Helimagnetism from competing intra- and interchain interactions in CrBr$_2$ and CrI$_2$

Despina Louca; John A. Schneeloch; Matthew B. Stone; Zachary Morgan

REVIEW 3 major objections 5 minor 51 references

Helimagnetism from competing intra- and interchain interactions in CrBr$_2$ and CrI$_2$

T0 review · 3 major / 5 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read In CrBr2 and CrI2, a two-bond rivalry sets the magnetic helix

desk verdict First fitted exchange parameters for CrBr2/CrI2, but the headline J1-J1' helix mechanism is only convincing for CrBr2; CrI2 misses the pitch by 20 degrees. read the letter →

arxiv 2608.10263 v1 pith:BRFYWBY3 submitted 2026-08-10 cond-mat.mtrl-sci cond-mat.str-el

John A. Schneeloch , Matthew B. Stone , Zachary Morgan , Despina Louca This is my paper · ORCID

classification cond-mat.mtrl-scicond-mat.str-el

keywords helimagnetismCrBr2I2inelasticneutronscatteringspin-wavedispersionexchangeinteractionssingle-ionanisotropyvanderWaalsmagnets

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

The paper sets out to identify which magnetic interactions produce the helimagnetic order in CrBr2 and CrI2, two layered chromium dihalides that can be made as bulk crystals, monolayers, and single chains. Using single-crystal inelastic neutron scattering, the authors map the spin-wave dispersions and fit them to a Heisenberg model. They find that the helix arises primarily not from the usual intrachain nearest-neighbor/next-nearest-neighbor competition but from two antiferromagnetic nearest-neighbor couplings: one along the ribbon chains ($J_1$) and one between chains ($J_1'$). The interlayer coupling is weak, while a sizable easy-axis single-ion anisotropy distorts the helix and creates avoided crossings in the spin-wave spectrum. Intralayer spin correlations survive well above the ordering temperature, up to at least 50 K.

What carries the argument

The load-bearing object is a Heisenberg Hamiltonian over the Cr lattice with bilinear exchange bonds $J_1$ (intrachain nearest neighbor), $J_1'$ (interchain nearest neighbor), $J_2$, $J_3$, $J_1''$, and a weak interlayer $J_c$, plus an easy-axis single-ion anisotropy $D$. The spin-wave dispersions are computed with linear spin-wave theory in finite supercells (5x1x1 for CrBr2 and 4x1x1 for CrI2, chosen to approximate the experimentally known helix angles by commensurate rotations) and fitted pixel-by-pixel to time-of-flight neutron data; the spin structure is relaxed to its energy minimum within the supercell so the anisotropy distorts the helix. The simplified $J_1$--$J_1'$ model carries the explanatory weight, because the helix-angle formula $\theta = 2\arccos(-J_1'/(2J_1))$ ties the pitch directly to the ratio of the two dominant AFM bonds.

What would settle it

Re-fit the same inelastic data with an incommensurate linear spin-wave formalism that treats the modulation wavevector exactly, without a supercell, and check whether $J_2$, $J_3$, and $J_1''$ change enough to alter the ratio $J_1'/J_1$; alternatively, measure the helix angle in a monolayer or under uniaxial strain and compare it with $\theta = 2\arccos(-J_1'/(2J_1))$ predicted from exchange constants determined at ambient bulk conditions.

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Extended reading notes

Core claim

The central claim is that in both CrBr2 and CrI2 the helimagnetic ground state is set by competition between the antiferromagnetic nearest-neighbor exchange along the ribbon chain, $J_1$, and the antiferromagnetic nearest-neighbor exchange between neighboring chains, $J_1'$. The fitted constants ($J_1 = 0.800(6)$ meV and $J_1' = 0.385(4)$ meV for CrBr2; $J_1 = 0.407(3)$ meV and $J_1' = 0.465(3)$ meV for CrI2) place the compounds near the AFM/AFM boundary of the $J_1$--$J_1'$ model, where the helical angle is minimized at $\theta = 2\arccos(-J_1'/(2J_1))$. The model reproduces the observed helix angle well for CrBr2 (153.3 degrees versus 147.0 degrees) and qualitatively for CrI2 (110.3 degrees versus 89.7 degrees). A substantial easy-axis single-ion anisotropy ($D = -0.159(4)$ meV for CrBr2 and $-0.1857(15)$ meV for CrI2) modulates the rotation of the helix, generating weak third-harmonic magnetic Bragg peaks and avoided crossings in the spin-wave branches. The exchange picture that emerges is quasi-2D: in-plane $J_1$ and $J_1'$ dominate, $J_2$, $J_3$, and $J_1''$ refine the dispersion, and the interlayer coupling $J_c$ is only 0.018--0.022 meV.

