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Bose–Einstein condensation of quasiparticles by rapid cooling

Nature Nanotechnology volume 15, pages 457–461 (2020)Cite this article

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Abstract

The fundamental phenomenon of Bose–Einstein condensation has been observed in different systems of real particles and quasiparticles. The condensation of real particles is achieved through a major reduction in temperature, while for quasiparticles, a mechanism of external injection of bosons by irradiation is required. Here, we present a new and universal approach to enable Bose–Einstein condensation of quasiparticles and to corroborate it experimentally by using magnons as the Bose-particle model system. The critical point to this approach is the introduction of a disequilibrium of magnons with the phonon bath. After heating to an elevated temperature, a sudden decrease in the temperature of the phonons, which is approximately instant on the time scales of the magnon system, results in a large excess of incoherent magnons. The consequent spectral redistribution of these magnons triggers the Bose–Einstein condensation.

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Fig. 1: Theoretical modelling of the BEC by rapid cooling and experimental approach.
Fig. 2: BLS measurements of BEC by rapid cooling.
Fig. 3: Threshold behaviour of the BEC.

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Data availability

The data that support the findings of this study are available from the corresponding author upon reasonable request.

References

  1. Anderson, M. H., Ensher, J. R., Matthews, M. R., Wieman, C. E. & Cornell, E. A. Observation of Bose–Einstein condensation in a dilute atomic vapor. Science 269, 198–201 (1995).

    Article  CAS  Google Scholar 

  2. Santra, B. et al. Measuring finite-range phase coherence in an optical lattice using Talbot interferometry. Nat. Commun. 8, 15601 (2017).

    Article  CAS  Google Scholar 

  3. Kasprzak, J. et al. Bose–Einstein condensation of exciton polaritons. Nature 443, 409–414 (2006).

    Article  CAS  Google Scholar 

  4. Lerario, G. et al. Room-temperature superfluidity in a polariton condensate. Nat. Phys. 13, 837–841 (2017).

    Article  CAS  Google Scholar 

  5. Klaers, J., Schmitt, J., Vewinger, F. & Weitz, M. Bose–Einstein condensation of photons in an optical microcavity. Nature 468, 545–548 (2010).

    Article  CAS  Google Scholar 

  6. Damm, T. et al. Calorimetry of a Bose–Einstein-condensed photon gas. Nat. Commun. 7, 11340 (2016).

    Article  CAS  Google Scholar 

  7. Nikuni, T., Oshikawa, M., Oosawa, A. & Tanaka, H. Bose–Einstein condensation of dilute magnons in TlCuCl3. Phys. Rev. Lett. 84, 5868–5871 (2000).

    Article  CAS  Google Scholar 

  8. Yin, L., Xia, J. S., Zapf, V. S., Sullivan, N. S. & Paduan-Filho, A. Direct measurement of the Bose-Einstein condensation universality class in NiCl2-4SC(NH2)2 at ultralow temperatures. Phys. Rev. Lett. 101, 187205 (2008).

    Article  CAS  Google Scholar 

  9. Giamarchi, T., Rüegg, C. & Tchernyshyov, O. Bose-Einstein condensation in magnetic insulators. Nat. Phys. 4, 198–204 (2008).

    Article  Google Scholar 

  10. Borovik-Romanov, A. S., Bunkov, Yu. M., Dmitriev, V. V. & Mukharskiǐ, Yu. M. Long-lived induction signal in superfluid 3He-B. JETP Lett. 40, 1033–1037 (1984).

    Google Scholar 

  11. Bunkov, Yu. M. & Volovik, G. E. Magnon condensation into a q ball in 3He-B. Phys. Rev. Lett. 98, 265302 (2007).

    Article  Google Scholar 

  12. Demokritov, S. O. et al. Bose–Einstein condensation of quasi-equilibrium magnons at room temperature under pumping. Nature 443, 430–433 (2006).

    Article  CAS  Google Scholar 

  13. Rezende, S. M. Theory of coherence in Bose-Einstein condensation phenomena in a microwave-driven interacting magnon gas. Phys. Rev. B 79, 174411 (2009).

    Article  Google Scholar 

  14. Serga, A. A. et al. Bose–Einstein condensation in an ultra-hot gas of pumped magnons. Nat. Commun. 5, 3452 (2014).

    Article  Google Scholar 

  15. Bozhko, D. A. et al. Supercurrent in a room temperature Bose–Einstein magnon condensate. Nat. Phys. 12, 1057–1062 (2016).

    Article  CAS  Google Scholar 

  16. Brächer, T., Pirro, P. & Hillebrands, B. Parallel pumping for magnon spintronics: amplification and manipulation of magnon spin currents on the micron-scale. Phys. Rep. 699, 1–34 (2017).

