2139-34

School on Synchrotron and Free-Electron-Laser Sources and their Multidisciplinary Applications

A. Perucchi

26 April - 7 May, 2010

Sincrotrone Trieste ITALY

IR spectroscopy and microscopy in material science Electrodynamics at high pressures of strongly correlated electron systems

IR spectroscopy and microscopy

in material scienceElectrodynamics at high pressures ofstrongly correlated electron systems

A. Perucchi

Outline - Selected applications of IRSR in

solid state physics

• IR light and IR synchrotron radiation• Basics of IR spectroscopy in condensed matter physics

1. From Reflectivity to Optical Conductivity2. The Lorentz-Drude Model

• High-pressure measurements• Strongly Correlated Electron Systems

1. Pressure-Induced Insulator to Metal Transition in VO2

2. The complexity of V2O3

3. Pressure vs Alloying effects in NiS24. Tuning a CDW instability in RE dichalchogenides

Electromagnetic Spectrum

FIR MIR NIR

Phonons; Drude absorption;

Gaps in superconductors;Molecular Rotations

Molecular Vibrations (“Fingerprints”);

Electronic excitations(polarons, CDW gaps,

d-bands)

Molecular Overtones andCombinations bands;

Excitons;Gaps in semiconductors

The “Terahertz gap”, Collective Excitations inMacromolecules and exotic electronic materials

IR Units: 200 cm-1=300 K= 25 meV = 50 μm = 7 THz

Advantages of IRSR

Brightness gain

•Small samples•Extreme experimental conditions(high pressure, high magnetic field)•Spatial resolution (microscopy)

Flux gain in the THz range

• � 10 with incoherent IRSR• > 104 with coherent IRSR (CSR) lecture by S. Lupi on May 7

Pulsed structure •Time resolved spectroscopy (�10 ps)•Pump-probe

Basics of infrared spectroscopy in

condensed matter physics

Refractive index and Optical constants

N~

= n + ik

Complex refractive index

Real refractive index(Snell’s law, dispersion)

Extinction coefficient(absorption)

N~

= �~

(�)�1 = n2 � k 2,

�2 = 2nk

�~

= i�

4�(1��

~

)�1 =

��2

4�,

� 2 = (1��1)�

4�

Complex dielectric constant

Complex optical conductivity

Absorbance, Optical Density and

the Lambert-Beer’s law

I0 Ik

A = �logI

I0

�

� �

�

�

Op.D.= �lnI

I0

�

� �

�

�

I = I0 exp(��d)

� =Op.D.

d = 2k�c

d

Optical Reflectivity

R(�) =Is(�)

I0(�)

R(�) = r(�)~ 2

=(n �1)2 + k 2

(n +1)2 + k 2

2

2

From Maxwell to Fresnel equations

By normal incidence

r~

=� N

~

� N~

� N ~

+ N~

Sample

Reference (Au, Al, Ag, … )

… and at vacuum interface

Kramers-Kronig Transformations

r~

(�) = R(�) exp i� (�)[ ] �(�) = ln r~

(�)�

� �

�

� � = ln R(�) + i (�)

� (�) = �2�

�P

ln R( � � )� � 2 �� 2 d � �

0

�

�

Following causality principle, the real and imaginary part of any linear responsefunction are univocally determined through Kramers-Kronig Transformations

To this aim one should measure R(�) over the broadest energy range:Extrapolation procedures are also used both at high and low frequencies

The Lorentz-Drude model

d2x

dt 2 + �dx

dt+ �0

2x = �e

mEloc,

r P e = �e

r r =�(�)

r E loc,

�(�) =e2 /m

�02�� 2 � i��

r D = �

r E =

r E + 4�

r P =

r E + 4�N

r P e = (1+ 4�N�)

r E

�(�) =1+ 4�N�(�) =1+4�Ne2

m

1

(�02 �� 2) � i��

�(�) =e2 /m

�02�� 2

r D = �

rE� =

r E + 4�

rP � =

r E + 4

�(�) =1+ 4�N�� �N (�) =1+4

�(�) =1�� pD

2

� 2 + i�D�+

4�N je2

m

1

(� j2�� 2) � i� j�j

�

Diamond Anvil Cell (DAC)

Force

Diamond

Gasket

Sample

Sample size<100 micron

T=IT / I0Op.D. = -ln(T) = �d

Rdia/sam=IR / I0

Infrared measurements at high pressure

Transmission Measurement:Op.D= - ln (I/I0)Since I=I0 exp(-� d) one has Op.D= � dDetermination of the absorption coefficient

