2010 06 10 Aussois Optics Lobo.ppt [Mode de …gdr-mico.cnrs.fr/UserFiles/file/Ecole/lobo_mico.pdfA...
Transcript of 2010 06 10 Aussois Optics Lobo.ppt [Mode de …gdr-mico.cnrs.fr/UserFiles/file/Ecole/lobo_mico.pdfA...
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Conductivité OptiqueConductivité Optique
Ricardo Lobocar LÉcole Supérieure de Physique et Chimie Industrielles
de la Ville de Paris
[email protected]@espci.fr
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Nichols, Phys. Rev. 1, 1 (1893)., y , ( )
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A few optical excitations in solidsA few optical excitations in solids
~ 2 cm-1 10 000 cm-1 20 000 cm-1 30 000 cm-1 40 000 cm-11 eV~ 0.25 meV 2 eV 3 eV 4 eV 5 eV
~ 5 mm 1 m 500 nm 250 nm333 nmSuperconducting gap
Plasmon SemiconductorsPhonons
Molecular Vibrations (biology and chemistry)Molecular Vibrations (biology and chemistry)
Density-wave gapPolarons
Gap Semiconductors
Density-wave gap
Plasmon oxidesGap Semiconductors
Oxides Charge TransferPlasmon metals
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OutlineOutline
The basics of optical conductivityThe optical conductivity of metalsp y fThe f-sum rule and gapsFermi liquid signaturesFermi liquid signaturesKinetic energyPh s d h s t siti sPhonons and phase transitionsDisordered Materials
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Preview: YBCO from an insulator to a conductorPreview: YBCO from an insulator to a conductor
1.0O7 - conducteur
0.8vi
tyO7 con uct ur
0 4
0.6
flec
tiv
0.2
0.4
Re
O6 - isolant
100 1000 100000.0
0.2
100 1000 10000
Frequency (cm-1)
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Optical C d i i
Optical C d i iConductivity
B ildi BlConductivity
B ildi BlBuilding Blocs Building Blocs
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Light scatteringLight scatteringSource
Black Box
Detector
Optical conductivityPhoton in Photon out
Detector
Optical conductivityHence the misnomer "center of zone" technique
B tt " t d" t h iBetter name: "momentum averaged" technique
Elastic light scattering
The interaction with the electric field dominates
Broadband (whitelight) spectroscopy
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Maxwell Equations – The Message in the "Photon Out"
Maxwell Equations – The Message in the "Photon Out"
I Maxwell Equations in matter In vacuum
Wave with speed "c"
In matter
Ohm's law
In matter
Wave with renormalized speedPlane wave
Wave with renormalized speed
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The common optical functionsThe common optical functions
Refraction index: light propagation and tt tiattenuation
Dielectric function: microscopic polarizability
Optical conductivity: high-frequency electrical transport
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Inside the Black Box – Fourier Transform Spectroscopy
Inside the Black Box – Fourier Transform Spectroscopy
Fixed mirror
Moving mirrorFellgett advantageMultiplex
Jacquinot advantageSlitless spectrometer
Nyquist theoremDiscrete FT is fine
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A Strange Choice for UnitsA Strange Choice for Units
W b 1/ 2 / 1Wavenumber = 1/ = 2c/ cm-1
Energy E = h = hcgy1 eV ~ 8000 cm-1
Wavelength = 1/Wavelength = 1/1 µm = 10000 cm-1
Temperature T = hc/kB10000 K ~ 7000 cm-1
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What else is in the black box?What else is in the black box?
