Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Polarized phonons carry angular momentum in ultrafast demagnetization

Abstract

Magnetic phenomena are ubiquitous in nature and indispensable for modern science and technology, but it is notoriously difficult to change the magnetic order of a material in a rapid way. However, if a thin nickel film is subjected to ultrashort laser pulses, it loses its magnetic order almost completely within femtosecond timescales1. This phenomenon is widespread2,3,4,5,6,7 and offers opportunities for rapid information processing8,9,10,11 or ultrafast spintronics at frequencies approaching those of light8,9,12. Consequently, the physics of ultrafast demagnetization is central to modern materials research1,2,3,4,5,6,7,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28, but a crucial question has remained elusive: if a material loses its magnetization within mere femtoseconds, where is the missing angular momentum in such a short time? Here we use ultrafast electron diffraction to reveal in nickel an almost instantaneous, long-lasting, non-equilibrium population of anisotropic high-frequency phonons that appear within 150–750 fs. The anisotropy plane is perpendicular to the direction of the initial magnetization and the atomic oscillation amplitude is 2 pm. We explain these observations by means of circularly polarized phonons that quickly absorb the angular momentum of the spin system before macroscopic sample rotation. The time that is needed for demagnetization is related to the time it takes to accelerate the atoms. These results provide an atomistic picture of the Einstein–de Haas effect and signify the general importance of polarized phonons for non-equilibrium dynamics and phase transitions.

Your institute does not have access to this article

Access options

Buy article

Get time limited or full article access on ReadCube.

$32.00

All prices are NET prices.

Fig. 1: Pump–probe electron diffraction measurements of atomic motions during ultrafast demagnetization.
Fig. 2: Time-resolved diffraction results.
Fig. 3: Molecular dynamics simulations.
Fig. 4: Sequence of events.

Data availability

The data supporting the findings of this study are available from the corresponding author upon request.

References

  1. Beaurepaire, E., Merle, J. C., Daunois, A. & Bigot, J. Y. Ultrafast spin dynamics in ferromagnetic nickel. Phys. Rev. Lett. 76, 4250–4253 (1996).

    ADS  CAS  PubMed  Google Scholar 

  2. Koopmans, B. et al. Explaining the paradoxical diversity of ultrafast laser-induced demagnetization. Nat. Mater. 9, 259–265 (2010).

    ADS  CAS  PubMed  Google Scholar 

  3. Wietstruk, M. et al. Hot-electron-driven enhancement of spin-lattice coupling in Gd and Tb 4f ferromagnets observed by femtosecond x-ray magnetic circular dichroism. Phys. Rev. Lett. 106, 127401 (2011).

    ADS  PubMed  Google Scholar 

  4. Graves, C. E. et al. Nanoscale spin reversal by non-local angular momentum transfer following ultrafast laser excitation in ferrimagnetic GdFeCo. Nat. Mater. 12, 293–298 (2013).

    ADS  CAS  PubMed  Google Scholar 

  5. von Korff Schmising, C. et al. Imaging ultrafast demagnetization dynamics after a spatially localized optical excitation. Phys. Rev. Lett. 112, 217203 (2014).

    ADS  Google Scholar 

  6. Frietsch, B. et al. Disparate ultrafast dynamics of itinerant and localized magnetic moments in gadolinium metal. Nat. Commun. 6, 8262 (2015).

    ADS  CAS  PubMed  Google Scholar 

  7. Frietsch, B. et al. The role of ultrafast magnon generation in the magnetization dynamics of rare-earth metals. Sci. Adv. 6, eabb1601 (2020).

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  8. Stanciu, C. D. et al. All-optical magnetic recording with circularly polarized light. Phys. Rev. Lett. 99, 047601 (2007).

    ADS  CAS  PubMed  Google Scholar 

  9. Radu, I. et al. Transient ferromagnetic-like state mediating ultrafast reversal of antiferromagnetically coupled spins. Nature 472, 205–208 (2011).

    ADS  CAS  PubMed  Google Scholar 

  10. Ostler, T. A. et al. Ultrafast heating as a sufficient stimulus for magnetization reversal in a ferrimagnet. Nat. Commun. 3, 666 (2012).

    ADS  CAS  PubMed  Google Scholar 

  11. Wienholdt, S., Hinzke, D., Carva, K., Oppeneer, P. M. & Nowak, U. Orbital-resolved spin model for thermal magnetization switching in rare-earth-based ferrimagnets. Phys. Rev. B 88, 020406(R) (2013).

