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arxiv: 2512.16014 · v1 · submitted 2025-12-17 · ❄️ cond-mat.mtrl-sci · physics.optics· quant-ph

Magneto-optical Kerr effect in pump-probe setups

Amir Eskandari-asl , Adolfo Avella (Dipartimento di Fisica 'E.R. Caianiello' , Universit\`a degli Studi di Salerno , Fisciano (SA) , Italy) This is my paper

Pith reviewed 2026-05-16 21:04 UTC · model grok-4.3

classification ❄️ cond-mat.mtrl-sci physics.opticsquant-ph
keywords time-resolved magneto-optical Kerr effectpump-probe setupdynamical projective operatorial approachsingle-particle density matrixultrafast dynamicsoptical conductivityn-photon resonances
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The pith

A framework based on the dynamical projective operatorial approach computes the time-resolved magneto-optical Kerr effect from the evolution of the single-particle density matrix.

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

The paper establishes a theoretical method to calculate the magneto-optical Kerr effect in time-resolved pump-probe experiments on complex materials. It uses the Dynamical Projective Operatorial Approach and its extension to the single-particle density matrix to express the optical conductivity after pumping. This approach reproduces both the rapid changes during the pump pulse and the slower relaxation afterward, while incorporating damping effects at low computational cost. A key insight is that measurements of Kerr rotation can experimentally reveal the n-photon resonances specific to the material under study.

Core claim

By formulating the time-resolved magneto-optical Kerr effect within the Dynamical Projective Operatorial Approach and expressing the post-pump optical conductivity in terms of the time-evolved single-particle density matrix, the framework provides an efficient way to simulate ultrafast spin-charge dynamics in multi-band systems, as demonstrated in both a simple tight-binding model and in weakly spin-polarized germanium.

What carries the argument

The Dynamical Projective Operatorial Approach (DPOA) extended via the single-particle density matrix (SPDM) to compute post-pump optical conductivity and Kerr rotation.

If this is right

  • The method captures short-time dynamics under the pump pulse envelope.
  • It also describes long-time dynamics after excitation.
  • Phenomenological damping can be included straightforwardly.
  • The Kerr rotation signal allows experimental identification of n-photon resonances.

Where Pith is reading between the lines

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

  • This approach may extend to other time-resolved optical spectroscopies in magnetic materials.
  • Applications could include guiding experiments on ultrafast magnetism in more complex compounds.
  • Comparisons with full many-body simulations could validate the approximations for specific systems.

Load-bearing premise

The essential physics of ultrafast spin-charge dynamics is captured by a two-band tight-binding model and a weakly spin-polarized germanium band structure without needing detailed many-body interactions.

What would settle it

Experimental Kerr rotation spectra from pump-probe measurements on germanium that fail to show the predicted positions of n-photon resonances or mismatch the calculated time evolution would falsify the framework's predictive power.

Figures

Figures reproduced from arXiv: 2512.16014 by Adolfo Avella (Dipartimento di Fisica 'E.R. Caianiello', Amir Eskandari-asl, Fisciano (SA), Italy), Universit\`a degli Studi di Salerno.

Figure 1
Figure 1. Figure 1: (a) Schematic representation of the system, the pump pulse, and the time-delayed probe pulse together with its [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: (a–d) Real and imaginary parts of δσ¯xx(ω, tpr) and δσ¯xy(ω, tpr) as functions of ω and tpr. The horizontal dashed lines mark the pump pulse frequency ℏωpu = 2.86 eV, while the vertical dashed lines indicate the probe pulse delay equal to the pump pulse FWHM, tpr = τpu = 10 fs [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: (a–d) The evolution of the Kerr rotation angle, [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: (a) Benchmark of the exact results for δθK(ω, tpr) against those obtained from the SPDM approach without damping (Υ = 0 in Eq. 31) for several probe pulse frequency cuts. The probe photon energy values of each cut, ℏω, are given in eV. An offset of 0.015 rad has been applied on increasing the probe photon energies. The pump photon energy is ℏωpu = 2.86 eV. (b) δθK(ω, tpr) at long delays without damping; th… view at source ↗
Figure 5
Figure 5. Figure 5: (a) Equilibrium Kerr rotation θ eq K (ω) of weakly spin-polarized germanium. (b) δθK(ω, tpr) at long delays without damping; the inset shows a cut at the two-photon resonant frequency ω = 2ωpu. (c) Same as (b) but including damping in SPDM with Υnm = δnm λ 4 + (1−δnm) λ 2 . The horizontal gray and black dashed lines in all panels mark the one and two-photon resonances, ℏω = ℏωpu = 1.55 eV and ℏω = 2ℏωpu = … view at source ↗
read the original abstract