I()
TR
R(ω) and T(ω) ~ |E|2
are real functions.R
Reflected Power (Real)
Kramers-Kronig, simulation; fit; R & T inversion... Other techniques using the same process:
Complex Optical Function
the same process:EllipsometryMach-ZehnderCoherent THzCoherent THz
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Kramers-Kronig relations & the ReflectivityKramers-Kronig relations & the Reflectivity
Cauchy theorem0
Hilbert transform
Kramers-KronigCausality:Causality:
Reflectivity:
But we need R() at all energies
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The optical The optical conductivity in conductivity in
metals metals
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Drude ModelDrude Model
Free electron gas
No electron-electron interactionsNo electron electron nteract ons
No electron-phonon interactions
Scattering through elastic collisions
Drude, Ann. Physik 306, 566 (1900)
Drude Modelg g
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Drude in lightly doped SiDrude in lightly doped Si
R Re 1 Hole dopedn ~ 10-15 cm-3
Electron doped
Im 1
n ~ 4 x 10-14 cm-3
Im 1
Dressel and Scheffler, Ann. Phys. 15, 535 (2006)
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Transparent conducting oxidesTransparent conducting oxides
0.8
1.0CdO
mis
sion
0 4
0.6
& Tr
ansm
0.2
0.4
efle
ctiv
ity &
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.50.0R
e
Energy (eV)
Keep n small (tweak materials) Increase (improve materials) Increase (improve materials) Play with m* (create materials)
Metz et al., JACS 126, 8477 (2004), , ( )
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Drude in metals (Silver)Drude in metals (Silver)
1.0
0.8
30000
35000
40000
0.6
efle
ctiv
ity
20000
25000
30000
-1 c
m-1]
0.4Re
0 2 5000
10000
15000
1 [
S. Biermann
0 0
0.2
0 2000 4000 6000 80000
5000
Frequency [cm-1]0
0.010000 20000 30000
Frequency [cm-1]
Frequency [cm ]
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But Drude fails in correlated matter…But Drude fails in correlated matter…
8000
60001/DC
4000cm-1)
2000 1 (
-1
YBCO – 100 K
0
Drude
0 500 1000 1500 2000 2500 30000
Fréquence (cm-1)
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Ignoring the elephantIgnoring the elephant
3500.0 0.1 0.2 0.3
500
Energy [eV]
200
250
300
300
400
2000
3000m
-1]
Bi2Sr2CaCu2O8
T = 100 K
m-1]
cm-1]
50
100
150
100
200
1000
1 [-1 c
m
[
-1 c
m
1/
[c
0 50 100 150 200 250 3000
50
00 1000 2000 3000
0
Frequency [cm-1] Temperature [K]
Coherent peak described by Drude
Mid IR response
The Drude temperature dependent scattering rate
Quijada et al PRB 60 14917 (1999)
Mid-IR response simulated as Lorentz oscillators
follows the resistivity
Quijada et al., PRB 60, 14917 (1999)
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The optical conductivity and multiband pnictidesThe optical conductivity and multiband pnictides
0 00 0 25 0 50 0 75 1 00
Energy [eV]
60000.00 0.25 0.50 0.75 1.00
Ag (divided by 100)Bi2212 (Quijada et al)
4000Bi2212 (Quijada et. al) Ba(Fe,Co)2As2
cm-1]
2000
1 [
-10 2000 4000 6000 8000
0
Frequency [cm-1]
Singh, PRB (2008).
Frequency [cm ]
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Multiband – pnictides DresselMultiband – pnictides Dressel
Using two Drude terms [two bands (??)] solves the problems
Wu et al., PRB 81, 100512 (2010)
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Can we take a look at the elephant?Can we take a look at the elephant?
8000
60001/DC
4000cm-1)
2000 1 (
-1
YBCO – 100 K
0
Drude
0 500 1000 1500 2000 2500 30000
Fréquence (cm-1)
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Patching the Drude ModelPatching the Drude ModelDrude, Ann. Physik 306, 566 (1900)
Allen, PRB 3, 305 (1971)
Drude Model Extended Drude Model
S tt i t MassScattering rate Massenhancement
"Optical self-energy"Optical self energy
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Is this extended Drude mambo-jambo of any use?Is this extended Drude mambo-jambo of any use?
