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SOLID STATE SPECTROSCOPY

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Presentation on theme: "SOLID STATE SPECTROSCOPY"— Presentation transcript:

1 SOLID STATE SPECTROSCOPY
SUMMER TERM 2014 Dr. Mathieu Le Tacon Prof. Dr. Bernhard Keimer Solid State Spectroscopy - Introduction 07/04/2014

2 Objective of this lecture
Provide a general background on some of the experimental spectroscopic techniques that are most commonly used to study materials Optical Spectroscopy (absorption/reflectivity/ellipsometry) Inelastic light scattering (Raman, Inelastic X-ray Scattering) X-ray absorption Spectroscopy (XAS) Nuclear Magnetic Resonance (NMR) Inelastic Neutron Scattering (INS) Tunneling Spectroscopy (STM/STS) Angle Resolved Photoemission Spectroscopy (ARPES) etc… Solid State Spectroscopy - Introduction

3 Non-exhaustive bibliography
Solid State Spectroscopy - Introduction 07/04/2014

4 Solid State Spectroscopy - Introduction
Material Science New materials: synthesis/design Original Physical Properties Technological applications 2006 Nature 410, 63 (2001) MgB2 2014 Solid State Spectroscopy - Introduction 07/04/2014

5 Solid State Spectroscopy - Introduction
Material Science New materials: synthesis/design Original Physical Properties Technological applications Solid State Spectroscopy - Introduction 07/04/2014

6 Materials for the future ?
Transition metal oxide superlattices Graphene BUT prior to application need to understand fundamental properties Solid State Spectroscopy - Introduction 07/04/2014

7 Solid State Spectroscopy - Introduction
Solid State Spectroscopy - Introduction 07/04/2014

8 Solid State Spectroscopy - Introduction
From the atomic building block… Nucleus : charge Ze + mass spin I (magnetic moment MI = -gmNI) Electrons : charge e spin S (magnetic moment MS = -gmBS) 𝜇 𝐵 = 𝑒ℏ 2 𝑚 𝑒 𝜇 𝑁 = 𝑒ℏ 2𝑀 ≪ 𝜇 𝐵 Weakly coupled spectator (NMR) Solid State Spectroscopy - Introduction 07/04/2014

9 Solid State Spectroscopy - Introduction
… to the solid STATIC PROPERTIES (GROUND STATE) Nuclei: Lattice structure - Local defects Charge: - Band structure ? - electronic structure of the defects Spin: - Magnetic structure (e.g. ferro-/ anti-ferromagnetic) Solid State Spectroscopy - Introduction 07/04/2014

10 Solid State Spectroscopy - Introduction
… to the solid DYNAMIC PROPERTIES (EXCITATIONS) Nuclei: individual: diffusion - Collective: phonons Charge: - Individual (Intra/Interband, Exciton) - Collective (plasmon) - topological (Vortex) Microscopic origin of THERMODYNAMIC Properties ! Spin: - individual: single spin flip - collective: spin waves/magnons - topological: skyrmions Solid State Spectroscopy - Introduction 07/04/2014

11 What Experimental techniques ?
Crystal/Magnetic Structure x-ray /Neutrons/NMR Electronic Structure ARPES STM XAS Ab-initio calculation Souma et al. Nature (2003) Kortus et al.PRL (2003) MgB2 Dynamical properties Charge electrodynamics: optics Phonon (lattice vibrations): optics, Raman, INS, IXS. Shukla, et al. PRL 90, (2003) 07/04/2014 Solid State Spectroscopy - Introduction

12 Experimental Method Interaction Response probe
Interesting system probe Interaction Response Linear response framework: Response = Susceptibility x Perturbation Intrinsic property of the system Solid State Spectroscopy - Introduction

13 Linear Response Theory
Consider an observable 𝑂( 𝑟 ,𝑡) (Magnetization, Current, Scattering Cross-section etc..) 𝑂( 𝑟 ,𝑡) = 1 𝑍 0 𝑇𝑟 𝜌𝑂 = 1 𝑍 0 𝑛 𝑛 𝑂 𝑛 𝑒 − 𝐸 𝑛 𝑘 𝐵 𝑇 =0 Assume in the absence of perturbation Consider a external perturbation (=weak) 𝑝( 𝑟 ,𝑡) Assuming system homogeneity and time translation invariance 𝑂( 𝑟 ,𝑡) = 𝑑 𝑟 ′ 𝑑 𝑡 ′ 𝜒 𝑟 − 𝑟 ′ , 𝑡− 𝑡 ′ 𝑝 𝑟 ′ , 𝑡 ′ It is often more convenient (and relevant) to work directly with Fourier transform 𝑂( 𝑞 ,𝜔) =𝜒 𝑞 ,𝜔 𝑝 𝑞 ,𝜔 𝜒 𝑞 ,𝜔 Important : is directly related to correlation functions Solid State Spectroscopy - Introduction

14 The Probes (pertubations)
1) Electro-magnetic field 𝐸 = 𝑒 𝐸 0 𝑒 𝑖( 𝑘 . 𝑟 −𝜔𝑡) 𝐵 = 1 𝜔 𝑘 × 𝐸 𝐸=ℏ𝜔= ℎ𝑐 𝜆 𝐸 𝜆=1Å =12.4 𝑘𝑒𝑉 2) Particles 𝜓~ 𝑒 𝑖 𝑘 . 𝑟 Particle electron positrons muons neutrons proton Nuclei 𝑍 𝐴 𝑋 ions 𝑍 𝐴 𝑋 𝑛± Mass me=9,1 ×10-31 kg mp=9,1 mm=1,88 ×10-28 kg MN=1,675 ×10-27 kg MP=1,673 Z.MP+ (A-Z).MN-EB/c2 ~Z.MP+ Charge -e +e +Ze ± ne Spin 1/2 0 if Z and A are even S > 1/2 for 75% of isotopes Depends on n (me >>mNucleus) (Internal probe) Solid State Spectroscopy - Introduction

15 Magnetic Susceptibility cm Spin-spin (static/uniform)
Perturbation Responding Observable ? Associated Susceptibility corresponding Correlations Magnetic Field H Magnetization M Magnetic Susceptibility cm Spin-spin (static/uniform) Spin of Neutrons Magnetic Scattering Cross section S(q,w) cm(q,w) (non-uniform) Electric Field E Polarization P Charge c(q=0,w) Charge-charge Electrical current j Electrical conductivity s(q=0,w) Current-current (uniform) (x-ray beam) Scattering Cross section c(q,w) NMR/ESR/mSR Neutron Scattering Raman Optics X-ray scattering Solid State Spectroscopy - Introduction

16 Experimental techniques: absorption
Ground State Excited State Incident photon ℏ𝜔𝐼, 𝑘 𝐼, 𝜀 𝐼 Interesting system e.g. light absorption (dipolar selection rules DJ = 0, ±1) Kortus et al.PRL (2003) e.g. NMR B = 0 B ≠ 0 IZ = -1/2 IZ = 1/2 DE ~ gn ħ Bloc with gn ~ few 10 MHz Bloc: local field at the nucleus position Includes surrounding e- through hyperfine coupling Solid State Spectroscopy - Introduction

17 Experimental techniques: Luminescence
Ground State Excited State Incident stimulus (photon/electron) Emitted photon Interesting system Solid State Spectroscopy - Introduction

18 Experimental techniques: Photo-emission
Ground State Excited State Incident Photon Photo-electron Interesting system Analysis of energy and momentum of the photo-electron allows to map out the band structure (here Ba2IrO4) Moser et al. NJP (2013) Solid State Spectroscopy - Introduction

19 Experimental techniques: Scattering
Ground State Excited State Incident Particule (photon/electron/neutron) Scatterd Particule Interesting system Distinct from luminescence ! Can be - elastic (without loss/gain of energy) e.g. Diffraction - inelastic e.g. Raman scattering, inelastic neutron scattering (INS) - coherent (e.g. diffraction) - incoherent (e.g. Compton scattering) Solid State Spectroscopy - Introduction

20 Solid State Spectroscopy - Introduction
The Probes 1) Electro-magnetic field 𝐸 = 𝑒 𝐸 0 𝑒 𝑖( 𝑘 . 𝑟 −𝜔𝑡) 𝐵 = 1 𝜔 𝑘 × 𝐸 𝐸=ℏ𝜔= ℎ𝑐 𝜆 𝐸 𝜆=1Å =12.4 𝑘𝑒𝑉 Solid State Spectroscopy - Introduction

21 Solid State Spectroscopy - Introduction
Absorption NMR ESR IR Photoemission XAS Scattering Raman diffraction IXS/RIXS 𝐸=ℏ𝜔= ℎ𝑐 𝜆 𝐸 𝜆=1Å =12.4 𝑘𝑒𝑉 Solid State Spectroscopy - Introduction

22 Appendix: the units Wavenumber Frequency Energy Temperature Wavenumber

23 Solid State Spectroscopy - Introduction
Absorption NMR ESR IR Photoemission XAS Scattering Raman diffraction IXS/RIXS 𝐸=ℏ𝜔= ℎ𝑐 𝜆 𝐸 𝜆=1Å =12.4 𝑘𝑒𝑉 Solid State Spectroscopy - Introduction

24 Photon Sources to cover the entire spectral range
Solid State Spectroscopy - Introduction

25 Blackbody radiation Radiance
W wire Radiance Radiation (in W) emitted per unit of area and solid angle unit in the frequency Interval 𝜔,𝜔+𝑑𝜔 (normal incidence) ℒ 𝜔, 𝑇 𝑑𝜔= 𝜔 2 4 𝜋 3 𝑐 2 ℏ𝜔𝑑𝜔 𝑒 ℏ𝜔/ 𝑘 𝐵 𝑇 −1 Continuous source in the near IR - visible range Limitation: Temperature Solid State Spectroscopy - Introduction

26 Solid State Spectroscopy - Introduction
Lamps Higher temperature emitters: ionized plasma up to 6000 K: Visible Low pressure: discrete spectral lines High pressure : continuum Solid State Spectroscopy - Introduction

27 L.A.S.E.R. (Light Amplification by Stimulated Emission of Radiation)
https://lasers.llnl.gov/ Solid State Spectroscopy - Introduction

28 L.A.S.E.R. (Light Amplification by Stimulated Emission of Radiation)
2 ℏ𝜔 1 Einstein coefficients fro absorption ( 𝐵 1→2 ), stimulated emission ( 𝐵 2→1 = 𝐵 1→2 = B) and spontaneous emission ( 𝐴 2→1 =A) 𝑑 𝑁 2 𝑑𝑡 =𝐵× 𝑁 1 ×𝜌 𝜔 −𝐵× 𝑁 2 ×𝜌 𝜔 −𝐴× 𝑁 2 𝑑 𝑁 2 𝑑𝑡 =− 𝑑 𝑁 1 𝑑𝑡 𝑁 2 𝑁 1 = 𝑒 − ℏ𝜔 𝑘 𝐵 𝑇 Equilibrium: and allow to retrieve Planck’s law LASER idea: If one can get 𝑁 2 > 𝑁 1 the number photons emitted by the system becomes greater than the number of photons absorbed by the system: ‘amplification’ ‘Inversion population’ => e.g. optical pumping Solid State Spectroscopy - Introduction

29 L.A.S.E.R. (Light Amplification by Stimulated Emission of Radiation)
en.wikipedia.org/wiki/Laser‎ Solid State Spectroscopy - Introduction

30 So far IR-visible-UV sources: a few orders of magnitude
Photon carries energy AND momentum 𝐸=ℏ𝜔= ℎ𝑐 𝜆 = ℏ𝑐𝑘 ℏ = 1.05 x m2kg s-1 c = 299 792 458 m s-1 1 eV = x J 𝐸[𝑒𝑉]~ 2×103 𝑘 [ Å −1 ] Solid in the real space 𝑎~ 3Å a b 𝑎 ∗ = 2𝜋 𝑎 ~1 Å −1 a* b* Solid in the reciprocal space Visible light only probes the center of the reciprocal space ! Equivalently l >> a No information at the atomic scale All unit cells are in phase Solid State Spectroscopy - Introduction

31 Brighter Photon Sources: Synchrotrons
Radiation of a relativistic accelerated charge Solid State Spectroscopy - Introduction

32 Brighter Photon Sources: Synchrotrons
Measuring the quality of the photon source: Brilliance ℬ 𝜔 = 𝑃ℎ𝑜𝑡𝑜𝑛𝑠/𝑠 𝑚𝑚2 × 𝑚𝑟𝑎𝑑 2×(0.1% 𝑏𝑎𝑛𝑑𝑤𝑖𝑑𝑡ℎ) Size of the source Beam angular divergence 𝜔 𝜔0 0.1%ℏ𝜔0 𝑃ℎ𝑜𝑡𝑜𝑛𝑠/𝑠 Solid State Spectroscopy - Introduction

33 Solid State Spectroscopy - Introduction
LCLS Free electron lasers 3rd Generation synchrotron (soft) 3rd Generation synchrotron (hard) ESRF 2nd Generation synchrotron NSLS X-ray tube Solid State Spectroscopy - Introduction

34 A world of synchrotrons
Solid State Spectroscopy - Introduction


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