We develop a general theoretical framework for computing the time-resolved magneto-optical Kerr effect in ultrafast pump-probe setups, formulated within the Dynamical Projective Operatorial Approach (DPOA) and its application to the generalized linear-response theory for pumped systems. Furthermore, we exploit this formalism to express the post-pump optical conductivity and consequently the Kerr rotation in terms of the time-evolved single-particle density matrix (SPDM), providing a transparent and computationally efficient description of photo-excited multi-band systems. This extension, in addition to its lower computational cost, has the advantage of allowing the inclusion of phenomenological damping. We illustrate the formalism using both (i) a two-band tight-binding model, which captures the essential physics of ultrafast spin-charge dynamics and the Kerr rotation, and (ii) weakly spin-polarized germanium, as a realistic playground with a complex band structure. The results demonstrate that, by exploiting DPOA and/or its SPDM extension, one can reliably reproduce both the short-time features under the pump-pulse envelope and the long-time dynamics after excitation, offering a versatile framework for analyzing time-resolved magneto-optical Kerr effect experiments in complex materials. Moreover, this analysis clearly shows that the Kerr rotation can be used to deduce experimentally the relevant n-photon resonances for a given specific material.

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 paper develops a general theoretical framework for the time-resolved magneto-optical Kerr effect in pump-probe setups using the Dynamical Projective Operatorial Approach (DPOA) and its extension to the time-evolved single-particle density matrix (SPDM) within generalized linear-response theory. It expresses the post-pump optical conductivity and Kerr rotation in terms of the SPDM, incorporates phenomenological damping, and illustrates the approach on a two-band tight-binding model and weakly spin-polarized germanium, claiming reliable reproduction of both short-time dynamics under the pump envelope and long-time post-excitation dynamics, plus the ability to deduce n-photon resonances from Kerr rotation.

Significance. If the central claims hold, the framework supplies a computationally efficient, damping-inclusive route to modeling TR-MOKE in multi-band systems that could aid experimental analysis of ultrafast spin-charge dynamics and resonance identification.

major comments (2)
  1. [Illustration sections (two-band TB model and Ge example)] The central claim that DPOA/SPDM reliably reproduces both sub-pulse and long-time Kerr dynamics rests on the two-band tight-binding and weakly spin-polarized Ge illustrations. These models replace electron-electron interactions, electron-phonon scattering, and multi-band hybridization with phenomenological damping and simplified dispersions; the manuscript must demonstrate that the omitted channels do not shift the time-evolved SPDM or the n-photon resonance positions that control the Kerr signal.
  2. [Results on resonance deduction] The assertion that Kerr rotation can be used to deduce the relevant n-photon resonances experimentally is load-bearing for the paper's utility claim, yet the provided models lack quantitative error bars, convergence checks with respect to damping strength, or direct comparison against full many-body or experimental spectra that would confirm resonance extraction remains robust.
minor comments (2)
  1. [Formalism section] Clarify the precise implementation of phenomenological damping inside the SPDM extension (e.g., how it enters the time-evolution operator) to ensure reproducibility.
  2. [Abstract and introduction] The abstract states the framework has 'lower computational cost' than alternatives; a brief scaling comparison or operation count would strengthen this point.

Simulated Author's Rebuttal

2 responses · 1 unresolved

We thank the referee for the detailed and constructive report. We address each major comment below and indicate the revisions we will make to strengthen the manuscript.

read point-by-point responses

  1. Referee: [Illustration sections (two-band TB model and Ge example)] The central claim that DPOA/SPDM reliably reproduces both sub-pulse and long-time Kerr dynamics rests on the two-band tight-binding and weakly spin-polarized Ge illustrations. These models replace electron-electron interactions, electron-phonon scattering, and multi-band hybridization with phenomenological damping and simplified dispersions; the manuscript must demonstrate that the omitted channels do not shift the time-evolved SPDM or the n-photon resonance positions that control the Kerr signal.

