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Cited by 68Advanced Condensed Matter PhysicsSolid-state spectroscopy and crystallographyThermal properties of materials

Magnetic Control of Soft Chiral Phonons in PbTe

Open access
Baydin, Andrey, Hernandez, Felix G. G., Rodriguez-Vega, Martin, Okazaki, Anderson K., Tay, Fuyang, Noe, G. Timothy, Katayama, Ikufumi, Takeda, Jun +5 more·2022·Physical Review Letters
DOI 10.1103/physrevlett.128.075901
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Abstract

PbTe crystals have a soft transverse optical phonon mode in the terahertz frequency range, which is known to efficiently decay into heat-carrying acoustic phonons, resulting in anomalously low thermal conductivity. Here, we studied this phonon via polarization-dependent terahertz spectroscopy. We observed softening of this mode with decreasing temperature, indicative of incipient ferroelectricity, which we explain through a model including strong anharmonicity with a quartic displacement term. In magnetic fields up to 25 T, the phonon mode splits into two modes with opposite handedness, exhibiting circular dichroism. Their frequencies display Zeeman splitting together with an overall diamagnetic shift with increasing magnetic field. Using a group-theoretical approach, we demonstrate that these observations are the result of magnetic field-induced morphic changes in the crystal symmetries through the Lorentz force exerted on the lattice ions. Thus, our Letter reveals a novel process of controlling phonon properties in a soft ionic lattice by a strong magnetic field.

Integrity signals

Registry

Crossref · 10.1103/physrevlett.128.075901

Cites

37 of 37 references verified0 citation errors · 0 not checkable

Statistics

Nothing to recompute.

Claims the paper makes

0 of 24 cited sources checked · 0 supported · 0 flagged

  • Findingown data

    The diamagnetic shift raises the energies of both Zeeman-split branches as the magnetic field increases.

    “The diamagnetic shift increases the energies of both Zeeman-split branches with increasing magnetic field.”
    Quote in the paperSubstantial claim
  • Findingcitation

    The temperature dependence of the transverse optical phonon frequency is sublinear.

    “This sublinear temperature dependence has been understood by strong anharmonic coupling between TO phonons and LA phonons with first principles calculations beyond the harmonic approximation [12,35].”
    Quote in the paperNot a substantial claim0 of 2 sources checked
    • cites [12] 12. G. A. S. Ribeiro, L. Paulatto, R. Bianco, I. Errea, F. Mauri, and M. Calandra, Phys. Rev. B 97, 014306 (2018).

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

    • cites [35] 35. P. T. Jochym, J. Łażewski, and W. Szuszkiewicz, Sci. Rep. 10, 19783 (2020).

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  • Findingown data

    The observed Zeeman splitting is three orders of magnitude larger than the value predicted for PbTe by density functional theory assuming harmonic phonons.

    “The observed Zeeman splitting was three orders of magnitude larger than what has been predicted for PbTe using density functional theory based on harmonic phonons”
    • Also stated in: § Abstract · plain
      “The value of g à we obtained (∼4 × 10 -2 ) is 3 orders of magnitude larger than the value (∼6 × 10 -5 ) predicted by using density functional theory in Ref. [2] assuming harmonic phonons.”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [2] 2. D. M. Juraschek and N. A. Spaldin, Phys. Rev. Mater. 3, 064405 (2019).

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  • Findingown data

    The temperature dependence of the transverse optical phonon linewidth is well fitted by a model in which a harmonic optical phonon decays into two acoustic phonons with finite momentum.

    “Interestingly, the TO phonon's linewidth temperature dependence is well fitted by the model for a harmonic optical phonon decaying into two acoustical phonons with finite momentum, as derived in Ref. [24]”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [24] 24. P. G. Klemens, Phys. Rev. 148, 845 (1966).

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  • Findingown data

    In the strong anharmonicity regime, theory and experimental data agree well for a constant phonon lifetime.

