Simo Huotari University of Helsinki, Finland TDDFT school, Benasque, Spain, January 2012

Transcription

1 Overview of spectroscopies III Simo Huotari University of Helsinki, Finland TDDFT school, Benasque, Spain, January 2012

2 Motivation: why we need theory Spectroscopy (electron dynamics) Theory of electronic structure and response TDDFT,... Electronic properties and dynamics Spectroscopy (atomic dynamics) Electron level structure, transition probabilities Theory of atomic level structure and dynamics DFT, MD simulations, QMC,... Better and new materials and applications Micro- and macroscopic structure and dynamics Simo Huotari, Benasque TDDFT school :53:08 2

3 Measurement vs. experiment Equipment for measurements Equipment for experiments Simo Huotari, Benasque TDDFT school :53:08 3

4 Probes and messengers Interaction H Incoming particles/radiation generic sample Transmission Simo Huotari, Benasque TDDFT school :53:08 4

5 Outline Part 1 Excitations and properties Part 2 Techniques (general) Part 3 Sample environments Tomorrow Techniques (examples) Simo Huotari, Benasque TDDFT school :53:08 5

6 Classification of excitations (non-exhaustive) Vibrational Collective Sound waves (phonons) Single particle Molecular bending, stretching... Spin Electronic Magnons, spin waves Plasmons, orbitons, polarons Spin flip Crystal fields, excitons, Compton, electron removal + multiples (bimagnons, double plasmons,...) Simo Huotari, Benasque TDDFT school :53:08 6

7 Properties Macroscopic dielectric function Complex refractive index Reflectivity Absorption coefficient = 4 Loss function Im Dynamic structure factor Spectral density function Resonant Raman spectra Im 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. Simo Huotari, Benasque TDDFT school :53:09 7

8 Energy-loss spectrum Average over Q, Im, elastic line phonons Crystalfield excitations charge transfer, band gap plasmon core excitations DOS ) X-ray Compton magnons Simo Huotari, Benasque TDDFT school :53:09 8

9 Magnons: spin waves Magnetic excitations: orbital physics in transition metal oxides Sr 2 IrO 4 J. Kim et al. 2011, arxiv: v1 [cond-mat.str-el] J. D. Perkins et al., PRB 52, R9863 (1995) Simo Huotari, Benasque TDDFT school :53:09 9

10 Plasmons ) W. Schülke: Electron dynamics by inelastic x-ray scattering (Oxford Univ. Press) Simo Huotari, Benasque TDDFT school :53:09 10

11 Band structure picture Both energy and momentum can be controlled Example: graphite N. Hiraoka et al., PRB 72, (2005) Simo Huotari, Benasque TDDFT school :53:09 11

12 Outline Part 1 Excitations and properties Part 2 Techniques (general) Part 3 Sample environments Tomorrow Techniques (examples) Simo Huotari, Benasque TDDFT school :53:09 12

13 Outgoing particle Nothing Photon Electron Nothing Skiing at the Pyrenees Light emission, photoluminescence Electron emission Incoming particle Photon Electron + Time-of-flights + Non-linear phenomena Absorption (IR, UV/vis, vacuum UV, x-ray..) CD; XMCD Electron absorption Ellipsometry, reflectometry, ATR, Raman, Brillouin, x-ray scattering, Compton scattering Inverse photoemission Cathodoluminescence Photoemission Auger spectroscopy Electron energy loss Tunneling 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) Simo Huotari, Benasque TDDFT school :53:09 13

14 Particle probing depth photons Simo Huotari, Benasque TDDFT school :53:09 14

15 Dynamic ranges for scattering Characteristic length scale (Å) = Energy or energy transfer (ev) Light scattering Electrons Synchrotron radiation Frequency (Hz) Momentum (Å -1 ) Simo Huotari, Benasque TDDFT school :53:09 15

16 Spectroscopy - interaction Photon-electron = + Electron-electron Scattering Absorption and emission in first order, resonant scattering in second order Transition rate from state A> to state B> is given by the Fermi s Golden Rule: W BA 2 2 E ) O( H 3 B A I A I B H I I H A B H A ( E E E i / 2 ) Simo Huotari, Benasque TDDFT school :53:09 16

17 Kramers-Heisenberg formula From - Non-resonant scattering (Raman, inelastic x-ray,...) From - Resonant scattering (Resonant Raman, resonant inelastic x-ray, fluorescence...) Simo Huotari, Benasque TDDFT school :53:09 17

18 Dynamic structure factor Average density-density correlation function = 1, 0 Dynamic structure factor Small Q interference effects are important (collective excitations) Large Q independent particle picture (Compton scattering) Simo Huotari, Benasque TDDFT school :53:09 18

19 Absorption and scattering Absorption Dipole selection rule Scattering Use the momentum transfer dependence of the scattering matrix element: as 0then =1+ 2 dipole Higher order multipoles Simo Huotari, Benasque TDDFT school :53:09 19

20 Outline Part 1 Excitations and properties Part 2 Techniques (general) Part 3 Sample environments Tomorrow Techniques (examples) Simo Huotari, Benasque TDDFT school :53:09 20

21 Phase diagram of water Simo Huotari, Benasque TDDFT school :53:09 21

22 Extremely high pressures pressure = force / area V.M.Giordano, T. Pylkkänen et al. ESRF ID16 photons in Experimental details 1 mm diamond tip (culet) 5 mm Be gasket 350 micron sample size sample X-ray beam µm 2 Ruby chip for P calibration Simo Huotari, Benasque TDDFT school :53:09 22

23 Liquid He Cryostat (4 K) Low temperatures Liquid nitrogen cryo-jet (77 K) He sorption pump (1 K) F. Albergamo et al., ESRF Simo Huotari, Benasque TDDFT school :53:09 23

24 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 Droplet of liquid basalt BCR-2 during levitation. The sample was heated from the top using a CO 2 -laser. The diameter of the sphere was ~2 mm. A. Pack et al., Geochemical transactions 2010, 11:4 Simo Huotari, Benasque TDDFT school :53:09 24

25 Modern 3rd generation synchrotrons Advanced Photon Source, USA Super Photon Ring 8 (Spring-8), Japan European Synchrotron Radiation Facility, France Simo Huotari, Benasque TDDFT school :53:09 25

26 Moore s law ma Diff. Limit X-Ray Source Brightness photons/sec/0.1%bw/sq.mm/mrad^ Brightness nd. Gen. 1st. Gen. Synch. Rad. CDC 6600 Cray 1 3rd. Gen. original design Cray T90 Computing speed Millions of operations per second Calendar Year Simo Huotari, Benasque TDDFT school :53:09 26