Spectroscopic ellipsometry is a technique for investigating the optical properties and electrodynamics of materials. It has several advantages over other optical techniques:
1) It provides an exact numerical inversion with no need for Kramers-Kronig transformations, allowing consistency checks.
2) Measurements are non-invasive and highly reproducible as they do not require reference samples.
3) It is very sensitive to thin film properties due to its ability to measure at oblique angles of incidence.
Ellipsometry has been used to study phenomena like superconductivity in cuprates and pnictides by measuring changes in spectral weight, and collective charge ordering in oxide superlattices.
We present an ab-initio real-time based computational approach to nonlinear optical properties in Condensed Matter systems. The equation of mot ions, and in particular the coupling of the electrons with the external electric field, are derived from the Berry phase formulation of the dynamical polarization. The zero-field Hamiltonian includes crystal local field effects, the renormalization of the independent particle energy levels by correlation and excitonic effects within the screened Hartree- Fock self-energy operator. The approach is validated by calculating the second-harmonic generation of SiC and AlAs bulk semiconductors : an excellent agreement is obtained with existing ab-initio calculations from response theory in frequency domain . We finally show applications to the second-harmonic generation of CdTe the third-harmonic generation of Si.
Reference :
Real-time approach to the optical properties of solids and nanostructures : Time-dependent Bethe-alpeter equation Phys. Rev. B 84, 245110 (2011)
Nonlinear optics from ab-initio by means of the dynamical Berry-phase
C. Attaccalite and M. Gruning Phys. Rev. B 88 (23), 235113 (2013)
Optical band gap measurement by diffuse reflectance spectroscopy (drs)Sajjad Ullah
Introduction to Optical band gap measurement
by electronic spectroscopy and diffuse reflectance spectroscopy (DRS) with comparison of the results obtained suing different equation and measurement techniques.
The role of scattering in extinction of light as it passes through media is briefly discussed.
Perovskite Solar Cells
a short general overview presentation
hadi maghsoudi
device structure
crystal structure
preparation synthesis method
review papers
We present an ab-initio real-time based computational approach to nonlinear optical properties in Condensed Matter systems. The equation of mot ions, and in particular the coupling of the electrons with the external electric field, are derived from the Berry phase formulation of the dynamical polarization. The zero-field Hamiltonian includes crystal local field effects, the renormalization of the independent particle energy levels by correlation and excitonic effects within the screened Hartree- Fock self-energy operator. The approach is validated by calculating the second-harmonic generation of SiC and AlAs bulk semiconductors : an excellent agreement is obtained with existing ab-initio calculations from response theory in frequency domain . We finally show applications to the second-harmonic generation of CdTe the third-harmonic generation of Si.
Reference :
Real-time approach to the optical properties of solids and nanostructures : Time-dependent Bethe-alpeter equation Phys. Rev. B 84, 245110 (2011)
Nonlinear optics from ab-initio by means of the dynamical Berry-phase
C. Attaccalite and M. Gruning Phys. Rev. B 88 (23), 235113 (2013)
Optical band gap measurement by diffuse reflectance spectroscopy (drs)Sajjad Ullah
Introduction to Optical band gap measurement
by electronic spectroscopy and diffuse reflectance spectroscopy (DRS) with comparison of the results obtained suing different equation and measurement techniques.
The role of scattering in extinction of light as it passes through media is briefly discussed.
Perovskite Solar Cells
a short general overview presentation
hadi maghsoudi
device structure
crystal structure
preparation synthesis method
review papers
Heterostructures, HBTs and Thyristors : Exploring the "different"Shuvan Prashant
This presentation aims at presenting the concepts of heterostructures : a structure resulting from semiconductors of different band gaps are used to form junctions. These junctions could have interesting effects due the potentials formed by the bands at the interfaces.
DPS material
DNG material ( Do not depend on the chemical composition, Depend on the geometry of the structure units, Metamaterials are artificial engineered composite structures, Not commonly found in nature)
MNG material
ENG material
This presentation summarizes history and recent development of perovskite solar cells. If you have any questions or comments, you can reach me at agassifeng@gmail.com
Science Cafe Discovers a New Form of Alternative EnergyEngenuitySC
These are the slides from the May Science Cafe featuring Dr. MVS Chandrashekhar. During this cafe he discussed his work with graphene a new, clean energy source.