Load-bearing premise

The conclusion rests on the assumption that the true incommensurate helix can be captured by a small commensurate supercell with g=2, S=2, and a single-k helix; if the supercell approximation biases the fitted exchange constants, the conclusion that $J_1$ and $J_1'$ dominate could shift.

Editorial extensions

If this is right

The helix wavelength in both compounds is set mainly by the ratio $J_1'/J_1$, so any perturbation that changes one bond more than the other will rotate the pitch in a predictable way.
Because interlayer coupling is only 2--5% of $J_1$, the intralayer exchange Hamiltonian should survive essentially unchanged in monolayer flakes, making the two-dimensional limit a direct test of the same constants.
The sizable single-ion anisotropy predicts weak third-harmonic magnetic Bragg peaks and avoided crossings at specific wavevectors, signatures that can be searched for in other ribbon-chain dihalides.
Above $T_N$, intralayer correlations persist to at least 50 K, so short-range helical fluctuations exist over a wide temperature window despite long-range order being lost near 17 K.
The same $J_1$--$J_1'$ logic, with $J_1 = J_1'$ by trigonal symmetry, reproduces the commensurate 120-degree spin spiral of VCl2 and VBr2, linking two families of helimagnets.

Reading between the lines

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

If the $J_1$--$J_1'$ balance is the helix driver, then the Jahn-Teller distortion that makes $J_1 \neq J_1'$ is the structural switch that turns a commensurate 120-degree spiral into an incommensurate helix; this suggests pressure or strain, which modifies the distortion, should tune the incommensurability continuously.
The 20.6-degree discrepancy between the $J_1$--$J_1'$ prediction and the observed helix angle in CrI2 hints that one of the smaller couplings ($J_2$, $J_1''$, or further-neighbor terms) plays a non-negligible role there; a re-fit including biquadratic or longer-range exchanges could test whether the primary-competition claim holds quantitatively.
A monolayer of CrBr2 or CrI2 should show the same in-plane helix but with the ordering temperature strongly suppressed; measuring its spin waves would isolate the intrachain and interchain couplings without the weak interlayer term.

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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

First, the thing to know: this is the first inelastic neutron scattering study to extract microscopic exchange constants for CrBr2 and CrI2, and the data are clearly good quality. The paper's specific claim—that helimagnetism comes mainly from competing intrachain J1 and interchain J1' AFM exchange—is well-supported for CrBr2 but much weaker for CrI2, where the fitted constants predict a helix pitch 20 degrees away from the measured one. The paper acknowledges this, but the abstract and conclusion state the mechanism more firmly than the evidence warrants.

What's genuinely new and good: the measurements themselves, the careful fitting with a multi-parameter Hamiltonian in Sunny, and several ancillary findings that hold up—weak interlayer coupling (Jc ~0.02 meV), persistence of intralayer correlations to at least 50 K, and a substantial easy-axis anisotropy that produces avoided crossings and a 3k harmonic. The comparison with VCl2/VBr2 and CuX2 is thoughtful and puts the results in context.

Where the soft spots are: the supercell approximation is the main one. The authors choose a 5x1x1 cell for CrBr2 and 4x1x1 for CrI2 to approximate the known helix angles (144 vs 147 degrees; 90 vs 89.7), then relax the spin structure within that fixed period and fit exchange constants. For CrI2, the resulting J1'/J1 ratio gives 110.3 degrees per step, not 89.7. That 20-degree miss is a direct signal that either the simple J1-J1' model is insufficient, or the supercell is biasing the fit, or both. The fit cannot correct the pitch because the period is fixed. So the central mechanism is not independently established for CrI2—other terms (J2, J1'', SIA) may be quantitatively essential. For CrBr2 the miss is only 6 degrees, which is less worrying, but the same circularity applies. Fixed g=2, S=2, and single-k helix are also assumptions, though S=2 with L=0 is well justified for Cr2+. Lack of public data and code is a minor reproducibility issue.

