1. ULTRAFAST DYNAMICAL RESPONSE OF THE PROTOTYPE MOTT COMPOUND V 2 O 3 B. Mansart 1, D. Boschetto 2 and M. Marsi 1 1Laboratoire de Physique des Solides, UMR 8502, Université Paris-Sud, 91405 Orsay, France 2 Laboratoire d’Optique Appliquée, ENSTA, CNRS, Ecole Polytechnique, 91761 Palaiseau, France

2. Ultrafast Dynamic Imaging of Matter II, Ischia 2009 Phase diagram and Mott transition in (V 1-x Cr x ) 2 O 3 Mott transition: localisation of electrons Coulomb Repulsion > Kinetic Energy. prototype Metal-Insulator transition: no symmetry breaking McWhan et al., PRL 27 (1971) Limelette et al., Science (2003) Paramagnetic Metal (PM) - Paramagnetic Insulator (PI): resistivity changes of 7 orders of magnitude V O o PMPI AFI Kuroda et al., PRB 16 (1977)

3. Ultrafast Dynamic Imaging of Matter II, Ischia 2009 Time-resolved reflectivity on V 2 O 3 wavelength: 800 nm pulse duration: 45 fs repetition rate 1 kHz Pump and probe polarizations orthogonal

4. Ultrafast Dynamic Imaging of Matter II, Ischia 2009 Time-resolved reflectivity on V 2 O 3 wavelength: 800 nm pulse duration: 45 fs repetition rate 1 kHz

5. Ultrafast Dynamic Imaging of Matter II, Ischia 2009 Time-resolved reflectivity on V 2 O 3 1. Ultrafast peak: electronic excitation wavelength: 800 nm pulse duration: 45 fs repetition rate 1 kHz

6. Ultrafast Dynamic Imaging of Matter II, Ischia 2009 Time-resolved reflectivity on V 2 O 3 1. Ultrafast peak: electronic excitation wavelength: 800 nm pulse duration: 45 fs repetition rate 1 kHz 2. Coherent Optical A 1g Phonon

7. Ultrafast Dynamic Imaging of Matter II, Ischia 2009 Time-resolved reflectivity on V 2 O 3 1. Ultrafast peak: electronic excitation wavelength: 800 nm pulse duration: 45 fs repetition rate 1 kHz 2. Coherent Optical A 1g Phonon 3. Coherent Acoustic wave propagation

8. Ultrafast Dynamic Imaging of Matter II, Ischia 2009 Ultrafast electronic excitation Electronic peak represents the ultrafast excitation and relaxation of electrons.

9. Ultrafast Dynamic Imaging of Matter II, Ischia 2009 Ultrafast electronic excitation Electronic peak represents the ultrafast excitation and relaxation of electrons.

10. Ultrafast Dynamic Imaging of Matter II, Ischia 2009 Ultrafast electronic excitation Electronic peak represents the ultrafast excitation and relaxation of electrons.

11. Ultrafast Dynamic Imaging of Matter II, Ischia 2009 Ultrafast electronic excitation Electronic peak represents the ultrafast excitation and relaxation of electrons. Electronic Peak: Intensity linear with pump fluence, width increasing with pump fluence.

12. Ultrafast Dynamic Imaging of Matter II, Ischia 2009 In V 2 O 3 compounds, the thermalization time depends on pump fluence. It is ~130 fs: faster than normal metals and others strongly correlated materials. Ultrafast electronic excitation analysis

13. Ultrafast Dynamic Imaging of Matter II, Ischia 2009 Relaxation of hot electrons: Two Temperatures Model (TTM). Ultrafast electronic excitation analysis In V 2 O 3 compounds, the thermalization time depends on pump fluence. It is ~130 fs: faster than normal metals and others strongly correlated materials.