Heterostructures, HBTs and Thyristors : Exploring the "different"Shuvan Prashant
This presentation aims at presenting the concepts of heterostructures : a structure resulting from semiconductors of different band gaps are used to form junctions. These junctions could have interesting effects due the potentials formed by the bands at the interfaces.
DPS material
DNG material ( Do not depend on the chemical composition, Depend on the geometry of the structure units, Metamaterials are artificial engineered composite structures, Not commonly found in nature)
MNG material
ENG material
This presentation summarizes history and recent development of perovskite solar cells. If you have any questions or comments, you can reach me at agassifeng@gmail.com
Science Cafe Discovers a New Form of Alternative EnergyEngenuitySC
These are the slides from the May Science Cafe featuring Dr. MVS Chandrashekhar. During this cafe he discussed his work with graphene a new, clean energy source.
Honest Reviews of Tim Han LMA Course Program.pptxtimhan337
Personal development courses are widely available today, with each one promising life-changing outcomes. Tim Han’s Life Mastery Achievers (LMA) Course has drawn a lot of interest. In addition to offering my frank assessment of Success Insider’s LMA Course, this piece examines the course’s effects via a variety of Tim Han LMA course reviews and Success Insider comments.
Synthetic Fiber Construction in lab .pptxPavel ( NSTU)
Synthetic fiber production is a fascinating and complex field that blends chemistry, engineering, and environmental science. By understanding these aspects, students can gain a comprehensive view of synthetic fiber production, its impact on society and the environment, and the potential for future innovations. Synthetic fibers play a crucial role in modern society, impacting various aspects of daily life, industry, and the environment. ynthetic fibers are integral to modern life, offering a range of benefits from cost-effectiveness and versatility to innovative applications and performance characteristics. While they pose environmental challenges, ongoing research and development aim to create more sustainable and eco-friendly alternatives. Understanding the importance of synthetic fibers helps in appreciating their role in the economy, industry, and daily life, while also emphasizing the need for sustainable practices and innovation.
Unit 8 - Information and Communication Technology (Paper I).pdfThiyagu K
This slides describes the basic concepts of ICT, basics of Email, Emerging Technology and Digital Initiatives in Education. This presentations aligns with the UGC Paper I syllabus.
How to Make a Field invisible in Odoo 17Celine George
It is possible to hide or invisible some fields in odoo. Commonly using “invisible” attribute in the field definition to invisible the fields. This slide will show how to make a field invisible in odoo 17.
Acetabularia Information For Class 9 .docxvaibhavrinwa19
Acetabularia acetabulum is a single-celled green alga that in its vegetative state is morphologically differentiated into a basal rhizoid and an axially elongated stalk, which bears whorls of branching hairs. The single diploid nucleus resides in the rhizoid.
Instructions for Submissions thorugh G- Classroom.pptxJheel Barad
This presentation provides a briefing on how to upload submissions and documents in Google Classroom. It was prepared as part of an orientation for new Sainik School in-service teacher trainees. As a training officer, my goal is to ensure that you are comfortable and proficient with this essential tool for managing assignments and fostering student engagement.
The French Revolution, which began in 1789, was a period of radical social and political upheaval in France. It marked the decline of absolute monarchies, the rise of secular and democratic republics, and the eventual rise of Napoleon Bonaparte. This revolutionary period is crucial in understanding the transition from feudalism to modernity in Europe.
For more information, visit-www.vavaclasses.com
Palestine last event orientationfvgnh .pptxRaedMohamed3
An EFL lesson about the current events in Palestine. It is intended to be for intermediate students who wish to increase their listening skills through a short lesson in power point.
1. Alexander BORIS
Max Planck Institute for Solid State Research
Stuttgart
Spectroscopic ellipsometry:
application to electrodynamics
of correlated electron materials
and oxide superlattices.