    Authors: We agree that the chosen illustrations employ simplified dispersions and phenomenological damping to represent scattering. The DPOA/SPDM approach is formulated to be extensible to more complete Hamiltonians; the present models serve to validate the formalism against exactly solvable limits. In the revised manuscript we will insert a new subsection discussing the limitations of the approximations, including how damping effectively captures dephasing from omitted channels and the conditions under which n-photon resonance locations remain stable. We will also add supplementary calculations that vary the damping parameter over a physically relevant range to illustrate the robustness of the extracted dynamics and resonance positions. revision: yes

  2. Referee: [Results on resonance deduction] The assertion that Kerr rotation can be used to deduce the relevant n-photon resonances experimentally is load-bearing for the paper's utility claim, yet the provided models lack quantitative error bars, convergence checks with respect to damping strength, or direct comparison against full many-body or experimental spectra that would confirm resonance extraction remains robust.

    Authors: We accept that quantitative error bars and explicit convergence tests with damping strength will strengthen the resonance-extraction claim. The revised version will include these analyses for both the two-band and germanium cases, together with error estimates derived from damping variations. Direct, quantitative comparisons to full many-body calculations or to experimental spectra lie outside the scope of the present work, which develops and benchmarks an efficient single-particle framework; such benchmarks are planned as follow-up studies. We will add a brief statement to this effect and reference existing experimental TR-MOKE data on germanium for qualitative context. revision: partial

standing simulated objections not resolved
  • Direct quantitative comparisons to full many-body calculations or experimental spectra confirming the robustness of n-photon resonance extraction from Kerr rotation.

Circularity Check

0 steps flagged

DPOA/SPDM extension for Kerr rotation is independent; minor self-citation only

full rationale

The paper formulates the time-resolved Kerr effect within DPOA and derives explicit expressions for post-pump optical conductivity and Kerr rotation directly in terms of the time-evolved single-particle density matrix (SPDM). This extension adds new content for pump-probe setups and phenomenological damping, without reducing any central prediction to a fitted input or self-defined quantity by construction. The two-band tight-binding model and weakly spin-polarized Ge serve as illustrative examples rather than sources of circular predictions. Self-citation to prior DPOA work is present but not load-bearing for the new SPDM-Kerr framework, which remains self-contained against external benchmarks. No uniqueness theorems, ansatze smuggling, or renaming of known results occur in the derivation chain.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

Abstract-only view limits visibility; framework rests on standard linear-response assumptions plus phenomenological damping and model-specific band structures.

free parameters (1)
  • phenomenological damping
    Introduced to account for energy loss in the SPDM evolution; value not specified in abstract but affects long-time dynamics.
axioms (1)
  • domain assumption Generalized linear-response theory applies to pumped systems within DPOA
    Invoked to connect post-pump conductivity to time-evolved SPDM.

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Reference graph

Works this paper leans on

58 extracted references · 58 canonical work pages

  1. [1]

    The horizontal solid and dashed lines in panels (b) and (c) are the same as those in Fig. 3 (a). Figure 5. (a) Equilibrium Kerr rotationθ eq K (ω)of weakly spin-polarized germanium. (b)δθ K(ω, tpr)at long delays without damping; the inset shows a cut at the two-photon resonant frequencyω= 2ωpu. (c) Same as (b) but including damping in SPDM withΥ nm =δ nm ...

    work page

  2. [2]

    g(ω)/h(ω)that mimics the Kerr functional dependence

    The horizontal gray and black dashed lines in all panels mark the one and two-photon resonances,ℏω=ℏω pu = 1.55 eVandℏω= 2ℏω pu = 3.10 eV, respectively. g(ω)/h(ω)that mimics the Kerr functional dependence. Upon pumping,g→g eq +δgandh→h eq +δh, which results in a variation,f→f eq +δf, which up to the first order readsδf=δg/h eq −(δh/h eq)f eq. Thus, even w...

    work page

  3. [3]