Overall: this is a solid experimental paper with an overreach in the central claim for one of the two compounds. It deserves serious peer review, and a good referee should push for a tempered abstract, a discussion of the CrI2 discrepancy's implications, and ideally a check with a different supercell size or an incommensurate method. The exchange constants themselves will likely survive scrutiny and be useful to the field.

Referee Report

3 major / 5 minor

Summary. The paper reports inelastic neutron scattering (INS) measurements on single crystals of CrBr2 and CrI2, together with fits of the spin-wave dispersions to a Heisenberg model including exchange couplings up to third-nearest-neighbor chains, an interchain coupling, an interlayer coupling (with a DM term for CrI2), and single-ion anisotropy. From the fitted exchange constants, the authors argue that the helimagnetic order in both compounds arises primarily from competing antiferromagnetic nearest-neighbor interactions within and between ribbon chains (J1 and J1'). They also report substantial easy-axis SIA, the presence of higher-harmonic (3k_M) features in the magnetic response, and the persistence of intralayer spin correlations above the ordering temperature. The paper is clearly written and contains a large amount of experimental data, but the central mechanistic claim is only partially supported by the quantitative analysis.

Significance. If the central claim were fully established, the paper would provide a clear microscopic explanation for helimagnetism in two van der Waals magnets that have been isolated in bulk, monolayer, and single-chain forms, offering a useful comparison to the copper dihalides and chromium trihalides. The experimental dataset is rich: the fits are performed carefully in Sunny, with documented procedures, and the inclusion of single-ion anisotropy and higher-harmonic effects goes beyond typical spin-wave analyses. Credit is due for the transparent reporting of the fit Hamiltonians and the reproducible computational framework. However, the claim that J1-J1' competition is 'primarily' responsible is only quantitatively supported for CrBr2, not for CrI2, where the simple two-parameter model predicts a helix angle 20.6° away from the measured value. Since the central claim is the paper's main contribution, the manuscript requires major revision before publication.

major comments (3)

[Spin waves (main text, para. 4)] The central claim that helimagnetic order arises primarily from competing J1 and J1' is not supported for CrI2. Using the fitted J1 = 0.407 meV and J1' = 0.465 meV from Table I, the J1-J1' model gives θ = 249.7°, i.e., a per-step rotation of 110.3°, versus the observed 89.7°—a discrepancy of 20.6°. The text explicitly acknowledges this, yet the abstract and conclusion still assert that the competition is the primary cause. For CrI2, the difference is large enough that either the fitted parameters are biased by the supercell approximation or the additional terms (J2, J1'', SIA) are quantitatively essential. The paper should either temper the claim to 'qualitatively explains' or provide additional evidence that the J1-J1' ratio is independently constrained by the data.
[Supplemental Material, Sec. H (Fitting inelastic data)] The supercell sizes are chosen directly from the experimentally known helix angles: a 5×1×1 cell for CrBr2 approximates 147.0° by 144°, and a 4×1×1 cell for CrI2 approximates 89.7° by 90°. The spin structure is then relaxed within that fixed period. This means the fitted exchange constants are conditioned on the observed pitch; the fit cannot independently measure the helix angle. The good reproduction of the pitch for CrBr2 is therefore partly built in, and the 20.6° disagreement for CrI2 is direct evidence of this limitation. The authors should demonstrate that the fitted J1/J1' ratio is robust to the supercell choice, for example by repeating fits with 3×1×1, 4×1×1, and 5×1×1 supercells and showing that the resulting helix angles are stable, or by using a method that allows an incommensurate propagation vector (while addressing the SIA issue that motivated the supercell approach).
[Spin waves and Table I] The paper fixes g = 2, S = 2, and a single-k helix, and adds a small easy-plane anisotropy (D2 = 0.0001 meV) to select a screw-like spin structure. These assumptions are plausible but not all are independently tested. In particular, a different g-factor would rescale the exchange constants and thus the relative weight of J1 versus J1', and the ad hoc D2 term, while small, influences the energy minimization that determines the relaxed spin configuration used in the fits. A sensitivity analysis showing how the helix angle changes under reasonable variations of g and D2 would strengthen the paper's conclusions.

