkin, Dynamics of domain walls in weak ferromagnets, Usp. Fiz. Nauk 146, 417 (1985)

work page 1985

[10] [10]

V. G. Bar’yakhtar, M. V. Chetkin, B. A. Ivanov, and S. N. Gadetskii, Dynamics of Topological Magnetic Soli- tons (Springer Berlin, Heidelberg, 2006)

work page 2006

[11] [11]

Bar’yakhtar, B

V. Bar’yakhtar, B. Ivanov, A. Sukstanskii, and E. V. Tartakovskaya, Nonequilibrium thermodynamics of a gas of solitons of kink type in quasione-dimensional systems, Theor Math Phys 74, 32 (1988)

work page 1988

[12] [12]

Popadiuk, E

D. Popadiuk, E. Tartakovskaya, M. Krawczyk, and K. Guslienko, Emergent magnetic field and nonzero gy- rovector of the toroidal magnetic hopfion, physica sta- tus solidi (RRL) – Rapid Research Letters 17, 2300131 (2023)

work page 2023

[13] [13]

Sobucki, M

K. Sobucki, M. Krawczyk, O. Tartakivska, and P. Graczyk, Magnon spectrum of bloch hopfion be- yond ferromagnetic resonance, APL Materials10, 091103 (2022)

work page 2022

[14] [14]

R. L. Stamps, Spin configurations and spin-wave excita- tions in exchange-coupled bilayers, Phys. Rev. B 49, 339 (1994)

work page 1994

[15] [15]

Ishibashi, Y

M. Ishibashi, Y. Shiota, T. Li, S. Funada, T. Moriyama, and T. Ono, Switchable giant nonreciprocal frequency shift of propagating spin waves in synthetic antiferromag- nets, Science Advances 6, eaaz6931 (2020)

work page 2020

[16] [16]

A. I. Akhiezer, V. G. Bar’yakhtar, and S. V. Peletmin- skii, Coupled magnetoelastic waves in ferromagnetic me- dia and ferroacoustic resonance, Soviet Physics JETP 8, 157 (1959)

work page 1959

[17] [17]

A. I. Akhiezer, V. Bar’yakhtar, and S. Peletminskii, Spin Waves (North-Holland Pub. Co., 1968)

work page 1968

[18] [18]

A. I. Akhiezer, V. G. Bar’yakhtar, and M. I. Kaganov, Spin waves in ferromagnets and antiferromagnets. ii in- teraction of spin waves with one another and with lattice vibrations; relaxation and kinetic processes, Sov. Phys. Usp. 3, 661 (1961)

work page 1961

[19] [19]

X. Zhou, E. V. Tartakovskaya, G. N. Kakazei, and A. O. Adeyeye, Engineering spin wave spectra in thick ni 80fe20 rings by using competition between exchange and dipolar fields, Phys. Rev. B 104, 214402 (2021)

work page 2021

[20] [20]

Szulc, J

K. Szulc, J. Kharlan, P. Bondarenko, E. V. Tar- takovskaya, and M. Krawczyk, Impact of surface anisotropy on the spin-wave dynamics in a thin ferro- magnetic film, Phys. Rev. B 109, 054430 (2024)

work page 2024

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R. E. D. Wames and T. Wolfram, Dipole-exchange spin waves in ferromagnetic films, J. Appl. Phys. 41, 987 (1970)

work page 1970

[22] [22]

Arias and D

R. Arias and D. L. Mills, Theory of spin excitations and the microwave response of cylindrical ferromagnetic nanowires, Phys. Rev. B 63, 134439 (2001)

work page 2001

[23] [23]

Rych ly, V

J. Rych ly, V. S. Tkachenko, J. W. K los, A. Kuchko, and M. Krawczyk, Spin wave modes in a cylindrical nanowire in crossover dipolar-exchange regime, Journal of Physics D: Applied Physics 52, 075003 (2018)

work page 2018

[24] [24]

Bar’yakhtar and B

V. Bar’yakhtar and B. Ivanov, Phase diagram of a ferro- magnetic plate in an external magnetic field, Zh. Eksp. Teor. Fiz. 72, 1504 (1977)

work page 1977

[25] [25]

B. A. Kalinikos and A. N. Slavin, Theory of dipole- exchange spin wave spectrum for ferromagnetic films with mixed exchange boundary conditions, J. Phys. C: Solid State Phys. 19, 7013 (1986)

work page 1986

[26] [26]

Hillebrands, C

B. Hillebrands, C. Mathieu, C. Hartmann, M. Bauer, O. Biittner, S. Riedling, B. Roos, S. Demokritov, B. Bartenlian, C. Chappert, D. Decanini, F. Rousseaux, E. Cambril, A. Miiller, B. Hoffmann, and U. Hartmann, Static and dynamic properties of patterned magnetic permalloy films, Journal of Magnetism and Magnetic Ma- terials 175, 10 (1997)

work page 1997

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Mathieu, J

C. Mathieu, J. Jorzick, A. Frank, S. O. Demokritov, A. N. Slavin, B. Hillebrands, B. Bartenlian, C. Chap- pert, D. Decanini, F. Rousseaux, and E. Cambril, Lateral quantization of spin waves in micron size magnetic wires, Phys. Rev. Lett. 81, 3968 (1998)

work page 1998

[28] [28]

Guslienko and A

K. Guslienko and A. Slavin, Spin-waves in cylindrical magnetic dot arrays with in-plane magnetization, Jour- nal of Applied Physics 87, 6337 (2000)

work page 2000

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