Resonant Inelastic X-Ray Scattering & Electron Dynamics
Jason N. Hancock University of Connecticut [email protected]
APS, Chicago
Neutron and X-ray Scattering School 2019 June 24, 2019, Argonne National Laboratory, Argonne, IL UConn Condensed Matter Physics
Gayanath Fernando Alexander Balatsky Boris Sinkovic Theory Theory Thin films synthesis Electron spectroscopy
Jason Hancock Ilya Sochnikov Elena Dormidontova THz, Infrared, X-ray Transport Soft Matter Theory Applied physics Scanning SQUID
Barrett Wells Niloy Dutta Menka Jain PLD films, Muons, Photonics Thin film synthesis Applied physics Neutrons, ARPES
Plus strong connections with: AMO group, UConn Institute for Materials Science, New UConn Tech Park Photon Science at UConn
• Additive manufacturing
Erin Curry Kaitlin Lyszak PhD student PhD student
• Negative thermal expansion near structural quantum phase transitions
Connor Occhialini BS ’18 Sahan Handunkanda (PhD ’18) (PhD @ MIT Aug 2018)
• f-electron physics via RIXS
Donal Sheets PhD student My PhD research does/will likely use… AA BB A B CC DD E Both X-rays and X-rays Neutrons Neither I am a theorist Neutrons C D My PhD research does/will likely regard… AA BB A B CC DD E Mostly structural Advanced imaging Still figuring it out None of these studies Spectroscopy and C electronicD structure Spectroscopy in a nutshell The Electromagnetic Field
• Photons are bosons, independent, luminal
• Described by Maxwell’s equations at low energy, QED at high energy
• Fully understood, quantized, modes are described as
Vector potential: Spectroscopy, general remarks
• Sample can exchange energy with EM field
(sample) (vacuum)
One photon Optical spectroscopy X-ray absorption
Neutron Related spectroscopies: n n
Two photon ARPES Raman Inelastic X-ray Scattering EELS Photon spectroscopies
One-photon Two-photon • Can measure from reflection or transmission in • IXS and RIXS (also REXS, Raman) time or frequency domain
• Probes electronic excitations in a • Use Fresnel’s equations to determine n + ik , momentum-resolved way . 1 i 2 , 1 + i 2 and relate to fundamental behavior • Technical advances making rapid progress • X-ray absorption collected differently, through total electron or total fluorescence yield Q
Reflection Synchrotron X-ray source
Energy- integrating Drain detector A Synchrotron Transmission current Measure Two-photon scattering examples Raman=inelastic light scattering
Raman/Stokes scattering
Raman Stokes scattering
Rayleigh/Thomson scattering Raman anti-Stokes scattering
https://www.nanophoton.net/ Modern Raman scattering Kung, et al Science 347, 1339 (2015)
• Laser source=high resolution Anti-Stokes Stokes scattering scattering • Lattice excitations easy to see
• Electronic and magnetic excitations possible High Energy Resolution Inelastic X-ray Scattering
• Sector 30, Advanced Photon Source, Argonne National Lab
• 23,724 eV incident energy
• <1 meV incident bandwidth
• Resolving power Ei/∆Ei= 2×107
• 9 analyzers sample, 9 momenta transfers simultaneously, 9m arm
• 1.5 meV energy resolution