minor comments (5)

[Abstract and Conclusion] The phrase 'arises primarily from competing' is stronger than the evidence presented; the main text already contains the caveat that the J1-J1' model 'qualitatively explains' the order. The abstract and conclusion should be aligned with the body's weaker claim.
[Main text, Spin waves] Typo: 'Dzayloshinskii-Moriya' should be 'Dzyaloshinskii-Moriya' (the same typo appears in the Supplemental Material, Sec. H).
[Fig. 4 and Fig. S9] The arrows marking avoided crossings in Fig. 4 are small and can be difficult to see in print; it would help to add labels or increase the arrow size, and to note in the caption that the matching crossings are identified in Fig. S9.
[Supplemental Material, Sec. B] The discussion of layer stacking disorder is thorough, but the phrase 'the amount of diffuse scattering observed (∼75%)' is ambiguous because the percentage refers to the fraction of the sample with random stacking, not to the scattered intensity. Clarify the wording.
[Main text, Discussion] The sentence 'This exchange constant is known, from INS, to be AFM in VCl2 and VBr2, from which the J1-J1' model implies a 120° helical angle' is slightly misleading: the 120° angle follows from the trigonal symmetry J1 = J1', not from the INS measurement itself. Rephrase to avoid the implication.

Circularity Check

1 steps flagged · score 4.0 of 10

Helix-angle validation is partly circular: the supercell periods in the spin-wave fit are chosen from the observed 147°/89.7° helix angles, and the fitted J1-J1' ratio is then said to 'qualitatively explain' those same angles; for CrI2 the predicted 110.3° pitch actually misses by 20.6°, so the reduction is incomplete and the dispersion fits supply independent content.

fitted input called prediction [Supplemental Sec. H (fitting inelastic data) and main text (Spin waves, Table I discussion)]
"These supercells were chosen so that spins would undergo an approximately whole number of rotations... for CrBr2, the helical rotation angle is 147.0° ≈ 360° × 5/2 = 144°; for CrI2, the helical rotation angle is 89.2° ≈ 360°/4 = 90°. ... Using the fitted exchange constants, we obtain θ= 206.7° for CrBr2 and θ= 249.7° for CrI2 ... differ from the experimental values (147.0° [17] and 89.7° [16]) by 6.3° and 20.6° ... showing that the J1-J1' qualitatively explains the helical order."

The experimentally determined helix angle is not an independent test of the model because it is used to set the supercell period for the spin-wave fit: 5×1×1 approximates 147° by 144°, and 4×1×1 approximates 89.7° by 90°. The fitted Hamiltonian is therefore constrained to a commensurate spin structure whose period derives from the target angle, so the later comparison of the J1-J1' pitch formula to the same experimental angles is partly self-referential. The circularity is incomplete: the predicted pitches (153.3° and 110.3°) are not equal to the imposed supercell angles, and for CrI2 the 20.6° discrepancy is explicitly acknowledged, so the prediction is not forced.

full rationale

The paper's central determination of exchange constants is based on fitting inelastic neutron scattering spin-wave dispersions in Sunny, using a Heisenberg Hamiltonian with J1, J1', J2, J3, J1'', Jc, and single-ion anisotropy. This is independent external data and does not reduce to the helical pitch by construction. No load-bearing self-citation chain is present: Refs. [16] and [17] supply the experimentally measured helix angles and interlayer phases, which are inputs rather than theoretical uniqueness claims, and the J1-J1' pitch formula is standard textbook material. The partial circularity lies specifically in the consistency check: the supercell sizes used in the fitting procedure are chosen from the observed helix angles (147.0° approximated by 144° for CrBr2, 89.7° approximated by 90° for CrI2), and the fitted exchange constants are then used to derive pitches that are compared with those same observed angles. Because the model's spin structure is constrained to be commensurate with the target period, this comparison is not an independent validation. The incompleteness of the circularity is important: for CrI2 the derived J1-J1' pitch (110.3°) misses the experimental value by 20.6°, which the authors acknowledge, so the fit does not actually reproduce the target pitch. This weakens the central claim for CrI2 but does not make the dispersion-based determination circular. Overall the score reflects one genuinely self-referential validation step, while the main derivation retains independent content.

