Two-dimensional Ferromagnetic van der Waals CrX3 (X=Cl, Br, I) Monolayers with Enhanced Anisotropy and Curie Temperature

Feng Xue; Ruqian Wu; Yusheng Hou; Zhe Wang

REVIEW 2 major objections 5 minor 41 references

Two-dimensional Ferromagnetic van der Waals CrX3 (X=Cl, Br, I) Monolayers with Enhanced Anisotropy and Curie Temperature

T0 review · 2 major / 5 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read The in-plane magnetic easy axis of a CrCl3 monolayer, long at odds with theory, is caused by magnetic shape anisotropy that outweighs its weak perpendicular magnetocrystalline anisotropy, and substituting tungsten for chromium produces a…

desk verdict A useful, plausible computational story about shape anisotropy and W doping in CrX3 monolayers, but the CrCl3 easy-axis punchline depends on a micro-eV-scale cancellation that the paper never quantifies. read the letter →

arxiv 1908.07710 v2 pith:AUSQVKXM submitted 2019-08-21 cond-mat.mtrl-sci

Feng Xue , Yusheng Hou , Zhe Wang , Ruqian Wu This is my paper · ORCID

classification cond-mat.mtrl-sci PACS 75.70.Ak75.30.Gw71.15.Mb

keywords CrCl3monolayertwo-dimensionalmagnetismvanderWaalsmagnetsmagneticshapeanisotropyperpendicularCurietemperaturefirst-principlescalculationsWCl6

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper resolves a puzzle: experiments see an in-plane magnetic easy axis in a CrCl3 monolayer, but every earlier first-principles calculation predicted out-of-plane. The authors show that the missing ingredient is magnetic shape anisotropy, the classical dipole-dipole energy of the ordered moments, which favors in-plane alignment and outweighs the weak perpendicular magnetocrystalline anisotropy in CrCl3. For CrBr3 and CrI3 the magnetocrystalline term wins, so their easy axis stays out-of-plane. The paper then proposes substituting isovalent tungsten for chromium, yielding CrWCl6, which has a perpendicular easy axis with a large anisotropy of 1071 µeV per magnetic atom and a Curie temperature as high as 76 K. A sympathetic reader would care because it demonstrates a design route for two-dimensional magnets for spintronic devices.

What carries the argument

The key object is the decomposition $E_{\rm MAE}=E_{\rm MCA}+E_{\rm MSA}$, where $E_{\rm MCA}$ is the magnetocrystalline anisotropy from spin-orbit coupling, obtained as the SOC total-energy difference between out-of-plane and in-plane magnetization, and $E_{\rm MSA}$ is the magnetic shape anisotropy from the classical dipole-dipole interaction. The paper computes the dipole sum with a real-space cutoff extended to 1000 Å so that the slowly converging shape term is numerically reliable. To explain the giant perpendicular anisotropy of CrWCl6, the authors use the torque method and a rigid-band shift to decompose $E_{\rm MCA}$ into atom and spin-channel contributions, identifying SOC between occupied spin-up $d_{xz}/d_{yz}$ and unoccupied spin-down $d_{z^2}$ states of W as the dominant source. Curie temperatures are obtained with the renormalized spin-wave theory (RSWT), which includes magnon-magnon interactions through a Holstein-Primakoff expansion to second order, in contrast to the linear spin-wave theory that overestimates $T_C$.

What would settle it

A torque-magnetometry or magneto-optical Kerr measurement that resolves the angular dependence of a CrCl3 monolayer's magnetization: if the data show the easy axis becomes out-of-plane once the sample is placed on a substrate that cancels or reduces the demagnetizing field, the paper's claim that shape anisotropy sets the in-plane axis would be falsified.

Watch

Extended reading notes

Core claim

The central discovery is that the net magnetic anisotropy of a two-dimensional magnet is the sum of a magnetocrystalline term from spin-orbit coupling and a magnetic shape term from dipole-dipole interactions, and the shape term, usually neglected, decides the easy axis when the spin-orbit term is weak. For a CrCl3 monolayer the calculated magnetocrystalline anisotropy is small and positive, favoring perpendicular magnetization, while the shape anisotropy is slightly larger and negative, favoring in-plane magnetization; the net result is an in-plane easy axis consistent with experiment. For CrBr3 and CrI3 the magnetocrystalline term is large enough to overcome shape anisotropy, preserving the perpendicular axis. In CrWCl6, made by replacing half the Cr with isovalent W, the spin-orbit coupling of W drives a perpendicular magnetocrystalline anisotropy of 1114 µeV per magnetic atom, which survives the shape correction to give a net MAE of 1071 µeV and a renormalized spin-wave Curie temperature of 76 K.