• 20µm x 5µm spot size
• Measures energy and momentum distribution of lattice vibrations S(~q , ! ) Scan101 {2.5, 1.5, 0} IXS from phonons 0.12
0.10
X 0.08 Molecular
dynamics ) � cts x (
0.06 M Li et al, PRL 107 195504 (2011) IXS signal • IXS measures collective modes 0.04 of lattice system: phonons
Energy of each mode X 0.02 at wavevector k
What about electronic or magnetic collective modes? Use RIXS! 0.00 -10 0 10 20 30 ΔE (meV) S. U. Handunkanda, et al PRB 92, 134101 (2015) What is this? AA BB A B CC DD E Balmer series of There is more than The emission A flat rainbow snake A fashionable belt spectrum of a emission by hydrogen one correct answer star atC z=0 redshift D What is this? AA BB A B CC DD E Balmer series of There is more than The absorption A flat rainbow snake A fashionable belt spectrum of a absorption by hydrogen one correct answer star atC z=0 redshift D Balmer series
• Describes transitions between quantized energy levels in hydrogen (one proton, one electron)
Schrodinger equation for 1/r potential:
Hydrogen wavefunctions:
Energy levels: Bohr radius: Quantum numbers: n, l, m
Generalize for nuclear charge +Ze:
2 Z RH na0 aZ,n = Ez,n = 2
Inner “core” electrons are 1s sees full nuclear much smaller than outer charge +Ze and can effectively screen nucleus for other electrons
1s Ze Core electrons much more 2s tightly bound than outer ones
2p
Lyman (1->n) series for multi-electron atoms form “K” X-ray edges 2p sees only unscreened +(Z-4)e Atomic transitions in solids Multi-electron Hydrogen atom atom in solid
Continuum E=0 3s,3p,3d M EF 2s,2p 3d 3p 3s
L 1s 2p Light absorption by water 2s
K
1s X-ray transition lines
Continuum M
L
K http://xdb.lbl.gov • Absorptive transitions of higher Z Absorption atoms lie in X-ray region X-ray absorptionQ spectroscopy (XAS)
Synchrotron X-ray source E=0 EF 3d 3p 3s X-ray Detector
Drain A
L current 2p 1 - 0.5 2s m H Near-edge 0.4 Extended X-ray structure 0.3 Fine Structure 0.2 Coefficient 1s 0.1 (Cu K edge example) 0.0 6500 7000 7500 8000 8500 9000 9500 10 000
Absorption 10 Energy eV 10 E c La2CuO4 d L 8 d 9 6 E||c H L 4 2 Count Rate (cts/sec) Count 8985 8990 8995 9000 9005 Energy (eV) X-ray absorption spectroscopy, uses to determine valence state
Example: Yb
Has two stable valence states Yb+2, has f14 full shell - nonmagnetic ion Yb+3 has f13 one hole in f shell - long j=7/2 mag moment
Real materials can have things in between, depends on interactions
Yb14MnSb11 - no magnetic moment coming from Yb
YbAl3 - long moment paramagnet from Yb+3 in f13 state X-ray edge absorption… and RIXS
4p 4p 4p e- e-h pair excitations
h+ 10 E c La2CuO4 8 6 E||c 4 2 Count Rate (cts/sec) Count 8985 8990 8995 9000 9005 Energy (eV)
X-ray absorption 1s process 1s
Copper K (example) Resonant Inelastic X-ray Scattering (RIXS)
• Resonant Raman spectroscopy, with resonance at an X-ray edge • Described by Kramers-Heisenberg formula • Large momentum transfer • Atomic-species and valence-specific information ~ i, ki ~ f , kf • Lots of control (polarization, angle, Q, Ei) ! = ! ! i f k = k k k i f ki kf
