ULTRAFAST DYNAMICAL RESPONSE OF THE PROTOTYPE MOTT COMPOUND

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

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

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

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

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

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

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

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

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

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

Ultrafast electronic excitation analysis In V 2 O 3 compounds, 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). Ultrafast Dynamic Imaging of Matter II, Ischia 2009

Ultrafast electronic excitation analysis In V 2 O 3 compounds, 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). Ultrafast Dynamic Imaging of Matter II, Ischia 2009

Ultrafast electronic excitation analysis In V 2 O 3 compounds, 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). With this model, one obtains a very high g value, 1000 times larger than gold. Possibly we underestimate the electron diffusion term k. E, which could be higher in the photoexcited state than at equilibrium. Ultrafast Dynamic Imaging of Matter II, Ischia 2009

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

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

Optical phonon: pump fluence study A 1 g mode V Phonon frequency: 8. 12 THz at 200 K Phonon lifetime: 630 fs at 200 K frequency blue-shifted with respect to Raman measurements (6. 23 THz, Kuroda et al. , PRB 16 (1977)). Consistent with previous measurements on undoped V 2 O 3. (Misochko et al. , PRB 58, (1998)). V Ultrafast Dynamic Imaging of Matter II, Ischia 2009

Optical phonon: pump fluence study A 1 g mode V Phonon frequency: 8. 12 THz at 200 K Phonon lifetime: 630 fs at 200 K frequency blue-shifted with respect to Raman measurements (6. 23 THz, Kuroda et al. , PRB 16 (1977)). Consistent with previous measurements on undoped V 2 O 3. (Misochko et al. , PRB 58, (1998)). V The frequency and lifetime of this mode don’t depend on thermodynamic phase (metal vs insulator). Ultrafast Dynamic Imaging of Matter II, Ischia 2009

Coherent Acoustic Wave: sample orientation effect Acoustic wave detection by Brillouin scattering: qphonon = 2 n kprobe cos qi We only detect the acoustic wave propagating along the incident plane symmetry axis. hexagonal c-axis V Oo Experimental geometry and c-axis orientation Ultrafast Dynamic Imaging of Matter II, Ischia 2009

Coherent Acoustic Wave: sample orientation effect Acoustic wave detection by Brillouin scattering: qphonon = 2 n kprobe cos qi We only detect the acoustic wave propagating along the incident plane symmetry axis. hexagonal c-axis V Oo Experimental geometry and c-axis orientation Ultrafast Dynamic Imaging of Matter II, Ischia 2009

Coherent Acoustic Wave: sample orientation effect Acoustic wave detection by Brillouin scattering: qphonon = 2 n kprobe cos qi We only detect the acoustic wave propagating along the incident plane symmetry axis. hexagonal c-axis V Oo Experimental geometry and c-axis orientation Ultrafast Dynamic Imaging of Matter II, Ischia 2009

Coherent Acoustic Wave: sample orientation effect Acoustic wave detection by Brillouin scattering: qphonon = 2 n kprobe cos qi We only detect the acoustic wave propagating along the incident plane symmetry axis. Along the c-axis, the detected acoustic wave is strongly reduced. hexagonal c-axis V Oo Experimental geometry and c-axis orientation Ultrafast Dynamic Imaging of Matter II, Ischia 2009

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

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

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

Conclusions and perspectives p We measured the ultrafast response of the prototype Mott compound V 2 O 3. p The coherent oscillations don’t depend on thermodynamic phase. p Coherent acoustic oscillations show a strong dependence on crystal orientation with respect to the laser propagation direction. p 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. p Perspectives: explore the dependence on the pump and probe wavelengths. Ultrafast Dynamic Imaging of Matter II, Ischia 2009

References p Pump-probe reflectivity measurements : § § § p 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) Ultrafast Dynamic Imaging of Matter II, Ischia 2009

Experimental Setup Reference Laser Synchronous detection: lock-in amplifier 0. 1 /2 P 90 Amplitude Phase chopper delay line PD 1 Sample L 2 probe pum p L 1 Ultrafast Dynamic Imaging of Matter II, Ischia 2009

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

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

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

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

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

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

Photoemission experiments on (V 1 -x. Crx)2 O 3 x=0. 011 Ultrafast Dynamic Imaging of Matter II, Ischia 2009

Spectromicroscopy experiments on (V 1 -x. Crx)2 O 3 x=0. 011 Phase separation observed photoemission experiments. in In agrement with the disapearrance of the coherent acoustic wave in the metallic phase of the sample. Ultrafast Dynamic Imaging of Matter II, Ischia 2009

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

Theoretical considerations on pump-probe reflectivity Principle of the pump-probe reflectivity: measure of the probe reflectivity as a function of time delay between pump and probe. detector pump probe Sample Dt 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: wp being the plasma frequency: and ne-ph is the electron-phonon collision frequency: Where ve is electron velocity, nph is phonon density and q is the atomic displacement. 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 ne and ne-ph, and so obtain an analytic expression for the transient reflectivity. 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: Ultrafast Dynamic Imaging of Matter II, Ischia 2009

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

Excitation and detection of coherent acoustic phonons Phenomenologic model of Thomsen 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)) 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) detector qphonon = 2 n ksonde cos qi qi probe Sample Sound velocity: w = vs q Final expression for the transient reflectivity: Ultrafast Dynamic Imaging of Matter II, Ischia 2009

Relaxation Times p p Manganites: spin-lattice relaxation: between 25 ps and 300 ps (as a function of temperature) Averitt and Taylor, J. Phys: Condens. Matter 14, R 1357 (2002) Blue Bronze: quasiparticle decay time 530 fs, Sagara, PHd thesis Ultrafast Dynamic Imaging of Matter II, Ischia 2009

Ccl: effet phase thermo p p p p 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 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 V 2 O 3 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) p Ultrafast Dynamic Imaging of Matter II, Ischia 2009