    “In particular, in the strong anharmonicity regime, λ ≫ k, where λ ¼ ℏλ=m 2 ω 3 0 and k ¼ k=mω 2 0 , and for a constant lifetime, theory and experimental data are in good agreement, as shown in Fig. 2(d).”
    Quote in the paperSubstantial claim
    • The authors state this as an assumption: The phonon lifetime is constant, or its temperature dependence does not affect the general conclusion.
  • May combine two claims. 14
  • Classified as probably not a substantial claim. 2
  • The quote only partly states this claim. 1

  • May combine two claims.

    Findingown data

    In magnetic fields up to 25 T, the transverse optical phonon mode splits into two modes of opposite handedness and exhibits circular dichroism.

    “In magnetic fields up to 25 T, the phonon mode splits into two modes with opposite handedness, exhibiting circular dichroism.”
    • Also stated in: § Abstract · plain
      “In conclusion, we observed circularly polarized phonons in PbTe in magnetic fields.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data

    The response to right-hand and left-hand polarized light varies, indicating magnetic circular dichroism of the transverse optical phonon.

    “Moreover, the response to right-hand and left-hand polarized light varies, which indicates MCD of the TO phonon.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data

    At high temperatures, the 0 T and 9 T data overlap, while at low temperatures the transverse optical phonon response in a magnetic field differs from that at zero field.

    “At high temperatures, the 0 T and 9 T data overlap, while at low temperatures, the TO phonon response in a magnetic field is different from that with no magnetic field.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data

    Harmonic first-principles calculations estimate phonon frequencies of about 1.25 THz for the doubly degenerate transverse optical phonons and about 3.32 THz for the longitudinal optical phonon.

    “Within harmonic first-principles calculations (see Supplemental Material [21] for details), we estimate the phonon frequencies to be ≈1.25 THz for the doubly degenerate TO phonons and ≈3.32 THz for the LO phonon.”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [21] 21. See Supplemental Material at http://link.aps.org/ supplemental/10.1103/PhysRevLett.128.075901 for details of the conductivity calculations, morphic effect group theory calculations, experimental methods, and additional figures, which includes Refs. [3,17,20,22-33].

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  • May combine two claims.

    Findingown data

    The frequencies of the split phonon modes show Zeeman splitting together with an overall diamagnetic shift as the magnetic field increases.

    “Their frequencies display Zeeman splitting together with an overall diamagnetic shift with increasing magnetic field.”
    • Also stated in: § Abstract · plain
      “We observed a Zeeman splitting as well as a diamagnetic shift in the phonon frequency as a function of magnetic field up to 25 T.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data

    The diamagnetic contribution becomes relevant for fields above 9 T, where the lower-energy branch reverses its decreasing trend.

    “In Fig. 3(c), this contribution appears to be relevant for fields above 9 T when the lower-energy branch reverses its decreasing trend.”
    • Also stated in: § Abstract · plain
      “On the other hand, the diamagnetic term only becomes important for fields above 9 T.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data

    The group theory analysis indicates that the irreducible representation of the optical mode is T1u, which is infrared active and triply degenerate without considering TO-LO splitting.

    “Our group theory analysis, performed using the Bilbao Crystallographic server [20], indicates that the irreducible representation of the optical mode is T 1u , which is infrared active and triply degenerate without considering the TO-LO splitting.”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [20] 20. E. Kroumova, M. Aroyo, J. Perez-Mato, A. Kirov, C. Capillas, S. Ivantchev, and H. Wondratschek, Phase Transit. 76, 155 (2003).

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  • May combine two claims.

    Findingown data

    Fitting Eq. 6 to the data yields an effective g factor of (4.3 ± 0.6) × 10^-2 and a diamagnetic shift coefficient of (1.9 ± 0.2) × 10^-4 meV/T^2.

    “We used Eq. ( 6) to fit the data in Fig. 3(c), as shown by dashed lines, to obtain g à ¼ ð4.3 Æ 0.6Þ × 10 -2 and σ dia ¼ ð1.9 Æ 0.2Þ × 10 -4 meV=T 2”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data

    The model does not contain explicit temperature dependence for magnetic circular dichroism, while the data show a continuous increase over the studied temperature range.