    Article  Google Scholar 

  17. Safranski, C. et al. Spin caloritronic nano-oscillator. Nat. Commun. 8, 117 (2017).

    Article  CAS  Google Scholar 

  18. Gurevich, A. G. & Melkov, G. A. Magnetization Oscillations and Waves (CRC, 1996).

  19. Hüser, J. Kinetic Theory of Magnon Bose-Einstein Condensation. PhD thesis, Westfälische Wilhelms-Universität Münster (2016).

  20. Dubs, C. et al. Sub-micrometer yttrium iron garnet LPE films with low ferromagnetic resonance losses. J. Phys. D 50, 204005 (2017).

    Article  Google Scholar 

  21. Sebastian, T., Schultheiss, K., Obry, B., Hillebrands, B. & Schultheiss, H. Micro-focused Brillouin light scattering: imaging spin waves at the nanoscale. Front. Phys. 3, 35 (2015).

    Article  Google Scholar 

  22. Cherepanov, V., Kolokolov, I. & L’vov, V. The saga of YIG. Phys. Rep. 229, 81–144 (1993).

    Article  CAS  Google Scholar 

  23. Olsson, K. S. et al. Temperature-dependent Brillouin light scattering spectra of magnons in yttrium iron garnet and permalloy. Phys. Rev. B 96, 024448 (2017).

    Article  Google Scholar 

  24. Bauer, G. E. W., Saitoh, E. & van Wees, B. J. Spin caloritronics. Nat. Mater. 11, 391–399 (2012).

    Article  CAS  Google Scholar 

  25. Bender, S. A. & Tserkovnyak, Y. Thermally driven spin torques in layered magnetic insulators. Phys. Rev. B 93, 064418 (2016).

    Article  Google Scholar 

  26. Tserkovnyak, Y., Bender, S. A., Duine, R. A. & Flebus, B. Bose-Einstein condensation of magnons pumped by the bulk spin Seebeck effect. Phys. Rev. B 93, 100402 (2016).

    Article  Google Scholar 

  27. Uchida, K., Kikkawa, T., Miura, A., Shiomi, J. & Saitoh, E. Quantitative temperature dependence of longitudinal spin Seebeck effect at high temperatures. Phys. Rev. X 4, 041023 (2014).

    Google Scholar 

  28. Demidov, V. E. et al. Magnetization oscillations and waves driven by pure spin currents. Phys. Rep. 673, 1–31 (2017).

    Article  CAS  Google Scholar 

  29. Chumak, A. V., Vasyuchka, V. I., Serga, A. A. & Hillebrands, B. Magnon spintronics. Nat. Phys. 11, 453–461 (2015).

    Article  Google Scholar 

  30. Cornelissen, L. J., Liu, J., Duine, R. A., Ben Youssef, J. & van Wees, B. J. Long-distance transport of magnon spin information in a magnetic insulator at room temperature. Nat. Phys. 11, 1022–1026 (2015).

    Article  Google Scholar 

  31. Kittel, C. Introduction to Solid State Physics (Wiley, 2005).

  32. Stancil, D. D. & Prabhakar, A. Spin Waves: Theory and Applications (Springer, 2009).

  33. Jungfleisch, M. B., Lauer, V., Neb, R., Chumak, A. V. & Hillebrands, B. Improvement of the yttrium iron garnet/platinum interface for spin pumping-based applications. Appl. Phys. Lett. 103, 022411 (2013).

  34. Pirro, P. et al. Spin-wave excitation and propagation in microstructured waveguides of yttrium iron garnet/Pt bilayers. Appl. Phys. Lett. 104, 012402 (2014).

    Article  Google Scholar 

  35. Snoke, D. Coherent questions. Nature 443, 403–404 (2006).

    Article  CAS  Google Scholar 

  36. Nowik-Boltyk, P., Dzyapko, O., Demidov, V. E., Berloff, N. G. & Demokritov, S. O. Spatially non-uniform ground state and quantized vortices in a two-component Bose-Einstein condensate of magnons. Sci. Rep. 2, 482 (2012).

    Article  CAS  Google Scholar 

  37. Bozhko, D. A. et al. Bogoliubov waves and distant transport of magnon condensate at room temperature. Nat. Commun. 10, 2460 (2019).

    Article  Google Scholar 

  38. Snoke, D. Polariton condensates: a feature rather than a bug. Nat. Phys. 4, 673–673 (2008).

    Article  CAS  Google Scholar 

  39. Eisenstein, J. P. & MacDonald, A. H. Bose–Einstein condensation of excitons in bilayer electron systems. Nature 432, 691–694 (2004).