0 00 0 25 0 50 0 75 1 000 00 0 05 0 10 0 15 0 20
Energy [eV]Energy [eV]
30.00 0.25 0.50 0.75 1.000.00 0.05 0.10 0.15 0.20
1000
Bi2212 - 300 Knon Fermi liquid (ω)
Correlations
1
2
500m-1]
Bi2212 300 K
= 1
+ YBCO 100 K
0
1500
1/
[cm
Cr - 320 K
m /
m* =
Fermi liquid (ω2)
Free electron
0 2000 4000 6000 8000-1
0 500 1000 1500 20000
Fermi liquid (ω )Interband
Frequency [cm-1] Frequency [cm-1]
Basov et al., PRB 65, 054516 (2002) Puchkov et al., JPCM 8, 10049 (1996)Basov et al., PRB 65, 054516 (2002) Puchkov et al., JPCM 8, 10049 (1996)
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One of the multiple versions of the cuprates phase diagram
One of the multiple versions of the cuprates phase diagram
TW i d t lW i d m t l
TW i d t lW i d m t l
PsPs
Weird metalWeird metal
PsPs
Weird metalWeird metal
“F i h”t
ins.
tt in
s.
Pseudoga
Pseudoga “F i h”t
ins.
tt in
s.
Pseudoga
Pseudoga “Fermish”liquid
“Fermish”liquidM
otM
ot
gapgap “Fermish”
liquid“Fermish”
liquidMot
Mot
gapgap
SCSCAFAF SCSCSCSCSCSCAFAF
Hole concentrationHole concentration
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From a Nodal Metal to a Bad Metal to a Fermi Liquid
From a Nodal Metal to a Bad Metal to a Fermi Liquid
1/: Fermi liquidness increases with doping
T
ins.
ins.
Pseudo
Pseudo
Weird metalWeird metalT
ins.
ins.
Pseudo
Pseudo
Weird metalWeird metal
Hwang, Nature 427, 714 (2004)
m*: Correlations decrease with increasing dopingSCSC
“Fermish”liquid
“Fermish”liquid
AFAF
Mot
t M
ott
dogapdogap
SCSCSCSCSCSC
“Fermish”liquid
“Fermish”liquid
AFAF
Mot
t M
ott
dogapdogap
Ma, PRB 73, 144503 (2006). Hole concentrationHole concentration
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Heavy Fermions and LF DrudeHeavy Fermions and LF Drude
300 neV 3 µeV 30 µeV
UPd2Al3
Awasthiet al. PRB 48, 10692 (1993).
Mass enhancement leads to scattering rate decrease
Dressel and Scheffler, Ann. Phys. 15, 535 (2006), ( )
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Gaps andGaps andGaps and the sum rule
Gaps and the sum rulethe sum rule the sum rule
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The Optical Conductivity Sum RuleThe Optical Conductivity Sum Rule
Sum rule
1() 1()
nedT2
)(
Sum rule
mdT
0 1 2),(
Fréquence (cm-1) 0 Fréquence (cm-1) 0 q ( )q ( )
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The charge transfer gap of (La,Sr)2CuO4The charge transfer gap of (La,Sr)2CuO4
Uchida et al. PRB 43, 7942 (1991).
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Density-wave like gapDensity-wave like gap
P4W14O50
CDW transition at T~140 K
CDW 1400 1 CDW gap at 1400 cm-1
Spectral weight transfer from low to high frequencies from low to h gh frequenc es
Zh l PRB 65 214519 (2002)Zhu et al., PRB 65, 214519 (2002)
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Hidden order in URu2Si2Hidden order in URu2Si2
Phase transition at 17K to an Phase transition at 17K to an unknown order parameter
Possible renormalization of th b d t tthe band structure
Order closely related to magnetismg
Gap opening at the Fermi surface
Bonn, PRL 61, 1305 (1988)E h d k h h Even when we do not know what the crap is the gap, it still creates a spectral weight transfer
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And let's go superconductingAnd let's go superconducting
0 5 10 15 20
Energy [meV]
15NbN18 K
103
-1 c
m-1]
5
1 [x10
9 K
0 50 100 1500
Frequency [cm-1]
Is the sum rule violated???
