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Femtosecond X-ray measurement of coherent lattice vibrations near the Lindemann stability limit

Nature volume 422, pages 287–289 (2003)Cite this article

Abstract

The study of phase-transition dynamics in solids beyond a time-averaged kinetic description requires direct measurement of the changes in the atomic configuration along the physical pathways leading to the new phase. The timescale of interest is in the range 10-14 to 10-12 s. Until recently, only optical techniques were capable of providing adequate time resolution1, albeit with indirect sensitivity to structural arrangement. Ultrafast laser-induced changes of long-range order have recently been directly established for some materials using time-resolved X-ray diffraction2,3,4,5,6,7,8. However, the measurement of the atomic displacements within the unit cell, as well as their relationship with the stability limit of a structural phase9,10,11, has to date remained obscure. Here we report time-resolved X-ray diffraction measurements of the coherent atomic displacement of the lattice atoms in photoexcited bismuth close to a phase transition. Excitation of large-amplitude coherent optical phonons gives rise to a periodic modulation of the X-ray diffraction efficiency. Stronger excitation corresponding to atomic displacements exceeding 10 per cent of the nearest-neighbour distance—near the Lindemann limit—leads to a subsequent loss of long-range order, which is most probably due to melting of the material.

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Figure 1: Geometrical structure factor |S(h, k, l)|2 of bismuth as a function of the distance d of the two basis atoms for diffraction from (111) and (222) lattice planes.
Figure 2: X-ray diffraction efficiency of the (222) reflection as a function of time delay between the optical pump pulse (fluence 6 mJ cm-2) and the X-ray probe pulse.
Figure 3: X-ray diffraction efficiency of the (111) reflection as a function of time delay between the optical pump pulse (fluence 6 mJ cm-2) and the X-ray probe pulse.
Figure 4

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References

  1. Bloembergen, N. From nanosecond to femtosecond science. Rev. Mod. Phys. 71, S283–S287 (1999)

    Article  CAS  Google Scholar 

  2. Chin, A. H. et al. Ultrafast structural dynamics in InSb probed by time-resolved X-ray diffraction. Phys. Rev. Lett. 83, 336–339 (1999)

    Article  ADS  CAS  Google Scholar 

  3. Siders, C. W. et al. Detection of non-thermal melting by ultrafast X-ray diffraction. Science 286, 1340–1342 (1999)

    Article  CAS  Google Scholar 

  4. Lindenberg, A. M. et al. Time-resolved X-ray diffraction from coherent phonons during a laser-induced phase transition. Phys. Rev. Lett. 84, 111–114 (2000)

    Article  ADS  CAS  Google Scholar 

  5. Rousse, A. et al. Non-thermal melting in semiconductors measured at femtosecond resolution. Nature 410, 65–68 (2001)

    Article  ADS  CAS  Google Scholar 

  6. Sokolowski-Tinten, K. et al. Femtosecond X-ray measurement of ultrafast melting and large acoustic transients. Phys. Rev. Lett. 87, 225701 (2001)

    Article  ADS  CAS  Google Scholar 

  7. Cavalleri, A. et al. Femtosecond structural dynamics in VO2 during an ultrafast solid-solid phase transition. Phys. Rev. Lett. 87, 237401 (2001)

    Article  ADS  CAS  Google Scholar 

  8. Feurer, T. et al. Femtosecond silicon Kα pulses from laser produced plasmas. Phys. Rev. E 65, 016412 (2002)

    Article  ADS  CAS  Google Scholar 

  9. Lindemann, F. A. Über die Berechnung molekularer Eigenfrequenzen. Phys. Z. 11, 609–612 (1910)

    CAS  MATH  Google Scholar 

  10. Born, M. Thermodynamics of crystals and melting. J. Chem. Phys. 7, 591–603 (1939)

    Article  ADS  CAS  Google Scholar 

  11. Tallon, J. L. A hierarchy of catastrophes as a succession of stability limits for the crystalline state. Nature 342, 658–660 (1989)

    Article  ADS  CAS  Google Scholar 

  12. Madelung, O. (ed.) Semiconductors: Physics of Non-tetrahedrally Bonded Elements and Binary Compounds I in Landolt-Börnstein, New Series, Group III: Crystal and Solid State Physics Vol. 17, Semiconductors, Part a (Springer, Berlin, 1983).