Kramers- Heisenberg: Q Diamond, UK LCLS, Stanford Soleil, Paris ... RIXS today CLS, Canada APS, Chicago NSLS-II, New York ESRF, Grenoble
SPring8, Japan
ALS, Berkeley
PETRA, Hamburg LCLS and SSRL, Stanford SLS, Switzerland • Immense worldwide investment
• BroadeningDaniel impact Mazzone Donal Sheets2000 1000 500 meV L
H 2000 2000 SIX instrument at NSLS-II (commissioning200 now)1000 1000 100 500 meV L
H 500 50 meV L H 200 NSLS-II
Resolution 200 20 100 2000 100 10 50 1000 1995 502000 2005 2010 2015 2020
Resolution 500 20 Cu L3 edgemeV L H Resolution 20 Year 10 200 199510 2000 2005 2010 2015 2020 1995 2000 1002005 2010 2015 2020 Year 50Year
Resolution 20 10 1995 2000 2005 2010 2015 2020 Year Energy dispersion in RIXS
4p L Raman-Stokes 150 Fluorescent Dispersion units
. Dispersion
arb 100 H
2s, 2p 50
Intensity 0 8970 8980 8990 9000 9010 Scattered Photon Energy eV
EmissionK 2 ,5line H L • Fluorescent-type energy dispersions 1s are independent of Ei Energy dispersion
4p L Raman-Stokes 150 Fluorescent Dispersion units
. Dispersion
arb 100 H
2s, 2p 50
Intensity 0 8970 8980 8990 9000 9010 Scattered Photon Energy eV
• Features following Ei represent HRamanL (RIXS) processes, connected to lower 1s energy (valence) physics Practical difference: Soft vs Hard RIXS
http://henke.lbl.gov/optical_constants/ Practical difference: Soft vs Hard RIXS
Tender X-ray
X-rays must be in vacuum X-rays can be in helium, air atmosphere
More scattering, lower penetration Less scattering, more bulk information
SIX instrument at NSLS-II (commissioning now) MERIX at APS, 29-I-D-B (world-leading) Technical difference: Soft vs Hard RIXS How to disperse the X-rays? Prism?
Grating? Crystal?
Index of Refraction = (1-delta)-i(beta)
If feature sizes can Feature size (atoms) of be on order wavelength order X-ray wavelength Inefficient Soft X-ray ~ 1 nm Index changes too small to be effective Hard X-ray << 1nm Technical difference: Soft vs Hard RIXS
ADRESS beamline at PSI (no spectrometer) ERIXS endstation at ESRF (no beamline shown)
MERIX spectrometer, sector 27-ID-B, APS Scientific difference: Soft vs Hard RIXS
Tender X-ray
3d transition metal K edges 3d transition metal L edges Rare-earth/4f L edges Rare-earth/4f M edges 5d transition metal L edges
tender
Edge and energy are determined by elements present and scientific question 3d 4d 4f 5d N-particle spectroscopy
Loosely bound itinerant states Direct RIXS
Optical States included 3d Neutron in Heff { Inverse ARPES photoemission
N-1 N N+1 Tightly bound 2p3/2 core electrons 2p1/2 2s
“Direct” RIXS at transition metal L edges N-particle spectroscopy
Loosely bound 4p itinerant states
States included { Indirect in Heff RIXS Direct RIXS
Optical Neutron Inverse ARPES photoemission
N-1 N N+1
Tightly bound electrons “Indirect” RIXS at transition metal K edges High-Tc cuprate superconductors
1/2-filled Hole-doped CuO2 planes CuO2 planes (La2-xSrxCuO4) (La2CuO4)
• Strong repulsion favors Hole doping a 2D Mott insulator induces antiferromagnetic state high-temperature superconductivity
• Hubbard model describes AFM Mott gap dispersion in high-Tc superconductors (Cu K edge)
Abbamonte et al. PRL 83, 860 (1999)
Kim et al. PRL 89, 177003 (2002) Hasan et al. Science 288, 1811 (2000) Incident energy and temperature dependence
Lu, JNH, et al. PRL 95, 217003 (2005) Ellis, et al. PRB 77, 060501 (2008) Lu, JNH, et al. PRB 74, 224509 (2006) Experimental realization of 0-D HTSC
CuO4 plaquettes O
B3+ ions Cu O O CuB2O4, <001> view
O • Low-Z nonresonant species
• Tractable electronic structure
• Ideal system for exploring RIXS phenomenology
Hancock et al. PRB 80, 092509 (2009) Hancock et al. NJP 12, 033001 (2010) B. Roessli et al, PRL 86, 1885 (2001) One hole, 8eV one plaquette
Many wavefunctions of varied angular • MO 4eV symmetry “Molecular Orbital” • Ground and molecular orbital states are the only ones of x2-y2 symmetry
• Simple RIXS selection rule (for indirect, “Ground state” K edge transitions): symmetry=constant
g 0eV Without core hole With core hole
PS “Poorly-screened”
MO
“Well-screened”
g WS 1-plaquette RIXS calculation 9005 9005 (a) low high (b) low high
9000 9000 9 4px,y d PS g eV absorption 8995 8995 absorption REXS REXS Energy RIXS 4p WS 8990 8990 z 2 2 Incident
Incident Energy (eV) Incident Energy x -y basis RIXS d10L¯ 8985 8985 with hybridization x2-y2 sector, Multi-orbital, 1-plaquette model withmulti-plaquette core holemodel 8980 8980 MO 2 0 2 4 6 8 0 2 4 6 8 10 12 14 Ei lineshape analysis capable of giving Energy Transfer eV • Energy Transfer eV phase information
A simple cuprate, CuB2O4
CuO2 planes CuO4 plaquette (La2CuO4) (CuB2O4) • Cluster modeling gave good, but imperfect agreement
MO
Hancock et al. PRB 80, 092509 (2009) g Hancock et al. NJP 12, 033001 (2010) Ê
Ê
Ê ÊÊ
Ê Ê
Ê Elusive properties of MO excitation
ÊÊ Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê 50 L 50 Ê Ê Lorentzian fit Ê
Ê cps Ê Ê Ê H Ê Ê 8984 eV Ê 40 Ê Ê Ê 8985 CuB2O4 ‡ Ê Ê ‡ Ê 40 8986 30 ‡‡‡ Ê Ê Ê ‡ 8987 Ê Ê ‡ Ê
Ê Intensity Ê ‡ Ê Ê 20 Ê Ê 8988 ‡‡ ‡ Ê Ê Ê 8989 Ê ‡ Ê 30 Ê Ê Ê Ê Ê ‡ ‡ Ê Ê 10 Ê Ê Ê 8990 Ê Ê Ê Ê ‡‡ ‡ Ê Ê ‡ ÊÊ ÊÊ ÊÊÊÊÊ ‡ ‡ 8993 ÊÊ Ê Ê Corrected Ê Ê ‡ ‡ Ê Ê ÊÊÊÊÊ ÊÊÊÊÊÊÊÊÊ ÊÊ0Ê Ê Ê Ê Ê Ê Ê ‡‡‡‡‡‡‡‡‡ ‡‡‡‡‡‡‡ 3 4 5 6 7 8 9 10 20 Ê ÊÊ Energy Transfer eV Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê 10
L 50 Ê Ê
H L Ê corrected (cps) RIXS Intensity,
cps Gaussian fit
Ê H Ê Ê Ê 40 Ê Ê Ê ‡ Ê Ê 0 ‡ Ê 30 ‡‡‡ Ê Ê 0 2 4 6 8 10 ‡ Ê Ê ‡ Ê
Intensity Ê ‡ Ê Energy Transfer (eV) Ê 20 Ê Ê ‡‡ ‡ Ê Ê Ê Ê ‡ Ê Ê Ê Ê Ê ‡ ‡ Ê Ê 10 Ê Ê Ê Ê Ê Ê Ê ‡‡ ‡ Ê Ê ‡ ÊÊ ÊÊ ÊÊÊÊÊ ‡ ‡ ÊÊ Ê Ê Corrected Ê Ê ‡ ‡ Ê Ê ÊÊÊÊÊ ÊÊÊÊÊÊÊÊÊ ÊÊ0Ê Ê Ê Ê Ê Ê Ê ‡‡‡‡‡‡‡‡‡ ‡‡‡‡‡‡‡ 3 4 5 6 7 8 9 10 Energy Transfer eV • Gaussian lineshape H L
• Shifting resonance behavior (eV) Peak Energy
Hancock et al. PRB 80, 092509 (2009) Hancock et al. NJP 12, 033001 (2010) Shen, etal,PRL93,267002(2004) Peak Energy (eV) • • Electron-phonon couplingattheMOexcitation Gives anestimate oftheelectron-phonon couplingparameter Simple Franck-Condon modelexplainsremaining features of thespectra Hancock etal.NJP12,033001(2010) Hancock etal.PRB80,092509(2009) Theory of RIXS in the cuprates
