pith. sign in

arxiv: 2507.23367 · v2 · submitted 2025-07-31 · ❄️ cond-mat.mtrl-sci

Terahertz spin-orbit torque as a drive of spin dynamics in the insulating antiferromagnet Cr₂O₃

R.M. Dubrovin , Z.V. Gareeva , A.V. Kimel , A.K. Zvezdin This is my paper

Pith reviewed 2026-05-19 02:34 UTC · model grok-4.3

classification ❄️ cond-mat.mtrl-sci
keywords terahertzspin-orbit torqueCr2O3antiferromagnetmagnetoelectricinsulatordisplacement currentNéel vector
0
0 comments X

The pith

The displacement current from a terahertz electric field generates a Néel spin-orbit torque in the insulating antiferromagnet Cr₂O₃.

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

In the magnetoelectric antiferromagnet Cr₂O₃, which is an insulator, a terahertz electric field drives a displacement current that couples to the antiferromagnetic spins through a Néel spin-orbit torque. This effect is uncovered by symmetry analysis combined with a Lagrangian approach that introduces an alternative electric dipole order parameter from the Cr³⁺ sites. The equations of motion show this torque competes with the linear magnetoelectric response, offering a pathway for ultrafast electric control of antiferromagnetic order in non-metallic systems. A sympathetic reader would care because this extends current-driven spin dynamics beyond metals to insulators.

Core claim

Contrary to conventional wisdom that spin dynamics induced by current are exclusive to metallic magnets, we theoretically predict that such phenomena can also be realized in magnetic insulators, specifically in the magnetoelectric antiferromagnet Cr₂O₃. We reveal that the displacement current driven by the THz electric field is able to generate a Néel spin-orbit torque in this insulating system. By introducing an alternative electric dipole order parameter arising from the dipole moment at Cr³⁺ sites, we combine symmetry analysis with a Lagrangian approach and uncover that the displacement current couples to the antiferromagnetic spins and enables ultrafast control of antiferromagnetic order

What carries the argument

Néel spin-orbit torque generated by displacement current, enabled by an alternative electric dipole order parameter at Cr³⁺ sites that couples the THz electric field to the antiferromagnetic spins.

If this is right

  • Insulating antiferromagnets such as Cr₂O₃ become viable platforms for electric-field-driven antiferromagnetic spintronics.
  • Ultrafast control of antiferromagnetic order becomes possible at terahertz frequencies without metallic current paths.
  • The displacement-current torque competes with the linear magnetoelectric response and can be distinguished in dynamics experiments.
  • General design principles are provided for identifying other non-metallic materials that support spin-orbit torque.

Where Pith is reading between the lines

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

  • The same symmetry-based coupling may be tested in other insulating magnetoelectric antiferromagnets to achieve similar THz control.
  • Experiments that separate the torque from magnetoelectric effects could use polarization or frequency dependence of the THz field.
  • This opens routes to antiferromagnetic devices that switch without net charge current flow.

Load-bearing premise

The assumption that an alternative electric dipole order parameter arising from the dipole moment at Cr^{3+} sites correctly captures the symmetry-allowed coupling between displacement current and antiferromagnetic spins.

What would settle it

Time-resolved measurement showing or failing to show ultrafast antiferromagnetic spin dynamics in Cr₂O₃ under a THz electric field that matches the predicted competition between the new torque and the linear magnetoelectric response.

Figures

Figures reproduced from arXiv: 2507.23367 by A.K. Zvezdin, A.V. Kimel, R.M. Dubrovin, Z.V. Gareeva.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
read the original abstract

Contrary to conventional wisdom that spin dynamics induced by current are exclusive to metallic magnets, we theoretically predict that such phenomena can also be realized in magnetic insulators, specifically in the magnetoelectric antiferromagnet $\mathrm{Cr}_{2}\mathrm{O}_{3}$. We reveal that the displacement current driven by the THz electric field is able to generate a N{\'e}el spin-orbit torque in this insulating system. By introducing an alternative electric dipole order parameter arising from the dipole moment at $\mathrm{Cr}^{3+}$ sites, we combine symmetry analysis with a Lagrangian approach and uncover that the displacement current couples to the antiferromagnetic spins and enables ultrafast control of antiferromagnetic order. The derived equations of motion show that this effect competes with the linear magnetoelectric response, offering a novel pathway for manipulating antiferromagnetic order in insulators. Our findings establish insulator antiferromagnets as a viable platform for electric field driven antiferromagnetic spintronics and provide general design principles for non-metallic spin-orbit torque materials.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 2 minor