Assumptions & free parameters 14 free parameters · 7 assumptions · 0 invented entities

The central claim rests on a Hamiltonian with fitted exchange parameters and a set of modeling assumptions (supercell approximation, g=2, S=2, single-k helix, fixed small easy-plane term, fixed DM ratio for CrI2). The exchange constants themselves are free parameters fitted to the spin wave data.

free parameters (14)

J1 (CrBr2) = 0.800(6) meV
Fitted to spin wave dispersions in Sunny; used in the Hamiltonian of Eq. 3.
J2 (CrBr2) = -0.105(6) meV
Fitted to spin wave dispersions in Sunny; included to capture dispersion details.
J3 (CrBr2) = -0.060(4) meV
Fitted to spin wave dispersions in Sunny; needed for curvature along (H,0,0).
J1' (CrBr2) = 0.385(4) meV
Fitted to spin wave dispersions in Sunny; central to the J1-J1' mechanism.
Jc (CrBr2) = 0.0181(4) meV
Fitted to interlayer dispersion along L.
D (CrBr2) = -0.159(4) meV
Fitted easy-axis single-ion anisotropy perpendicular to chains.
J1 (CrI2) = 0.407(3) meV
Fitted to spin wave dispersions in Sunny; used in the Hamiltonian of Eq. 3.
J2 (CrI2) = 0.0862(18) meV
Fitted to spin wave dispersions in Sunny; sign opposite to CrBr2.
J1' (CrI2) = 0.465(3) meV
Fitted to spin wave dispersions in Sunny; central to the J1-J1' mechanism.
J1'' (CrI2) = 0.0259(15) meV
Fitted to reproduce curvature along (0.75,K,0).
Jc (CrI2) = 0.0216(8) meV
Fitted to interlayer dispersion along L.
Jc,DM (CrI2) = 0.0122 meV
Fixed during fitting to reproduce the 210 degree interlayer phase; not freely fitted.
D (CrI2) = -0.1857(15) meV
Fitted easy-axis single-ion anisotropy perpendicular to chains.
D2 (both) = 0.0001 meV
Hand-chosen small easy-plane term to select a screw-like helix; not fitted.

assumptions (7)

domain assumption The magnetic Hamiltonian is a Heisenberg model with bilinear exchange couplings plus single-ion anisotropy (Eq. 3).
The paper assumes this Hamiltonian to fit the spin waves; if biquadratic or other terms are important, the fitted exchange constants could be effective only.
domain assumption Linear spin wave theory is valid for the ordered helix at 5 K.
The fitting uses Sunny's linear spin wave theory; anharmonic effects are neglected.
domain assumption The magnetic structure is a single-k helix with spins rotating in the (yz) plane, perpendicular to the ribbon chains.
Based on previous diffraction and the observed peaks; used to set the spin structure in the supercell.
domain assumption The Cr2+ ion has L=0, S=2, and g=2.
Used in the model and in the magnetic form factor; CrI2's susceptibility moment is lower, indicating covalency.
ad hoc to paper A fixed small easy-plane SIA (D2=0.0001 meV) is added to select a screw-like helix.
The value is not fitted and is set just to break degeneracy; it may affect the dispersion at low energy.
ad hoc to paper For CrI2, the interlayer DM coupling Jc,DM is fixed relative to Jc to reproduce the 210 degree interlayer phase.
This ratio is imposed, not fitted from the spin wave data.
domain assumption The finite supercell with periodic boundaries approximates the incommensurate helix.
The supercell sizes are chosen from the experimental helix angle; the spin structure is relaxed within the supercell.