Reflectivity Measurement:

With nd=2.43 being the diamond refractive index

Rsd =(n + ik) � nd

(n + ik) + nd

2

Rsd =

1 measured quantity

(n ++ ik)

2 optical constantsto be determined

1 measured quantity

2 optical constantsto be determined

Infrared spectroscopy is a bulk, contactless technique which probesboth electronic and phononic excitations over a broad energy range

The full determination of the optical constants can be achieved through:• Simultaneous measurement of R and T• Lorentz-Drude fitting• Kramers-Kronig Transformations

Electrodynamics at high pressures of

strongly correlated electron systems

Band insulators

EF

EFEgap

Conduction band Conduction band

Valence bandValence band

Metal Insulator

The band theory is properly defined in the one-electron approximation,i.e. when W is much larger than other electronic energy scales

W >> U,e � ph

W

Mott-Hubbard insulators

U prevents double on-site occupancy.

the opening of a gap in the

spectra of excitations is induced

Electron-electron interaction and insulator to

metal transition (MIT)

Electronic correlation: failure of band modelHubbard model

Pressure may increase the W/U ratio inducing a MIT

W: bandwidth or kinetic energy (strongly dependent on atomic distances)

U : coulomb repulsion

Strongly correlated electron systems

Cuprates

Manganites

FeSe

Mott insulators (V203, Bechgaard salts, NiS2)

P-Induced Insulator to Metal Transition in

Vanadium Dioxide - VO2

The metal-insulator transition in VO2

Insulatordimers along c

High Pressure may disentangle the two mechanismsChosen techniques: IR and Raman

so to monitor independently electronic and structural changes

Strong Interplay between electron-lattice and electron-electron interactionsDriving MIT mechanism Hubbard or Peierls?

M.M. Qazilbash et al, PRB 2007

Metal T-dependent MIT at TMIT= 340 KConcomitant lattice modification

from a low-T monoclinic (M1)phase to a high-T rutile (R) phase.

Both phases are non-magnetic

P-dependent reflectance and transmittance of VO2

Simultaneous measurements of reflectance andtransmittance at 300 K in the M1 monoclinic

insulating phase on a thin VO2 sampleKBr pellet

VO2 slab

E. Arcangeletti et al, PRL 98, 196406 (2007)

Onset Onset of aof ametallization processmetallization process

around around 10 10 GPaGPa

Main questionMain question::is is the the metallization processmetallization processassociated to associated to a (M1-->R)a (M1-->R)

symmetry changesymmetry change??

Optical conductivity of VO2 under high pressure

0 1500 3000 4500 60000

50

100

150

200

250

0

50

100

150

200

� (cm-1)

0.5 GPa

2.8 GPa

6.4 GPa

9,2 GPa

10.7 GPa

13.1GPa

14.4 GPa

� 1 (�

-1

cm-

1

)

0.2 GPa

4.6 GPa

5.9 GPa

10.1 GPa

11.9 GPa

12.9 GPa

13.9 GPa

0.5 GPa

14.4 GPa

11.9 GPa

13.9 GPa

10.1 GPa

� 1 (�

-1

cm-

1

)

0.2 GPa

9.2 GPa

o o o

•Different extent of Peierls distortion•Negligible effects on electronic properties at P=0

•• Structural transition Structural transition and MITand MITdecoupled decoupled at high at high pressurepressure

••Weakened relevance Weakened relevance of of PeierlsPeierlsdistortion distortion in in leading leading the MIT inthe MIT infavours favours of of electronic correlationelectronic correlation

•• Strong impact on Strong impact on theoretical modelstheoretical modelsCr=0.7% Cr=2.5%pristine

Raman spectroscopy on VO2

Raman spectroscopy on VO2 under high pressure

Metallization process in a new Mxmonoclinic structure

Insulator to metal transition and monoclinic to rutile transition aredecoupled at high pressure

Electron correlation is the main localizationmechanism (at least at high-P) in VO2

T

P

E. Arcangeletti et al, PRL98, 196406 (2007)C. Marini et al, PRB 2008

The complex phase diagram of

Vanadium Sesquioxide - V2O3

Vanadium Sesquioxide - V2O3

Pressure vs Alloying effects in

Nickel Disulfide - NiS2

Cubic structure

� = �0 + A �T 2

Simple cubic structureHomogeneous NiS2-xSex solution

No structural transition!Charge Transfer Insulator

Se increases bandwidth while expanding the lattice!Surprising similarities in the T-x, T-P phase diagrams