Summary. The manuscript theoretically predicts that in the insulating magnetoelectric antiferromagnet Cr₂O₃, a THz electric field can drive spin dynamics via displacement current generating a Néel spin-orbit torque. By introducing an alternative electric dipole order parameter P_Cr arising from local Cr³⁺ dipole moments, symmetry analysis combined with a Lagrangian formulation shows that displacement current J_d = ε ∂E/∂t couples to the antiferromagnetic Néel vector L, enabling ultrafast control of AF order. The derived equations of motion indicate this torque competes with the linear magnetoelectric response, establishing a pathway for electric-field-driven antiferromagnetic spintronics in insulators.

Significance. If the central construction holds, the work opens a route to non-metallic, electric-field-driven spin-orbit torques in antiferromagnetic insulators, with potential implications for THz-speed AF spintronics. The combination of crystal symmetry analysis and Lagrangian derivation is a methodological strength that yields falsifiable equations of motion and general design principles for similar materials.

major comments (2)
  1. [Symmetry analysis and Lagrangian formulation] Symmetry analysis and Lagrangian sections: the claim that P_Cr generates a distinct, symmetry-allowed bilinear or trilinear invariant coupling to displacement current J_d and the Néel vector L (beyond standard linear magnetoelectric terms) is load-bearing for the new torque mechanism. The magnetic point group R-3c of Cr₂O₃ must be shown explicitly to permit such invariants that are not redundant with existing ME couplings; otherwise the derived torque reduces to known effects and the central claim of a competing drive vanishes.
  2. [Equations of motion] Equations of motion: the competition between the proposed Néel SOT term proportional to J_d and the linear magnetoelectric response is asserted but lacks quantitative estimates of relative magnitudes or parameter ranges where the new term dominates. Without this, the practical relevance of the predicted ultrafast control remains unclear.
minor comments (2)
  1. [Abstract] Abstract: the phrasing 'alternative electric dipole order parameter' is introduced without a prior definition or reference to its microscopic origin at Cr³⁺ sites; a brief clarifying sentence would improve readability.
  2. [Throughout] Notation: consistent use of symbols for the Néel vector (L) and electric dipole order parameter (P_Cr) should be checked throughout; minor inconsistencies in subscripts appear in the provided text.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of our manuscript and for the constructive comments, which help us clarify the novelty and practical implications of the proposed mechanism. We address each major comment below.

read point-by-point responses

  1. Referee: Symmetry analysis and Lagrangian sections: the claim that P_Cr generates a distinct, symmetry-allowed bilinear or trilinear invariant coupling to displacement current J_d and the Néel vector L (beyond standard linear magnetoelectric terms) is load-bearing for the new torque mechanism. The magnetic point group R-3c of Cr₂O₃ must be shown explicitly to permit such invariants that are not redundant with existing ME couplings; otherwise the derived torque reduces to known effects and the central claim of a competing drive vanishes.

    Authors: We thank the referee for this important observation. Our symmetry analysis was performed under the magnetic point group R-3c, and the local dipole order parameter P_Cr was introduced precisely to capture additional invariants permitted by the crystal symmetry that involve the displacement current. These terms arise from the local Cr³⁺ site dipoles and are distinct from the conventional linear magnetoelectric coupling. To make this explicit and address the concern directly, we will add to the revised manuscript a supplementary table enumerating the symmetry-allowed invariants under R-3c, highlighting those that couple J_d to L via P_Cr and confirming they are not redundant with standard ME terms. This will also include a brief derivation sketch showing how the Lagrangian incorporates these new contributions. revision: yes

  2. Referee: Equations of motion: the competition between the proposed Néel SOT term proportional to J_d and the linear magnetoelectric response is asserted but lacks quantitative estimates of relative magnitudes or parameter ranges where the new term dominates. Without this, the practical relevance of the predicted ultrafast control remains unclear.