Load-bearing premise

Everything hinges on the calculated magnetocrystalline anisotropy of CrCl3 being accurate to a few tens of micro-electronvolts per atom, because the in-plane easy axis is the tiny net difference between a slightly larger in-plane shape term and a slightly smaller out-of-plane spin-orbit term.

Editorial extensions

If this is right

Shape anisotropy must be included in first-principles studies of two-dimensional magnets with weak spin-orbit coupling; neglecting it flips the predicted easy axis for CrCl3.
CrWCl6 is predicted to be a perpendicular ferromagnet with a MAE of 1071 µeV per magnetic atom, comparable to transition-metal films, and a Curie temperature of 76 K.
Intermediate W concentrations (x = 4–6 in Cr8-xWxCl24) are energetically stable and synthetically accessible under W-rich conditions.
A 5% in-plane tensile strain enhances the perpendicular anisotropy of CrWCl6 to 2375 µeV per magnetic atom.
The enhanced ferromagnetic superexchange in CrWCl6 originates from a reduced energy separation between occupied W t2g and empty Cr eg states, raising the nearest-neighbor exchange J1 to 14.8 meV.

Reading between the lines

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

By the same logic, other van der Waals magnets with small magnetocrystalline anisotropy should show easy-axis reorientation as a function of flake thickness or lateral size, since the dipolar term is shape-dependent; this is a testable corollary the paper does not spell out.
The tungsten-substitution recipe may transfer to CrBr3 and CrI3 monolayers, potentially raising their Curie temperatures further; the paper only demonstrates it on CrCl3.
The predicted 76 K ordering could be verified by magneto-optical Kerr effect or nitrogen-vacancy magnetometry on exfoliated or grown CrWCl6 flakes.
Because the shape anisotropy term is independent of spin-orbit coupling, the CrCl3 in-plane easy axis should persist at low temperatures; deviations seen in future measurements would reveal additional anisotropy contributions such as magnetoelastic terms.

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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

The thing to know about this paper is that it does two real things well: it adds magnetic shape anisotropy (MSA) to the usual magnetocrystalline anisotropy (MCA) for CrX3 monolayers, and it works through a Cr1-xWxCl3 alloy design with formation energies, a chemical potential phase diagram, and a U-dependence check. The MSA point is legitimate and often neglected in 2D magnet calculations, and the W-substitution route to a perpendicular easy axis is concrete and experimentally actionable. The paper also cross-checks its torque-method MAE against total-energy differences and gives a plausible orbital decomposition of the W-driven anisotropy. That is solid, useful work.

The soft spot is exactly where the reader's stress-test lands. The CrCl3 in-plane easy axis is obtained as the net of a negative MSAE and a positive MCAE, each of order tens of μeV per atom, and the paper quotes no uncertainty on either. A small error in the Hubbard U, the SOC total-energy convergence, or the dipole cutoff could flip the sign. Table 1 shows the values, but there is no sensitivity analysis for the anisotropy of pure CrCl3 with respect to U or k-mesh. The statement that shape anisotropy dominates is plausible, but it is not demonstrated to the precision the claim needs. This is the central physical conclusion for CrCl3, so it matters. If the sign flipped under a controlled variation, the paper's headline resolution of the puzzle would be wrong, even though the CrWCl6 design could survive independently.

Two smaller concerns. First, the relation to ref [39] is under-clarified: the paper cites it for energy separations that justify the alloy, but it never states whether CrWCl6 itself was already predicted there. The new contribution may be the systematic alloy study rather than the bare compound, and the text should say so. Second, the Curie temperature is a model prediction from RSWT with fitted exchange parameters. That is standard practice, and the paper does not tune anything to experimental TC, so I do not see circularity. But the 76 K number should be treated as a rough estimate, not a quantitative prediction.

Who is this for? Computational 2D magnetism people and experimentalists looking for dopant strategies in chromium trihalides. It deserves a serious referee: the physics question is real, the calculations are mostly careful, and the flaws are addressable rather than fatal. I would send it to review, with the request that the authors add an error bar or a U-sensitivity test for the CrCl3 MCAE/MSAE balance and clarify the overlap with ref [39].

Referee Report

2 major / 5 minor

Summary. This manuscript uses DFT+U and renormalized spin-wave theory (RSWT) to investigate monolayer CrX3 (X = Cl, Br, I) magnets. The authors compute magnetocrystalline anisotropy (EMCA) and magnetic shape anisotropy (MSAE) separately and show that for CrCl3 the net anisotropy is negative (in-plane) because the in-plane shape anisotropy overcomes the weak perpendicular EMCA, thereby explaining the experimentally observed easy axis. They then propose an ordered CrWCl6 alloy, obtained by substituting half the Cr with isovalent W, which exhibits a perpendicular MAE of 1071 µeV per magnetic atom and a Curie temperature of 76 K. The paper also presents a formation-energy and chemical-potential phase diagram for Cr8-xWxCl24 to support experimental feasibility.

Significance. If the CrCl3 conclusion holds, the paper resolves a long-standing discrepancy between DFT and experiment and establishes magnetic shape anisotropy as an essential term for 2D magnets with weak spin-orbit coupling. The proposed CrWCl6 design, with a large perpendicular MAE and a Curie temperature comparable to CrI3, is a useful candidate for 2D spintronics. The computational pipeline is standard and internally consistent, and the authors cross-check EMCA with the torque method and examine the phase stability against U variations. However, the central CrCl3 result depends on a delicate cancellation of two small energies, and the RSWT implementation is not fully documented, so the quantitative claims require additional validation.

major comments (2)

[Section 3, Table 1] The in-plane easy axis of CrCl3 is obtained as the sign of EMCA + MSAE, where both terms are of order tens of µeV per atom and the net value is not explicitly stated in the text. No error estimates or convergence tests are given for the SOC total-energy difference that defines EMCA, nor for the sensitivity of MSAE to the DFT local magnetic moments. Because a systematic error of a few µeV can change the sign, the claim that shape anisotropy is responsible for the in-plane easy axis is plausible but not quantitatively demonstrated. Please report the net MAE with an uncertainty estimate, and provide convergence tests for EMCA with respect to k-mesh and SOC integration, as well as a U-dependent study (e.g., U = 2, 3, 4 eV) for CrCl3.
[Section 4, Eqs. (2), (5)-(7)] The RSWT calculation is not fully specified. Equation (2) contains only exchange couplings, but a finite Curie temperature in a 2D isotropic Heisenberg model would contradict the Mermin-Wagner theorem; therefore the magnon spectrum must include an anisotropy term. The manuscript does not state how EMCA is incorporated into the spin Hamiltonian, how the anisotropy constant is related to the values in Table 1, or how the 'assumed out-of-plane magnetization' for CrCl3 (footnote to Table 1) is implemented. Please write the complete spin Hamiltonian used in the RSWT, including any single-ion anisotropy, and specify all input parameters. Without this information, the reported Curie temperatures are not reproducible.

minor comments (5)

[Section 2] The sentence 'The electron correlation effect for the localized d orbitals of Mn and W atoms' should read 'Cr and W atoms'.
[Introduction] The word 'silicone' should be 'silicene', and 'topotronic' appears to be a typographical or nonstandard term that should be checked.
[Section 3, Eq. (1)] The text around Eq. (1) contains garbled notation and grammatical errors, for example 'Since the this energy converges'; please proofread and ensure all mathematical symbols are rendered correctly.
[Table 1] The units of the exchange parameters J1, J2, and J3 are not specified in the table; please state them (presumably meV) and define the meaning of 'per magnetic atom' for the anisotropy energies.
[References] Reference [22] is formatted inconsistently (the author list appears as 'J. K. Yusheng Hou, Ruqian Wu') and should be corrected to the standard citation format.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity; the central predictions are derived from first-principles energies rather than fitted to the explained observations.

full rationale

The paper's derivation chain is self-contained: exchange parameters J1-J3 are obtained by mapping DFT total energies of four magnetic configurations onto the Heisenberg Hamiltonian (Eq. 2), and MCAE is a direct spin-orbit total-energy difference; MSAE is computed from the dipole-dipole formula (Eq. 1) with DFT local moments, not fitted to the experimental easy axis. The Curie temperatures are then produced by the renormalized spin-wave theory (Eq. 7) using those J values, with no adjustable parameter aimed at the reported Tc. The self-citations ([22], [36]-[38]) are methodological (torque method, comparison to thin-film MAEs) and do not supply the paper's premises; in particular, no uniqueness theorem or prior ansatz is imported that would force the result. The paper even flags its own limitation that the CrCl3 monolayer cannot sustain long-range order and that its hypothetical out-of-plane Tc is obtained by ignoring MSAE, which is an honest caveat rather than a circular move. The experimentally relevant fragility is the small energy difference between competing anisotropy terms; however, a lack of error bars is a robustness/correctness concern, not circularity, because the conclusion is not defined in terms of the experiment it explains.