    TOPological Qubit In driveN and reconfig- urable heterostructures

    TOPQIN “TOPological Qubit In driveN and reconfig- urable heterostructures”. Appendix A: Derivation of Eq. 29 In this appendix, we derive Eq. 29. Settingtfin =t pr in Eq. (23), we obtainσ(1),a.p. out,in (ω, tfin, tpr)→σ (1) out,in (ω, tpr) where σ(1) out,in (ω, tpr) =− ie ℏV × × X k {Wk (ω, tpr) + Tr (Qk (ω, tpr)·S k (tpr, tpr))}. (A1) Using Eqs. 24, 25 an...

    work page

  4. [4]

    Brabec and F

    T. Brabec and F. Krausz, Reviews of Modern Physics 72, 545 (2000)

    work page 2000

  5. [5]

    Krausz and M

    F. Krausz and M. Ivanov, Reviews of modern physics81, 163 (2009)

    work page 2009

  6. [6]

    Krausz and M

    F. Krausz and M. I. Stockman, Nature Photonics8, 205 (2014)

    work page 2014

  7. [7]

    Calegari, G

    F. Calegari, G. Sansone, S. Stagira, C. Vozzi, and M. Nisoli, Journal of Physics B: Atomic, Molecular and Optical Physics49, 062001 (2016)

    work page 2016

  8. [8]

    Gandolfi, G

    M. Gandolfi, G. L. Celardo, F. Borgonovi, G. Ferrini, A. Avella, F. Banfi, and C. Giannetti, Physica Scripta 92, 034004 (2017)

    work page 2017

  9. [9]

    Borrego-Varillas, M

    R. Borrego-Varillas, M. Lucchini, and M. Nisoli, Reports on Progress in Physics85, 066401 (2022)

    work page 2022

  10. [10]

    Inzani, L

    G. Inzani, L. Adamska, A. Eskandari-asl, N. Di Palo, G. L. Dolso, B. Moio, L. J. D’Onofrio, A. Lamperti, A. Molle, R. Borrego-Varillas,et al., Nature Photonics 17, 1059 (2023)

    work page 2023

  11. [11]

    Inzani, A

    G. Inzani, A. Eskandari-asl, L. Adamska, B. Moio, G. L. Dolso, N. D. Palo, L. J. D’Onofrio, A. Lamperti, A. Molle, C. A. Rozzi, R. Borrego-Varillas, M. Nisoli, S. Pittalis, A. Avella, and M. Lucchini, IL NUOVO CI- MENTO C46, 1 (2023)

    work page 2023

  12. [12]

    Zürch, H.-T

    M. Zürch, H.-T. Chang, L. J. Borja, P. M. Kraus, S. K. Cushing, A. Gandman, C. J. Kaplan, M. H. Oh, J. S. Prell, D. Prendergast, C. D. Pemmaraju, D. M. Neu- mark, and S. R. Leone, Nature Communications8, 15734 (2017)

    work page 2017

  13. [13]

    C. J. Kaplan, P. M. Kraus, A. D. Ross, M. Zürch, S. K. Cushing, M. F. Jager, H.-T. Chang, E. M. Gullikson, D. M. Neumark, and S. R. Leone, Phys. Rev. B97, 205202 (2018)

    work page 2018

  14. [14]

    Perfetti, P

    L. Perfetti, P. A. Loukakos, M. Lisowski, U. Bovensiepen, M. Wolf, H. Berger, S. Biermann, and A. Georges, New Journal of Physics10, 053019 (2008)

    work page 2008

  15. [15]

    G. P. Zhang, W. Hübner, G. Lefkidis, Y. Bai, and T. F. George, Nature Physics5, 499 (2009)

    work page 2009

  16. [16]

    Sato and T

    K. Sato and T. Ishibashi, Frontiers in Physics10, 946515 (2022)

    work page 2022

  17. [17]

    Beaurepaire, J.-C

    E. Beaurepaire, J.-C. Merle, A. Daunois, and J.-Y. Bigot, Phys. Rev. Lett.76, 4250 (1996)

    work page 1996

  18. [18]

    A. V. Kimel, A. Kirilyuk, P. A. Usachev, R. V. Pisarev, A. M. Balbashov, and T. Rasing, Nature435, 655 (2005)

    work page 2005

  19. [19]