  13. Peierls, R. More Surprises in Theoretical Physics (Princeton Univ. Press, Princeton, 1991)

    Google Scholar 

  14. Shick, A. B., Ketterson, J. B., Novikov, D. L. & Freeman, A. J. Electronic structure, phase stability, and semimetal-semiconductor transitions in Bi. Phys. Rev. B 60, 15484–15487 (1999)

    Article  ADS  CAS  Google Scholar 

  15. Zeiger, H. J. et al. Theory for displacive excitation of coherent phonons. Phys. Rev. B 45, 768–778 (1992)

    Article  ADS  CAS  Google Scholar 

  16. Hunsche, S., Wienecke, K., Dekorsy, T. & Kurz, H. Impulsive softening of coherent phonons in tellurium. Phys. Rev. Lett. 75, 1815–1818 (1995)

    Article  ADS  CAS  Google Scholar 

  17. Garrett, G. A., Albrecht, T. F., Whitaker, J. F. & Merlin, R. Coherent THz phonons driven by light pulses and the Sb problem: what is the mechanism? Phys. Rev. Lett. 77, 3661–3664 (1996)

    Article  ADS  CAS  Google Scholar 

  18. Hase, M., Mizoguchi, K., Harima, H. & Nakashima, S. Dynamics of coherent phonons in bismuth generated by ultrashort light pulses. Phys. Rev. B 58, 5448–5452 (1998)

    Article  ADS  CAS  Google Scholar 

  19. DeCamp, M. F., Reis, D. A., Bucksbaum, P. H. & Merlin, R. Dynamics and coherent control of high-amplitude phonons in bismuth. Phys. Rev. B 64, 092301 (2001)

    Article  ADS  Google Scholar 

  20. Hase, M., Kitajima, M., Nakashima, S. & Mizoguchi, K. Dynamics of coherent anharmonic phonons in bismuth using high density photoexcitation. Phys. Rev. Lett. 88, 067401 (2002)

    Article  ADS  Google Scholar 

  21. Von der Linde, D. et al. ‘Ultrafast’ extended to X-rays: Femtosecond time-resolved X-ray diffraction. Z. Phys. Chem. 215, 1527–1541 (2001)

    CAS  Google Scholar 

Download references

Acknowledgements

Financial support by the Deutsche Forschungsgemeinschaft, the European Community (Research and Training Network XPOSE) and the German Academic Exchange Service (DAAD) is acknowledged.

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Authors and Affiliations

  1. Institut für Laser- und Plasmaphysik, Universität Essen, 45117, Essen, Germany

    Klaus Sokolowski-Tinten, Christian Blome, Juris Blums, Clemens Dietrich, Alexander Tarasevitch, Michael Horn-von-Hoegen & Dietrich von der Linde

  2. Materials Science Division, Lawrence Berkeley National Laboratory, Berkeley, California, 94720, USA

    Andrea Cavalleri

  3. Forschungsgruppe Röntgenoptik, Institut für Optik und Quantenelektronik, Friedrich-Schiller-Universität Jena, 07743, Jena, Germany

    Ingo Uschmann & Eckhard Förster

  4. Institut für Halbleitertechnologie, Universität Hannover, 30167, Hannover, Germany

    Martin Kammler

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  1. Klaus Sokolowski-Tinten
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Correspondence to Klaus Sokolowski-Tinten.

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Sokolowski-Tinten, K., Blome, C., Blums, J. et al. Femtosecond X-ray measurement of coherent lattice vibrations near the Lindemann stability limit. Nature 422, 287–289 (2003). https://doi.org/10.1038/nature01490

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