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Superconducting gap – Back to DrudeSuperconducting gap – Back to Drude
Area transfered toth ( ) functi n
1.0
b.)
the () function = 0 not accessible
to optics
The "Lost area" 0.6
0.8
vity
(arb
The Lost area gives superfluid density
0 2
0.4
Con
duct
iv
1/
0 5 10 150.0
0.2C
Energy / 2 Energy /
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Manifestation of the superconducting gap in the infrared
Manifestation of the superconducting gap in the infrared
s-wave (Pr,Ce)2CuO4 - Tc = 21 KZimmers et al., PRB 70, 132502 (2004)
d-wave
NbN – Tc = 16.5 KSomal et al., PRL 76, 1525 (1996)
Mazin, Nature 464, 183 (2010).s-multiband
Pnictides:s ? d? Multiband?
MgB2 – Tc = 39 KPerucchi et al., PRL 89, 097001 (2002).
s±? d? Multiband?Extended s?
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The gap in the cupratesThe gap in the cuprates
Tc changes by a factor 3 and the thing that looks like the gap stays put ?!?!?!?!
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Clean and DirtyClean and Dirty
Clean superconductor
0 75
1.00N
0.50
0.75
dc NS
In a clean superconductor you do
0.25
1 /
SN
In a clean superconductor you do not see the gap because there is no optical conductivity left at that frequency
0 2 4 60.00
SS
Nq y
The important feature in the optical conductivity is the determination of the superfluid
Energy / determination of the superfluid density.
The gap is a bonus!!!
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The gap in the cupratesThe gap in the cuprates
Tc changes by a factor 3 and the thing that looks like the gap stays put ?!?!?!?!Yep! Cause it ain't the gap, stupid!!
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Pnictides Gap ReviewPnictides Gap Review
Claim: 2 gap BCS H t l Xi 0912 0636 1van Heuman et al., arXiv:0912.0636v1
Claim: Good agreement with s-wave BCSGorshunov et al., PRB 81, 060509 (2010)
Claim: 3 gap BCSKim et al., arXiv:0912.0140
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s ± gap: Interband scattering is pair breakings± gap: Interband scattering is pair breaking
Interband scattering annihilates Cooper pairsp p
Residual Drude peak in the superconducting state
Lobo et al (2010)Lobo et al. (2010)
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The infamous The infamous cuprate
dcuprate
dpseudogap pseudogap
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The pseudogapThe pseudogapT
. PsPs
Weird metalWeird metalT
. PsPs
Weird metalWeird metal
“Fermish”liquid
“Fermish”liquidM
ott
ins.
Mot
t in
s .
Pseudogap
Pseudogap “Fermish”liquid
“Fermish”liquidM
ott
ins.
Mot
t in
s .
Pseudogap
Pseudogap
SCSC
Hole concentration
liquidliquidAFAF SCSCSCSCSCSC
Hole concentration
liquidliquidAFAF
Nd2-xCexCuO4Bi-2212
95 K
Alloul, PRL 63, 1700 (1989)Hole concentrationHole concentration
120 K
95 K
Armitage et al PRL 81 257001 (2002) Norman et al. Nature 392, 157 (1998).
180 K
Armitage et al. PRL 81, 257001 (2002). , ( )
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Restricted Spectral Weight or Partial Sum RuleRestricted Spectral Weight or Partial Sum Rule
nedT2
0 1 2),(
Sum rule
m0 2
1() 1()
Restricted spectral i ht
W (T)
[0, 2.5/2 cm-1]W (300K)
weight
1.3
1 15
[ , 2 ]
dTW c
c )(),,0(0 1
1.15
1
0 50 100 150 200 250 300
TempératureFréquence (cm-1) 0 Fréquence (cm-1) 0
c
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The Sum Rule when a Gap OpensThe Sum Rule when a Gap Opens
Ec0 8
1.0
Wei
ght
0.6
0.8
uctiv
ity
Spec
tral
W
0.4Con
du
S
0.0
0.2
Temperature0.0 0.2 0.4 0.6 0.8 1.0
Energy
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(Pr,Ce)2CuO4 - A well behaved normal state (pseudo) gap
(Pr,Ce)2CuO4 - A well behaved normal state (pseudo) gap
Energy [eV]
0.00 0.25 0.50 0.75
3 Pr2-xCexCuO4
Energy [eV]
Partial Sum Rule
2 25 K 300 K
1 ]
1.8
H,3
00K) 0-500 cm-1
0.17
0
1
x 10
3 -1cm
-1
1.4
1.6
/ RSW
(L,
(a)0.15
0
1[x
1.2
W (
L,H,T
) /
0.13
0
0 2000 4000 60000
(b) 0 100 200 300
1.0
RSW
Temperature (K)
Zimmers et al EPL 70 225 (2005)
Wavenumber [cm-1]
Zimmers et al., EPL 70, 225 (2005).