Kramers-Heisenberg Formula
• Calculations model RIXS cross section to understand electronic structure of high-Tc superconductors Chen, ... Hancock, ... et al. PRL 105, 177401 (2010) Magnetically-ordered states
• Magnetic interactions between magnetic ions can lead to ordered states
• Disturbance in order forms “spin waves” or “magnons”
• Like sound, magnons carry momentum and energy
• Dispersion relation is important Magnetic excitations via RIXS
• 2008 Cu K edge RIXS showed La CuO bi-magnon feature, consistent 2 4 with Raman q=0 result
• 2009 Cu L edge (soft X-ray) RIXS showed a shoulder of elastic line Hill, Blumberg, et al, PRL 100 097001 (2008) consistent with single-magnon excitation
Braicovich, Ghiringhelli, et al, PRL 102 167401 (2009) Extended interactions in a Mott insulator Sr2CuO2Cl2
Excitation energy
Sr2CuO2Cl2
Crystal field excitations • Suggestive of extended magnetic interactions in 2D Mott insulator
Guarise, ...JNH,... et al. PRL 12, 033001 (2010) Wells, et al, PRL 74, 964 (1994) Iron pnictide superconductors and Correlated 5d systems
BaFe2As2 SrIr2O4
Raw data
2nd derivative
Zhou, et al, Nature Comm. 4, 1470 (2013) Kim, et al, Phys. Rev. Lett. 108, 177003 (2012) Other RIXS highlights
• Orbiton dispersion
• Phonons excited through core hole intermediates
• Spin-2 (triplon) excitations
• Incipient CDW effect at Tc in YBCO Ulrich, et al PRL 103, 107205 (2009) Schlappa, et al PRL 103, 047401 (2009) • Paramagnon fluctuations in doped cuprates
Ghiringhelli, et al Science 337, 821 (2012) Le Tacon, et al, Nat. Phys. 2011 Yavas, et al JPCM 22, 485601 (2010) Soft X-ray RIXS work L s sec
60 12 1 Yb M5 RIXS H • Rediscovery of the Kondo gap w YbInCu4 L H (now with X-rays) 10
photons ê 40 8 H 3 W -
20 4 1 cm T<40 K -
• 1st mapping of magnon spectra in Intensity > 1 0 T 40 K 0 L Sr2CuO2Cl2 (non-local exchange) 0 1 2 RIXS Energy eV Single crystals from John Sarrao, LANL • Connected RIXS to edge singularity physics H L
Sr2CuO2Cl2
Single crystals from Helmut Berger, EPFL
Hancock et al. (2011) Kotani, in review (2011) Guarise et al. PRL 12, 033001 (2010) Single crystals from Enrico Giannini group, Geneva Hancock et al. PRB 82, 020513R (2010) Future technique directions with RIXS
• Time-resolved RIXS - XFEL • Higher energy resolution
Energy scales in correlated electron systems Schematic UF-RIXS setup at LCLS • Tender X-ray RIXS - new edges and opportunities • Polarization analysis of scattered photon
High potential to resolve subtle changes, identify In-vacuum RIXS spectrometer at DESY excitation channels Summary/outlook
• RIXS is a 21st century technique, deep probe of exotic excitations
• Many opportunities on horizon for new generation of synchrotron scientists
• APS and NSLS-II have world-leading opportunities in hard and soft RIXS science
• New opportunities for science of correlated electron materials
• Mixed-valent/Kondo lattice physics
• High-temperature superconductivity
• Search for exotic phases for quantum information science Thank you!