Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Letter
  • Open Access

Electron magnetic moment of transient chiral phonons in KTaO3

R. Matthias Geilhufe1 and Wolfram Hergert2

  • 1Department of Physics, Chalmers University of Technology, SE-412 96 Gothenburg, Sweden
  • 2Institute of Physics, Martin Luther University Halle-Wittenberg, D-06120 Halle, Germany

Phys. Rev. B 107, L020406 – Published 18 January, 2023

DOI: https://doi.org/10.1103/PhysRevB.107.L020406

Abstract

High-intensity THz lasers allow for the coherent excitation of individual phonon modes. The ultrafast control of emergent magnetism by means of phonons opens up new tuning mechanisms for functional materials. While theoretically predicted phonon magnetic moments are tiny, recent experiments hint towards a significant magnetization in various materials. To explain these phenomena, we derive a coupling mechanism between the phonon angular momentum and the electron spin. This coupling introduces the transient level splitting of spin-up and spin-down channels and a resulting magnetization. We estimate this magnetization on the example of the lowest infrared active mode in the perovskite KTaO3. Our results show an electronic magnetic moment of ≈10−1µB per unit cell, depending on the doping level and electron temperature.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (56)

  1. L. Zhang and Q. Niu, Angular Momentum Of Phonons and The Einstein–de Haas Effect, Phys. Rev. Lett. 112, 085503 (2014).
  2. A. McLellan, Angular momentum states for phonons and a rotationally invariant development of lattice dynamics, J. Phys. C 21, 1177 (1988).
  3. D. M. Juraschek, M. Fechner, A. V. Balatsky, and N. A. Spaldin, Dynamical multiferroicity, Phys. Rev. Mater. 1, 014401 (2017).
  4. D. M. Juraschek, T. c. v. Neuman, and P. Narang, Giant effective magnetic fields from optically driven chiral phonons in 4f paramagnets, Phys. Rev. Res. 4, 013129 (2022).
  5. D. M. Juraschek, D. S. Wang, and P. Narang, Sum-frequency excitation of coherent magnons, Phys. Rev. B 103, 094407 (2021).
  6. D. M. Juraschek, P. Narang, and N. A. Spaldin, Phonomagnetic analogs to optomagnetic effects, Phys. Rev. Res. 2, 043035 (2020).
  7. Yu. T. Rebane, Faraday effect produced in the residual ray region by the magnetic moment of an optical phonon in an ionic crystal, Zh. Eksp. Teor. Fiz. 84, 2323 (1983).
  8. R. M. Geilhufe, V. Juričić, S. Bonetti, J.-X. Zhu, and A. V. Balatsky, Dynamically induced magnetism in KTaO3, Phys. Rev. Res. 3, L022011 (2021).
  9. D. M. Juraschek and N. A. Spaldin, Orbital magnetic moments of phonons, Phys. Rev. Mater. 3, 064405 (2019).
  10. B. Cheng, T. Schumann, Y. Wang, X. Zhang, D. Barbalas, S. Stemmer, and N. Armitage, A large effective phonon magnetic moment in a Dirac semimetal, Nano Lett. 20, 5991 (2020).
  11. A. Baydin, F. G. G. Hernandez, M. Rodriguez-Vega, A. K. Okazaki, F. Tay, G. T. Noe, I. Katayama, J. Takeda, H. Nojiri, P. H. O. Rappl, E. Abramof, G. A. Fiete, and J. Kono, Magnetic Control Of Soft Chiral Phonons In PbTe, Phys. Rev. Lett. 128, 075901 (2022).
  12. F. G. Hernandez, A. Baydin, S. Chaudhary, F. Tay, I. Katayama, J. Takeda, H. Nojiri, A. K. Okazaki, P. H. Rappl, E. Abramof et al., Chiral phonons with giant magnetic moments in a topological crystalline insulator, arXiv:2208.12235.
  13. M. Basini, M. Pancaldi, B. Wehinger, M. Udina, T. Tadano, M. C. Hoffmann, A. V. Balatsky, and S. Bonetti, Terahertz electric-field driven dynamical multiferroicity in SrTiO3, arXiv:2210.01690.
  14. R. J. Elliott, Theory of the effect of spin-orbit coupling on magnetic resonance in some semiconductors, Phys. Rev. 96, 266 (1954).