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Cite this review

Pith. "Pith review of Helimagnetism from competing intra- and interchain interactions in CrBr$_2$ and CrI$_2$." pith.science (2026). https://pith.science/paper/BRFYWBY3

@misc{pith2026260810263,
  author       = {Pith},
  title        = {Pith review of: Helimagnetism from competing intra- and interchain interactions in CrBr$_2$ and CrI$_2$},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/BRFYWBY3}},
  note         = {Machine review of arXiv:2608.10263}
}

abstract

CrBr$_2$ and CrI$_2$ are promising platforms for studying the effect of dimensionality on magnetic order, having been isolated in a 3-, 2-, and 1-dimensional form as bulk crystals, monolayers, and individual chains encapsulated in carbon nanotubes. However, the interactions that give rise to their helimagnetic order are unknown. Via inelastic neutron scattering on single crystals, we have determined the exchange interactions of these compounds from the spin wave dispersions, finding that the helimagnetic order arises primarily from competing antiferromagnetic interactions between intrachain and interchain nearest-neighbors. Single-ion anisotropy is substantial, modulating the helical spin rotation and gapping the inelastic intensity at points of branch crossings. As temperature increases, long-range order vanishes but intralayer correlations remain detectable up to at least 50 K.

Figures

Figures reproduced from arXiv: 2608.10263 by the authors.

**Figure 2.** Elastic intensity within the H0L plane for CrBr [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗

**Figure 4.** Spin wave intensity at 5 K for CrBr2 (a,e,g) and CrI2 (b,f,j), along with the dispersion for simplified single-layer spin-wave models that omit single-ion anisotropy and interlayer coupling. Data were taken on SEQUOIA. Intensity is plotted as a function of energy transfer E, and wavevector along the directions in reciprocal space shown on the horizontal axis, corresponding to the ribbon-chain axis (a,b), the perpend… view at source ↗

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Peigen Li, Jihai Zhang, Di Zhu, Cui-Qun Chen, Enkui Yi, Bing Shen, Yusheng Hou, Zhongbo Yan, Dao-Xin Yao, Donghui Guo, and Dingyong Zhong, “Observation of In-Gap States in a Two-Dimensional CrI2/NbSe2 Het- 5 erostructure,” Nano Letters24, 9468–9476 (2024)

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Magnetic ordering in the frustrated Heisen- berg chain system cupric chloride CuCl 2,

M. G. Banks, R. K. Kremer, C. Hoch, A. Simon, B. Ouladdiaf, J.-M. Broto, H. Rakoto, C. Lee, and M.-H. Whangbo, “Magnetic ordering in the frustrated Heisen- berg chain system cupric chloride CuCl 2,” Physical Re- view B80, 024404 (2009)

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CuBr 2 – A New Multiferroic Ma- terial with High Critical Temperature,

Li. Zhao, Tsu-Lien Hung, Ching-Chien Li, Yang- Yuan Chen, Maw-Kuen Wu, Reinhard K. Kre- mer, Michael G. Banks, Arndt Simon, Myung-Hwan Whangbo, Changhoon Lee, Jun Sung Kim, Ingyu Kim, and Kee Hoon Kim, “CuBr 2 – A New Multiferroic Ma- terial with High Critical Temperature,” Ad...

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Heli- magnetism in the candidate ferroelectric CrI 2,

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Helimagnetism in CrBr 2 and CrIBr,

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2025
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Structure cristalline de l’iodure de chrome, CrI 2,

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Helimagnetism and weak ferromag- netism in edge-shared chain cuprates,

S. L. Drechsler, J. Richter, R. Kuzian, J. M´ alek, N. Tristan, B. B¨ uchner, A. S. Moskvin, A. A. Gippius, A. Vasiliev, O. Volkova, A. Prokofiev, H. Rakoto, J. M. Broto, W. Schnelle, M. Schmitt, A. Ormeci, C. Loi- son, and H. Rosner, “Helimagnetism and weak ferromag- netism i...

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Discussion— Our results clarify the magnetic inter- actions in CrBr 2 and CrI 2

and CrCl 2 [28], where somewhat lower values of the SIA cause gaps of∼2 meV at the bottom of the inelastic intensity. Discussion— Our results clarify the magnetic inter- actions in CrBr 2 and CrI 2. The dominant interactions are the AFM intrachainJ 1 and the interchainJ ′ 1, a...
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VESTA 3 for three- dimensional visualization of crystal, volumetric and mor- phology data,

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M. B. Stone, J. L. Niedziela, D. L. Abernathy, L. DeBeer- Schmitt, G. Ehlers, O. Garlea, G. E. Granroth, M. Graves-Brook, A. I. Kolesnikov, A. Podlesnyak, and B. Winn, “A comparison of four direct geometry time-of- flight spectrometers at the Spallation Neutron Source,” Review...