    “Nevertheless, the model does not contain any explicit temperature dependence for the MCD, as seen in Fig. 3(b), where a continuous increase occurs in the studied temperature range.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Study design and conductcitation

    For a model with a temperature-dependent phonon lifetime, the general conclusion remains valid, although some details depend on the lifetime assumptions.

    “For a model with a temperature-dependent phonon lifetime the general conclusion remains valid, although some details hinge on the assumptions for the lifetime, as discussed in the Supplemental Material [21].”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [21] 21. See Supplemental Material at http://link.aps.org/ supplemental/10.1103/PhysRevLett.128.075901 for details of the conductivity calculations, morphic effect group theory calculations, experimental methods, and additional figures, which includes Refs. [3,17,20,22-33].

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

    • The authors state this as an assumption: The phonon lifetime is constant, or its temperature dependence does not affect the general conclusion.

  • May combine two claims.

    Interpretationreasoning

    The magnetic phonon moment in this study comes from phonon anharmonicity and morphic effects due to high magnetic fields, rather than from resonant electron-phonon coupling.

    “The magnetic phonon moment in the present Letter, instead, comes from phonon anharmonicity and morphic effects due to high magnetic fields, as explained below.”
    • Also stated in: § Abstract · plain
      “In our case, the high magnetic field moves the free-carrier cyclotron frequency completely out of our frequency range, and thus, this mechanism is irrelevant.”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [3] 3. B. Cheng, T. Schumann, Y. Wang, X. Zhang, D. Barbalas, S. Stemmer, and N. P. Armitage, Nano Lett. 20, 5991 (2020).

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

    • Rests on an assumption: At the high magnetic fields used, the free-carrier cyclotron frequency lies completely outside the measurement frequency range.

  • May combine two claims.

    Premisecitation

    PbTe belongs to the space group Fm-3m with Oh point group.

    “PbTe belongs to the space group Fm 3m with O h point group.”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [19] 19. S.-Y. Xu et al., Nat. Commun. 3, 1192 (2012). source

      Not checked in the free run.

  • Classified as probably not a substantial claim.

    Premisecitation

    The unusually low thermal conductivity of PbTe is linked to anomalous lattice dynamics involving strong anharmonic coupling between longitudinal acoustic and transverse optical phonon modes.

    “Reports have related the low thermal conductivity to anomalous lattice dynamics with giant anharmonic coupling of the longitudinal acoustic (LA) modes with the transverse optical (TO) phonon mode [9][10][11][12].”
    Quote in the paperSubstantial claim0 of 3 sources checked
    • cites [9] 9. O. Delaire, J. Ma, K. Marty, A. F. May, M. A. McGuire, M.-H. Du, D. J. Singh, A. Podlesnyak, G. Ehlers, M. D. Lumsden, and B. C. Sales, Nat. Mater. 10, 614 (2011).

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

    • cites [10] 10. Y. Xia, Appl. Phys. Lett. 113, 073901 (2018).

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

    • cites [11] 11. Y. Lu, T. Sun, and D.-B. Zhang, Phys. Rev. B 97, 174304 (2018).

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation

    The Pb and Te atoms form interpenetrating face-centered cubic lattices.

    “The Pb and Te atoms form an arrangement of interpenetrating face-centered cubic lattices [19].”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [19] 19. S.-Y. Xu et al., Nat. Commun. 3, 1192 (2012). source

      Not checked in the free run.

  • May combine two claims.

    Premisereasoning

    An incident light beam propagating in the [111] direction couples linearly to the transverse optical phonon modes and induces ionic oscillations in a perpendicular plane.

    “An incident light beam propagating in the [111] direction couples linearly to these TO phonon modes, inducing ionic oscillations in a perpendicular plane.”
    Quote in the paperSubstantial claim

  • The quote only partly states this claim.