14. Ultrafast Dynamic Imaging of Matter II, Ischia 2009 Ultrafast electronic excitation analysis In V 2 O 3 compounds, the thermalization time depends on pump fluence. It is ~130 fs: faster than normal metals and others strongly correlated materials. Relaxation of hot electrons: Two Temperatures Model (TTM).

15. Ultrafast Dynamic Imaging of Matter II, Ischia 2009 Ultrafast electronic excitation analysis With this model, one obtains a very high g value, 1000 times larger than gold. Possibly we underestimate the electron diffusion term  E, which could be higher in the photoexcited state than at equilibrium. In V 2 O 3 compounds, the thermalisation time depends on pump fluence. It is ~130 fs: faster than normal metals and others strongly correlated materials. Relaxation of hot electrons: Two Temperatures Model (TTM).

16. Ultrafast Dynamic Imaging of Matter II, Ischia 2009 Optical phonon: pump fluence study

17. Ultrafast Dynamic Imaging of Matter II, Ischia 2009 Optical phonon: pump fluence study

18. Ultrafast Dynamic Imaging of Matter II, Ischia 2009 V V Optical phonon: pump fluence study A 1g mode Phonon frequency: 8.12 THz at 200K Phonon lifetime: 630 fs at 200K frequency blue-shifted with respect to Raman measurements (6.23THz, Kuroda et al., PRB 16 (1977)). Consistent with previous measurements on undoped V 2 O 3.( Misochko et al., PRB 58, (1998)).

19. Ultrafast Dynamic Imaging of Matter II, Ischia 2009 V V Optical phonon: pump fluence study A 1g mode The frequency and lifetime of this mode don’t depend on the thermodynamic phase (metal vs insulator). Phonon frequency: 8.12 THz at 200K Phonon lifetime: 630 fs at 200K frequency blue-shifted with respect to Raman measurements (6.23THz, Kuroda et al., PRB 16 (1977)). Consistent with previous measurements on undoped V 2 O 3.( Misochko et al., PRB 58, (1998)).

20. Ultrafast Dynamic Imaging of Matter II, Ischia 2009 Coherent Acoustic Wave: sample orientation effect hexagonal c-axis V O o Experimental geometry and c-axis orientation Acoustic wave detection by Brillouin scattering: q phonon = 2 n k probe cos  i We only detect the acoustic wave propagating along the incident plane symmetry axis.

21. Ultrafast Dynamic Imaging of Matter II, Ischia 2009 Coherent Acoustic Wave: sample orientation effect hexagonal c-axis V O o Experimental geometry and c-axis orientation Acoustic wave detection by Brillouin scattering: q phonon = 2 n k probe cos  i We only detect the acoustic wave propagating along the incident plane symmetry axis.

22. Ultrafast Dynamic Imaging of Matter II, Ischia 2009 Coherent Acoustic Wave: sample orientation effect hexagonal c-axis V O o Experimental geometry and c-axis orientation Acoustic wave detection by Brillouin scattering: q phonon = 2 n k probe cos  i We only detect the acoustic wave propagating along the incident plane symmetry axis.

23. Ultrafast Dynamic Imaging of Matter II, Ischia 2009 Coherent Acoustic Wave: sample orientation effect hexagonal c-axis V O o Experimental geometry and c-axis orientation Acoustic wave detection by Brillouin scattering: q phonon = 2 n k probe cos  i We only detect the acoustic wave propagating along the incident plane symmetry axis. Along the c-axis, the detected acoustic wave is strongly reduced.

24. Ultrafast Dynamic Imaging of Matter II, Ischia 2009 Acoustic wave: Thermodynamic phase effects Insulating phase (PI)Metallic phase (PM) PM PI

25. Ultrafast Dynamic Imaging of Matter II, Ischia 2009 Acoustic wave: Thermodynamic phase effects Insulating phase (PI)Metallic phase (PM) PM PI Coherent acoustic oscillation intensity linear in pump fluence, identical in metal and insulator. The lifetime is longer in the Insulating phase.