September 1, 2011, Vancouver
MAX-PLANCK-UBC CENTRE FOR QUANTUM MATERIALS
International Summer School on Surfaces and Interfaces in Correlated Oxides
2. Outline Outline
• the complex dielectic function spectra -
one of the first steps in research of the
physical properties of a new material
• spectroscopic ellipsometry -
basic principles and experimental implementation
• advantages of ellipsometry - illustrative examples -
i) exact numerical inversion, no i) superconductivity-induced
Kramers-Kronig transformation, transfer of the spectral weight in
allows for K-K consistency check high temperature cuprate SCs
ii) no reference measurements, very ii) superconductivity-induced optical
accurate and highly reproducible anomalies and iron pnictide
superconductors
iii) oblique and variable angle of iii) dimensionality-controlled
incidence, very sensitive to collective charge and spin* order
thin-film properties in nickel-oxide superlattices
* combined with low-energy muons which serve as a sensitive
local probe of the internal magnetic field distribution
3. Outline Outline
• the complex dielectic function spectra -
one of the first steps in research of the
physical properties of a new material
6. 4π
Electrodynamics of ∂E
∇× H = j + ε 0ε Solids
Maxwell’s equations for wave c ∂t
propagation in a conductor: ∂H
∇ × E = −µ0
∂t
∂E ∂ 2E
⇒ ∇ × (∇ × E) = −∇ E = − µ0 σ
2
+ ε 0ε 2
∂t ∂t
plane wave : ܧ = ܧ ݁ [(ఠ௧ିk ݔାఋ)] ⇒ k ଶ = ߤ ݅߱ߪ + ߤ ߝ ߝ߱ଶ
4ߨ 1
SI → CGS: ߤ → ଶ , ߝ →
ܿ 4ߨ
ఠమ ସగ ఠ ସగ
k ଶ = ߝ+݅ ߪ , k ≡ N, Nଶ = ߝ + ݅ ߪ
మ ఠ ఠ
Complex dielectric function optical conductivity
ߝ̃ ߱ = ߝଵ (߱) + ݅ ∙ ߝଶ (߱) ߪ ߱ = ߪଵ ߱ + ݅ ∙ ߪଶ (߱)
4ߨ
ߝଶ ߱ = ߪଵ (߱)
߱
7. Dielectric response of Drude metal
dv mb
equation of motion for electrons mb = eE − v
dt τ
damping term
momentum transferred to phonons
and impurities per unit time
eτ 1
solution v= E
mb 1 − iωτ
nb e 2 τ
current density j = nb e v = E
mb 1 − iωτ
σ0 γ = 1/ τ ω pl
2
σ (ω) = ε1 (ω) = 1 − 2 2
1 − iωτ ω +γ
4π nbe2
ne2τ ω pl =
2
ω pl γ 2
2
σ0 = mb σ1 (ω) =
1
mb collective oscillations of 4π γ ω 2 + γ 2
electron charge density
9. Optical sum rules: ∞
Spectral Weight and Sum Rules π ne e 2
f-sum rule: SW (0, ∞) = ∫ σ 1 (ω )dω = = const
0
2me
݊ - total number of electrons in the system, ݉ - free electron mass
D.Y. Smith and E. Shiles,
PRB 17, (1978) 4689-4694
Ω
= 2 Al ∫ σ (ω )dω
2m
neff
πe N 0
Ω
ω pl
2
π nb e 2
intra-band spectral weight: SW intra
(0, ∞) = = = f (T ) ≠ const
8 2mb
13. Analogy with electric circuit electric circuit admittance
Analogy with impedance
Lissajous figure
a b resistance & reactance
(complex impedance)
X Y
Z = R+iωL
R Vmaxsinωt