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Bi-2212 – Where is the pseudogap?Bi-2212 – Where is the pseudogap?
6 80 K
Optical conductivity Partial sum rule
T 70 K 7 7
4
6 80 K 150 K 250 K
Tc = 70 K
Bi2Sr2CaCu2O8+δ7.6
7.7
cm
)
Over Tc = 63K Under Tc = 70KOver T = 67K
0
2
3 -1
cm
-1]
2 2 2 8+δ
7.5
ht (
106
.c Over Tc 67K
Under Tc = 66K
1 [103
491 K 143 K 300 K
Tc = 86 K
7.3
7.4
Santander-Syro et al PRL '02ectra
l wei
gh0 500 1000 1500
0
2
50 100 150 200 250 3007.2
Santander Syro et al., PRL 02 Molegraaf et al., Science '02Sp
eT (K)0 500 1000 1500
Frequency (cm-1)
Santander Syro et al PRL 88 097005(2002)
Temperature (K)
Santander-Syro et al., PRL 88, 097005(2002).
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Why the difference?Why the difference?
The ab-plane optical probes mostly the nodal ( ) directions() directions
Bi-221295 K
120 K
95 K
(La,Sr)2CuO4
Armitage et al PRL 81 257001 (2002)
Nd2-xCexCuO4
Norman et al. Nature 392, 157 (1998).
180 K
Armitage et al. PRL 81, 257001 (2002). , ( )
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The pseudogap in the scattering rateThe pseudogap in the scattering rate
2500.0 0.1 0.2 0.3
3
Energy [eV]
200
(b)
K]
Bi2223
1
2
3
300 K(a)
200 K
100
150
pera
ture
[K
Bi22120
0
1
x103 c
m-1]
1
150 K
73 K
50
100
Tem
p
Bi2201
1 /
[x
0
1
20 K
0
1
73 K
0.1 0.2 0.30
Bi2212 - UD - Tc = 67 K
0 1000 2000 30000
1
0
Doping
Lobo et al. (2009)
Frequency [cm-1]
Hwang et al., Nature 427, 714 (2004)
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The pseudogap along the c-axis of YBCO (Tc = 63 K)
The pseudogap along the c-axis of YBCO (Tc = 63 K)
Spectral weight decrease
Knight shift
Homes et al., PRL 71, 1645 (1993).Homes et al., RL 7 , 6 5 ( 993).
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AND NOW FOR SOMETHING AND NOW FOR SOMETHING AND NOW FOR SOMETHING COMPLETELY DIFFERENT
AND NOW FOR SOMETHING COMPLETELY DIFFERENT
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Light and Matter interaction in an Insulator
Light and Matter interaction in an Insulatorin an Insulatorin an Insulator
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Phonons and the Harmonic ApproximationPhonons and the Harmonic Approximation
And for many phonons
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Phonons & the f-sum rulePhonons & the f-sum rule
The f-sum rule (particle conservation):
The f-sum rule for phonons:
The f-sum rule for decoupled phonons:
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Soft Mode & Phase TransitionsSoft Mode & Phase TransitionsQ is a dynamic variable of the system
Order parameter = < Q > = 0, T > Tc 0 T T
Order parameter Q ≠ 0, T < Tc
<Q>Energie libre QgT > Tc
TTc
T ~ Tc
T < Tc
= < Q0 > (paramètre d’ordre)
c
TT
Q (variable dynamique)
TTc
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SrTiO3 – A wannabe ferroelectricSrTiO3 – A wannabe ferroelectric
1001.0
60
80
m-1)
0.6
0.8
vity
20
40
WTO
(1) (
c
0.4
0.6
Ref
lect
i
20 K 180 K 250 K 300 K
0 50 100 150 200 250 3000
20W
Temperature0 200 400 600 800
0.0
0.2
F ( -1) TemperatureFrequency (cm )
Incipient soft mode driven f l ferroelectric transition
TC ~ -15 K
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Soft mode and FerroelectricsSoft mode and Ferroelectrics
BaTiO3100
Vogt et al, PRB 1982.