    ADS  Google Scholar 

  12. Siegrist, F. et al. Light-wave dynamic control of magnetism. Nature 571, 240–244 (2019).

    CAS  PubMed  Google Scholar 

  13. Malinowski, G. et al. Control of speed and efficiency of ultrafast demagnetization by direct transfer of spin angular momentum. Nat. Phys. 4, 855–858 (2008).

    CAS  Google Scholar 

  14. Battiato, M., Carva, K. & Oppeneer, P. M. Superdiffusive spin transport as a mechanism of ultrafast demagnetization. Phys. Rev. Lett. 105, 027203 (2010).

    ADS  CAS  PubMed  Google Scholar 

  15. Melnikov, A. et al. Ultrafast transport of laser-excited spin-polarized carriers Au/Fe/MgO(001). Phys. Rev. Lett. 107, 076601 (2011).

    ADS  PubMed  Google Scholar 

  16. Rudolf, D. et al. Ultrafast magnetization enhancement in metallic multilayers driven by superdiffusive spin current. Nat. Commun. 3, 1037 (2012).

    ADS  PubMed  Google Scholar 

  17. Eschenlohr, A. et al. Ultrafast spin transport as key to femtosecond demagnetization. Nat. Mater. 12, 332–336 (2013).

    ADS  CAS  PubMed  Google Scholar 

  18. Koopmans, B., Ruigrok, J. J. M., Dalla Longa, F. & De Jonge, W. J. M. Unifying ultrafast magnetization dynamics. Phys. Rev. Lett. 95, 267207 (2005).

    ADS  CAS  PubMed  Google Scholar 

  19. Carva, K., Battiato, M. & Oppeneer, P. M. Ab initio investigation of the Elliott-Yafet electron-phonon mechanism in laser-induced ultrafast demagnetization. Phys. Rev. Lett. 107, 207201 (2011).

    ADS  CAS  PubMed  Google Scholar 

  20. La-O-Vorakiat, C. et al. Ultrafast demagnetization measurements using extreme ultraviolet light: Comparison of electronic and magnetic contributions. Phys. Rev. 2, 011005 (2012).

    Google Scholar 

  21. Hinzke, D. et al. Multiscale modeling of ultrafast element-specific magnetization dynamics of ferromagnetic alloys. Phys. Rev. B 92, 054412 (2015).

    ADS  Google Scholar 

  22. Dornes, C. et al. The ultrafast Einstein-de Haas effect. Nature 565, 209–212 (2019).

    ADS  CAS  PubMed  Google Scholar 

  23. Roth, T. et al. Temperature dependence of laser-induced demagnetization in Ni: a key for identifying the underlying mechanism. Phys. Rev. 2, 021006 (2012).

    Google Scholar 

  24. Schellekens, A. J., Verhoeven, W., Vader, T. N., Koopmans, B. Investigating the contribution of superdiffusive transport to ultrafast demagnetization of ferromagnetic thin films. Appl. Phys. Lett. 102, 252408 (2013).

    ADS  Google Scholar 

  25. Stamm, C. et al. Femtosecond modification of electron localization and transfer of angular momentum in nickel. Nat. Mater. 6, 740–743 (2007).

    ADS  CAS  PubMed  Google Scholar 

  26. Maldonado, P. et al. Tracking the ultrafast nonequilibrium energy flow between electronic and lattice degrees of freedom in crystalline nickel. Phys. Rev. B 101, 100302 (2020).

    ADS  CAS  Google Scholar 

  27. Chen, Z. & Wang, L.-W. Role of initial magnetic disorder: a time-dependent ab initio study of ultrafast demagnetization mechanisms. Sci. Adv. 5, eaau8000 (2019).

    ADS  PubMed  PubMed Central  Google Scholar 

  28. Kealhofer, C. et al. All-optical control and metrology of electron pulses. Science 352, 429–433 (2016).

    ADS  MathSciNet  CAS  PubMed  MATH  Google Scholar 

  29. Wang, X. et al. Temperature dependence of electron-phonon thermalization and its correlation to ultrafast magnetism. Phys. Rev. B 81, 220301 (2010).

    ADS  Google Scholar 

  30. Zhang, L. F. & Niu, Q. Angular momentum of phonons and the Einstein-de Haas effect. Phys. Rev. Lett. 112, 085503 (2014).