ϕ Imaxsin(ωt-ϕ)
L Vmax
Imax
ϕ= arctan(ωL/R)=
= arcSin(a/b)
Time
14. Polarization of light Electrodynamics of Solids
ࡱ-field vector ࡱ = ࡱ࢞ + ࡱ࢟
Y
Linear polarization
phase delay ߮=0 X
Y
Curcular polarization
phase delay ߮=ߨ/2
X
Y
Elliptical polarization Ψ
ܧ௫
phase delay ߮=0.35·2ߨ
X
ܧ௬
19. ANKA Synchrotron, Karlsruhebeamline at ANKA
IR IT
IR-1 beamline
Y.-L. Mathis, B. Gasharova, D. Moss
Current: 80 -180 mA
lifetime: 12-23 hours
20. ANKA Synchrotron, Karlsruhebeamline at ANKA
IR IT
IR-1 beamline
Y.-L. Mathis, B. Gasharova, D. Moss
1.5
Magnetic Field [T]
Magnetic profile
1.0
of a dipole
0.5 Edge and dipole
Spatial distribution radiation in the visible
from the edge at
0.0
3 m from the source
(calculated for 100µm) 1.0m 0.5 0.0 -0.5 -1.0
Position on particle trajectory [m]
Photons/s/.1%bw/mm^2 x10
40 150
20
at λ=10 µm
y [mm]
100
0
-20 50
-40mm
9
0
-40mm -20 0 20 40
x [mm]
21. wide-band spectroscopic ellipsometry THz to UV
Ellipsometry: from
ANKA Synchrotron
edge radiation
1m 10m 100m 1 eV 6.2
0.2 THz 1 2
far-IR mid-IR near-IR UV
10 100 1000 10000 cm-1
near-IR to deep-UV
far-IR homebuilt ellipsometer spectroscopic
at ANKA IR1- beam line, ellipsometer (VASE)
@ Karlsruhe IT Woollam Co., @ MPI-FKF
IR homebuilt ellipsometer
based on Bruker 66v/S FTIR
spectrometer, @ MPI-FKF
22. wide-band spectroscopic ellipsometry THz to UV
Ellipsometry: from
ANKA Synchrotron
edge radiation
1m 10m 100m 1 eV 6.2
0.2 THz 1 2
far-IR mid-IR near-IR UV
10 100 1000 10000 cm-1
near-IR to deep-UV
far-IR homebuilt ellipsometer spectroscopic
at ANKA IR1- beam line, ellipsometer (VASE)
@ Karlsruhe IT Woollam Co., @ MPI-FKF
IR homebuilt ellipsometer
based on Bruker 66v/S FTIR
spectrometer, @ MPI-FKF
23. Outline Outline
• advantages of ellipsometry -
i) exact numerical inversion, no
Kramers-Kronig transformation,
allows for K-K consistency check
ii) no reference measurements, very
accurate and highly reproducible
iii) oblique and variable angle of
incidence, very sensitive to
thin-film properties
24. Outline Outline
• advantages of ellipsometry - illustrative examples -
i) exact numerical inversion, no i) superconductivity-induced
Kramers-Kronig transformation, transfer of the spectral weight in
allows for K-K consistency check high temperature cuprate SCs
25. Kramers-Kronig consistency check
∆σ 1Exp (ω ')
∞
∆ε 1Exp (ω0 ) ∆ε KK
(ω0 ) = 8 ⋅ P ∫ 2 2 dω '
0 ω ' −ω0
1
This additional constraint unique to ellipsometry allows one to determine
with high accuracy changes in the spectral weight in the extrapolation
region beyond the experimentally accessible spectral range:
hω < 10 meV ......... hω > 6.6 eV
27. T-dependent Drude SW ω pl π e 2 nb
2
SW Drude = =
8 2 mb
electron correlation effects
σDC
UHB
Daniel Khomslii’s lecture
0
nb
= f (T ) ≠ const
-20 mb
ε1
-40
0.0 0.5 1.0 1.5 2.0
hν (eV)
28. Kramers-Kronig consistency check
1.2
1.0 σ1,A- σ1,B
0.8
A ωp= 1.5 eV
∆σ1 (10 Ω cm )
6 SWA-SWB
-1
0.6
-1
+0.1 %
γΑ = 0.05 eV
3
σ1 (10 Ω cm )
-1
0.4 -0.25 %
4
γB = 0.06 eV
-1
B 0.2
3
0.0
2
-0.2
0.00 0.02 0.04 0.06 0.08
photon energy (eV)
0
0.00 0.05 0.10 0.15 0.20 0.0
photon energy (eV)
-0.5
∆σ (ω ')
∞
ε1,A- ε1,B
∆ε 1 (ω0 ) = 8 ⋅ P ∫ 2 1 2 dω '
-1.0
∆ε1
0 ω ' −ω0
-1.5 SWA-SWB
+0.1 %
-2.0
-0.25 %
0.18 0.21 0.24 0.27
photon energy (eV)
29. in-plane Ba2Sr2CaCu2Oin-plane Ba2Sr2CaCu2O8
8 Tc=91 K
Tc = 91 K
6000
10 K
100K
200 K
σ1 (Ω cm )
4000
-1
0
-1
2000
-1000
ε1b
10 K
0 100 K
0.01 0.1 -2000 200 K
Photon energy (eV)
-3000
0.01 0.1
Photon energy (eV)
30. in-plane Ba2Sr2CaCu2O8 (T>Tc)
8
exp
N
∆ε1
0 ∆SW > 0
6 exp
from ∆σ1 (0 < ω < 1.0 eV)
as measured
∆σ1 (mΩ cm )
-2 100K 200K
-1
extrapolated with with SW = SW
4 100K
SW > SW
200K
-4
-1
(by ≈ 1.5%)
∆ε1
SW head = − SW tail 2
-6
SW head
> − SW tail
-8
∆T = 200 K - by ≈ 1.5%
100 K (0.007eV 2 ) 0
-10
0.00 0.02 0.04 0.06 0.08 0.10
0.1 0.2 0.3 0.4 0.5
Photon energy (eV)
Photon energy (eV)
∆SW total > 0
SW 100 K = SW 200 K + 0.007 eV 2
31. Perfect conductor
ω plτ → ∞
σ0 σ0 ne2
purely reactive σ(ω) = = =
1 − iωτ iωτ iωm*
Cooper pairs ms = 2m, es = 2e, ns = n / 2
1 ns es2 r 1 1 r
j (ω) = E(ω) = E(ω)
r
iω ms iω µ0λ2
ms r r i ( kr⋅rr −ωt )
penetration depth λ= , E = E0e
µ0ns es
2
r
dj
The first London equation: E = µ0λ2
r
dt
35. in-plane Ba2Sr2CaCu2Oin-plane Ba2Sr2CaCu2O8
8 Tc=91 K
Tc = 91 K
6000
10 K
100K
200 K
σ1 (Ω cm )
4000
-1
0
-1
2000
-1000
ε1b
10 K
0 100 K
0.01 0.1 -2000 200 K
Photon energy (eV)
-3000
0.01 0.1
Photon energy (eV)
36. in-plane Ba2Sr2CaCu2O8 (T<Tc)
∆σ 1Exp (ω ')
∞ ∞
∆ε 1 (ω ) = 2 2 + 8 ⋅ P ∫ 2 = 8 ∫ ∆σ 1Exp (ω ')dω ' ( FGT − sum rule)
1 1
dω ' with
λLω 0+
ω ' −ω 2
λ2
L 0+
8
exp
∆ε1
as measured 6 exp
from ∆σ1 (0 < ω < 1.0 eV)
extrapolated with
∆σ1 (mΩ cm )
2
1/λ L=∆SW
-1
°
with
λL = 2300 Α 4
-1
°
λL = 2000 Α
∆ε1
2
∆T = 100 K - 10 K
0
SC
0 ∆SW ≈0
0.00 0.02 0.04 0.06 0.08 0.10
Photon energy (eV) 0.1 0.2 0.3 0.4 0.5
Photon energy (eV)
∞
≈ 8 ∫ ∆σ 1Intra (ω ')dω '
1
λ2
L 0+
37. in-plane Ba2Sr2CaCu2O8 (T<Tc)
∆σ 1Exp (ω ')
∞ ∞
∆ε 1 (ω ) = 2 2 + 8 ⋅ P ∫ 2 = 8 ∫ ∆σ 1Exp (ω ')dω ' ( FGT − sum rule)
1 1
dω ' with
λLω 0+
ω ' −ω 2
λ2
L 0+
8
exp
∆ε1
as measured 6 exp
from ∆σ1 (0 < ω < 1.0 eV)
extrapolated with
∆σ1 (mΩ cm )
2
1/λ L=∆SW+1%
-1
°
with
λL = 2300 Α 4 2
1/λ L=∆SW-1%
-1
°
λL = 2000 Α
∆ε1
2
∆T = 100 K - 10 K
0
SC
0 ∆SW ≈0
0.00 0.02 0.04 0.06 0.08 0.10
Photon energy (eV) 0.1 0.2 0.3 0.4 0.5
Photon energy (eV)
∞
= 8 ∫ ∆σ 1Intra (ω ')dω ' ± 0.5% (0.0008 eV 2 )
1
λ2
L 0+
38. SW transfer in Ba2Sr2CaCu2O8 Ba2Sr2CaCu2O8
in-plane Tc=91 K
SW 100 K = SW 200 K + 0.007 eV 2
8
exp
∆ε1 (∆T=200K-100K)
6 exp
∆ε1 (∆T=100K-10K)
4
N
∆SW > 0
∆ε1
2
0
SC
∆SW ν0
0.1 0.2 0.3 0.4 0.5
Photon energy (eV)
∞
= ∫ ∆σ 1Intra (ω ')dω ' ± 0.0008 eV 2
1
λ2
L 0+
H.J.A. Molegraaf & D. van der Marel,
Science, 295, 2239 (2002)
39. SW transfer in Ba2Sr2CaCu2O8 Ba2Sr2CaCu2O8
in-plane Tc=91 K
Bi2212
H.J.A. Molegraaf & D. van der Marel,
Science, 295, 2239 (2002)
40. SW transfer in Ba2Sr2CaCu2O8 Ba2Sr2CaCu2O8
in-plane Tc=91 K
Bi2212
Y123
H.J.A. Molegraaf & D. van der Marel,
Science, 295, 2239 (2002)
42. Outline Outline
• advantages of ellipsometry - illustrative examples -
ii) no reference measurements, very ii) superconductivity-induced optical
accurate and highly reproducible anomalies and iron pnictide
superconductors
43. Iron arsenide superconductors
Ba
lattice structure
multiband electronic structure
Fe As
superconductivity
Ba0.68K0.32Fe2As2
Tc=38.5 K
49. SC-induced lowering of the chemical potential
Single band BCS: e.g. D.J. Scalapino, “SC-ty” (1969)
1 ∆ SC
2
µ SC ≈ µN −
4 µN
∆ SC / ε F ~ ∆F SC (0) ~ 0.1 meV
2
50. SC-induced lowering of the chemical potential
Single band BCS: e.g. D.J. Scalapino, “SC-ty” (1969)
1 ∆ SC
2
µ SC ≈ µN −
4 µN
∆ SC / ε F ~ ∆F SC (0) ~ 0.1 meV
2
Multi band BCS: ∆iSC ≠ ∆ jSC
j→
⇒ nSC = nN + ∆nSC i
i i
µ = µ = µ SC
i j
• self-consistent treatment of a variable chemical potential at
the SC transition is required
51. SC-induced inter-band charge transfer
Single band BCS: e.g. D.J. Scalapino, “SC-ty” (1969)
1 ∆ SC
2
µ SC ≈ µN −
4 µN
∆ SC / ε F ~ ∆F SC (0) ~ 0.1 meV
2
Multi band BCS: ∆iSC ≠ ∆ jSC
j→
⇒ nSC = nN + ∆nSC i
i i
µ = µ = µ SC
i j
Two el’s subsystems in cuprates:
D. I. Khomskii and F.V. Kusmartsev, PRB 46 (1992)
N CuO2 ∆2
µ SC = µ N −
N CuO2 + N chain 4µ N
N CuO2 ∆2
nSC
=n N 1 + ~ 1%
CuO2 CuO2
N CuO + N chain 4µ N
2
2
52. SC-induced inter-band charge transfer
Fe3dxz,zy+Fe3dxy
∆SC < ∆SC
h e nh < nh
SC N
⇒
mh < me h ∆F SC (0) > ∆ SC / ε F
* * 2
Fe3dxy
53. Conclusions
Ba0.68K0.32Fe2As2 - SC-reduced absorption in visible:
• assigned to excitations from As-px,y/Fe-dz2 to Fe-dyz,zx and Fe-dxy states
• charge transfer between the Fe-dyz,zx and Fe-dxy bands
below Tc could explain the optical anomaly
• self-consistent treatment of a variable chemical potential
at the SC transition is required
• in the presence of large Fe-As bond polarizability it can potentially
enhance superconductivity in iron pnictides.
54. Outline Outline
• advantages of ellipsometry - illustrative examples -
iii) oblique and variable angle of iii) dimensionality-controlled
incidence, very sensitive to collective charge and spin* order
thin-film properties in nickel-oxide superlattices
* combined with low-energy muons which serve as a sensitive
local probe of the internal magnetic field distribution
55. 2D e-gas in semiconductors
Band Bending picture
QHE v Klitzing 1980
FQHE H. Störmer 1984
Jochen Mannhart’s lecture
56. Dimentionality control in oxides
LaAlO3
“solid-state chemistry approach” wide-band-gap
(~ 5eV) insulator
LaNiO3
Ruddlesden–Popper (R–P) homologous paramagnetic
series of Srn+1RunO3n+1 metal
57. Why RNiO3?
J.-S. Zhou, J.B. Goodenough et al., LaAlO3
PRL 84, 526 (2000)
wide-band-gap
(~ 5eV) insulator
Ni3+ 3d7 t62ge1g
∆CF >> JH
eg LaNiO3
S=1/2
W ~ EG~ JH ~ U paramagnetic
t2g metal
58. RNiO3-based Heterosctructures
LaAlO3
wide-band-gap
Possible 3D-to-2D- and interface- (~ 5eV) insulator
induced “engineered” properties
of correlated electrons:
• metal- insulator transition with unusual
magnetic and charge ordering
• orbital reconstruction
• multiferroicity
G. Giovannetti et al., PRL 103, 156401 (2009)
• superconductivity
J. Chaloupka and G. Khaliullin, PRL 100, 016404 (2008)
P. Hansmann et al., PRL 103, 016401 (2009)
“… possible orbital occupancy analogous to the cuprates …”
LaNiO3
paramagnetic
metal
59. Theory Experiment
Perfect sample Real sample
Technology
Extrinsic properties
Intrinsic properties (stacking faults, inter-diffusion
(collective quantum phases) substrate contribution)
high oxygen pressure PLD, MPI-FKF
G. Cristiani and H.-U. Habermeier
60. LaNiO3|LaAlO3 superlattices
compressive
tensile
(001) LaSrAlO4
(001) SrTiO3
N = 4 u.c. x 10, d = 290 ± 10 Å N = 3 u.c. x 13, d = 312 ± 10 Å
MF-MPI beam line @ANKA, A. Frano, E. Benckiser, P. Wochner
62. Reciprocal-space maps
N = 4 u.c. N = 2 u.c. N = 2 u.c.
TEM: MF-MPI StEM E. Detemple, W. Sigle, P. van Aken
63. Theory Experiment
Perfect sample Real sample
Technology
Extrinsic properties
Intrinsic properties faults, inter-diffusion
(stacking
(collective quantum phases) contribution)
substrate
inevitable defects
+ local probes! vs. macro probes
optical spectroscopy dc conductivity
charge:
(ellipsometry) and permittivity
muon-SR magnetic
spin:
(slow muons) susceptibility
AFM, charge order FM, ferroelectric, SC
64. Charge dynamics via spectroscopic ellipsometry
Y
Ai
sample detector
E Es analyzer
IrsI
P Ep ϕ IrpI
~
~ r p (ω )
polarizer ρ (ω ) = ~
= tan Ψ (ω )ei∆ (ω )
light source
r s (ω )
oblique incidence
- sensitive to thin-film properties
intrinsic SL’s electrodynamics
is not flawed by a substrate, contacts and
extended defects
65. Isotropic film on isotropic substrate in vacuum
⁄
ଶ ଶ
߮ ܰ cos ߮ − ܰ − sin ࣐
ݎଵ = ⁄
01 ܰ ଶ cos ߮ + ܰ ଶ − sin ࣐
d
ܰ SL ଶ ଶ
⁄
12 −݊ cos ߚ + ܰ ݊ − ࡺࡿ sin ࢼ
ݎଵଶ = ⁄
ߚ ݊ଶ cos ߚ +ܰ ݊ଶ − ࡺࡿ sin ࢼ
ࡺ࢙ substrate
⁄
cos ߮ − ܰ ଶ − sin ࣐
ݎଵೞೞ =
ݎ (߱)
̃ cos ߮ + ܰ ଶ − sin ࣐
⁄
ߩ ߱ =
= tan Ψ(߱) ݁ ∙(ఠ)
ݎ௦ (߱)
̃ ⁄
ଶ
−ࡺࡿ cos ߚ + ܰ − ࡺࡿ sin ࢼ
ݎଵ + ݎଵଶ ݁ ିଶఈ ݎଵଶೞೞ = ⁄
ݎ (߱) =
̃ cos ߚ + ܰ ଶ − ࡺࡿ sin ࢼ
1 + ݎଵ ݎଵଶ ݁ ିଶఈ
ݎଵೞೞ + ݎଵଶೞೞ ݁ ିଶఈ Snell‘s law: sin ߮ = ܰ௦ sin ߚ
ݎ௦ (߱) =
̃
1 + ݎଵೞೞ ݎଵଶೞೞ ݁ ିଶఈ ⁄
ௗ ଶ
Phase thickness: ߙ = 2ߨ ܰ − sin ࣐
ఒ
Known: ߩ ߱ , ߮, ࡺࡿ
߱
Unkown: ࡺ ߱ , ݀
66. complex dielectric function of bare SLs
numerical inversion
Drude parameters:
N = 4: ω p ≈ 1.10 eV , γ ≈ 87 meV m*
= 10
N = 2: ω p ≈ 1.05 eV , γ ≈ 196 meV m
V
EF = 0.5eV , VF = 1.33 ⋅107 cm , l = F
s 2π cγ
o o
mean free path: N = 4: l = 9.7 A, N = 2: l = 4.4 A
69. from itinerant to localized electrons
LaNiO3
ΔNeff=0.03
Effective number of electrons localized:
ω
∆N eff (ω ) = 2 0 ∫ ∆σ (ω ′)dω ′
2m
π e N Ni 0
70. from itinerant to localized electrons
LaNiO3
ΔNeff=0.03
Effective number of electrons localized:
bulk NdNiO3 - ΔNeff=0.058 ω
∆N eff (ω ) = 2 0 ∫ ∆σ (ω ′)dω ′
2m
T.Katsufuji, Y.Tokura et al., (1995): π e N Ni 0
71. from itinerant to localized electrons
LaNiO3
ΔNeff=0.03
Effective number of electrons localized:
bulk NdNiO3 - ΔNeff=0.058 ω
∆N eff (ω ) = 2 0 ∫ ∆σ (ω ′)dω ′
2m
T.Katsufuji, Y.Tokura et al., (1995): π e N Ni 0
72. Metal – Insulator Transition (MIT) in LaNiO3
Continuing the analogy with bulk RNiO3 series, one would then expect another
second-order transition due to the onset of antiferromagnetic ordering at TN < TMI
in the N = 2 SLs, as in RNiO3 with small R (Lu through Sm).
73. Low-Energy µSR measurements
Rob Kiefl’s lecture
Thomas Prokscha, Zaher Salman,
Andreas Suter, Elvezio Morenzoni
74. LaNiO3|LaAlO3 SLs : µ+ Spin Relaxation
F (t ) − B (t ) BTF = 0
AZF (t ) = = aoG (t )
F (t ) + B(t )
G(t) is the Fourier transform of the field
distribution averaged over all muon sites.
Fast depolarization rate:
Ni spins are AFM ordered
75. LaNiO3|LaAlO3 SLs : µ+ Spin Rotation
BTF=100 G
The time evolution of the muon
polarisation in a transverse field BTF is
µ+
F (t ) − B(t )
ATF (t ) = = aoG (t ) cos(ω L t )
F (t ) + B (t )
where Larmor frequency ωL= γµBTF ,
γµ= 2π×13.55 MHz/kG
76. LaNiO3|LaAlO3 SLs : µ+ Spin Rotation
BTF > 0
The time evolution of the muon
polarisation in a transverse field BTF is
µ+
F (t ) − B(t )
ATF (t ) = = aoG (t ) cos(ω L t )
F (t ) + B (t )
where Larmor frequency ωL= γµBTF ,
γµ= 2π×13.55 MHz/kG
BTF =100 Gauss BTF =1000 Gauss BTF =3000 Gauss
81. SUMMARY
i) superconductivity-induced
transfer of the spectral weight in
high temperature cuprate SCs
ii) superconductivity-induced
optical anomalies and iron-based
pnictide superconductors
iii) dimensionality-controlled
collective charge and spin* order
in nickel-oxide superlattices