m-1)
50
(c
m
Merz, PR 91, 513 (1953)0300 500 700300 500 700
T(K)
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The Multiferroic Materials TotemThe Multiferroic Materials Totem
Coexistence of at least two ferroic orders [ferromagnetic,
P
ferroelectric, ferroelastic, ferrotoroidal (??)] *
P
F l t iMagnetoelectricsPiezoelectrics
Schmid, Ferroelectrics 162, 317 (1994).
Ferroelectric
FerromagneticFerroelastic
Magnetostriction
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Magneto-electric MultiferroicsMagneto-electric MultiferroicsEerenstein et al., Nature 442, 759 (2006).
Multiferroics
FM FEMagnetoelectricsMagnetoelectric
Magnetict i l
Electricl
Multiferroics(Control of either
polarization materials materials
pby either field)
*antiferromagnets also accepted.
Small coupling – 4 state memory Large coupling – “E” write / “M” read
also accepted.
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Ying & YangYing & YangFerroelectricity & Magnetism coexist
Magnetism causes Ferroelectricity
BiFeO3Large moments High temperature transitions
TbMnO3Small momentsLow temperaturesHigh temperature transitions
Weak couplingmp
Strong coupling
Lebeugle et al. APL 2007 Kimura, Nature 2003
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Yang (TbMnO3) is more fun!Yang (TbMnO3) is more fun!
Kimura Nature 2003Kimura, Nature 2003.
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TbMnO3 Phonon Spectra (T = 5 K)TbMnO3 Phonon Spectra (T = 5 K)
0.8
1.0
115
116
117
E // a
0.4
0.6
112
113
114
204
cm-1)
0.0
0.2
vity
E // a
0.4201
202
203
est T
O m
ode
(c
E // b
Ref
lect
iv
0 0
0.2
E // b199
200
201
eque
ncy
of lo
we
168
0.0
0.2
0.4
E // c
Fre
165
166
167
168
0 200 400 600 800 10000.0
Frequency (cm-1)
E // c
0 50 100 150 200 250 300
164
165
Temperature (K)
E // c
q y ( )
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So, where is the action?So, where is the action?
Pimenov et al., Nat. Phys, 2006.
M ti it ti
Senff et al. PRL 2007
Magnetic excitation
Activated by electric field of light only
Suppressed by an external magnetic field Suppressed by an external magnetic field
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Magnons and PhononsMagnons and Phonons
Stronger electromagnon at 60 cm-1 coupled to phonon at 110 cm-1
Takahashi et al PRL 101 187201 (2008)
Stronger electromagnon at 60 cm coupled to phonon at 110 cm
Takahashi et al. PRL 101, 187201 (2008)
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Phonon and magnon optical responsePhonon and magnon optical response
1 0 0 6
0.8
1.0
TbMnO3 E // a
0 4
0.5
0.6
n
50K 25K5K
0.4
0.6
flect
ivity
0.3
0.4
smis
sion 5K
simulation 5K
0.2
Ref
6.5 K 60 K 0.1
0.2
Tran
s
0 50 100 150 200 2500.0
Wavenumber (cm-1)
0 50 100 150 2000.0
Wavenumber (cm-1)( )
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Phonon spectral weigthsPhonon spectral weigths
2 )
100 1 2 3
1 0
K) (
1 cm2
-100
0
0.8
1.0
E // aT = 5K
100
200
T)-W
(60K
4 7 5 86 9
0 4
0.6
efle
ctiv
ity
T 5K
0
100
(T) =
W(T 6 9
0.2
0.4Re
-200
-100
W (
0 200 400 600 800 10000.0
Frequency (cm-1)
0 20 40 60Temperature (K)
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The electromagnon is built from two phononsThe electromagnon is built from two phonons
200
0
100
-1cm
-2)
All phonons MagnonPhonons 1 & 3
200
-100
T)-W
(50K
) ( Phonons 1 & 3
-300
-200
W (T
) = W
(T TNTC
0 10 20 30 40 50 60-500
-400W
0 10 20 30 40 50 60Temperature (K)
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DiSordEredDiSordEredDiSordEred MEdiA
DiSordEred MEdiAMEdiAMEdiA
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Disorder in (Y,Pr)Ba2Cu3O7Disorder in (Y,Pr)Ba2Cu3O7
8000
(P Y )B C O
4000
6000 (PrxY1-x)Ba2Cu3O7
100 K
)
2000
4000
x = 0 0-1cm
-1
Pr is an underdoping agent
Empties CuO2 planes
0
40 K x = 0 4
x = 0.0
1 ( p p
Localizes charges along chains
0
040 K
50 K
x 0.4
x = 0.50 500 1000 1500
0
Frequency (cm-1)Lobo et al. PRB 65, 104509 (2002).
