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

2

Laboratoire d’Optique Appliquée, ENSTA, CNRS, Ecole Polytechnique, 91761 Palaiseau, France

Phase diagram and Mott transition in (V 1-x Cr x ) 2 O 3 Mott transition: localisation of electrons Coulomb Repulsion > Kinetic Energy.

PI PM AFI

prototype Metal-Insulator transition:

no symmetry breaking

Kuroda et al. , PRB 16 (1977) McWhan et al., PRL 27 (1971)

Paramagnetic Metal (

PM

) Paramagnetic Insulator (

PI

): resistivity changes of 7 orders of magnitude

Limelette et al., Science (2003)

Ultrafast Dynamic Imaging of Matter II, Ischia 2009

V  O o

Time-resolved reflectivity on V 2 O 3 wavelength: 800 nm pulse duration: 45 fs repetition rate 1 kHz 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 kHz

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

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 1g Phonon wavelength: 800 nm pulse duration: 45 fs repetition rate 1 kHz

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 1g Phonon 3.

Coherent propagation Acoustic wave wavelength: 800 nm pulse duration: 45 fs repetition rate 1 kHz

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, the 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, 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).

C E C L



T E



t

 2

l s A I

(

t

)   

z



T L



t



g



T E



T L

 

E



T E



z



g



T E



T L



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).

C E C L



T E



t

 2

l s A I

(

t

)   

z



T L



t



g



T E



T L

 

E



T E



z



g



T E



T L



Ultrafast Dynamic Imaging of Matter II, Ischia 2009

Ultrafast electronic excitation analysis 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).

C E C L



T E



t

 2

l s A I

(

t

)   

z



T L



t



g



T E



T L

 

E



T E



z



g



T E



T L

 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 equilibrium .

state than at

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 1g mode

V

Phonon frequency: 8.12 THz at 200K Phonon lifetime: 630 fs at 200K frequency blue-shifted measurements (6.23THz

,

with respect to Raman

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 1g mode

V V

Phonon frequency: 8.12 THz at 200K Phonon lifetime: 630 fs at 200K frequency blue-shifted measurements (6.23THz

,

with respect to Raman

Kuroda et al., PRB 16 (1977)).

Consistent with previous measurements on undoped V 2 O 3 .( Misochko et al., PRB 58, (1998)).

The frequency and lifetime of this mode don’t depend on the 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: q phonon = 2 n k probe cos q i We only detect the acoustic wave propagating along plane symmetry axis.

the incident hexagonal c-axis V  O o

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: q phonon = 2 n k probe cos q i We only detect the acoustic wave propagating along plane symmetry axis.

the incident hexagonal c-axis V  O o

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: q phonon = 2 n k probe cos q i We only detect the acoustic wave propagating along plane symmetry axis.

the incident hexagonal c-axis V  O o

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: q phonon = 2 n k probe cos q i We only detect the acoustic wave propagating along plane symmetry axis.

the incident

Along the c-axis, the detected acoustic wave is strongly reduced.

hexagonal c-axis V  O o

Experimental geometry and c-axis orientation

Ultrafast Dynamic Imaging of Matter II, Ischia 2009

Acoustic wave: Thermodynamic phase effects

Insulating phase (PI) PI PM Metallic phase (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 the 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  We measured the ultrafast response of the prototype Mott compound V 2 O 3.

 The coherent oscillations phase.

don’t depend on the thermodynamic  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.

Ultrafast Dynamic Imaging of Matter II, Ischia 2009

References  Pump-probe reflectivity measurements :      R.Merlin, Solid State Commun. D.Boschetto

et al

C.Thomsen et al., Phys.Rev.B

102

Y-X.Yan and K.A.Nelson, J.Chem.Phys. ., Phys.Rev.Lett.

34

L. Brillouin, Ann. de Phys. (Paris)

100

, 4129 (1986)

17

, 207 (1997)

87

, 6257 (1987) , 027404 (2008) , 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

Md.Motin Seikh ., Phys.Rev.B

et al

., Solid State Commun. S.R.Hassan, A.Georges (2005)

et al

58

, 12789 (1998)

138

., Phys.Rev.Lett.

94

, 466 (2006) , 036402

Ultrafast Dynamic Imaging of Matter II, Ischia 2009

Experimental Setup Synchronous detection: lock-in amplifier 0.1

90 Amplitude Phase Laser Sample Reference  /2 P L2 PD1 chopper L1 delay line

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 Cr x ) 2 O 3

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

métal 200K isolant 300K Ag -2.0

-1.5

-1.0

-0.5

binding energy (eV) 0.0

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 photoemission experiments.

in In agrement with the disapearrance of the coherent acoustic wave in the metallic phase of the same 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 electronic density Excitation of coherent phonons Variation of electron-phonon collision rate Variation of the dieletric function 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 D t

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:   1  w 2 w  n 2

p e

2 

ph



i

w 2 w

p

2  n

e

2 

ph

n

e



ph

w  

r



i



i

w p being the plasma frequency: w 2

p

 4 

e

2

n e m

*

e

(

t

) and n e-ph is the electron-phonon collision frequency: n

e



ph



n ph

(

t

)

q

2 (

t

)

v e

Where v e is electron velocity, n ph displacement.

is phonon density and q is the atomic

Ultrafast Dynamic Imaging of Matter II, Ischia 2009

The reflectivity is always given by Fresnel equations:

R

   1 / 2 1 / 2  1  1 2 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: D

R

   

R

 

r

  

n e r

 

R

 

i

  

n e i

  D

n e

 

R

 

r

  n 

e



r ph

 

R

 

i

 n  

i e



ph

D n

e



ph

If we know the expression of dielectric function, we can get the derivatives with respect to n e and n e-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: D

n e

(

t

) 

n e

D

T e

(

t

)

T e

max The excited phonon density is proportional to the lattice temperature, Debye temperature and atomic density as:

n ph

(

t

) 

T l

(

T D t

)

n a

So for the electron-phonon collision rate: D n n

e



e

0 

ph

(

t

)

ph

 D

T l

(

t

)

T

0  2 D

q

(

t

)

q

0

Ultrafast Dynamic Imaging of Matter II, Ischia 2009

Finally, the electronic and lattice temperatures can be given by the Two-Temperature Model equations:

C e



T e



t

 2

l s A I

(

t

)   

z

   

e



T e



z

   

g



T e



T l



C l



T l



t



g



T e



T l

 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: D

R



A e T e

(

t

) 

A l T l

(

t

) 

A ph

cos  w 0 2   2

t



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 q phonon = 2 n k sonde cos q i q i probe Sample Sound velocity: w = v s q Final expression for the transient reflectivity: D

R

(

t

) 

A ac

cos 4 

nv s

cos 

sonde

q

i t

 

e

 

t

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

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) 

Ultrafast Dynamic Imaging of Matter II, Ischia 2009