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Supplemental Material includes Refs

See Supplemental Material at [URL will be inserted by the production group] for experimental details; details on fitting the inelastic data; a discussion of the ordering temperature of CrBr 2, and data relevant to layer stack- ing, the temperature dependence of the magnetic or...
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S= 2 quasi-one-dimensional spin waves in CrCl2,

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Low-Dimensional Metal–Organic Magnets as a Route toward the S = 2 Haldane Phase,

Jem Pitcairn, Andrea Iliceto, Laura Ca˜ nadillas-Delgado, Oscar Fabelo, Cheng Liu, Christian Balz, Andreas Weil- hard, Stephen P. Argent, Andrew J. Morris, and Matthew J. Cliffe, “Low-Dimensional Metal–Organic Magnets as a Route toward the S = 2 Haldane Phase,” Journal of the ...

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Sunny.jl: A Julia Package for Spin Dynamics,

David Dahlbom, Hao Zhang, Cole Miles, Sam Quinn, Alin Niraula, Bhushan Thipe, Matthew Wilson, Sakib Matin, Het Mankad, Steven Hahn, Daniel Pajerowski, Steve Johnston, Zhentao Wang, Harry Lane, Ying Wai Li, Xiaojian Bai, Martin Mourigal, Cristian D. Batista, and Kipton Barros, ...

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and VBr 2 [36], from which theJ 1-J ′ 1 model implies a 120 ◦ helical angle. Thus, the incommensurate helical angles of CrBr 2 and CrI 2 can be seen as a consequence of Jahn-Teller distortion, or, conversely, that VCl 2 and VBr2 have spin spiral ordering similar to CrBr2 and C...
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Massless Dirac magnons in the two dimensional van der Waals honeycomb magnet CrCl3,

Lebing Chen, Matthew B. Stone, Alexander I. Kolesnikov, Barry Winn, Wonhyuk Shon, Pengcheng Dai, and Jae-Ho Chung, “Massless Dirac magnons in the two dimensional van der Waals honeycomb magnet CrCl3,” 2D Materials9, 015006 (2021)

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Topological magnon insulator spin ex- citations in the two-dimensional ferromagnet CrBr 3,

Zhengwei Cai, Song Bao, Zhao-Long Gu, Yi-Peng Gao, Zhen Ma, Yanyan Shangguan, Wenda Si, Zhao-Yang Dong, Wei Wang, Yizhang Wu, Dongjing Lin, Jinghui Wang, Kejing Ran, Shichao Li, Devashibhai Adroja, Xi- aoxiang Xi, Shun-Li Yu, Xiaoshan Wu, Jian-Xin Li, and Jinsheng Wen, “Topolo...

2021
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Magnetic Field Ef- fect on Topological Spin Excitations in CrI 3,

Lebing Chen, Jae-Ho Chung, Matthew B. Stone, Alexan- der I. Kolesnikov, Barry Winn, V. Ovidiu Garlea, Dou- glas L. Abernathy, Bin Gao, Mathias Augustin, Elton J. G. Santos, and Pengcheng Dai, “Magnetic Field Ef- fect on Topological Spin Excitations in CrI 3,” Physical Review X...

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Chong Wang, Daiwei Yu, Xiaoqiang Liu, Rongyan Chen, Xinyu Du, Biaoyan Hu, Lichen Wang, Kazuki Iida, Kazuya Kamazawa, Shuichi Wakimoto, Ji Feng, Nanlin Wang, and Yuan Li, “Observation of magnetoelastic ef- fects in a quasi-one-dimensional spiral magnet,” Physical 6 Review B96, ...

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The crystal structure of chromium(II) io- dide,

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Armando di Biase, John A. Schneeloch, Qiang Zhang, and Despina Louca, “Persistent Jahn-Teller distortion across a high-temperature phase transition in CrX 2 (X = Br, I),” Physical Review B113, 064110 (2026)

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Mag- netic and structural investigations on NiI 2 and CoI 2,

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John A. Schneeloch, Luke Daemen, and Despina Louca, “Antiferromagnetic-ferromagnetic homostructures with Dirac magnons in the van der Waals magnet CrI3,” Phys- ical Review B109, 024409 (2024)

2024
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Role of stacking defects on the mag- netic behavior of CrCl3,

John A. Schneeloch, Adam A. Aczel, Feng Ye, and Despina Louca, “Role of stacking defects on the mag- netic behavior of CrCl3,” Physical Review B110, 144439 (2024). 7 SUPPLEMENT AL MA TERIALS A. Experimental Details Crystals of CrBr2 and CrI2, were synthesized from the elements...