26. Ultrafast Dynamic Imaging of Matter II, Ischia 2009 Acoustic wave: Thermodynamic phase effects Insulating phase (PI)Metallic phase (PM) PM PI Strong effects of the thermodynamic phase (metal vs insulator) on the mean value (baseline) of the coherent oscillation.

27. Ultrafast Dynamic Imaging of Matter II, Ischia 2009 Conclusions and perspectives  We measured the ultrafast response of the prototype Mott compound V 2 O 3.  The coherent oscillations don’t depend on the thermodynamic phase.  Coherent acoustic oscillations show a strong dependence on crystal orientation with respect to the laser propagation direction.  Difference between metal and insulator: mean value of the reflectivity on the picosecond time-scale. Potentially important also for other materials presenting metal-insulator transitions.  Perspectives: explore the dependence on the pump and probe wavelengths.

28. Ultrafast Dynamic Imaging of Matter II, Ischia 2009 References  Pump-probe reflectivity measurements :  R.Merlin, Solid State Commun. 102, 207 (1997)  Y-X.Yan and K.A.Nelson, J.Chem.Phys. 87, 6257 (1987)  D.Boschetto et al., Phys.Rev.Lett. 100, 027404 (2008)  C.Thomsen et al., Phys.Rev.B 34, 4129 (1986)  L. Brillouin, Ann. de Phys. (Paris) 17, 88 (1922)  Phonons in V 2 O 3 :  N.Kuroda and H.Y.Fan, Phys.Rev.B 16, 5003 (1977)  O.V.Misochko et al., Phys.Rev.B 58, 12789 (1998)  Md.Motin Seikh et al., Solid State Commun. 138, 466 (2006)  S.R.Hassan, A.Georges et al., Phys.Rev.Lett. 94, 036402 (2005)

29. Ultrafast Dynamic Imaging of Matter II, Ischia 2009 Synchronous detection: lock-in amplifier Laser Reference pump probe delay line chopper Sample PD1 P P L1 L2 /2 0.190 Amplitude Phase Experimental Setup

30. Ultrafast Dynamic Imaging of Matter II, Ischia 2009 N.Kuroda and H.Y.Fan, Phys.Rev.B 16, 5003 (1977) Raman spectrum of V 2 O 3

31. Ultrafast Dynamic Imaging of Matter II, Ischia 2009 Reflectivity of V 2 O 3 L. Baldassarre et al., PRB 77, 113107 (2008)

32. Ultrafast Dynamic Imaging of Matter II, Ischia 2009 Difference Metal-Insulator: coherent acoustic wave

33. Ultrafast Dynamic Imaging of Matter II, Ischia 2009 Difference Metal-Insulator: coherent acoustic wave

34. Ultrafast Dynamic Imaging of Matter II, Ischia 2009 DMFT calculations for Mott compounds Georges et al. RMP (1996)

35. Ultrafast Dynamic Imaging of Matter II, Ischia 2009 DMFT calculations for (V 1-x Cr x ) 2 O 3

36. Ultrafast Dynamic Imaging of Matter II, Ischia 2009 Photoemission experiments on (V 1-x Cr x ) 2 O 3 x=0.011 (V 1-x Cr x ) 2 O 3 x=0.011

37. Ultrafast Dynamic Imaging of Matter II, Ischia 2009 Spectromicroscopy experiments on (V 1-x Cr x ) 2 O 3 x=0.011 Phase separation observed in photoemission experiments. In agrement with the disapearrance of the coherent acoustic wave in the metallic phase of the same sample.