NiS2insulator

NiSe2metal

Ni pyrite and its Se alloys NiS2-xSex

S.Miyasaka et al, J. Phys. Soc. Jpn. 69, 3166 (2000)

Coherent vs Incoherent excitations in NiS2-xSex

Mott-Hubbard

Charge Transfer

Bandwidth vs CT controlled transition

Two different MITs:1) under pressure, W /� = const. and W /Udecreases, triggering the MIT;2) Se alloying: W /U = const. whereas W /�increases inducing the MIT;

Tuning a CDW instability in Rare-Earth

Dichalchogenides

Nesting wavevectors and the Peierls transition

Hydrostatic pressure vs. chemical pressure

A. Sacchetti et al., PRL 98, 026401 (2007)

With increasing P, R(�)increases between 2000and 5000 cm-1

The same kind of behavior isobserved by applying chemicalpressure (substitution of theRare Earth ion).

Optical conductivity

A. Sacchetti et al., PRL 98, 026401 (2007)

The optical conductivity isrecovered through a fitting ofthe reflectivity data.

It is then possible to give anestimate for the singleparticle-gap energy.

Single-particle gap

A. Sacchetti et al., PRL 98, 026401 (2007)

V (P) = V (0) 1+B'

B0

P�

� �

�

�

�1/ B '

B(P) = B0 + B'P

� = (2� 2 /5)kB (2� � kB /hvs)3

� is known from specific heat

vs= 1923 m/s

B0 = �vs2, �=6873 kg/m3

B0 = 25 GPa

�(P)= �(0)x[V(P)/V(0)]1/3

V (P) = V (0) 1+B'

B0

P�

����

��

�

���

��

�1/ B '

B(P) = B0 + B'P

� = (2� 2 /5)kB (2� � kB /hvs)3

� is known from specific heat

vs= 1923 m/s

B0 = �vs2, �=6873 kg/m3

B0 = 25 GPa

�(P)= �(0)x[V(P)/V(0)]1/3

The high pressure measurement permits to study the evolution of the SP gap asa function of the lattice parameter by using one single sample.

Pressure vs. Alloying

VO2Cr-doping changes structure within the insulating phase but does not affect

electronic properties. Independently on the level of Cr-doping Pressure drives ametallic monoclinic phase

V2O3Besides expanding the lattice, Cr-doping induces phase separation. Pressure drives amore homogeneous metallic phase but does not completely restore the pristine V2O3

homogeneous metallic state. Pressure vs doping scaling does not hold

NiS2Se expands the lattice contrary to Pressure

Se drives metallicity through a reduction of �: merging of Ni-eg and chalchogen pp� bandsPressure increases bandwidth of Ni-eg

CeTe3Pressure and Rare Earth substitution have the same effect on CDW:

Reduced nesting because of increased 3-D character

References

•Review on T- and P-induced MITs on vanadium oxide compounds:Journal of Physics: Condensed Matter 21, 323202 (2009)

•VO2 and Cr-doped VO2:Phys. Rev. Lett. 98, 196406 (2007); Phys. Rev. B 77, 235111 (2008)

• T-dependence of pure V2O3 (Cr-V2O3 still unpublished):Phys. Rev. Lett. 75, 105 (1995); Phys. Rev. B 77, 113107 (2008)

•NiS2 as a function of alloying and pressurePhys. Rev. B 80, 073101 (2009)

•Pressure dependence of RE chalchogenidesPhys. Rev. Lett. 98, 026401 (2007); Phys. Rev. B 77, 165132 (2008);Phys. Rev. B 79, 075117 (2009)

Acknowledgements

P. Calvani and A. Nucara,

IRS Group, University of Rome

“La Sapienza”

M. Ortolani

CNR-IFN

U. Schade

Synchrotron BESSY II Berlin

P. Postorino

HP Group, University of Rome

“La Sapienza”

L. Degiorgi

ETH Zurich

L. Malavasi

Dip. di Chimica, Università di Pavia

M. Marsi

CNRS-LPSU, France

V.A. Sidorov

Institute for High Pressure Physics

Troitsk, Moscow Region Russia

and many others…….

The SISSI@ELETTRA group

L. Baldassarre

G. Birarda

M. Kiskinova

S. Lupi

F. Piccirilli

L. Vaccari