    Interpretationown data

    A model that includes strong quartic anharmonicity accounts for the temperature dependence of the transverse optical phonon frequency and line shape.

    “which we explain through a model including strong anharmonicity with a quartic displacement term.”
    • Also stated in: § Abstract · boosted
      “In particular, in the strong anharmonicity regime, λ ≫ k, where λ ¼ ℏλ=m 2 ω 3 0 and k ¼ k=mω 2 0 , and for a constant lifetime, theory and experimental data are in good agreement, as shown in Fig. 2(d).”
    Quote in the paperSubstantial claim
    • The authors state this as an assumption: The phonon Hamiltonian can be modeled with a quartic anharmonic term.

  • May combine two claims.

    Premisecitation

    Interactions between atoms in a crystal produce a finite energy potential that sets the harmonic phonon frequency, and a magnetic field can add symmetry-allowed terms that alter this frequency.

    “The interactions between the atoms in a crystal lead to a finite energy potential, which determines the frequency of harmonic phonons.The presence of a magnetic field can induce additional symmetry-allowed terms, which, in turn, modify the phonon frequency.”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [17] 17. E. Anastassakis and E. Burstein, J. Phys. Chem. Solids 32, 563 (1971).

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

17 of 17

  • The authors state this as an assumption.

    The phonon Hamiltonian can be modeled with a quartic anharmonic term.

    “where H ph is the phonon Hamiltonian including a quartic anharmonic term [25]”

  • The authors state this as an assumption.

    The phonon Born effective charge can depend on the applied magnetic field according to the symmetries of the system.

    “Z Ã ¼ Z Ã ðHÞ is the phonon Born effective charge, which can depend on the applied magnetic field H, depending on the symmetries of the system.”

  • The authors state this as an assumption.

    The phonon lifetime is constant, or its temperature dependence does not affect the general conclusion.

    “for a constant lifetime, theory and experimental data are in good agreement”
    “some details hinge on the assumptions for the lifetime”

  • The paper relies on this without support.

    At the high magnetic fields used, the free-carrier cyclotron frequency lies completely outside the measurement frequency range.

    “In our case, the high magnetic field moves the free-carrier cyclotron frequency completely out of our frequency range”
4 of 4

Claims other papers make about this one

Each is checked against this paper’s own text: does it say what the citing paper says it does?

  • The truncated-data transmittance exhibits characteristic PbTe thin-film behavior at 120 K, showing a broad absorption band centered near 0.75 THz attributed to a transverse optical (TO) phonon mode.

    “The truncated-data transmittance exhibits characteristic PbTe thin-film behavior at 120 K, showing a broad absorption band centered near 0 . 75 THz attributed to a transverse optical (TO) phonon mode [36, 41].”

    From Windowing in Terahertz Time-Domain Spectroscopy: Resolving Resonances in Thin-Film Samples (2025) · cites this paper as [36]

    Experimental — accuracy not yet measured

  • This ε2 peak is in reasonable agreement with literature values for PbTe thin films (e.g., real conductivity peaks in Ref. [36]).

    “This is in reasonable agreement with literature values for PbTe thin films (e.g., real conductivity peaks in Ref. [36]).”

    From Windowing in Terahertz Time-Domain Spectroscopy: Resolving Resonances in Thin-Film Samples (2025) · cites this paper as [36]

  • The measured g factor in PbTe related to a soft phonon at terahertz frequencies was found to be three orders of magnitude larger than predicted by theory.

    “In another work28, the measured g factor in PbTe related to a soft phonon at terahertz frequencies was found to be three orders of magnitude larger than predicted by theory.”

    From Terahertz electric-field-driven dynamical multiferroicity in SrTiO3 (2024) · cites this paper as [28]

  • Only the Gaussian-windowed signal provides a realistic amplitude, with extracted ε2 peak estimated as (42 ± 1) × 10^3, closely matching values reported in Ref. [36].