  15. Y. Yafet, g Factors and Spin-Lattice Relaxation of Conduction Electrons, in Solid State Physics, Vol. 14, edited by F. Seitz and D. Turnbull (Academic Press, 1963).
  16. J. Fransson, D. Thonig, P. F. Bessarab, S. Bhattacharjee, J. Hellsvik, and L. Nordström, Microscopic theory for coupled atomistic magnetization and lattice dynamics, Phys. Rev. Mater. 1, 074404 (2017).
  17. J. Fransson, Vibrational origin of exchange splitting and chiral-induced spin selectivity, Phys. Rev. B 102, 235416 (2020).
  18. J. Son, B. C. Park, C. H. Kim, H. Cho, S. Y. Kim, L. J. Sandilands, C. Sohn, J.-G. Park, S. J. Moon, and T. W. Noh, Unconventional spin-phonon coupling via the Dzyaloshinskii-Moriya interaction, npj Quantum Mater. 4, 17 (2019).
  19. M. C. Weber, M. Guennou, D. M. Evans, C. Toulouse, A. Simonov, Y. Kholina, X. Ma, W. Ren, S. Cao, M. A. Carpenter, B. Dkhil, M. Fiebig, and J. Kreisel, Emerging spin-phonon coupling through cross-talk of two magnetic sublattices, Nat. Commun. 13, 443 (2022).
  20. H. Katsura, N. Nagaosa, and A. V. Balatsky, Spin Current And Magnetoelectric Effect In Noncollinear Magnets, Phys. Rev. Lett. 95, 057205 (2005).
  21. M. Mostovoy, Ferroelectricity In Spiral Magnets, Phys. Rev. Lett. 96, 067601 (2006).
  22. M. Mochizuki, N. Furukawa, and N. Nagaosa, Theory of spin-phonon coupling in multiferroic manganese perovskites RMnO3, Phys. Rev. B 84, 144409 (2011).
  23. Y. Ren, C. Xiao, D. Saparov, and Q. Niu, Phonon Magnetic Moment From Electronic Topological Magnetization, Phys. Rev. Lett. 127, 186403 (2021).
  24. D. Xiao, J. Shi, and Q. Niu, Berry Phase Correction To Electron Density Of States In Solids, Phys. Rev. Lett. 95, 137204 (2005).
  25. T. Thonhauser, D. Ceresoli, D. Vanderbilt, and R. Resta, Orbital Magnetization In Periodic Insulators, Phys. Rev. Lett. 95, 137205 (2005).
  26. R. Resta, Electrical polarization and orbital magnetization: The modern theories, J. Phys.: Condens. Matter 22, 123201 (2010).
  27. R. M. Geilhufe, Dynamic electron-phonon and spin-phonon interactions due to inertia, Phys. Rev. Res. 4, L012004 (2022).
  28. M. Matsuo, J. Ieda, K. Harii, E. Saitoh, and S. Maekawa, Mechanical generation of spin current by spin-rotation coupling, Phys. Rev. B 87, 180402(R) (2013).
  29. M. Matsuo, J. Ieda, E. Saitoh, and S. Maekawa, Effects Of Mechanical Rotation On Spin Currents, Phys. Rev. Lett. 106, 076601 (2011).
  30. M. Matsuo, J. Ieda, E. Saitoh, and S. Maekawa, Spin-dependent inertial force and spin current in accelerating systems, Phys. Rev. B 84, 104410 (2011).
  31. S. R. Tauchert, M. Volkov, D. Ehberger, D. Kazenwadel, M. Evers, H. Lange, A. Donges, A. Book, W. Kreuzpaintner, U. Nowak et al., Polarized phonons carry angular momentum in ultrafast demagnetization, Nature (London) 602, 73 (2022).
  32. S. Streib, Difference between angular momentum and pseudoangular momentum, Phys. Rev. B 103, L100409 (2021).
  33. H. Vogt, Refined treatment of the model of linearly coupled anharmonic oscillators and its application to the temperature dependence of the zone-center soft-mode frequencies of KTaO3 and SrTiO3, Phys. Rev. B 51, 8046 (1995).
  34. A. S. Barker and J. J. Hopfield, Coupled-optical-phonon-mode theory of the infrared dispersion in BaTiO3, SrTiO3, and KTaO3, Phys. Rev. 135, A1732 (1964).
  35. M. Kozina, M. Fechner, P. Marsik, T. van Driel, J. M. Glownia, C. Bernhard, M. Radovic, D. Zhu, S. Bonetti, U. Staub, and M. C. Hoffmann, Terahertz-driven phonon upconversion in SrTiO3, Nat. Phys. 15, 387 (2019).
  36. R. D. King-Smith and D. Vanderbilt, Theory of polarization of crystalline solids, Phys. Rev. B 47, 1651 (1993).
  37. M. Gajdoš, K. Hummer, G. Kresse, J. Furthmüller, and F. Bechstedt, Linear optical properties in the projector-augmented wave methodology, Phys. Rev. B 73, 045112 (2006).
  38. G. Kresse and J. Furthmüller, Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set, Phys. Rev. B 54, 11169 (1996).
  39. A. Togo and I. Tanaka, First principles phonon calculations in materials science, Scr. Mater. 108, 1 (2015).
  40. J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized Gradient Approximation Made Simple, Phys. Rev. Lett. 77, 3865 (1996).
  41. P. Pershan, J. Van der Ziel, and L. Malmstrom, Theoretical discussion of the inverse Faraday effect, Raman scattering, and related phenomena, Phys. Rev. 143, 574 (1966).
  42. M. Hamada and S. Murakami, Conversion between electron spin and microscopic atomic rotation, Phys. Rev. Res. 2, 023275 (2020).
  43. I. G. Gurtubay, A. Iturbe-Beristain, and A. Eiguren, Magnetic oscillations induced by phonons in non-magnetic materials, Commun. Phys. 3, 22 (2020).
  44. X. Li, J. Cheng, J. Cheng, H. Chen, L. Zhang, and J. Zhou, Chiral phonon activated spin seebeck effect, arXiv:2105.08485.
  45. A. V. Podolskiy and P. Vogl, Compact expression for the angular dependence of tight-binding hamiltonian matrix elements, Phys. Rev. B 69, 233101 (2004).
  46. J. C. Slater and G. F. Koster, Simplified LCAO method for the periodic potential problem, Phys. Rev. 94, 1498 (1954).
  47. R. M. Geilhufe and W. Hergert, GTPack: A Mathematica group theory package for application in solid-state physics and photonics, Frontiers Phys. 6, 86 (2018).
  48. W. Hergert and R. M. Geilhufe, Group Theory in Solid State Physics and Photonics: Problem Solving with Mathematica (Wiley-VCH, Weinheim, Germany, 2018).
  49. G. E. Jellison, I. Pauluskas, L. A. Boatner, and D. J. Singh, Optical functions of KTaO3 as determined by spectroscopic ellipsometry and comparison with band structure calculations, Phys. Rev. B 74, 155130 (2006).
  50. M. Choi, F. Oba, and I. Tanaka, Hybrid density functional study of oxygen vacancies in KTaO3 and NaTaO3, Phys. Rev. B 83, 214107 (2011).
  51. P. Modak and B. Modak, Energetic, electronic, and optical properties of intrinsic charge carrier-trapping defects in KTaO3: Insights from a hybrid DFT study, J. Phys. Chem. C 125, 24067 (2021).
  52. K. Ueno, S. Nakamura, H. Shimotani, H. Yuan, N. Kimura, T. Nojima, H. Aoki, Y. Iwasa, and M. Kawasaki, Discovery of superconductivity in KTaO3 by electrostatic carrier doping, Nat. Nanotechnol. 6, 408 (2011).
  53. L. Alber, V. Scalera, V. Unikandanunni, D. Schick, and S. Bonetti, Ntmpy: An open source package for solving coupled parabolic differential equations in the framework of the three-temperature model, Comput. Phys. Commun. 265, 107990 (2021).
  54. V. Unikandanunni, F. Rigoni, M. C. Hoffmann, P. Vavassori, S. Urazhdin, and S. Bonetti, Ultrafast electron dynamics in platinum and gold thin films driven by optical and terahertz fields, Appl. Phys. Lett. 120, 021601 (2022).
  55. T. Tsatsoulis, C. Illg, M. Haag, B. Y. Mueller, L. Zhang, and M. Fähnle, Ultrafast demagnetization after femtosecond laser pulses: Transfer of angular momentum from the electronic system to magnetoelastic spin-phonon modes, Phys. Rev. B 93, 134411 (2016).
  56. B. Koopmans, G. Malinowski, F. Dalla Longa, D. Steiauf, M. Fähnle, T. Roth, M. Cinchetti, and M. Aeschlimann, Explaining the paradoxical diversity of ultrafast laser-induced demagnetization, Nat. Mater. 9, 259 (2010).

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation