Resolving the Line Shape of Orbitons in Mott Insulators

Report
New paradigms for RIXS: 30meV resolution, and
reading the quantum interference pattern
L. Andrew Wray
Advanced Light Source, Lawrence Berkeley National Laboratory
8/14/2013
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Collaborators
LBNL
Princeton University
APS
Zahid Hussain
Yi-De Chuang
Jonathan Denlinger
Shih-Wen Huang
Wanli Yang
Ruimin Qiao
Elke Arenholz
M. Zahid Hasan
Yuqi Xia
Su-Yang Xu
Nasser Alidoust
Madhab Neupane
Yuri Shvyd’ko
SPring-8
Special thanks to
UC Berkeley
Z. Q. Qiu
Jia Li
R. Ramesh
Jian Liu
8/14/2013
K. Ishii
K. Ikeuchi
BNL
Ignace Jarrige
Jinsheng Wen
Zhijun Xu
Genda Gu
IXS 2013
Harvard University
Charles Mathy
AIST
Hiroshi Eisaki
Takami Tohyama
Kenji Tsutsui
R. Eder
K. Wohlfeld
Dung-Hai Lee
Ronny Thomale
Suman Hossain
Sujoy Roy
Padraic Shafer
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Talk outline
1. Introduction
2. RIXS at high resolution: dd modes in CoO
• “pseudo-anti-Stokes” radiation
How does high resolution change
what you can study with RIXS?
• beyond the atomic multiplet
3. Quantum interference in RIXS spectra
• 2-slit interference in cuprates
• transforming into the time domain
Where does quantum interference fit
into RIXS analysis and simulation?
•interference in arbitrary experimental spectra
4. Future directions: into the time domain!
• A non-Kramers-Heisenberg calculation
• New physics with ultrashort pulses
• A momentum-resolved thermometer
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ALS MERLIN beamline (4.0.3)
RIXS at hv~40-120eV
>~10meV RIXS resolution
Polarization control
ARPES at hv~14-120eV
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RIXS at the M-edge
SrCuO
2
M2,3: 3p½3d (Mn 47eV to Cu 77eV)
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2
RIXS at high resolution
dd modes in CoO
t2g-eg dd mode
eg
t2g
200meV resolution
dd mode
30meV resolution
Temperature dependence from “any old excitation”
Temperature dependence in a
large spin 3D AF Mott insulator
LSMO MI transition
K. Ishii, PRB 2004
C. Monney, PRL 2013
Inter-site ZRS in quasi-0D
The observation of effects like this is of
existential importance for future pumpprobe time resolved RIXS
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Pseudo-anti-Stokes
pAS will instantly show where the
energy is in pump-probe RIXS
(AS will show where energy is after 1-2
scattering events)
CoO AS states:
20meV: spin
38meV: spin-orbit
47meV: mixed
Wray et al., Phys. Rev. B 88, 035105 (2013)
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Shaking up the neighbors
Model vs. Data
12 states/Co
atom from
0-150meV
Poisson
AM calc
Wray et al., Phys. Rev. B 88, 035105 (2013)
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Mini-Summary
RIXS at high resolution:
• Observed “final state shake-up” excitations
• Identified a likely role of electronic instabilities
• First identification of “pseudo-anti-Stokes”
• Will be an important q-independent signal in the time domain
• Just one of many kinds of temperature dependence yet to be seen in RIXS
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3
Quantum interference in RIXS spectra
When a particle follows two different paths that
arrive at the same place, at the same time
Cuprate orbitons (SrCuO2)
RIXS with just two core hole symmetries!
You don’t need a ‘real’ AM calculation to understand cuprate RIXS: see Sala et al., New J. Phys. 13, 043026 (2011)
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Transforming to the time domain
Knowing amplitudes and phases lets you take
Kramers-Heisenberg into the time domain!
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RIXS with a 100as X-ray pulse:
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Direct, indirect and elastic scattering
SIAM Charge Transfer (NiO)
~0.2fs~1/ESOC
See definitions in L. Ament review
[RMP 83, 705 (2011)]
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Quantum interference in complex spectra
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Future directions
into the time domain!
Have you ever seen the momentum-vs-energy dispersion relation of a Cooper pair?
RIXS gives information other spectroscopies are blind to
RIXS with sub-fs pulses and time-resolved (pump-probe) capabilities will take X-ray
science to new places
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Self consistent lifetime correction (SCLC)
SCLC(1): the natural answer for
Kramers-Heisenberg
SCLC(∞): the non-perturbative
answer for a Hamiltonian
K. Okada, A. Kotani, H. Ogasawara, Y.
Seino, B. T. Thole, PRB 47, 6203 (1993);
L. A. Wray et al., PRB 86, 195130 (2012).
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Beyond Kramers-Heisenberg
Another way to get a coherent core hole is to use a coherent, sub-femtosecond X-ray pulse.
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Changing the core hole clock
2π/4eV=1fs
L-edge
Γtot (eV)
2.5
2
SCLC(∞)
A
KH
1.5
1
B
0
1
Time (fs)
2
Core hole decay is ~20% faster on a small
time scale, during overlap with the 100as
incident pulse.
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Same effect at the L- and K- edges!
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Tracking energy in time and momentum
pAS will instantly show where the
energy is in pump-probe RIXS
(AS will show where energy is after 1-2
scattering events)
CoO AS states:
20meV: spin
38meV: spin-orbit
47meV: mixed
Wray et al., Phys. Rev. B 88, 035105 (2013)
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K
Excitation Mechanisms
1. Atomic monopole shake-up
Features:
1. Broad Q-dependence
2. Large resolving power
L
Excitation Mechanisms
1. Atomic multipole
2. Intersite/intraband monopole
Features:
1. High throughput!
2. Weak elastic line!
Now
M
Excitation Mechanisms
1. Strong atomic multipole
2. 10-30meV resolution:
•Final state shake-up
•T-dependence
Features:
Strong quantum interference
Surface sensitivity to several unit
cells
Near Future
Resolution similar to kBT!
Resolution similar to ARPES
• resolving electronic
superstructure and
susceptibility features
Flux
δE~5meV
Laser coherence
?
A cleaner elastic tail?
Summary
Color code
RIXS at high resolution:
• Observed temperature dependence in a simple orbiton
black: M only
blue: M, L and K!
• First observation of “pseudo-anti-Stokes” radiation
• Identified many-body spectral structure in simple orbitons
Quantum interference
• Fitted phase information from 2-slit interference in cuprates
• Experimental RIXS data transformed into the time domain for the first time
• Introduced ζ function to identify interference in arbitrary experimental spectra
• QI in core hole decay improves multiplet and ultrafast simulations
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M vs L vs K
M
Fast resonance processes
Elastic Fano effect
1/q~20nm
Best current resolution (10meV)
L
• 1/q~10nm
• Best flux
• Large spin-orbit
coupling gives strong
spin cross section
K
1/q<< lattice constant
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Energy resolution and the time scale of dynamics
Energy resolution sets the observable time scale. With 200meV resolution, you have ~3fs.
With 20meV resolution, you have ~30fs
Low energy resolution:
local physics
High energy resolution:
less local physics
Excitations that take a long time to emerge can only be studied with high resolution
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Fano tails
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The dynamics of RIXS
“What is the RIXS spectral function?”
RIXS reveals a spectral decomposition
of the many-body quantum state in
the time window of core hole decay.
Kramers-Heisenberg equation
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When is a core hole not a core hole?
Ni orbitals in NiO
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Electron probability density
8
2p
7
6
5
4
3s
3
3p
2
3d
1
0
0
0.5
1
1.5
Radial distance (Angstroms)
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