Assumptions & free parameters 3 free parameters · 6 assumptions · 0 invented entities

The central claims rest on DFT+U with a hand-chosen Hubbard U=3 eV and on model assumptions (Heisenberg Hamiltonian, classical dipole shape anisotropy, RSWT). No parameter is fitted to experimental targets; the easy-axis direction and TC emerge from the ab initio derived energies and exchange couplings.

free parameters (3)

Hubbard U = 3 eV
Applied to Cr and W d orbitals in PBE+U; affects band gap, MCAE, exchange couplings, and stability. The paper checks the phase diagram versus U but does not scan U for the anisotropy values.
r_max for dipole sum = 1000 Å
Cutoff for the magnetic dipole-dipole interaction in Eq. (1); chosen to achieve numerical convergence, not a physical model parameter.
Configurational entropy temperature = 300 K
Used in Eq. (4) for the formation enthalpy phase diagram; a modeling choice for the synthesis discussion.

assumptions (6)

standard math Mermin-Wagner theorem: isotropic 2D Heisenberg magnets have no long-range order at finite T; anisotropy is required.
Used in the introduction to motivate the importance of magnetic anisotropy.
domain assumption Goodenough-Kanamori-Anderson rules: near-90-degree superexchange paths give ferromagnetic coupling.
Used in Section 3 to explain the dominant ferromagnetic J1.
domain assumption Classical dipole-dipole interaction (Eq. 1) captures all magnetic shape anisotropy of the monolayer.
Central to the CrCl3 easy-axis resolution; assumes no other anisotropy source changes the balance.
domain assumption The Heisenberg Hamiltonian with J1, J2, J3 (Eq. 2) and four DFT spin configurations determine the magnetic interactions.
Used to extract exchange parameters for the TC calculation; assumes the model is complete and the mapping is unique.
domain assumption Renormalized spin-wave theory (refs [40,41]) predicts reliable Tc for 2D magnets, as validated on Cr2Ge2Te6.
Basis for the claimed Tc values; the method is cited from prior work, not re-derived here.
domain assumption PBE+U with U=3 eV adequately describes the electronic structure and magnetism of Cr/W chlorides.
Underpins all DFT results; U is a chosen parameter and the paper only partially checks its sensitivity.

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Cite this review

Pith. "Pith review of Two-dimensional Ferromagnetic van der Waals CrX3 (X=Cl, Br, I) Monolayers with Enhanced Anisotropy and Curie Temperature." pith.science (2026). https://pith.science/paper/AUSQVKXM

@misc{pith2026190807710,
  author       = {Pith},
  title        = {Pith review of: Two-dimensional Ferromagnetic van der Waals CrX3 (X=Cl, Br, I) Monolayers with Enhanced Anisotropy and Curie Temperature},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/AUSQVKXM}},
  note         = {Machine review of arXiv:1908.07710}
}

read the original abstract

Among the recently widely studied van der Waals layered magnets CrX3 (X=Cl, Br, I), CrCl3 monolayer (ML) is particularly puzzling as it is solely shown by experiments to have an in-plane magnetic easy axis and, furthermore, all of previous first-principles calculation results contradict this. Through systematical first-principles calculations,we unveil that its in-plane shape anisotropy that dominates over its weak perpendicular magnetocrystalline anisotropy is responsible for the in-plane magnetic easy axis of CrCl3 ML. To tune the in-plane ferromagnetism of CrCl3 ML into the desirable perpendicular one, we propose substituting Cr with isovalent tungsten (W). We find that CrWCl6 has a strong perpendicular magnetic anisotropy and a high Curie temperature up to 76 K. Our work not only gives insight into understanding the two-dimensional ferromagnetism of van der Waals MLs but also sheds new light on engineering their performances for nanodevices.

Figures

Figures reproduced from arXiv: 1908.07710 by the authors.

**Figure 2.** (a) Formation energy   ΔEf x x Cr W Cl 8 24  as a function of W concentration (x) in Cr8-xWxCl24. Inserts show the lowest-energy configurations for x  2 ~ 4 . (b) The phase diagram of the stable region of Cr8-xWxCl24 (x = 0~8) with different W concentrations. The number of W atoms in Cr8-xWxCl24 ML is labeled by x. The right (bottom) and left (top) boundaries of chromium (tungsten) chemical potential correspond … view at source ↗

**Figure 4.** (a) The renormalized magnetization   0 MT M as a function of temperature T. TC is determined by the temperature at MT   0 . (b) Spin-wave excitation (magnon) spectrums of CrCl3 ML and CrWCl6 M. Finally, we determined the TC of CrWCl6 using the renormalized spin-wave theory (RSWT) [40,41] to show the benefit of Cr-W intermixing. It is recognized that the linear spin-wave theory (LSWT) typically overestimates TC … view at source ↗

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Pith tools

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

[1] [39]

Huang, J

C. Huang, J. Feng, F. Wu, D. Ahmed, B. Huang, H. Xiang, K. Deng, and E. Kan, Journal of the American Chemical Society 140, 11519 (2018)

work page 2018

[2] [1]

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2004

[3] [2]

C. R. Dean, A. F. Young, I. Meric, C. Lee, L. Wang, S. Sorgenfrei, K. Watanabe, T. Taniguchi, P. Kim, K. L. Shepard, and J. Hone, Nature Nanotechnology 5, 722 (2010)

work page 2010

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