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REVIEW 3 major objections 4 minor 1 cited by

Chiral Phonons Enhance Ferromagnetism

T0 review · 3 major / 4 minor · reviewed 2026-08-11 · deepseek-v4-flash

Pith's one-line read Chiral phonons absorb thermal energy that would otherwise excite magnons, strengthening ferromagnetic order as temperature rises.

desk verdict Novel mechanism, but a load-bearing sign inconsistency between the Hartree shift and the magnon gap undermines the central claim. read the letter →

arxiv 2412.13787 v1 pith:H7IDMPO4 submitted 2024-12-18 cond-mat.mtrl-sci physics.chem-ph

classification cond-mat.mtrl-sciphysics.chem-ph
keywords chiralphononsmagnon-phononcouplingcoercivityenhancementmagneticanisotropyinducedspinselectivityferromagnetismHolstein-Primakofftransformationmagnetite
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

Coating a ferromagnet with chiral molecules has been seen to raise its coercivity and to make that coercivity grow with temperature, against the usual rule that heat destroys magnetic order. This paper proposes a microscopic mechanism: lattice vibrations (phonons) that gain chirality from the broken inversion symmetry of the adsorbed layer couple to the magnetic spin excitations (magnons) and act as an energy sink. Thermal energy that would have excited magnons is instead absorbed into these phonons, so the magnon gap effectively widens as temperature rises. On the paper's account, ferromagnetic order is not merely preserved but stabilized by heating, which is the effect reported in chiral-molecule-coated magnetite and nickel.

What carries the argument

The load-bearing object is the Hartree self-energy $\Sigma^{(H)}$ of Eq. (6), computed from a Holstein-Primakoff expansion of an anisotropic Heisenberg magnet coupled to phonon displacements. $\Sigma^{(H)}$ is a phonon-mediated magnon-magnon interaction: a magnon scatters off the phonon-shifted spin density, and the correction shifts the magnon energy $\varepsilon_k$ by an amount that grows with temperature (Eq. (7)). The companion object is the entropy-production rate of Eq. (11), whose negative sign expresses that magnons continually lose energy to the phonon reservoir; together these two expressions convert chiral phonons into an effective temperature-dependent anisotropy $\tilde I_0$.

What would settle it

Measure the magnon gap by inelastic neutron scattering or Brillouin light scattering in a chiral-molecule-coated ferromagnet between 273 K and 343 K: the proposed mechanism requires the gap to widen and the magnon population to stay low as temperature rises, while phonon modes gain spectral weight; a flat or shrinking gap would refute the energy-sink claim.

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Extended reading notes

Core claim

The paper's central claim is that chiral phonons, not the bare electronic structure, provide the extra magnetic anisotropy that lets ferromagnetic order survive at room temperature and strengthens it as temperature increases. A layer of chiral molecules breaks inversion symmetry and couples phonon displacements to local spin moments; expanding the anisotropic Heisenberg model with Holstein-Primakoff magnons, the phonon-mediated magnon-magnon interaction generates a Hartree self-energy that shifts the magnon energy by a temperature-dependent amount. The paper reads this shift as an increased out-of-plane anisotropy $\tilde I_0$, and its entropy-production analysis shows magnons losing entropy to the phonon reservoir. This is the proposed explanation for the observed near-doubling of coercivity in magnetite and for the linear coercivity increase with temperature on nickel substrates.

Load-bearing premise

The derivation needs the uniaxial anisotropy parameter $I_0$ to be negative wherever the phonon shift stabilizes the magnet, while the magnon spectrum shown has an energy gap at $k=0$ only when $I_0$ is positive; the paper never states which sign convention is physical.

Editorial extensions

If this is right

  • The coercivity of a chiral-coated ferromagnet should rise approximately linearly with temperature in the window where the Hartree shift dominates, matching the measurements on magnetite and nickel.
  • Replacing the chiral layer with an achiral one should switch off the phonon-mediated anisotropy shift, so the anomalous coercivity-temperature slope should disappear.
  • The magnon energy gap should be measurably larger in the coated film than in the bare ferromagnet at the same temperature, and should increase with temperature under the coating.
  • The mechanism gives a microscopic identification of the chiral heat engine: the entropy drop from spin filtering is balanced by phonon heating, so a heat current into chiral phonons sustains the ordered spin state.

Reading between the lines

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

  • A direct time-resolved test would be to apply a heat pulse to a coated ferromagnet and observe a transient rise in phonon occupation with little or no rise in magnon population, whereas the bare magnet should show the opposite.
  • The sign conflict over $I_0$ suggests the published derivation may be using opposite sign conventions for the anisotropy term in the spectrum versus the Hartree shift; a first-principles calculation of $I_0$ for magnetite would settle whether the mechanism survives quantitatively.
  • If the energy-sink picture is right, materials with different phonon densities of states, or isotopic substitutions that shift phonon energies, should show systematically different coercivity-temperature slopes, giving a materials-design handle.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 4 minor

Summary. The paper proposes a microscopic mechanism by which chiral phonons, coupled to magnons through a spin-phonon interaction, act as a thermal energy sink that reduces magnon occupation and increases the uniaxial magnetic anisotropy, thereby enhancing ferromagnetic order. Starting from an anisotropic Heisenberg model with a magnon-phonon coupling (Eq. (1)), the authors derive second-order self-energy corrections to the magnon Green function (Eqs. (4)-(7)), argue that the Hartree term gives a positive temperature-dependent anisotropy contribution (Eq. (7)), and compute an entropy production rate (Eqs. (8)-(11)) that they claim is negative for a ferromagnet with I0<0. The results are connected to experimental observations of coercivity enhancement in chiral-molecule-coated magnetite and Ni.

Significance. If the mechanism were correct, the paper would be a conceptually interesting challenge to the standard view that phonons only degrade magnetic order, and it would provide a microscopic counterpart to the authors' earlier thermodynamic 'chiral heat engine' model. The perturbative setup is transparent and the diagrammatic formulation is standard, which makes the model easy to follow. However, the central result relies on an internal sign inconsistency: the same anisotropy parameter I0 must be negative for the claimed positive Hartree shift and negative entropy production, yet positive for a stable magnon gap. The entropy-production calculation also uses equilibrium Bose-Einstein occupations to infer a directional energy flow, which is not physically justified. No quantitative comparison with the cited experiments is provided, so the explanatory claim is not backed by a parameter-based estimate.

major comments (3)
  1. [Magnons, Eqs. (6)-(7)] The claimed positive Hartree contribution to the anisotropy requires I0<0. In Eq. (6), the logarithm ln[(1-e^{-2M\beta(I0-\alpha p_c^2)})/(1-e^{-2M\beta I0})] is positive only when both arguments in the exponentials are negative, i.e., when I0<0 (since \alpha p_c^2>0); for a positive I0 the log is negative and the Hartree shift would reduce, not increase, the anisotropy. At the same time, Eq. (3) gives the magnon energy at k=0 as \varepsilon_0=2M I0, so a stable ferromagnetic state with a positive magnon gap requires I0>0. The manuscript thus requires I0 to be both negative (for the enhancement and entropy reduction) and positive (for the ground-state gap), but it never resolves this conflict. The introductory statement that an out-of-plane ferromagnet requires negative I_mn is also inconsistent with the Hamiltonian in Eq. (1), where a positive I lowers the out-of-plane energy. This sign inconsistency is load-bearing for the entire mechanism.
  2. [Entropy production rate, Eqs. (8)-(11)] The entropy production rate is computed using equilibrium Bose-Einstein distribution functions n_B for both magnons and phonons. For an isolated system described by the Hamiltonian in Eq. (1), detailed balance in equilibrium implies that the net energy current between the magnon and phonon subsystems vanishes; a negative entropy production cannot emerge from a calculation that assumes both subsystems are in equilibrium at the same temperature. The paper does not specify a nonequilibrium drive, such as a phonon bath at a different temperature or a steady chiral-phonon source, nor does it derive the occupation functions from a kinetic equation. Therefore the conclusion that the phonon subsystem acts as an energy sink 'with increasing temperature further stabilizes' the ferromagnet is not established by Eqs. (9)-(11). This is central to the claimed energy-diversion mechanism.
  3. [Results and Discussion, Fig. 4] The numerical illustration uses freely chosen parameters (the magnon-phonon coupling A_k, the phonon mode range, the broadening \Gamma_ph, and the cutoff p_c) and is not applied to magnetite or Ni, the materials invoked in the abstract and conclusion. The paper makes a qualitative claim to explain the experimentally observed increase of coercivity with temperature, but without a material-specific estimate of the anisotropy shift or of the entropy reduction, the connection between the model and the experiments remains illustrative. This lack of quantitative anchoring compounds the technical issues above, because the sign of the effect is the main experimental discriminant.
minor comments (4)
  1. [Introduction] The sentence 'on the one hand show stable room temperature ferromagnetism and one the other hand small, if not vanishing, magnetic moment at low' contains a typo ('one the other hand' should be 'on the other hand').
  2. [Magnons, Eq. (3)] The notation J0 is overloaded: J0 is defined through a sum over J_mn, but the text says 'with J = J or I', so the same symbol J0 is used for both the exchange and the anisotropy sums. This makes Eq. (3) and the subsequent condition I0<0 difficult to interpret.
  3. [Results and Discussion, Fig. 4] The caption states that a broadening Gamma_ph = 0.03J is included for smoothening, but Gamma_ph is not introduced in the Hamiltonian or in the self-energy definitions (Eqs. (5a)-(5c)); the reader cannot tell how the Lorentzian broadening is implemented.
  4. [Results and Discussion, Fig. 4] The plots in Fig. 4(b,c) show the Hartree self-energy with the value Sigma^(X)(omega=0) subtracted, but the text does not explain why this subtraction is made or whether the plotted quantity is the full anisotropy correction; this should be clarified.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the phonon-induced anisotropy shift is derived from the model Hamiltonian and illustrative parameters, not fitted to the data; self-citations are contextual rather than load-bearing.

full rationale

The paper's central derivation is self-contained given the model Hamiltonian in Eq. (1). The claimed enhancement of magnetic anisotropy is obtained by computing the Hartree and lowering-raising self-energies from the assumed magnon-phonon coupling, and the entropy reduction is derived from the sign analysis of Eq. (11). No parameter is fitted to the experimental coercivity data; the coupling strengths and phonon frequencies are explicitly illustrative, so the 'prediction' is not statistically forced by a fit. The self-citations (Refs. [5,6,7,29,30,31]) are used for physical motivation, prior context, and the broken-inversion-symmetry requirement, but the mathematical core of the paper does not reduce to an unverified uniqueness theorem or to an ansatz smuggled in through citation. The internal sign issue concerning I0 (negative for the Hartree and entropy signs but positive for a stable k=0 magnon gap) is a physical consistency/correctness concern, not a circular reduction: it does not make the output equivalent to the input by construction. Therefore, under the hard rules, there is no identifiable circular step and the appropriate score is 0.

Assumptions & free parameters 6 free parameters · 7 assumptions · 0 invented entities

The paper's central result depends on a set of ad hoc coupling and cutoff choices, a harmonic phonon assumption, and a sign convention for I0 that is not reconciled with the magnon spectrum. No new physical entities are introduced; the chiral phonons are a known concept.

free parameters (6)
  • Magnon-phonon coupling strength A = A_z = 3 J x 10^-6, A_+ = J/500 (chosen for Fig. 4)
    The coupling tensor is not derived or fit; the plotted self-energies use these illustrative values.
  • Phonon mode range and count = 500 modes, omega_m/J in [1/30, 50/3]
    The phonon sum is truncated to an arbitrary range and number of modes.
  • Anisotropy parameter I0 = No value given; sign taken as I0<0 in Eq. (11)
    The sign of I0 is load-bearing for the Hartree shift and entropy production, but conflicts with the gap condition.
  • Magnon dispersion curvature alpha = Not specified numerically
    alpha controls the q-integral in Eq. (6); no material value is provided.
  • Momentum cutoff p_c = Not specified
    The logarithmic Hartree shift depends on p_c; its value is not given.
  • Phonon broadening Gamma_ph = 0.03 J in Fig. 4(a)
    Added for smoothening; its physical origin and value are not justified.
assumptions (7)
  • domain assumption Adsorbed chiral molecules break inversion symmetry, enabling a linear coupling between local spin moments and phonons (sum M_m * A_mn * Q_n).
    The whole mechanism depends on this coupling, which is asserted from refs. [6,7] rather than derived.
  • domain assumption The phonon background is harmonic (H_ph = sum omega_m b^dagger_m b_m).
    Used in Eq. (1); anharmonicity is not included.
  • standard math The Holstein-Primakoff expansion is truncated at quadratic order in magnon operators.
    Standard approximation valid for low magnon density; limits validity.
  • ad hoc to paper The Fock self-energy Sigma^(F) is omitted because it is pinned to phonon energies and does not add to anisotropy.
    The neglect is justified qualitatively, not by an error estimate.
  • domain assumption Magnon and phonon distributions are Bose-Einstein at the same temperature during the entropy production calculation.
    Eqs. (10)-(11) use equilibrium n_B functions while claiming a directional energy flow; no drive is specified.
  • domain assumption The interface is treated as a two-dimensional system with quadratic dispersion near Gamma.
    Used to derive Eq. (6); 3D effects are ignored.
  • ad hoc to paper The sign of I0 is set to I0<0 in Eq. (11) so the claimed negative entropy production holds.
    This sign is required for the conclusion and conflicts with the magnon gap condition; it is not derived from material parameters.

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Cite this review

Pith. "Pith review of Chiral Phonons Enhance Ferromagnetism." pith.science (2026). https://pith.science/paper/H7IDMPO4

@misc{pith2026241213787,
  author       = {Pith},
  title        = {Pith review of: Chiral Phonons Enhance Ferromagnetism},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/H7IDMPO4}},
  note         = {Machine review of arXiv:2412.13787}
}
read the original abstract

Recent experiments suggest that the conditions for ferromagnetic order in, e.g., magnetite, can be modified by adsorption of chiral molecules. Especially, the coercivity of magnetite was increased by nearly 100 \%, or 20 times the earth magnetic flux density, at room temperature. The coercivity was, moreover, demonstrated to increase linearly with temperature in a finite range around room temperature. Based on these results, a mechanism is proposed for providing the necessary enhancement of the magnetic anisotropy. It is shown that nuclear vibrations (phonons) coupled to ferromagnetic spin excitations (magnons) absorb the thermal energy in the system, thereby diverting the excess energy that otherwise would excite magnons in the ferromagnet. This energy diversion, not only restores the ferromagnetic order but also enhances its stability by increasing the anisotropy energy for magnon excitations. The coupling between phonons with magnons is enabled by chirality due to the lack of inversion symmetry.

Figures

Figures reproduced from arXiv: 2412.13787 by the authors.

Figure 1
Figure 1. FIG. 1. We present an illustration depicting the coupling between [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Magnon spectrum (a) without and (b) with coupling to chiral [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 4
Figure 4. FIG. 4. Examples of the self-energies (a) [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗

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Forward citations

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Reference graph

Works this paper leans on

31 extracted references · 26 canonical work pages · cited by 1 Pith paper

  1. [1]

    Ke ffer, Handbuch der Physik (Springer-Verlag, New York, 1966)

    F. Ke ffer, Handbuch der Physik (Springer-Verlag, New York, 1966)

  2. [2]

    Ahmmad, M

    B. Ahmmad, M. Z. Islam, A. Billah, and M. A. Basith, Anoma- lous coercivity enhancement with temperature and tunable ex- change bias in gd and ti co-doped bifeo3 multiferroics, Journal of Physics D: Applied Physics 49, 095001 (2016)

  3. [3]

    Dhara, K

    B. Dhara, K. Tarafder, P. K. Jha, S. N. Panja, S. Nair, P. M. Oppeneer, and N. Ballav, Possible room-temperature ferromag- netism in self-assembled ensembles of paramagnetic and dia- magnetic molecular semiconductors, The Journal of Physical Chemistry Letters 7, 4988 (2016)

  4. [4]

    A. K. Mondal, N. Brown, S. Mishra, P. Makam, D. Wing, S. Gilead, Y . Wiesenfeld, G. Leitus, L. J. W. Shimon, R. Carmieli, D. Ehre, G. Kamieniarz, J. Fransson, O. Hod, L. Kronik, E. Gazit, and R. Naaman, Long-range spin-selective transport in chiral metal–organic crystals with temperature- activated magnetization, ACS Nano 14, 16624 (2020)

  5. [5]

    Fransson, Vibrationally induced magnetism in supramolecu- lar aggregates, The Journal of Physical Chemistry Letters 14, 2558 (2023)

    J. Fransson, Vibrationally induced magnetism in supramolecu- lar aggregates, The Journal of Physical Chemistry Letters 14, 2558 (2023)

  6. [6]

    Fransson, Chiral phonon induced spin polarization, Phys

    J. Fransson, Chiral phonon induced spin polarization, Phys. Rev. Res. 5, L022039 (2023)

  7. [7]

    J. Fransson, Temperature activated chiral induced spin selectivity, The Journal of Chemical Physics 159, 084115 (2023), https: //pubs.aip.org/aip/jcp/article- pdf/doi/10.1063/5.0155854/18100799/084115 1 5.0155854.pdf

  8. [8]

    Fransson and L

    J. Fransson and L. Turin, Current induced spin-polarization in chiral molecules, The Journal of Physical Chemistry Letters15, 6370 (2024)

Show all 31 references
  1. [9]

    ˇCervenka, M

    J. ˇCervenka, M. I. Katsnelson, and C. F. J. Flipse, Room- temperature ferromagnetism in graphite driven by two- dimensional networks of point defects, Nature Physics 5, 840 (2009)

  2. [10]

    Bonilla, S

    M. Bonilla, S. Kolekar, Y . Ma, H. C. Diaz, V . Kalappattil, R. Das, T. Eggers, H. R. Gutierrez, M.-H. Phan, and M. Batzill, Strong room-temperature ferromagnetism in vse2 monolayers on van der waals substrates, Nature Nanotechnology 13, 289 6 (2018)

  3. [11]

    Huang, J

    C. Huang, J. Feng, F. Wu, D. Ahmed, B. Huang, H. Xiang, K. Deng, and E. Kan, Toward intrinsic room-temperature ferro- magnetism in two-dimensional semiconductors, Journal of the American Chemical Society 140, 11519 (2018)

  4. [12]

    Q. Xu, H. Schmidt, S. Zhou, K. Potzger, M. Helm, H. Hochmuth, M. Lorenz, A. Setzer, P. Esquinazi, C. Mei- necke, and M. Grundmann, Room temperature ferromagnetism in zno films due to defects, Applied Physics Letters 92, 082508 (2008)

  5. [13]

    S.-J. Han, J. W. Song, C.-H. Yang, S. H. Park, J.-H. Park, Y . H. Jeong, and K. W. Rhie, A key to room-temperature ferromag- netism in fe-doped zno: Cu, Applied Physics Letters 81, 4212 (2002)

  6. [14]

    Y . Wang, Y . Huang, Y . Song, X. Zhang, Y . Ma, J. Liang, and Y . Chen, Room-temperature ferromagnetism of graphene, Nano Letters 9, 220 (2009)

  7. [15]

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

  8. [16]

    Huang, G

    B. Huang, G. Clark, E. Navarro-Moratalla, D. R. Klein, R. Cheng, K. L. Seyler, D. Zhong, E. Schmidgall, M. A. McGuire, D. H. Cobden, W. Yao, D. Xiao, P. Jarillo-Herrero, and X. Xu, Layer-dependent ferromagnetism in a van der waals crystal down to the monolayer limit, Nature 54...

  9. [17]

    Chang, Marriage of topology and magnetism, Nature Ma- terials 19, 484 (2020)

    C.-Z. Chang, Marriage of topology and magnetism, Nature Ma- terials 19, 484 (2020)

  10. [18]

    B. A. Bernevig, C. Felser, and H. Beidenkopf, Progress and prospects in magnetic topological materials, Nature 603, 41 (2022)

  11. [19]

    U. K. R ¨oßler, A. N. Bogdanov, and C. Pfleiderer, Spontaneous skyrmion ground states in magnetic metals, Nature 442, 797 (2006)

  12. [20]

    M ¨uhlbauer, B

    S. M ¨uhlbauer, B. Binz, F. Jonietz, C. Pfleiderer, A. Rosch, A. Neubauer, R. Georgii, and P. B ¨oni, Skyrmion lattice in a chiral magnet, Science 323, 915 (2009)

  13. [21]

    X. Z. Yu, Y . Onose, N. Kanazawa, J. H. Park, J. H. Han, Y . Mat- sui, N. Nagaosa, and Y . Tokura, Real-space observation of a two-dimensional skyrmion crystal, Nature 465, 901 (2010)

  14. [22]

    Tokura and N

    Y . Tokura and N. Kanazawa, Magnetic skyrmion materials, Chemical Reviews 121, 2857 (2021)

  15. [23]

    Y . Sang, F. Tassinari, K. Santra, W. Zhang, C. Fontanesi, B. P. Bloom, D. H. Waldeck, J. Fransson, and R. Naaman, Chiral- ity enhances oxygen reduction, Proceedings of the National Academy of Sciences 119, e2202650119 (2022)

  16. [24]

    Gupta, Y

    A. Gupta, Y . Sang, C. Fontanesi, L. Turin, and R. Naaman, A possible unitary mechanism for general anesthesia, bioRxiv 10.1101/2022.11.29.518334 (2022)

  17. [25]

    S. F. Ozturk and D. D. Sasselov, On the origins of life’s ho- mochirality: Inducing enantiomeric excess with spin-polarized electrons, Proceedings of the National Academy of Sciences 119, e2204765119 (2022)

  18. [26]

    S. F. Ozturk, Z. Liu, J. D. Sutherland, and D. D. Sasselov, Ori- gin of biological homochirality by crystallization of an rna pre- cursor on a magnetic surface, Science Advances 9, eadg8274 (2023)

  19. [27]

    Chou, S.-K

    W.-Y . Chou, S.-K. Peng, F.-H. Chang, H.-L. Cheng, J.-J. Ruan, and T.-Y . Ho, Ferromagnetism above room temperature in a ni-doped organic-based magnetic semiconductor, ACS Applied Materials & Interfaces 13, 34962 (2021)

  20. [28]

    Kondou, M

    K. Kondou, M. Shiga, S. Sakamoto, H. Inuzuka, A. Niho- nyanagi, F. Araoka, M. Kobayashi, S. Miwa, D. Miyajima, and Y . Otani, Chirality-induced magnetoresistance due to thermally driven spin polarization, Journal of the American Chemical So- ciety 144, 7302 (2022)

  21. [29]

    Kapon, L

    Y . Kapon, L. Brann, S. Yochelis, J. Fransson, D. D. Sas- selov, Y . Paltiel, and S. F. Ozturk, Non-classical tempera- ture dependence of chirality-induced magnetization and its im- plications for rna’s homochirality (2024), arXiv:2412.05720 [physics.chem-ph]

  22. [30]

    S. F. Ozturk, D. K. Bhowmick, Y . Kapon, Y . Sang, A. Kumar, Y . Paltiel, R. Naaman, and D. D. Sasselov, Chirality-induced avalanche magnetization of magnetite by an rna precursor, Na- ture Communications 14, 6351 (2023)

  23. [31]

    Fransson, D

    J. Fransson, D. Thonig, P. F. Bessarab, S. Bhattacharjee, J. Hellsvik, and L. Nordstr ¨om, Microscopic theory for coupled atomistic magnetization and lattice dynamics, Phys. Rev. Mate- rials 1, 074404 (2017)

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