ULTRAFAST DYNAMICAL RESPONSE OF THE PROTOTYPE MOTT COMPOUND V 2 O 3 B. Mansart 1, D. Boschetto 2 and...

ULTRAFAST DYNAMICAL RESPONSE OF THE PROTOTYPE MOTT COMPOUND V2O3

B. Mansart1,

D. Boschetto2 and M. Marsi1

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

Ultrafast Dynamic Imaging of Matter II, Ischia 2009

Phase diagram and Mott transition in (V1-xCrx)2O3

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)


Time-resolved reflectivity on V2O3

wavelength: 800 nmpulse duration: 45 fsrepetition rate 1 kHzPump and probe polarizations orthogonal



wavelength: 800 nmpulse duration: 45 fsrepetition rate 1 kHz



1. Ultrafast peak: electronic excitation






2. Coherent Optical A1g Phonon





2. Coherent Optical A1g Phonon

3. Coherent Acoustic wave propagation


Ultrafast electronic excitation

Electronic peak represents the ultrafast excitation and relaxation of electrons.


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.


In V2O3 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


Relaxation of hot electrons: Two Temperatures Model (TTM).


LEL

L TTgt

TC

LEE

Es

EE TTg

z

T

ztI

l

A

t

TC

)(2




LEL

L TTgt

TC

LEE

Es

EE TTg

z

T

ztI

l

A

t

TC

)(2





LEL

L TTgt

TC

LEE

Es

EE TTg

z

T

ztI

l

A

t

TC

)(2

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 V2O3 compounds, the thermalisation time depends on pump fluence. It is ~130 fs: faster than normal metals and others strongly correlated materials.



Optical phonon: pump fluence study


V

V


A1g

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 V2O3.(Misochko et al., PRB 58, (1998)).


V

V


A1g

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 V2O3.(Misochko et al., PRB 58, (1998)).


Coherent Acoustic Wave: sample orientation effect

hexagonal c-axis

V

O o Experimental geometry and c-axis orientation

Acoustic wave detection by Brillouin scattering: qphonon = 2 n kprobe cos i

We only detect the acoustic wave propagating along the incident plane symmetry axis.


Coherent Acoustic Wave: sample orientation effect

hexagonal c-axis

V

O o Experimental geometry and c-axis orientation

Acoustic wave detection by Brillouin scattering: qphonon = 2 n kprobe 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.


Acoustic wave: Thermodynamic phase effects

Insulating phase (PI) Metallic phase (PM)

PM

PI




PM

PI

Coherent acoustic oscillation intensity linear in pump fluence, identical in metal and insulator.

The lifetime is longer in the Insulating phase.




PM

PI

Strong effects of the thermodynamic phase (metal vs insulator) on the mean value (baseline) of the coherent oscillation.


Conclusions and perspectives

We measured the ultrafast response of the prototype Mott compound V2O3.

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.


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 V2O3:

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)


Synchronous detection:lock-in amplifier

LaserLaser

ReferenceReference

pumppump

probeprobe

delay linedelay linechopper

Sample

PD1PD1

PP

L1L1

L2L2

/2/20.1 90

Amplitude Phase

Experimental Setup


N.Kuroda and H.Y.Fan, Phys.Rev.B 16, 5003 (1977)

Raman spectrum of V2O3


Reflectivity of V2O3

L. Baldassarre et al., PRB 77, 113107 (2008)


Difference Metal-Insulator: coherent acoustic wave


DMFT calculations for Mott compounds

Georges et al. RMP (1996)


DMFT calculations for (V1-xCrx)2O3


Photoemission experiments on (V1-xCrx)2O3 x=0.011

-2.0 -1.5 -1.0 -0.5 0.0binding energy (eV)

métal 200K isolant 300K Ag

(V1-xCrx)2O3 x=0.011


Spectromicroscopy experiments on (V1-xCrx)2O3 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.


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


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

Sample

detector

pump

probe


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 ve is electron velocity, nph is phonon density and q is the atomic displacement.

ephphe vtqtn )( )( 2

irphe

phe

p

phe

p ii

1

22

2

22

2

*

22 )(4

e

ep m

tne


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 e-ph, and so obtain an analytic expression for the transient reflectivity.

2

2/1

2/1

11

R

phephe

i

iphe

r

re

e

i

ie

r

r

RRn

n

R

n

RR


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:

max

)( )(e

e

e

e

TtT

ntn

a

D

lph n

TtTtn )()(

000

)(2)()(q

tqT

tTt l

phe

phe


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, e the heat diffusivity of electrons and g the electron-phonon coupling constant.

And changes in reflectivity can be written in the form:

lee

es

ee TTg

z

T

ztI

l

A

t

TC

)(2

lel

l TTgt

TC

tAtTAtTAR phllee cos )( )( 220


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))


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)

qphonon = 2 n ksonde cos i

Sound velocity: = vs q

Final expression for the transient reflectivity:t

sonde

isac etnvAtR

cos4cos)(

Sample

detector

probe

i


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


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 DYNAMICAL RESPONSE OF THE PROTOTYPE MOTT COMPOUND V 2 O 3 B. Mansart 1, D. Boschetto 2 and...

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