    Article  CAS  Google Scholar 

Download references

Acknowledgements

This research was funded by ERC Starting Grant 678309 MagnonCircuits and ERC Advanced Grant 694709 Super-Magnonics, as well as by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) TRR 173—268565370 and Project DU 1427/2-1, by grants no. EFMA-1641989 and no. ECCS-1708982 from the National Science Foundation of the United States, and by the U.S. AFOSR under the MURI grant # FA9550-19-1-0307.

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Authors and Affiliations

  1. Fachbereich Physik and Landesforschungszentrum OPTIMAS, Technische Universität Kaiserslautern, Kaiserslautern, Germany

    Michael Schneider, Thomas Brächer, David Breitbach, Viktor Lauer, Philipp Pirro, Halyna Yu. Musiienko-Shmarova, Björn Heinz, Qi Wang, Thomas Meyer, Frank Heussner, Sascha Keller, Evangelos Th. Papaioannou, Alexander A. Serga, Burkard Hillebrands & Andrii V. Chumak

  2. Department of Physics and Energy Science, University of Colorado at Colorado Springs, Colorado Springs, CO, USA

    Dmytro A. Bozhko

  3. Graduate School Materials Science in Mainz, Mainz, Germany

    Björn Heinz

  4. Faculty of Physics, University of Vienna, Wien, Austria

    Qi Wang & Andrii V. Chumak

  5. THATec Innovation GmbH, Dresden, Germany

    Thomas Meyer

  6. Institut für Physik, Martin-Luther-Universität Halle-Wittenberg, Halle, Germany

    Evangelos Th. Papaioannou

  7. Nano Structuring Center, Technische Universität Kaiserslautern, Kaiserslautern, Germany

    Bert Lägel & Thomas Löber

  8. INNOVENT e.V. Technologieentwicklung, Jena, Germany

    Carsten Dubs

  9. Department of Physics, Oakland University, Rochester, MI, USA

    Andrei N. Slavin & Vasyl S. Tiberkevich

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  1. Michael Schneider
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Contributions

M.S. and D.B. performed the measurements and analysed the experimental results. T.B. and A.V.C. supervised the measurements. T.B., P.P., A.A.S. and A.V.C. planned the experiment. M.S., B. Heinz and T.M. developed the experimental setup. V.L. performed FMR characterizations and preliminary experiments. C.D. grew the LPE YIG films. S.K. and E.Th.P. deposited the Pt overlayer. M.S., B. Heinz, B.L., T.L. and D.B. fabricated the structures under investigation. V.S.T. developed the quasi-analytical model of the magnon spectral redistribution. D.A.B., H.Yu.M.-S., V.S.T. and A.N.S. performed the theoretical calculations. M.S. and F.H. performed the COMSOL simulations. Q.W. and P.P. performed the MuMax3 simulations. B. Hillebrands and A.V.C. led the project. All authors discussed the results and wrote the manuscript.

Corresponding authors

Correspondence to Michael Schneider or Andrii V. Chumak.

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Extended data

Extended Data Fig. 1 Parameters used for the calculations of the magnon density.

The table shows the parameters according to the developed quasi-analytical theoretical model for two different experimentally investigated strips.

Extended Data Fig. 2 Temperature profile and time evolution of the temperature gradient.

a, Temperature across the layers at the end of a 120-ns-long heating pulse simulated with COMSOL (corresponding to the experiment shown in Fig. 2b in the main manuscript). b, Temperature (red curve, left axis) and temperature gradient (black curve, right axis) as a function of time simulated with COMSOL (corresponding to the experiment shown in Fig. 2b in the main manuscript).

Extended Data Fig. 3 Rapid cooling BEC generated in an Au/Al/YIG structure.

a, Time resolved BLS spectrum for the case when a 50-ns-long pulse is applied b, Integrated BLS intensity over the frequency range shown in a.

Extended Data Fig. 4 BEC by rapid cooling for different geometries of the external field.

a, BLS spectrum as a function of time. The BLS signal (colour-coded, log scale) is proportional to the density of magnons. FM indicates the fundamental mode, EM – the edge mode, and 1st M – the first thickness mode. The vertical dashed lines indicate the start and the end of the pulse (τP = 150 ns, U = 0.9 V). The external field was parallel to the short axis of the strip (B||y). c, BLS spectrum as a function of time for the case when the external magnetic field is parallel to long axis of the strip (B||x), (τP = 120 ns, U = 0.9 V). b,d, Normalized magnon intensity integrated from 4.95 GHz to 8.1 GHz as a function of time for the cases in a,c. The insets show the sample and measurement geometry.

Supplementary information

Supplementary Information

Supplementary discussion, Figs. 1–11 and Tables 1–2.

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Schneider, M., Brächer, T., Breitbach, D. et al. Bose–Einstein condensation of quasiparticles by rapid cooling. Nat. Nanotechnol. 15, 457–461 (2020). https://doi.org/10.1038/s41565-020-0671-z

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