    “only the latter provides a realistic amplitude, with the extracted ϵ 2 peak estimated as (42 ± 1) × 10 3 , closely matching the values reported in Ref. [36].”

    From Windowing in Terahertz Time-Domain Spectroscopy: Resolving Resonances in Thin-Film Samples (2025) · cites this paper as [36]

    The optical-conductivity discussion (section labeled Abstract, page unavailable) reports a PbTe phonon resonance but gives no ε₂ peak value. Searches for the Gaussian window, ε₂, and (42 ± 1) × 10³ found no passage establishing that the cited paper reports a closely matching value. (LLM, conf=0.76)

    Experimental — accuracy not yet measured

Self-check

Percentages, sums and reported differences re-computed from the paper’s own numbers.

Each contradiction between two passages listed here was confirmed by an independent check.

  • Diamagnetic coefficient has one too few permeability factors

    Minor

    In Eq. (5), the quadratic frequency shift is proportional to K2H_z2. Eq. (6) writes the corresponding energy shift as σ_diaμ02H_z2, so the stated conversion from K2 to σ_dia should divide by μ02, not μ0.

1 of 1

Cites

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Research works printed but not linked: 1

  1. 1980, Disordered Solids, Optical Properties

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Related

Authors
Baydin, A., Hernandez, F. G. G., Rodriguez-Vega, M., Okazaki, A. K., Tay, F., Noe, G. T., Katayama, I., Takeda, J., Nojiri, H., Rappl, P. H. O., Abramof, E., Fiete, G. A., & Kono, J.
Affiliations
  • Rice University (US)
  • Instituto de Física, Universidade de São Paulo, São Paulo, São Paulo 05508-090, Brazil
  • Los Alamos National Laboratory (US)
  • Instituto Nacional de Pesquisas Espaciais (BR)
  • Yokohama National University (JP)
  • Tohoku University (JP)
  • Northeastern University (US)
ORCID
Venue
Physical Review Letters
Publisher
American Physical Society (APS)
Published
2022-02-15
Volume
128
Issue
7
Pages
075901-075901
ISSN
  • 0031-9007 (ISSN-L)
  • 1079-7114
DOI
10.1103/physrevlett.128.075901
OpenAlex
W3185707187
Cited by
68
References
37
Citations by year
2026: 2 · 2025: 15 · 2024: 23 · 2023: 21 · 2022: 7
FWCI
6.17
Type
journal article
Language
en
Open access
Licence
Locations
  • Physical Review Letters (publishedVersion)
  • PubMed (publishedVersion)
  • arXiv (Cornell University) (submittedVersion)
  • OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information) (submittedVersion)
  • Figshare (submittedVersion, cc-by)
  • Institutional Repositories DataBase (IRDB) (submittedVersion, cc-by-nc-nd)
  • Biblioteca Digital da Memória Científica do INPE (National Institute for Space Research) (submittedVersion)
  • Yokohama National University Repository (Yokohama National University) (submittedVersion, cc-by-nc-nd)
  • arXiv (Cornell University)
  • Texas Digital Library (University of Texas)
Funders
  • National Science Foundation
  • Materials Research Science and Engineering Center, Harvard University (DMR-1720595)
  • Fundação de Amparo à Pesquisa do Estado de São Paulo (2015/16191-5, 2018/06142-5, 307737/2020-9)
  • Conselho Nacional de Desenvolvimento Científico e Tecnológico
  • Laboratory Directed Research and Development
  • U.S. Department of Energy
  • Office of Science
  • Basic Energy Sciences
  • Japan Society for the Promotion of Science (20H05662)
Topics
  • Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Advanced Condensed Matter Physics
  • Physical Sciences › Materials Science › Materials Chemistry › Solid-state spectroscopy and crystallography
  • Physical Sciences › Materials Science › Materials Chemistry › Thermal properties of materials
Keywords
PbTe, chiral phonons, circular dichroism, Zeeman splitting, diamagnetic shift, incipient ferroelectricity, anharmonicity, phonon softening, low thermal conductivity, crystal symmetry breaking

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