    ADS  Google Scholar 

  31. Garanin, D. A. & Chudnovsky, E. M. Angular momentum in spin-phonon processes. Phys. Rev. B 92, 024421 (2015).

    ADS  Google Scholar 

  32. Zhu, H. et al. Observation of chiral phonons. Science 359, 579–582 (2018).

    ADS  MathSciNet  CAS  PubMed  Google Scholar 

  33. Birgeneau, R. J., Cordes, J., Dolling, G. & Woods, A. D. B. Normal modes of vibration in nickel. Phys. Rev. A 136, 1359–1365 (1964).

    ADS  CAS  Google Scholar 

  34. Zahn, D. et al. Lattice dynamics and ultrafast energy flow between electrons, spins, and phonons in a 3D ferromagnet. Phys. Rev. Res. 3, 023032 (2021).

    CAS  Google Scholar 

  35. Tengdin, P. et al. Critical behavior within 20 fs drives the out-of-equilibrium laser-induced magnetic phase transition in nickel. Sci. Adv. https://doi.org/10.1126/science.aaw9486 (2018).

  36. Hofherr, M. et al. Induced versus intrinsic magnetic moments in ultrafast magnetization dynamics. Phys. Rev. B 98, 174419 (2018).

    ADS  Google Scholar 

  37. Fechner, M. et al. Magnetophononics: ultrafast spin control through the lattice. Phys. Rev. Mater. 2, 064401 (2018).

    CAS  Google Scholar 

  38. Disa, A. S. et al. Polarizing an antiferromagnet by optical engineering of the crystal field. Nat. Phys. 16, 937–941 (2020).

    CAS  Google Scholar 

  39. Gao, M. N., Zhang, W. & Zhang, L. F. Nondegenerate chiral phonons in graphene/hexagonal boron nitride heterostructure from first-principles calculations. Nano Lett. 18, 4424–4430 (2018).

    ADS  CAS  PubMed  Google Scholar 

  40. Grissonnanche, G. et al. Chiral phonons in the pseudogap phase of cuprates. Nat. Phys. 16, 1108–1111 (2020).

    CAS  Google Scholar 

  41. Hirashita, N., Kinoshita, M., Aikawa, I. & Ajioka, T. Effects of surface hydrogen on the air oxidation at room temperature of HF treated Si (100) surfaces. Appl. Phys. Lett. 56, 451–453 (1990).

    ADS  CAS  Google Scholar 

  42. Mazzara, C. et al. Hydrogen-terminated Si(111) and Si(100) by wet chemical treatment: linear and non-linear infrared spectroscopy. Surf. Sci. 427–428, 208–213 (1999).

    ADS  Google Scholar 

  43. Ji, J.-Y., Shen, T.-C. Low-temperature silicon epitaxy on hydrogen-terminated Si(001) surfaces. Phys. Rev. B 70, 115309 (2004).

    ADS  Google Scholar 

  44. Kreuzpaintner, W., Störmer, M., Lott, D., Solina, D. & Schreyer, A. Epitaxial growth of nickel on Si(100) by dc magnetron sputtering. J. Appl. Phys. 104, 114302 (2008).

    ADS  Google Scholar 

  45. Kreuzpaintner, W., Störmer, M., Lott, D., Solina, D. & Schreyer, A. Epitaxial growth of nickel on Si(100) by dc magnetron sputtering. J. Appl. Phys. 104, 114302 (2008).

    ADS  Google Scholar 

  46. Schmehl, A. et al. Design and realization of a sputter deposition system for the in situ- and in operando-use in polarized neutron reflectometry experiments. Nucl. Instrum. Methods Phys. Res. A 883, 170–182 (2018).

    ADS  CAS  Google Scholar 

  47. Jiang, H., Klemmer, T. J., Barnard, J. A. & Payzant, E. A. Epitaxial growth of Cu on Si by magnetron sputtering. J. Vac. Sci. Technol. A 16, 3376–3383 (1998).

    ADS  CAS  Google Scholar 

  48. Chang, C.-A. Reversed magnetic anisotropy in deformed (100) Cu/Ni/Cu structures. J. Appl. Phys. 68, 4873–4875 (1990).

    ADS  CAS  Google Scholar 

  49. Chang, C.-A. Reversal in magnetic anisotropy of (100)Cu-Ni superlattices. J. Magn. Magn. Mater. 97, 102–106 (1991).

    ADS  CAS  Google Scholar 

  50. Ye, J. et al. Design and realization of a sputter deposition system for the in situ and in operando use in polarized neutron reflectometry experiments: novel capabilities. Nucl. Instrum. Methods Phys. Res. A 964, 163710 (2020).

    CAS  Google Scholar 

  51. Hull, C. M., Switzer, J. A. Electrodeposited epitaxial cu(100) on si(100) and lift-off of single crystal-like Cu(100) foils. ACS Appl. Mater. Interfaces 10, 38596–38602 (2018).

    CAS  PubMed  Google Scholar 

  52. Warren, B. E. X-Ray Diffraction (Dover, 1990).

  53. Björck, M. & Andersson, G. GenX: an extensible X-ray reflectivity refinement program utilizing differential evolution. J. Appl. Crystallogr. 40, 1174–1178 (2007).

    Google Scholar 

  54. Cemin, F. et al. Epitaxial growth of Cu(001) thin films onto Si(001) using a single-step HiPIMS process. Sci. Rep. 7, 1655 (2017).

    ADS  PubMed  PubMed Central  Google Scholar 

  55. Chen, L., Andrea, L., Timalsina, Y. P., Wang, G.-C. & Lu, T.-M. Engineering epitaxial-nanospiral metal films using dynamic oblique angle deposition. Cryst. Growth Des. 13, 2075–2080 (2013).

    CAS  Google Scholar 

  56. Seidel, M. et al. Efficient high-power ultrashort pulse compression in self-defocusing bulk media. Sci. Rep. 7, 1410 (2017).

    ADS  PubMed  PubMed Central  Google Scholar 

  57. Srinivasan, R., Lobastov, V. A., Ruan, C.-Y. & Zewail, A. H. Ultrafast electron diffraction (UED). Helv. Chim. Acta 86, 1761–1799 (2003).

    Google Scholar 

  58. Miller, R. J. D. Femtosecond crystallography with ultrabright electrons and x-rays: capturing chemistry in action. Science 343, 1108–1116 (2014).

    ADS  CAS  PubMed  Google Scholar 

  59. Kasmi, L., Kreier, D., Bradler, M., Riedle, E. & Baum, P. Femtosecond single-electron pulses generated by two-photon photoemission close to the work function. New J. Phys. 17, 033008 (2015).

    ADS  Google Scholar 

  60. Ehberger, D. et al. Terahertz compression of electron pulses at a planar mirror membrane. Phys. Rev. Appl. 11, 024034 (2019).

    ADS  CAS  Google Scholar 

  61. Simerska, M. The temperature dependence of the characteristic Debye temperature of nickel. Czech. J. Phys. B 12, 858–859 (1962).

    ADS  Google Scholar 

  62. Plimpton, S. Fast parallel algorithms for short-range molecular dynamics. J. Comput. Phys. 117, 1–19 (1995).

    ADS  CAS  MATH  Google Scholar 

  63. Foiles, S. M., Baskes, M. I. & Daw, M. S. Embedded-atom-method functions for the fcc metals Cu, Ag, Au, Ni, Pd, Pt, and their alloys. Phys. Rev. B 33, 7983–7991 (1986).

    ADS  CAS  Google Scholar 

  64. Sandia National Laboratories LAMMPS (Large-scale Atomic/Molecular Massively Parallel Simulator) https://lammps.sandia.gov/doc/Intro.html (2019).

  65. Coleman, S. P., Spearot, D. E. & Capolungo, L. Virtual diffraction analysis of Ni [010] symmetric tilt grain boundaries. Model. Simul. Mater. Sci. Eng. 21, 055020 (2013).

    ADS  CAS  Google Scholar 

  66. Danan, H., Herr, A. & Meyer, A. J. New determinations of the saturation magnetization of nickel and iron. J. Appl. Phys. 39, 669–670 (1968).

    ADS  CAS  Google Scholar 

  67. Scott, G. G. The gyromagnetic ratios of the ferromagnetic elements. Phys. Rev. 87, 697–699 (1952).

    ADS  CAS  Google Scholar 

  68. You, W. et al. Revealing the nature of the ultrafast magnetic phase transition in Ni by correlating extreme ultraviolet magneto-optic and photoemission spectroscopies. Phys. Rev. Lett. 121, 077204 (2018).