38. Ultrafast Dynamic Imaging of Matter II, Ischia 2009 Pump pulse Excitation of electrons close to Fermi level Variation of electronic density Excitation of coherent phonons Variation of electron-phonon collision rate Variation of the dieletric function Variation of the reflectivity Excitation and detection of coherents optical phonons

39. Ultrafast Dynamic Imaging of Matter II, Ischia 2009 Principle of the pump-probe reflectivity: measure of the probe reflectivity as a function of time delay between pump and probe. Theoretical considerations on pump-probe reflectivity tt Sample detector pump probe

40. Ultrafast Dynamic Imaging of Matter II, Ischia 2009 Out of equilibrium, optical properties of solids depends on several parameters: electron density, electronic effective mass and electron-phonon collision rate. In metals, a good approximation is the Drude model, giving the dielectric function in terms of these three parameters:  p being the plasma frequency: and e-ph is the electron-phonon collision frequency: Where v e is electron velocity, n ph is phonon density and q is the atomic displacement.

41. Ultrafast Dynamic Imaging of Matter II, Ischia 2009 The reflectivity is always given by Fresnel equations: After electron excitation by the pump pulse, electron density and electron-phonon collision rate change, and so the dielectric function changes as well. This causes variations in reflectivity, as the following equation: If we know the expression of dielectric function, we can get the derivatives with respect to n e and e-ph, and so obtain an analytic expression for the transient reflectivity.

42. Ultrafast Dynamic Imaging of Matter II, Ischia 2009 The electron density is proportional to electronic temperature: The excited phonon density is proportional to the lattice temperature, Debye temperature and atomic density as: So for the electron-phonon collision rate:

43. Ultrafast Dynamic Imaging of Matter II, Ischia 2009 Finally, the electronic and lattice temperatures can be given by the Two-Temperature Model equations: Where C e and C l are respectively heat capacity of electrons and lattice, A is absorption coefficient, l s the penetration depth,  e the heat diffusivity of electrons and g the electron-phonon coupling constant. And changes in reflectivity can be written in the form:

44. Ultrafast Dynamic Imaging of Matter II, Ischia 2009 Phenomenologic model of Thomsen Excitation and detection of coherent acoustic phonons Pump pulse arriving along z-axis Deposition of energy in the skin depth Temperature gradient: z-dependent thermic constraint Creation of a deformation wave along z-axis (longitudinal acoustic phonon))

45. Ultrafast Dynamic Imaging of Matter II, Ischia 2009 Detection of acoustic waves: Diffraction of the probe beam on acoustic waves propagating in the material (the probe acts as a filter by selecting the measured wave) q phonon = 2 n k sonde cos  i Sound velocity:  = v s q Final expression for the transient reflectivity: Sample detector probe ii

46. Ultrafast Dynamic Imaging of Matter II, Ischia 2009 Relaxation Times  Manganites: spin-lattice relaxation:between 25 ps and 300 ps (as a function of temperature) Averitt and Taylor, J. Phys:Condens. Matter 14, R1357 (2002)  Blue Bronze: quasiparticle decay time 530 fs, Sagara, PHd thesis

47. Ultrafast Dynamic Imaging of Matter II, Ischia 2009 Ccl: effet phase thermo  Electron-phonon coupling fundamental in Mott transition and in general in strongly correlated systems  Electronic excitation peak  e-ph coupling from ultrafast response  Optical phonon and acoustic phonon have to be understood in order to completely describe the ultrafast response and the correct lineshape of the electronic excitation  Show how one can extract e-ph coupling from electronic excitation (one exemple)  optical phonon: (no) polarization dependence  Acoustic phonon: (strong) polarization dependence (?)  Optical phonon: (very weak) phase dependence (normal for Mott material)  Acoustic phonon: thermodynamic phase dependence  Conclusions:  1) we measured e-ph coupling for prototype Mott compound V2O3  2) in order to correctly measure it, understand overall ultrafast response  3) overall ultrafast response depends on LATTICE oscillations (polarization AND phase dependence) even for purely ELECTRONIC Mott system  4) these effects may in general contribute to the ultrafast response of all strongly correlated materials (even those where electronic transitions are associated to structural symmetry changes) 