    J. Wang, C. Sun, Y. Hashimoto, J. Kono, G. A. Khoda- parast, Ł. Cywiński, L. Sham, G. D. Sanders, C. J. Stan- ton, and H. Munekata, Journal of Physics: Condensed Matter18, R501 (2006)

    work page 2006

  20. [20]

    Kirilyuk, A

    A. Kirilyuk, A. V. Kimel, and T. Rasing, Rev. Mod. Phys.82, 2731 (2010)

    work page 2010

  21. [21]

    M.W.Wu, J.H.Jiang,andM.Q.Weng,PhysicsReports 493, 61 (2010)

    work page 2010

  22. [22]

    Hennecke, D

    M. Hennecke, D. Schick, T. Sidiropoulos, F. Willems, A. Heilmann, M. Bock, L. Ehrentraut, D. Engel, P. Hess- ing, B. Pfau,et al., Physical Review Research4, L022062 (2022)

    work page 2022

  23. [23]

    Němec, M

    P. Němec, M. Fiebig, T. Kampfrath, and A. V. Kimel, Nat. Phys.14, 229 (2018)

    work page 2018

  24. [24]

    I. Gray, Q. Deng, Q. Tian, M. Chilcote, J. S. Dodge, M. Brahlek, and L. Wu, Applied Physics Letters125 (2024)

    work page 2024

  25. [25]

    Eskandari-asl, J

    A. Eskandari-asl, J. I. Facio, O. Janson, A. Avella, and J. van den Brink, Phys. Rev. B112, 024401 (2025)

    work page 2025

  26. [26]

    Kampfrath, M

    T. Kampfrath, M. Battiato, P. Maldonado, G. Eil- ers, J. Nötzold, S. Mährlein, V. Zbarsky, F. Freimuth, Y. Mokrousov, S. Blügel,et al., Nat. Nanotechnol.8, 256 (2013)

    work page 2013

  27. [27]

    Zhang, Y

    S. Zhang, Y. Sun, and B. Yan, Phys. Rev. B101, 035138 (2020)

    work page 2020

  28. [28]

    De Giovannini, G

    U. De Giovannini, G. Brunetto, A. Castro, J. Walken- horst, and A. Rubio, ChemPhysChem14, 1298 (2013)

    work page 2013

  29. [29]

    De Giovannini, H

    U. De Giovannini, H. Hubener, and A. Rubio, Nano let- ters16, 7993 (2016)

    work page 2016

  30. [30]

    De Giovannini, A

    U. De Giovannini, A. Castro,et al., Attosecond Molecu- lar Dynamics13, 424 (2018)

    work page 2018

  31. [31]

    Schlaepfer, M

    F. Schlaepfer, M. Lucchini, S. A. Sato, M. Volkov, L. Kasmi, N. Hartmann, A. Rubio, L. Gallmann, and U. Keller, Nature Physics14, 560 (2018)

    work page 2018

  32. [32]

    S. A. Sato, M. Lucchini, M. Volkov, F. Schlaepfer, L. Gallmann, U. Keller, and A. Rubio, Physical Review B98, 035202 (2018). 14

    work page 2018

  33. [33]

    Broers and L

    L. Broers and L. Mathey, Physical Review Research4, 013057 (2022)

    work page 2022

  34. [34]

    Eskandari-asl and A

    A. Eskandari-asl and A. Avella, Physical Review B110, 094309 (2024)

    work page 2024

  35. [35]

    Eskandari-asl and A

    A. Eskandari-asl and A. Avella, Physical Review A110, 043520 (2024)

    work page 2024

  36. [36]

    Eskandari-Asl and A

    A. Eskandari-Asl and A. Avella, Materials18, 1310 (2025)

    work page 2025

  37. [37]

    Eskandari-asl and A

    A. Eskandari-asl and A. Avella, inAdvances in Ultrafast Condensed Phase Physics IV, Vol. 12992 (SPIE, 2024) pp. 65–68

    work page 2024

  38. [38]

    Schüler, J

    M. Schüler, J. A. Marks, Y. Murakami, C. Jia, and T. P. Devereaux, Physical Review B103, 155409 (2021)

    work page 2021

  39. [39]