2024
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(doubled along thecaxis and swapping thexandy axes), for which ∆ = 0. Writing out the structure factor explicitly and simplifying, we have FM (G±k M ) = 2γnr0f(G±k M )(ˆz±iˆy)× (1 +e iπ(H+K) )(1 +e iαei2πK∆ eiπL).(2) Here,e iα allows for an arbitrary phase between layers. An i...
[51]

Inelastic data at 5 K, similar to Fig

near (0.5,0,0), a crossing between theω(Q−k M ), ω(Q+k M ), andω(Q+ 3k M ) branches; and 3) near 13 (a) (b) (c) (d) (e) (f) (g) (h) Figure S9. Inelastic data at 5 K, similar to Fig. 4, but with theω(Q±3k M ) branches included in the simplified dispersion plots (c,d,g,h). Arrow...

Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.

[1] [1]

Interactions are quasi-2D, result- ing in intralayer spin correlations being detectable up to at least 50 K, well above the loss of 3D long-range order atT N

There is a substantial easy-axis single-ion anisotropy (SIA) that distorts the spin helix and creates avoided crossings in the spin-wave dispersion. Interactions are quasi-2D, result- ing in intralayer spin correlations being detectable up to at least 50 K, well above the loss of 3D long-range order atT N . Elastic neutron scattering— We grew crystals of ...

work page

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Layer-dependent ferromag- netism in a van der Waals crystal down to the monolayer limit,

Bevin Huang, Genevieve Clark, Efr´ en Navarro- Moratalla, Dahlia R. Klein, Ran Cheng, Kyle L. Seyler, Ding Zhong, Emma Schmidgall, Michael A. McGuire, David H. Cobden, Wang Yao, Di Xiao, Pablo Jarillo- Herrero, and Xiaodong Xu, “Layer-dependent ferromag- netism in a van der Waals crystal down to the monolayer limit,” Nature546, 270–273 (2017)

work page 2017

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J 1-J ′ 1

The interlayer coupling is weak; in both CrBr2 and CrI 2,J c is around 0.02 meV, and the acous- tic dispersion alongLreaches a maximum of∼1.1 meV. Additional intralayer interactions were included to repro- duce certain details. For CrBr2, the 3rd-nearest-neighbor intrachain couplingJ 3 was needed to capture the curva- ture of the dispersion along (H,0,0),...

work page

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The crystal structure of chromium(II) chloride,

J. W. Tracy, N. W. Gregory, E. C. Lingafelter, J. D. Dunitz, H.-C. Mez, R. E. Rundle, C. Scheringer, H. L. Yakel, and M. K. Wilkinson, “The crystal structure of chromium(II) chloride,” Acta Crystallographica14, 927– 929 (1961), number: 9

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Structural and mag- netic characterization of a new phase of CrCl 2,

M. Winkelmann, M. Baehr, M. Reehuis, M. Steiner, M. Hagiwara, and K. Katsumata, “Structural and mag- netic characterization of a new phase of CrCl 2,” Journal of Physics and Chemistry of Solids58, 481–489 (1997)

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Ising-Type Mag- netic Ordering in Atomically Thin FePS3,

Jae-Ung Lee, Sungmin Lee, Ji Hoon Ryoo, Soonmin Kang, Tae Yun Kim, Pilkwang Kim, Cheol-Hwan Park, Je-Geun Park, and Hyeonsik Cheong, “Ising-Type Mag- netic Ordering in Atomically Thin FePS3,” Nano Letters 16, 7433–7438 (2016)

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thesis, Aalto University School of Science (2023)

Antti Karjasilta,Molecular beam epitaxy growth and scanning tunneling microscopy characterization of CrBr2-SnTe van der Waals heterostructures, Ph.D. thesis, Aalto University School of Science (2023)

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2D van der Waals magnets: From fundamental physics to applications,

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work page 2026