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Effective Medium TheoriesEffective Medium Theories
Gold evaporated onto hot (600K)
hi b t tsapphire substrates
Cranberry glass (Ruby gold glass)Cranberry glass (Ruby gold glass)
Maxwell-Garnett Theory
insul.
metal
J. C. Maxwell Garnett, Colours in Metal Glasses and in Metallic Films Philos Trans R Soc 203 385 (1904) Metallic Films, Philos. Trans. R. Soc. 203, 385 (1904).
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Superconducting MoGe: Field Dependent Transmission
Superconducting MoGe: Field Dependent TransmissionTransmissionTransmission
2.0
K)
Far IR
1.5
K,H
)/T(8
B
1.0atio
T(3
K
0 5ssio
n R
a
0 T 6 T 1 T 7 T 2 T 8 T3 T 9 T0.5
Tran
smi 3 T 9 T
4 T 10 T 5 T
10 20 30 400.0
T
Frequency [cm-1]Frequency [cm ]
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S d t2.5
Br ggeman
Effective Medium Models for a Superconductor with Vortices
Effective Medium Models for a Superconductor with Vortices
1.5
2.0
Superconductor& Normal metalin parallel
o T S(
f)/T N
1 5
2.0
BruggemanEffective MediumApproximation
T S(f)/T
N
0.5
1.0
Tran
smis
sion
Rat
io
= f +(1 f ) 1.0
1.5
smis
sion
Rat
io
10 20 300.0
0.5T
Frequency [cm-1]
= f N+(1-f ) S
0 10 20 300.0
0.5
Tran
s
super
normal
Frequency [cm-1]
2.0
2.5Garnett TheoryNormal withSuperconductinginclusions
f)/T N
1.0
1.5
mis
sion
Rat
io T
S(f
0 10 20 300.0
0.5Tran
sm super
normal
Frequency [cm-1]
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Effective Medium Models for a Superconductor with Vortices
Effective Medium Models for a Superconductor with Vortices
2.5
Garnett TheorySuperconductor
/ N l i l i2.0 w/ Normal inclusionsT S(
f)/T N
1.5
on R
atio
T
1.0
ansm
issi
o
super0.5Tr
a super
normal
10 20 300.0
Frequency [cm-1]Frequency [cm ]
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SummarySummary1 01 0
0.6
0.8
1.0
ctiv
ity
O7 - conducteur
0.6
0.8
1.0
ctiv
ity
O7 - conducteur Optics is mostly an electrical measurement
Momentum averaged technique 0.2
0.4
Refl
ec
O6 - isolant0.2
0.4
Refl
ec
O6 - isolant
measurement
100 1000 100000.0
Frequency (cm-1)
100 1000 100000.0
Frequency (cm-1)
The optical conductivity specgtral weight is always conservedalways conserved
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RappelsRappels
Technique moyennée en impulsionq y pMesure de la conductivité électrique aux hautes
fréquencesf q Pic à fréquence nulle = charge mobile Pic à fréquence finie charge localisée Pic à fréquence finie = charge localiséeAccès aux états électroniques et à leur distribution
é ien énergieRègle de somme de la conductivité