    Authors: We agree that quantitative estimates are needed to assess the practical relevance. Although the manuscript derives the equations of motion analytically, we can provide order-of-magnitude estimates using established material parameters for Cr₂O₃ (e.g., magnetoelectric susceptibility, dielectric constant, and typical THz field strengths from experiments). In the revision we will insert a new paragraph in the discussion section that compares the torque magnitudes, identifies the frequency and amplitude regimes where the displacement-current term becomes competitive or dominant, and references relevant experimental literature on Cr₂O₃ to anchor the estimates. revision: yes

Circularity Check

0 steps flagged

Derivation from crystal symmetry and Lagrangian is self-contained; minor self-citation risk but central claim independent

full rationale

The paper's core derivation combines symmetry analysis of the magnetic point group with a Lagrangian formulation that introduces an alternative electric dipole order parameter P_Cr tied to Cr^{3+} sites. This leads to equations of motion showing competition between displacement-current-driven Néel torque and linear magnetoelectric response. No steps reduce by construction to fitted parameters, self-predictions, or load-bearing self-citations that are themselves unverified. The approach relies on external symmetry principles and standard Lagrangian methods rather than renaming known results or smuggling ansatzes via prior self-work. A score of 2 accounts for possible routine self-citation of related magnetoelectric studies by overlapping authors, but this is not load-bearing for the central claim. The derivation remains falsifiable against external benchmarks such as known Cr2O3 point-group invariants and does not collapse to its inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 1 invented entities

Central claim rests on symmetry-allowed couplings and the validity of the introduced dipole order parameter; no explicit free parameters or data fits mentioned.

axioms (2)
  • domain assumption Symmetry analysis of Cr2O3 crystal structure determines allowed magnetoelectric and spin-orbit couplings
    Invoked to establish that displacement current generates Néel torque.
  • domain assumption Lagrangian formulation accurately describes the coupled spin and electric dipole dynamics
    Used to derive equations of motion.
invented entities (1)
  • alternative electric dipole order parameter from Cr^{3+} sites no independent evidence
    purpose: To mediate coupling between displacement current and antiferromagnetic spins
    Newly introduced to enable the torque description beyond standard magnetoelectric terms.

pith-pipeline@v0.9.0 · 5725 in / 1306 out tokens · 59409 ms · 2026-05-19T02:34:46.761817+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

54 extracted references · 54 canonical work pages

  1. [1]

    J. Han, R. Cheng, L. Liu, H. Ohno, and S. Fukami, Co- herent antiferromagnetic spintronics, Nat. Mater.22, 684 (2023)

    work page 2023

  2. [2]

    B. H. Rimmler, B. Pal, and S. S. P. Parkin, Non-collinear antiferromagnetic spintronics, Nat. Rev. Mater. 10, 109 (2025)

    work page 2025

  3. [3]

    Dal Din, O

    A. Dal Din, O. Amin, P. Wadley, and K. W. Edmonds, Antiferromagnetic spintronics and beyond, npj Spintron- ics 2, 25 (2024)

    work page 2024

  4. [5]

    Baltz, A

    V. Baltz, A. Hoffmann, S. Emori, D.-F. Shao, and T. Jungwirth, Emerging materials in antiferromagnetic spintronics, APL Mater. 12, 10.1063/5.0184580 (2024)

    work page doi:10.1063/5.0184580 2024

  5. [6]

    A. K. Zvezdin, Dynamics of domain walls in weak ferro- magnets, JETP Lett. 29, 553 (1979)

    work page 1979

  6. [7]

    A. F. Andreev and V. I. Marchenko, Symmetry and the macroscopic dynamics of magnetic materials, Sov. Phys. Usp. 130, 39 (1980)

    work page 1980

  7. [8]

    A. K. Zvezdin and A. A. Mukhin, New nonlinear dynam- ics effects in antiferromagnets, Bull. Lebedev Phys. Inst. 12, 10 (1981)

    work page 1981

  8. [9]

    Satoh, S.-J

    T. Satoh, S.-J. Cho, R. Iida, T. Shimura, K. Kuroda, H. Ueda, Y. Ueda, B. A. Ivanov, F. Nori, and M. Fiebig, Spin Oscillations in Antiferromagnetic NiO Triggered by Circularly Polarized Light, Phys. Rev. Lett. 105, 077402 (2010)

    work page 2010

  9. [10]

    V. R. Bilyk, R. M. Dubrovin, A. K. Zvezdin, A. I. Kiri- lyuk, and A. V. Kimel, Control of spins in collinear an- 8 tiferromagnet Cr2O3 by terahertz electric fields, Newton 1, 100132 (2025)

    work page 2025

  10. [11]

