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Temperature and magnetic field dependent g-factors in electron spin resonance spectroscopy

Sebastian Kalhöfer*

  • *Contact author: sebastian.kalhofer@physics.uu.se
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Phys. Rev. B 112, 125104 – Published 2 September, 2025

DOI: https://doi.org/10.1103/bjfk-wlf2

Abstract

We propose that phonons coupled to electrons play an important role in both the fundamental phenomenology of electron spin resonance as well as the interpretation of such measurements. By including spin-dependent electron-phonon interactions originating from spin-orbit coupling, we demonstrate that the g-f actor acquires emergent temperature dependencies that are in excellent agreement with experimental observations. Moreover, we predict that at low temperatures, the g-factor will exhibit a nontrivial dependence on the magnetic field, indicating a dynamic property that has not been previously considered in electron-phonon systems. We further predict the influence of phonons to be negligible at very low and very high temperatures, with the former requiring experimental verification.

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References (69)

  1. J. H. Freed, New technologies in electron spin resonance, Annu. Rev. Phys. Chem. 51, 655 (2000).
  2. J. E. Wertz, Electron Spin Resonance, Second ed. (Chapman and Hall, London, England, 1986).
  3. D. Griller and K. U. Ingold, Electron paramagnetic resonance and the art of physical-organic chemistry, Acc. Chem. Res. 13, 193 (1980).
  4. B. A. Goodman and J. B. Raynor, Electron spin resonance of transition metal complexes, in Advances in Inorganic Chemistry and Radiochemistry, Vol. 13 (Academic Press, Cambridge, 1970), pp. 135–362.
  5. I. D. Sahu, R. M. McCarrick, and G. A. Lorigan, Use of electron paramagnetic resonance to solve biochemical problems, Biochemistry 52, 5967 (2013).
  6. J. R. Mallard and M. Kent, Electron spin resonance in biological tissues, Phys. Med. Biol. 14, 373 (1969).
  7. M. Bennati and T. F. Prisner, New developments in high field electron paramagnetic resonance with applications in structural biology, Rep. Prog. Phys. 68, 411 (2005).
  8. S. Bader and S. Parkin, Spintronics, Annu. Rev. Condens. Matter Phys. 1, 71 (2010).
  9. D. D. Awschalom, L. C. Bassett, A. S. Dzurak, E. L. Hu, and J. R. Petta, Quantum spintronics: Engineering and manipulating atom-like spins in semiconductors, Science 339, 1174 (2013).
  10. S. Sanvito, Molecular spintronics, Chem. Soc. Rev. 40, 3336 (2011).
  11. M.-C.-i. Lee, Biomedical application of electron spin resonance (ESR) spectroscopy–Assessment of antioxidant property for development of drugs, Yakugaku Zasshi 128, 753 (2008).
  12. H. Bolvin and J. Autschbach, in Handbook of Relativistic Quantum Chemistry (Springer, Berlin, Heidelberg, 2015), pp. 1–39.
  13. P. H. Rieger, Electron Spin Resonance (Royal Society of Chemistry, Cambridge, England, 2007).
  14. B. C. Gilbert, Electron Paramagnetic Resonance (Royal Society of Chemistry, 2008), Vol. 21.
  15. S. A. Al'tshuler and B. M. Kozyrev, Electron Paramagnetic Resonance (Academic Press, San Diego, CA, 2013).
  16. H. M. Assenheim, in Introduction to Electron Spin Resonance (Springer US, Boston, MA, 1966), pp. 1–7.
  17. J. E. Harriman, Theoretical Foundations of Electron Spin Resonance: Physical Chemistry: A Series of Monographs (Academic Press, San Diego, CA, 2013).
  18. F. E. Mabbs and D. Collison, Electron Paramagnetic Resonance of d Transition Metal Compounds (Elsevier, Amsterdam, London, New York, Tokyo, 2013).
  19. S. K. Misra, in Multifrequency Electron Paramagnetic Resonance, Second ed., edited by S. K. Misra (Wiley-VCH Verlag, Weinheim, Germany, 2011).
  20. G. Lancaster, Electron Spin Resonance in Semiconductors, Monographs on Electron Spin Resonance (Springer US, New York, 1967).
  21. A. Abragam and B. Bleaney, Electron Paramagnetic Resonance of Transition Ions, Oxford Classic Texts in the Physical Sciences (Oxford University Press, London, England, 2012).
  22. S. Poncé, E. Margine, C. Verdi, and F. Giustino, EPW: Electron–phonon coupling, transport and superconducting properties using maximally localized Wannier functions, Comput. Phys. Commun. 209, 116 (2016).
  23. F. Giustino, M. L. Cohen, and S. G. Louie, Electron-phonon interaction using Wannier functions, Phys. Rev. B 76, 165108 (2007).
  24. F. Giustino, Electron-phonon interactions from first principles, Rev. Mod. Phys. 89, 015003 (2017).
  25. G. D. Mahan, Many-Particle Physics (Springer Science & Business Media, Berlin, Heidelberg, 2012).
  26. F. Marsiglio, Eliashberg theory: A short review, Ann. Phys. 417, 168102 (2020).
  27. E. R. Margine and F. Giustino, Anisotropic Migdal-Eliashberg theory using Wannier functions, Phys. Rev. B 87, 024505 (2013).
  28. J. Noffsinger, E. Kioupakis, C. G. Van de Walle, S. G. Louie, and M. L. Cohen, Phonon-assisted optical absorption in silicon from first principles, Phys. Rev. Lett. 108, 167402 (2012).
  29. J. Fransson, Vibrational origin of exchange splitting and ”chiral-induced spin selectivity, Phys. Rev. B 102, 235416 (2020).
  30. J. Fransson, Chirality-induced spin selectivity: The role of electron correlations, J. Phys. Chem. Lett. 10, 7126 (2019).
  31. J. Fransson, Chiral phonon induced spin polarization, Phys. Rev. Res. 5, L022039 (2023).
  32. D. L. Huber, The effects of anisotropy and Yb–Yb interactions on the low-field electron spin resonance in Yb2Rh2Si2 and YbIr2Si2, J. Phys.: Condens. Matter 21, 322203 (2009).
  33. U. Schaufuß, V. Kataev, A. A. Zvyagin, B. Büchner, J. Sichelschmidt, J. Wykhoff, C. Krellner, C. Geibel, and F. Steglich, Evolution of the Kondo state of YbRh2Si2 probed by high-field ESR, Phys. Rev. Lett. 102, 076405 (2009).
  34. L. Holanda, J. Duque, E. Bittar, C. Adriano, P. Pagliuso, C. Rettori, R. Hu, C. Petrovic, S. Maquilon, Z. Fisk, D. Huber, and S. Oseroff, Field-dependent collective ESR mode in YbRh2Si2, Phys. B: Condens. Matter 404, 2964 (2009).
  35. M. Maslov, M. Lemeshko, and E. Yakaboylu, Synthetic spin-orbit coupling mediated by a bosonic environment, Phys. Rev. B 101, 184104 (2020).
  36. C. Bray, K. Maussang, C. Consejo, J. A. Delgado-Notario, S. Krishtopenko, I. Yahniuk, S. Gebert, S. Ruffenach, K. Dinar, E. Moench, J. Eroms, K. Indykiewicz, B. Jouault, J. Torres, Y. M. Meziani, W. Knap, A. Yurgens, S. D. Ganichev, and F. Teppe, Temperature-dependent zero-field splittings in graphene, Phys. Rev. B 106, 245141 (2022).
  37. F. S. Ham, Effect of linear Jahn-Teller coupling on paramagnetic resonance in a E2 state, Phys. Rev. 166, 307 (1968).
  38. W. Nolting, Grundkurs Theoretische Physik 5 Quantenmechanik, Third ed. (Springer Vieweg, Wiesbaden, Germany, 1997).
  39. J. Wheatley and D. Halliday, Paramagnetic absorption in single crystals of copper sulfate pentahydrate, Phys. Rev. 75, 1412 (1949).
  40. S. Wang, J. Zhong, and W. Liu, Temperature measurement based on electron paramagnetic resonance of magnetic nanoparticles, IEEE Trans. Instrum. Meas. 71, 1 (2022).
  41. N. Marzari, A. A. Mostofi, J. R. Yates, I. Souza, and D. Vanderbilt, Maximally localized Wannier functions: Theory and applications, Rev. Mod. Phys. 84, 1419 (2012).
  42. C. M. Iaru, A. Brodu, N. J. J. van Hoof, S. E. T. ter Huurne, J. Buhot, F. Montanarella, S. Buhbut, P. C. M. Christianen, D. Vanmaekelbergh, C. de Mello Donega, J. G. Rivas, P. M. Koenraad, and A. Y. Silov, Fröhlich interaction dominated by a single phonon mode in CsPbBr3, Nat. Commun. 12, 5844 (2021).
  43. R. Mondal, M. Berritta, C. Paillard, S. Singh, B. Dkhil, P. M. Oppeneer, and L. Bellaiche, Relativistic interaction Hamiltonian coupling the angular momentum of light and the electron spin, Phys. Rev. B 92, 100402 (2015).
  44. W. Nolting, Grundkurs Theoretische Physik 5/1, Eighth ed., Springer-Lehrbuch (Springer, Berlin, Germany, 2012).
  45. J. W. Negele and H. Orland, Quantum Many-particle Systems, Frontiers in Physics (Westview Press, Philadelphia, PA, 1998).
  46. A. Altland and B. D. Simons, Condensed Matter Field Theory, Second ed. (Cambridge University Press, Cambridge, 2010).
  47. H. Bruus and K. Flensburg, Many-body Quantum Theory in Condensed Matter Physics, Oxford Graduate Texts (Oxford University Press, London, England, 2004).
  48. M. Kardar, Statistical Physics of Fields (Cambridge University Press, Cambridge, England, 2007).
  49. F. Schwabl, Statistische Mechanik, Third ed., Springer-Lehrbuch (Springer, Berlin, Germany, 2006).
  50. P. Zdeb, N. Rebrova, and P. J. Dereń, Discovering the potential of high phonon energy hosts in the field of visible-to-ultraviolet C upconversion, J. Phys. Chem. Lett. 15, 9356 (2024).
  51. H. Chandrasekar, K. L. Ganapathi, S. Bhattacharjee, N. Bhat, and D. N. Nath, Optical-phonon-limited high-field transport in layered materials, IEEE Trans. Electron Devices 63, 767 (2016).
  52. P. Wu, F.-R. Fan, M. Hagihala, M. Kofu, K. Peng, Y. Ishikawa, S. Lee, T. Honda, M. Yonemura, K. Ikeda, T. Otomo, G. Wang, K. Nakajima, Z. Sun, and T. Kamiyama, Strong lattice anharmonicity exhibited by the high-energy optical phonons in thermoelectric material, New J. Phys. 22, 083083 (2020).
  53. B. Wei, X. Zhang, W. Li, J. Li, Y. Li, Q. Gao, J. Hong, C.-W. Nan, and Y.-H. Lin, Optical phonons on thermal conduction in advanced materials, Appl. Phys. Rev. 12, 011324 (2025).
  54. M. Mohr, J. Maultzsch, E. Dobardžić, S. Reich, I. Milošević, M. Damnjanović, A. Bosak, M. Krisch, and C. Thomsen, Phonon dispersion of graphite by inelastic x-ray scattering, Phys. Rev. B 76, 035439 (2007).
  55. H. Zhang, C. Bao, M. Schüler, S. Zhou, Q. Li, L. Luo, W. Yao, Z. Wang, T. P. Devereaux, and S. Zhou, Self-energy dynamics and the mode-specific phonon threshold effect in Kekulé-ordered graphene, Natl. Sci. Rev. 9, nwab175 (2021) .
  56. R. Lucrezi, P. P. Ferreira, S. Hajinazar, H. Mori, H. Paudyal, E. R. Margine, and C. Heil, Full-bandwidth anisotropic Migdal-Eliashberg theory and its application to superhydrides, Commun. Phys. 7, 33 (2024).
  57. O. Pfingsten, J. Klein, L. Protesescu, M. I. Bodnarchuk, M. V. Kovalenko, and G. Bacher, Phonon interaction and phase transition in single formamidinium lead bromide quantum dots, Nano Lett. 18, 4440 (2018).
  58. R. Heid, I. Y. Sklyadneva, and E. V. Chulkov, Electron-phonon coupling in topological surface states: The role of polar optical modes, Sci. Rep. 7, 1095 (2017) .
  59. V. Brizé, C. Autret-Lambert, J. Wolfman, M. Gervais, P. Simon, and F. Gervais, Temperature dependence of electron spin resonance in CaCu3Ti4O12 substituted with transition metal elements, Solid State Sci. 11, 875 (2009).
  60. A. Koitzsch, G. Blumberg, A. Gozar, B. Dennis, A. P. Ramirez, S. Trebst, and S. Wakimoto, Antiferromagnetism in CaCu3Ti4O12 studied by magnetic Raman spectroscopy, Phys. Rev. B 65, 052406 (2002).
  61. L. He, J. B. Neaton, M. H. Cohen, D. Vanderbilt, and C. C. Homes, First-principles study of the structure and lattice dielectric response of CaCu3Ti4O12, Phys. Rev. B 65, 214112 (2002).
  62. C. Kant, T. Rudolf, F. Mayr, S. Krohns, P. Lunkenheimer, S. G. Ebbinghaus, and A. Loidl, Broadband dielectric response of CaCu3Ti4O12: From dc to the electronic transition regime, Phys. Rev. B 77, 045131 (2008).
  63. A. V. Semeno, V. V. Glushkov, A. V. Bogach, N. E. Sluchanko, A. V. Dukhnenko, V. B. Fillippov, N. Y. Shitsevalova, and S. V. Demishev, Electron spin resonance in EuB6, Phys. Rev. B 79, 014423 (2009).
  64. S. K. Gupta, N. Pathak, P. Ghosh, B. Rajeshwari, V. Natarajan, and R. Kadam, Temperature dependent electron paramagnetic resonance (EPR) of SrZrO3, J. Magn. Magn. Mater. 391, 101 (2015).
  65. J. Sichelschmidt, J. Wykhoff, H.-A. K. v. Nidda, I. I. Fazlishanov, Z. Hossain, C. Krellner, C. Geibel, and F. Steglich, Electron spin resonance of YbIr2Si2x below the Kondo temperature, J. Phys.: Condens. Matter 19, 016211 (2007).
  66. C. Autret-Lambert, M. Gervais, M. Zaghrioui, S. Roger, F. Gervais, N. Raimboux, and P. Simon, Temperature dependence of phase separation and magnetic anisotropy by electron spin resonance in Pr0.6 Ca0.4 Mn0.9 Ru0.1O3, Eur. Phys. J. B 47, 207 (2005).
  67. W. Nolting, Grundkurs Theoretische Physik 6, Seventh ed., Springer-Lehrbuch (Springer, Berlin, Germany, 2012).
  68. T. Fliebach, Statistische Physik, Sixth ed. (Springer Spektrum, Berlin, Heidelberg, 2018).
  69. S. Kalhöfer, Data for “temperature and magnetic field dependent g-factors in electron spin resonance spectroscopy” (Version V5) [Data set], Zenodo (2025), https://doi.org/10.5281/zenodo.16892607.

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Phys. Rev. B 112, 125104– Published 2 September, 2025
  • Received 16 January 2025
  • Revised 21 May 2025
  • Accepted 14 August 2025
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