    Koopmans, M

    B. Koopmans, M. van Kampen, J. T. Kohlhepp, and W. J. M. de Jonge, Phys. Rev. Lett.85, 844 (2000)

    work page 2000

  40. [40]

    P. M. Oppeneer and A. Liebsch, Journal of Physics: Con- densed Matter16, 5519 (2004)

    work page 2004

  41. [41]

    Mukamel,Principles of Nonlinear Optical Spec- troscopy, Oxford series in optical and imaging sciences (Oxford University Press, 1995)

    S. Mukamel,Principles of Nonlinear Optical Spec- troscopy, Oxford series in optical and imaging sciences (Oxford University Press, 1995)

    work page 1995

  42. [42]

    J. W. Freeland, R. H. Kodama, M. Vedpathak, S. C. Erwin, D. J. Keavney, R. Winarski, P. Ryan, and R. A. Rosenberg, Phys. Rev. B70, 033201 (2004)

    work page 2004

  43. [43]

    sourceforge.net/(2000)

    ELK Developers, The elk code,http://elk. sourceforge.net/(2000)

    work page 2000

  44. [44]

    Pizzi, V

    G. Pizzi, V. Vitale, R. Arita, S. Blügel, F. Freimuth, G. Géranton, M. Gibertini, D. Gresch, C. Johnson, T. Koretsune,et al., Journal of Physics: Condensed Mat- ter32, 165902 (2020)

    work page 2020

  45. [45]

    J. D. Jackson,Classical Electrodynamics, 3rd ed. (John Wiley & Sons, 1998)

    work page 1998

  46. [46]

    Born and E

    M. Born and E. Wolf,Principles of Optics, 7th ed. (Cam- bridge University Press, 1999)

    work page 1999

  47. [47]

    Zangwill,Modern Electrodynamics(Cambridge Uni- versity Press, 2012)

    A. Zangwill,Modern Electrodynamics(Cambridge Uni- versity Press, 2012)

    work page 2012

  48. [48]

    Hecht,Optics, 5th ed

    E. Hecht,Optics, 5th ed. (Pearson, 2017)

    work page 2017

  49. [49]

    Landau and E

    L. Landau and E. M. Lifshitz,Electrodynamics of con- tinuous media, Course of theoretical physics (Pergamon, 1960)

    work page 1960

  50. [50]

    P. S. Pershan, Journal of Applied Physics38, 1482 (1967)

    work page 1967

  51. [51]

    Dolgov and E

    O. Dolgov and E. Maksimov, inThe Dielectric Function of Condensed Systems, Modern Problems in Condensed Matter Sciences, Vol. 24, edited by L. Keldysh, D. Kirzh- nitz, and A. Maradudin (Elsevier, 1989) pp. 221–298

    work page 1989

  52. [52]

    Oppeneer, inHandbook of Magnetic Materials 13, Handbook of Magnetic Materials, Vol

    P. Oppeneer, inHandbook of Magnetic Materials 13, Handbook of Magnetic Materials, Vol. 13 (Elsevier, 2001) pp. 229–422

    work page 2001

  53. [53]

    P. N. Argyres, Physical Review97, 334 (1955)

    work page 1955

  54. [54]

    J. L. Erskine and E. A. Stern, Physical Review B8, 1239 (1973)

    work page 1973

  55. [55]

    Beaurepaire, J.-C

    E. Beaurepaire, J.-C. Merle, A. Daunois, and J.-Y. Bigot, Physical Review Letters76, 4250 (1996)

    work page 1996

  56. [56]

    A. K. Zvezdin and V. A. Kotov,Modern Magnetooptics and Magnetooptical Materials(CRC Press, 1997)

    work page 1997

  57. [57]

    Z. Q. Qiu and S. D. Bader, Review of Scientific Instru- ments71, 1243 (2000)

    work page 2000

  58. [58]

    Weber, S

    M. Weber, S. Wust, L. Haag, A. Akashdeep, K. Leckron, C. Schmitt, R. Ramos, T. Kikkawa, E. Saitoh, M. Kläui, et al., arXiv preprint arXiv:2408.05187 (2024)

    work page arXiv 2024