Overview of spectroscopies III

Overview of spectroscopies III

Simo Huotari

University of Helsinki, Finland

15.1.2012

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. experiment

Equipment for measurements

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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)

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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)

Properties

Macroscopic dielectric function Complex refractive index

Reflectivity

Absorption coefficient = 4 Loss function Im

Dynamic structure factor Im

Spectral 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 .

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Energy-loss spectrum

elastic line

magnons phonons

Crystal- field excitations

charge transfer, band gap

core excitations

DOS ) plasmon

, Im ,

Average 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

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Plasmons

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

)

Both energy and momentum can be controlled

Band structure picture

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

15.1.2012

Outline

Part 1 – Excitations and properties Part 2 – Techniques (general)

Part 3 – Sample environments

Tomorrow – Techniques (examples)

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 Auger

spectroscopy

Electron Electron absorption

Inverse

photoemission Cathodo-

luminescence

Electron energy loss

Tunneling Differences in:

Outgoing particle

In c o m in g p a rt ic le

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Particle probing depth

photons

Dynamic ranges for scattering

10⁴

10² 10

1 10^-1 10^-2

10¹⁸

10¹³ 10¹⁶ 10¹⁵ 10¹⁴ 10¹⁷ 10³

1 0.1

10² 10 10³

10⁴

Frequency (Hz)

ergy or energy transfer (eV)

Characteristic length scale (Å) = 2

Synchrotron radiation

cattering

Electrons

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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 ² ₃

H O E

i E E E

A H I I H A B

H B

W _{B A}

I A I

BA

Kramers-Heisenberg formula

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

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Small Q

interference effects are important (collective excitations)

Large Q

independent 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

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

= 1 + 2

15.1.2012

Outline

Part 1 – Excitations and properties Part 2 – Techniques (general)

Part 3 – Sample environments

Tomorrow – Techniques (examples)

Phase diagram of water

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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 pressures

pressure = 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)

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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

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1960 1970 1980 1990 2000

10⁷ 10⁸ 10⁹ 10¹⁰ 10¹¹ 10¹² 10¹³ 10¹⁴ 10¹⁵ 10¹⁶ 10¹⁷ 10¹⁸ 10¹⁹ 10²⁰ 10²¹ 10²² 10²³

Computing speed

Millions of operations per second X-Ray Source Brightness

photons/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

Brightness

Moore’s law