    ADS  CAS  PubMed  Google Scholar 

  69. Volkov, M. et al. Attosecond screening dynamics mediated by electron localization in transition metals. Nat. Phys. 15, 1145–1149 (2019).

    CAS  Google Scholar 

  70. Lee, E. W. Magnetostriction and magnetomechanical effects. Rep. Prog. Phys. 18, 184–229 (1955).

    ADS  Google Scholar 

  71. Guo, G. Y. Orientation dependence of the magnetoelastic coupling constants in strained FCC Co and Ni: an ab initio study. J. Magn. Magn. Mater. 209, 33–36 (2000).

    ADS  CAS  Google Scholar 

  72. Grossinger, R., Turtelli, R. S. & Mehmood, N. Materials with high magnetostriction. In 13th International Symposium on Advanced Materials (ISAM 2013) 60, 012002 (2014).

  73. Pateras, A. et al. Room temperature giant magnetostriction in single-crystal nickel nanowires. NPG Asia Mater. 11, 59 (2019).

    ADS  CAS  Google Scholar 

  74. Farle, M., Mirwald-Schulz, B., Anisimov, A. N., Platow, W. & Baberschke, K. Higher-order magnetic anisotropies and the nature of the spin-reorientation transition in face-centered-tetragonal Ni(001)/Cu(001). Phys. Rev. B 55, 3708–3715 (1997).

    ADS  CAS  Google Scholar 

  75. Kittel, C. On the gyromagnetic ratio and spectroscopic splitting factor of ferromagnetic substances. Phys. Rev. 76, 743–748 (1949).

    ADS  CAS  MATH  Google Scholar 

  76. Van Vleck, J. H. Concerning the theory of ferromagnetic resonance absorption. Phys. Rev. 78, 266–274 (1950).

    ADS  MATH  Google Scholar 

  77. Scott, G. G. Review of gyromagnetic ratio experiments. Rev. Mod. Phys. 34, 102–109 (1962).

    ADS  Google Scholar 

Download references

Acknowledgements

We thank I. Wimmer for magnetic hysteresis data, B.-H. Chen for help with the optics, S. Geprägs for access to his X-ray diffractometer and F. Krausz for laboratory infrastructure. This research was supported by the European Union’s Horizon 2020 research and innovation program via CoG 647771 and by the German Research Foundation (DFG) via SFB 1432.

Author information

Authors and Affiliations

Authors

Contributions

P.B. and U.N. conceived the experiment. S.T., M.V. and D.E. performed the diffraction experiments and analyzed the data. A.B. and S.T. produced the specimen under supervision of W.K. A.B. and W.K. characterized the epitaxial growth. D.K. performed the ultrafast optical measurements and thermal simulations. U.N. conceived the theory and M.E., H.L. and A.D. performed the simulations. P.B., U.N. and S.T. wrote the manuscript with help of all co-authors.

Corresponding author

Correspondence to P. Baum.

Ethics declarations

Competing interests

The authors declare no competing interests.

Peer review information

Nature thanks Georg Woltersdorf and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Peer reviewer reports are available.

Additional information

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Extended data figures and tables

Extended Data Fig. 1 X-ray characterization of the nickel thin-film structure.

a, X-ray reflectivity data and fit of the sample using a four-layer model with the scattering length density profile shown in the inset. The dashed lines in the inset indicate the slab model of the corresponding layers. The best fit parameters obtained by fitting the XRR intensities are shown in the table. The errors are estimated by a 5% increase over the optimum logarithmic figure of merit. b, Out-of-plane XRD scan in the angular regime of 40° ≤ 2θ ≤60°. The observed intensities at 2θ ≈ 50.53° and 2θ ≈ 52.13° correspond to Cu(002) and Ni(002). The lack of any Cu(111) and Ni(111) intensities shows the epitaxial growth. The inset graph shows the rocking-scans over the Cu(002) and Ni(002) peak positions. c, In-plane XRD scan at an inclination angle Δχ = 54.51°. The intensities at 2θ ≈ 43.41° and 2θ ≈ 44.47° correspond to the Cu(111) and Ni(111) reflections, respectively. d, ϕ scans for the Ni(111), Cu(111) and Si(111) ip peaks, obtained at an inclination angle of Δχ = 54.74°. A clear fourfold symmetry of the Cu(111) and Ni(111) ip reflections is observed with an offset angle of 45° to the Si(111) substrate reflections. For reasons of clarity, the scans are shifted in intensity by a factor of two each. e, ϕ scans for the Cu(111) and Ni(111) reflections, obtained at inclination angles of Δχ = 15.80°, Δχ = 54.74° and Δχ = 79.00°. For clarity, the scans are shifted in intensity by 0.1 each. Cu(111) intensities are shown in the angular regime of 0° ≤ ϕ ≤180°, while the Ni(111) intensities are shown for 180° ≤ ϕ ≤360°.