    Wadley, B

    P. Wadley, B. Howells, J. ˇZelezn` y, C. Andrews, V. Hills, R. P. Campion, V. Nov´ ak, K. Olejn´ ık, F. Maccherozzi, S. Dhesi, et al., Electrical switching of an antiferromag- net, Science 351, 587 (2016)

    work page 2016

  11. [12]

    S. Y. Bodnar, L. ˇSmejkal, I. Turek, T. Jungwirth, O. Gomonay, J. Sinova, A. A. Sapozhnik, H.-J. Elmers, M. Kl¨ aui, and M. Jourdan, Writing and reading anti- ferromagnetic Mn 2Au by N´ eel spin-orbit torques and large anisotropic magnetoresistance, Nat. Commun. 9, 348 (2018)

    work page 2018

  12. [13]

    Manchon, J

    A. Manchon, J. ˇZelezn´ y, I. M. Miron, T. Jungwirth, J. Sinova, A. Thiaville, K. Garello, and P. Gambardella, Current-induced spin-orbit torques in ferromagnetic and antiferromagnetic systems, Rev. Mod. Phys. 91, 035004 (2019)

    work page 2019

  13. [14]

    R. E. Troncoso, K. Rode, P. Stamenov, J. M. D. Coey, and A. Brataas, Antiferromagnetic single-layer spin-orbit torque oscillators, Phys. Rev. B 99, 054433 (2019)

    work page 2019

  14. [15]

    Selzer, L

    S. Selzer, L. Salemi, A. De´ ak, E. Simon, L. Szunyogh, P. M. Oppeneer, and U. Nowak, Current-induced switch- ing of antiferromagnetic order in Mn 2Au from first prin- ciples, Phys. Rev. B 105, 174416 (2022)

    work page 2022

  15. [16]

    Kaˇ spar, M

    Z. Kaˇ spar, M. Sur` ynek, J. Zub´ aˇ c, F. Krizek, V. Nov´ ak, R. P. Campion, M. S. W¨ ornle, P. Gambardella, X. Marti, P. Nˇ emec, K. W. Edmonds, S. Reimers, O. J. Amin, F. Maccherozzi, S. S. Dhesi, P. Wadley, J. Wunderlich, K. Olejn´ ık, and T. Jungwirth, Quenching of an antifer- romagnet into high resistivity states using electrical or ultrashort opti...

    work page 2021

  16. [17]

    Freimuth, S

    F. Freimuth, S. Bl¨ ugel, and Y. Mokrousov, Laser-induced torques in metallic antiferromagnets, Phys. Rev. B 103, 174429 (2021)

    work page 2021

  17. [18]

    Behovits, A

    Y. Behovits, A. L. Chekhov, S. Y. Bodnar, O. Gueck- stock, S. Reimers, Y. Lytvynenko, Y. Skourski, M. Wolf, T. S. Seifert, O. Gomonay, M. Kl¨ aui, M. Jourdan, and T. Kampfrath, Terahertz n´ eel spin-orbit torques drive nonlinear magnon dynamics in antiferromagnetic Mn2Au, Nat. Commun. 14, 6038 (2023)

    work page 2023

  18. [19]

    J. L. Ross, P.-I. Gavriloaea, F. Freimuth, T. Adaman- topoulos, Y. Mokrousov, R. F. Evans, R. Chantrell, R. M. Otxoa, and O. Chubykalo-Fesenko, Ultrafast antiferro- magnetic switching of Mn 2Au with laser-induced optical torques, npj Comput. Mater. 10, 234 (2024)

    work page 2024

  19. [20]

    Olejn´ ık, Z

    K. Olejn´ ık, Z. Kaˇ spar, J. Zub´ aˇ c, S. Telkamp, A. Farkaˇ s, D. Kriegner, K. V` yborn` y, J.ˇZelezn` y, Z.ˇSob´ aˇ n, P. Zeng, et al. , Quench switching of Mn 2As, arXiv preprint arXiv:2411.01930 10.48550/arXiv.2411.01930 (2024)

    work page doi:10.48550/arxiv.2411.01930 2024

  20. [21]

    Th¨ ole, A

    F. Th¨ ole, A. Keliri, and N. A. Spaldin, Concepts from the linear magnetoelectric effect that might be useful for antiferromagnetic spintronics, J. Appl. Phys. 127, 10.1063/5.0006071 (2020)

    work page doi:10.1063/5.0006071 2020

  21. [22]

    I. E. Dzyaloshinskii, On the magneto-electrical effects in antiferromagnets, Sov. Phys. JETP 10, 628 (1960)

    work page 1960

  22. [23]

    D. N. Astrov, The magnetoelectric effect in antiferromag- netics, Sov. Phys. JETP 11, 708 (1960)

    work page 1960

  23. [24]

    D. N. Astrov, Magnetoelectric effect in chromium oxide, Sov. Phys. JETP 13, 729 (1961)

    work page 1961

  24. [25]

    G. T. Rado and V. J. Folen, Observation of the Mag- netically Induced Magnetoelectric Effect and Evidence for Antiferromagnetic Domains, Phys. Rev. Lett. 7, 310 (1961)

    work page 1961

  25. [26]

    Volger, Anomalous specific heat of chromium oxide (Cr2O3) at the antiferromagnetic Curie temperature, Na- ture 170, 1027 (1952)

    J. Volger, Anomalous specific heat of chromium oxide (Cr2O3) at the antiferromagnetic Curie temperature, Na- ture 170, 1027 (1952)

    work page 1952

  26. [27]

    T. R. McGuire, E. J. Scott, and F. H. Grannis, Antifer- romagnetism in a Cr 2O3 Crystal, Phys. Rev. 102, 1000 (1956)

    work page 1956

  27. [28]

    B. N. Brockhouse, Antiferromagnetic structure in Cr2O3, J. Chem. Phys. 21, 961 (1953)

    work page 1953

  28. [29]

    L. M. Corliss, J. M. Hastings, R. Nathans, and G. Shi- rane, Magnetic structure of Cr 2O3, J. Appl. Phys. 36, 1099 (1965)

    work page 1965

  29. [30]

    Bousquet, E

    E. Bousquet, E. Leli` evre-Berna, N. Qureshi, J.-R. Soh, N. A. Spaldin, A. Urru, X. H. Verbeek, and S. F. Weber, On the sign of the linear magnetoelectric coefficient in Cr2O3, J. Phys. Condens. Matter 36, 155701 (2024)

    work page 2024

  30. [31]

    Z. V. Gabbasova, M. D. Kuz’min, A. K. Zvezdin, I. S. Dubenko, V. A. Murashov, D. N. Rakov, and I. B. Krynetsky, Bi1−xRxFeO3 (R = rare earth): a family of novel magnetoelectrics, Phys. Lett. A 158, 491 (1991)

    work page 1991

  31. [32]

    Ederer and N

    C. Ederer and N. A. Spaldin, Influence of strain and oxy- gen vacancies on the magnetoelectric properties of multi- ferroic bismuth ferrite, Phys. Rev. B 71, 224103 (2005)

    work page 2005

  32. [33]

    A. K. Zvezdin, Z. V. Gareeva, and X. M. Chen, Mul- tiferroic order parameters in rhombic antiferromagnets RCrO3, J. Phys. Condens. Matter 33, 385801 (2021)

    work page 2021

  33. [34]

    Resta and D

    R. Resta and D. Vanderbilt, Theory of polarization: a modern approach, in Physics of ferroelectrics: a modern perspective (Springer, 2007) pp. 31–68

    work page 2007

  34. [35]

    Kittel, Theory of antiferroelectric crystals, Phys

    C. Kittel, Theory of antiferroelectric crystals, Phys. Rev. 82, 729 (1951)

    work page 1951

  35. [36]

    A. K. Tagantsev, K. Vaideeswaran, S. B. Vakhrushev, A. V. Filimonov, R. G. Burkovsky, A. Shaganov, D. An- dronikova, A. I. Rudskoy, A. Q. R. Baron, H. Uchiyama, D. Chernyshov, A. Bosak, Z. Ujma, K. Roleder, A. Ma- jchrowski, J.-H. Ko, and N. Setter, The origin of antifer- roelectricity in PbZrO 3, Nat. Commun. 4, 2229 (2013)

    work page 2013

  36. [37]

    E. A. Turov, A. V. Kolchanov, V. V. Menshenin, I. F. Mirsaev, and V. V. Nikolaev, Symmetry and Physi- cal Properties of Antiferromagnets, Fizmatlit, Moscow (2001)

    work page 2001

  37. [38]

    E. A. Turov and V. V. Nikolaev, New physical phenom- ena caused by magnetoelectricand antiferroelectric inter- actions in magnets, Phys.-Usp. 48, 431 (2005)

    work page 2005

  38. [39]

    Manchon, H

    A. Manchon, H. C. Koo, J. Nitta, S. M. Frolov, and R. A. Duine, New perspectives for rashba spin–orbit coupling, Nat. Mater. 14, 871 (2015)

    work page 2015

  39. [40]

    ˇZelezn´ y, H

    J. ˇZelezn´ y, H. Gao, A. Manchon, F. Freimuth, Y. Mokrousov, J. Zemen, J. Maˇ sek, J. Sinova, and T. Jungwirth, Spin-orbit torques in locally and globally noncentrosymmetric crystals: Antiferromagnets and fer- romagnets, Phys. Rev. B 95, 014403 (2017)

    work page 2017

  40. [41]

    Salemi, M

    L. Salemi, M. Berritta, A. K. Nandy, and P. M. Oppe- neer, Orbitally dominated rashba-edelstein effect in non- centrosymmetric antiferromagnets, Nat. Commun. 10, 5381 (2019)

    work page 2019

  41. [42]

    Bihlmayer, P

    G. Bihlmayer, P. No¨ el, D. V. Vyalikh, E. V. Chulkov, and A. Manchon, Rashba-like physics in condensed matter, Nat. Rev. Phys. 4, 642 (2022)

    work page 2022

  42. [43]

    A. K. Zvezdin, A. V. Kimel, D. I. Plokhov, and K. A. Zvezdin, Ultrafast spin dynamics in the iron borate easy- plane weak ferromagnet, J. Exp. Theor. Phys. 131, 130 (2020)

    work page 2020

  43. [44]

    Landau and E

    L. Landau and E. Lifshitz, Electrodynamics of continuous media, Vol. 8 (Pergamon, 1984). 9

    work page 1984

  44. [45]

    D. V. Sivukhin, A Course of General Physics. Vol. III, Electricity (Nauka, Moscow (in Russian), 1996)

    work page 1996

  45. [46]

    O. D. Jefimenko, Electricity and magnetism: An in- troduction to the theory of electric and magnetic fields (Appleton-Century-Crofts, 1966)

    work page 1966

  46. [47]

    Lucovsky, R

    G. Lucovsky, R. J. Sladek, and J. W. Allen, Infrared- active phonons in Cr 2O3, Phys. Rev. B 16, 4716 (1977)

    work page 1977

  47. [48]

    Fradkin, Field theories of condensed matter physics (Cambridge University Press, 2013)

    E. Fradkin, Field theories of condensed matter physics (Cambridge University Press, 2013)

    work page 2013

  48. [49]

    A. K. Zvezdin, R. M. Dubrovin, and A. V. Kimel, Giant Parametric Amplification of the Inverse Cotton–Mouton Effect in Antiferromagnetic Crystals, JETP Lett. 119, 363 (2024)

    work page 2024

  49. [50]

    Foner, High-Field Antiferromagnetic Resonance in Cr2O3, Phys

    S. Foner, High-Field Antiferromagnetic Resonance in Cr2O3, Phys. Rev. 130, 183 (1963)

    work page 1963

  50. [51]

    A. A. Mukhin, V. D. Travkin, and S. P. Lebedev, BWO quasi-optical spectroscopy of Cr2O3: Gyrotropic birefrin- gence at antiferromagnetic resonance, Ferroelectrics 204, 261 (1997)

    work page 1997

  51. [52]

    R. V. Pisarev, B. B. Krichevtsov, and V. V. Pavlov, Op- tical study of the antiferromagnetic-paramagnetic phase transition in chromium oxide Cr 2O3, Phase Transitions 37, 63 (1991)

    work page 1991

  52. [53]

    B. B. Krichevtsov, V. V. Pavlov, R. V. Pisarev, and V. N. Gridnev, Spontaneous non-reciprocal reflection of light from antiferromagnetic Cr2O3, J. Phys. Condens. Matter 5, 8233 (1993)

    work page 1993

  53. [54]

    B. B. Krichevtsov, V. V. Pavlov, R. V. Pisarev, and V. N. Gridnev, Magnetoelectric Spectroscopy of Elec- tronic Transitions in Antiferromagnetic Cr 2O3, Phys. Rev. Lett. 76, 4628 (1996)

    work page 1996

  54. [55]

    D. M. Juraschek, D. S. Wang, and P. Narang, Sum- frequency excitation of coherent magnons, Phys. Rev. B 103, 094407 (2021)

    work page 2021