Overview of spectroscopies III Simo Huotari University of Helsinki, Finland TDDFT school, Benasque, Spain, January 2012
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 2012 23:53:08 2
Measurement vs. experiment Equipment for measurements Equipment for experiments Simo Huotari, Benasque TDDFT school 2012 23:53:08 3
Probes and messengers Interaction H Incoming particles/radiation generic sample Transmission Simo Huotari, Benasque TDDFT school 2012 23:53:08 4
Outline Part 1 Excitations and properties Part 2 Techniques (general) Part 3 Sample environments Tomorrow Techniques (examples) Simo Huotari, Benasque TDDFT school 2012 23:53:08 5
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 2012 23:53:08 6
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 2012 23:53:09 7
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 2012 23:53:09 8
Magnons: spin waves Magnetic excitations: orbital physics in transition metal oxides Sr 2 IrO 4 J. Kim et al. 2011, arxiv:1110.0759v1 [cond-mat.str-el] J. D. Perkins et al., PRB 52, R9863 (1995) Simo Huotari, Benasque TDDFT school 2012 23:53:09 9
Plasmons ) W. Schülke: Electron dynamics by inelastic x-ray scattering (Oxford Univ. Press) Simo Huotari, Benasque TDDFT school 2012 23:53:09 10
Band structure picture Both energy and momentum can be controlled Example: graphite N. Hiraoka et al., PRB 72, 075103 (2005) Simo Huotari, Benasque TDDFT school 2012 23:53:09 11
Outline Part 1 Excitations and properties Part 2 Techniques (general) Part 3 Sample environments Tomorrow Techniques (examples) Simo Huotari, Benasque TDDFT school 2012 23:53:09 12
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 2012 23:53:09 13
Particle probing depth photons Simo Huotari, Benasque TDDFT school 2012 23:53:09 14
Dynamic ranges for scattering Characteristic length scale (Å) = 2 10 4 10 3 10 2 10 1 0.1 Energy or energy transfer (ev) 10 4 10 3 10 2 10 1 10-1 10-2 10-3 Light scattering Electrons Synchrotron radiation 10 18 10 17 10 16 10 15 10 14 10 13 10 12 Frequency (Hz) 10-3 10-2 10-1 1 10 100 Momentum (Å -1 ) Simo Huotari, Benasque TDDFT school 2012 23:53:09 15
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 2012 23:53:09 16
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 2012 23:53:09 17
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 2012 23:53:09 18
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 2012 23:53:09 19
Outline Part 1 Excitations and properties Part 2 Techniques (general) Part 3 Sample environments Tomorrow Techniques (examples) Simo Huotari, Benasque TDDFT school 2012 23:53:09 20
Phase diagram of water Simo Huotari, Benasque TDDFT school 2012 23:53:09 21
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 100 50 µm 2 Ruby chip for P calibration Simo Huotari, Benasque TDDFT school 2012 23:53:09 22
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 2012 23:53:09 23
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 2012 23:53:09 24
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 2012 23:53:09 25
Moore s law 10 23 10 22 10 21 10 20 200 ma Diff. Limit X-Ray Source Brightness photons/sec/0.1%bw/sq.mm/mrad^2 10 15 10 14 10 13 10 12 Brightness 10 19 10 18 10 17 10 16 10 15 10 14 10 13 10 12 10 11 10 10 10 9 10 8 10 7 2nd. Gen. 1st. Gen. Synch. Rad. CDC 6600 Cray 1 3rd. Gen. original design Cray T90 Computing speed Millions of operations per second 1960 1970 1980 1990 2000 Calendar Year 10 11 10 10 10 9 10 8 10 7 10 6 10 5 10 4 10 3 10 2 10 1 10 0 10-1 Simo Huotari, Benasque TDDFT school 2012 23:53:09 26