Extended Data Fig. 2 Rocking curve, magnetic hysteresis and optical penetration depth.

a, Rocking scan data obtained with the femtosecond electron beam. Shown is the Ni(200) peak when rotating the specimen around the [010] axis. b, Magnetic hysteresis curve of our nickel specimen, obtained by an in-plane SQUID measurement. c, Simulated optical energy disposition as a function of penetration depth. Upper panel: solid line, normalized electric field amplitude; dotted line, real part of the refractive index; dashed line, imaginary part of the refractive index. The laser comes from the left. Lower panel: absorption as a function of depth. The green, red, blue and grey areas denote nickel, copper, silicon and NiOx, respectively.

Extended Data Fig. 3 Second-harmonic-generation FROG measurements of the optical pulses after compression.

a, Measured FROG trace. b, Retrieved FROG trace at 0.3% FROG error. c, Evaluated spectrum (blue) and spectral phase (green). d, Retrieved pulse shape (blue) with temporal phase (green). The pulse duration is 93 fs.

Extended Data Fig. 4 Numerical simulation of heat flow.

a, Temperature profile at 20 ps after laser excitation. Drawing is not to scale. b, Radial profile of the temperature increase ΔT due to quasi-static heat accumulation. c, Cooling dynamics of the front surface at r = 0.

Extended Data Fig. 5 Magneto-optical Faraday effect and fluence dependency of the electron diffraction results.

a, Magnetic hysteresis curves for a negative (black) and slightly positive pump–probe delay (blue). b, Magnetization as a function of delay time. c, Debye–Waller effect as a function of the applied laser excitation fluence. d, Bragg spot anisotropy as a function of the applied laser excitation fluence. e, Simulated anisotropy as function of the degree of demagnetization.

Extended Data Fig. 6 Changes of Bragg spots angles as a function of pump–probe delay.

Dots, changes Δαx along the x axis; squares, changes Δαy along the y axis (see Fig. 1d).

Extended Data Fig. 7 Absence of beam deflection effects.

a, Two time-delayed electron beams on the screen. b, Intensity changes in the reference pulse (black) and probe pulse (blue), showing a Debye–Waller effect in the probe beam only. c, Differences of the beam positions before and after laser excitation as a function of the pump–probe delay, converted to angle changes at the specimen. All changes remain below 5 µrad.

Extended Data Fig. 8 Control experiment.

Analysis of the anisotropy of the silicon and copper spots as function of the pump–probe delay. a, isotropic Debye–Waller effect of Ni. b, Anisotropy of Si and Cu as a function of time.

Extended Data Fig. 9 Monte Carlo analysis of the time constants.

a, Distribution of the fitted response times for the Bragg spot asymmetry (blue) and the Debye–Waller effect (black). b, Correlation plot of the asymmetry fit parameters.

Extended Data Fig. 10 Additional molecular dynamics simulations results.

a, Finite-size effects of the anisotropy of crystallographically equivalent peaks comparing open boundary conditions (OBC) with periodic ones (PBC). For OBC a finite-size effect is observed: the relaxation time of the contrast increases with system size. PBC do not show this effect. b, Long-time evolution for N = 50 testing the three cases (OBC, PBC, and global rotation according to the Einstein–de Hass effect (EdH)) (blue, solid lines). Also shown is the anisotropy of the mean-squared velocities \(2{v}_{y}^{2}/({v}_{x}^{2}+{v}_{z}^{2})\) (green, dotted lines). c, Temperature dependence; anisotropy of crystallographically equivalent peaks for the same angular momentum L0 (same demagnetization) but different energy transfers to the lattice, leading to a temperature increase of ΔT = 15 K and 60 K, respectively.

Supplementary information

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Tauchert, S.R., Volkov, M., Ehberger, D. et al. Polarized phonons carry angular momentum in ultrafast demagnetization. Nature 602, 73–77 (2022). https://doi.org/10.1038/s41586-021-04306-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41586-021-04306-4

Comments

By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.

Search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing