Overview of spectroscopies III -...

Overview of spectroscopies III

Simo HuotariUniversity of Helsinki, Finland

TDDFT school, Benasque, Spain, January 2012

15.1.2012 23:53:08Simo Huotari, Benasque TDDFT school 2012 2

Motivation: why we need theory

Spectroscopy (electron

dynamics)

Theory of electronic

structure and response

Electronic properties and

dynamics

Micro- and macroscopic structure and

dynamics

Theory of atomic level structure and dynamics

DFT, MD simulations,QMC, ...

TDDFT, ...

Electron level structure, transition probabilities

Better and new materials and applications

Spectroscopy (atomic

dynamics)

Equipment for experiments


Measurement vs. experimentEquipment for measurements


Incoming particles/radiation

generic sample

Transmission

Probes and messengers

Interaction H


Outline

Part 1 – Excitations and properties

Part 2 – Techniques (general)

Part 3 – Sample environments

Tomorrow – Techniques (examples)


Collective ”Single particle”

Vibrational Sound waves(phonons)

Molecular bending, stretching...

Spin Magnons, spin waves

Spin flip

Electronic Plasmons, orbitons,polarons

Crystal fields,excitons,Compton, electron removal

+ multiples (bimagnons, double plasmons, ...)

Classification of excitations(non-exhaustive)


PropertiesMacroscopic dielectric functionComplex refractive indexReflectivity Absorption coefficient = 4Loss function ImDynamic structure factor ImSpectral density function Resonant Raman spectra

Dynamic structure factor is also the Fourier transform of the density correlation function - which is the probability to find two different particles separated by and .


Energy-loss spectrum

elastic line

magnons

phonons

Crystal-field

excitations

charge transfer,

band gap

core excitations

DOS )plasmon

,Im

, X-ray Compton

Aver

age

over

Q


Magnetic excitations: orbital physics in transition metal oxides

J. D. Perkins et al., PRB 52, R9863 (1995)

J. Kim et al. 2011, arXiv:1110.0759v1 [cond-mat.str-el]

Sr2IrO4

Magnons: spin waves


Plasmons

W. Schülke: Electron dynamics by inelastic x-ray scattering (Oxford Univ. Press)

)


Both energy and momentum can be controlledBand structure picture

N. Hiraoka et al., PRB 72, 075103 (2005)Example: graphite


Outline






Nothing Photon Electron

Nothing Skiing at the Pyrenees

Light emission, photoluminescence

Electron emission

Photon Absorption (IR, UV/vis, vacuum UV, x-ray..)CD; XMCD

Ellipsometry, reflectometry, ATR, Raman, Brillouin, x-ray scattering, Compton scattering

Photoemission Augerspectroscopy

Electron Electron absorption

Inverse photoemissionCathodo-luminescence

Electron energylossTunneling

+ Time-of-flights+ Non-linear phenomena

Differences in:- Dynamic range of Q and E, coupling to spin, nuclei, … - Bulk or surface sensitivity- Resolving power in energy, momentum, time, space…- Element specifity (useful for complicated systems)

Outgoing particleIn

com

ing

parti

cle


Particle probing depth

photons


Dynamic ranges for scattering

104

102

10

1

10-1

10-2

1018

1013

1016

1015

1014

1017

101210-3

103

10 100110-110-210-3

1 0.110102103104

Frequency (Hz)

Ene

rgy

or e

nerg

y tra

nsfe

r (eV

)

Characteristic length scale (Å) = 2

Momentum (Å-1)

Synchrotron radiation

Ligh

t sca

tterin

gElectrons


Spectroscopy - interaction

= +Photon-electron

Electron-electron

Absorption and emission in first order, resonant scattering in second order

Scattering

Transition rate from state |A> to state |B>is given by the Fermi’s Golden Rule:

)()(2/

2 3

2

HOEEiEE

AHIIHBAHBW AB

I IABA


Kramers-Heisenberg formulaFrom - Non-resonant scattering (Raman, inelastic x-ray, ....)

From - Resonant scattering (Resonant Raman, resonant inelastic x-ray, fluorescence....)


Small Qinterference effects are important

(collective excitations)

Large Qindependent particle picture

(Compton scattering)

Dynamic structure factor

Average density-density correlation function

=1

, 0

Dynamic structure factor


Absorption and scattering

Scattering

Absorption Dipole selection rule

dipole Higher order multipoles

Use the momentum transfer dependence of the scattering matrix element: as 0 then

= 1 + 2


Outline






Phase diagram of water


Experimental details•1 mm diamond tip (culet)

• 5 mm Be gasket• 350 micron sample size•X-ray beam 100 50 µm2

•Ruby chip for P calibration

sample

photons in

Extremely high pressurespressure = force / area V.M.Giordano, T. Pylkkänen et al. ESRF ID16


Low temperatures

Liquid nitrogen cryo-jet (77 K)

Liquid He Cryostat (4 K)

He sorption pump (1 K)

F. Albergamo et al., ESRF


Droplet of liquid basalt BCR-2 during levitation. The sample was heated from the top using a CO2-laser. The diameter of the sphere was ~2 mm. A. Pack et al., Geochemical transactions 2010, 11:4

Extremely high temperatures (thousands of deg): Laser heating and aerodynamic levitation

High temperatures (up to 1000 deg C): furnaces, hot air guns

Wikipedia: Aerodynamic levitation

ESRF, Sample group


Advanced Photon Source, USA Super Photon Ring 8 (Spring-8), Japan

European Synchrotron Radiation Facility, France

Modern 3rd generation synchrotrons


1960 1970 1980 1990 2000107

108

109

1010

1011

1012

1013

1014

1015

1016

1017

1018

1019

1020

1021

1022

1023

Computing speedMillions of operations per second

X-Ray Source Brightnessphotons/sec/0.1%bw/sq.mm/mrad^2

200 mA Diff. Limit

3rd. Gen.original design

2nd. Gen.

1st. Gen. Synch. Rad.

CDC 6600

Cray 1

Cray T90

Calendar Year

10-1

100

101

102

103

104

105

106

107

108

109

1010

1011

1012

1013

1014

1015

Brig

htne

ssMoore’s law

Overview of spectroscopies III -...

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