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 IXS 2013 1

Collaborators 8/14/2013

LBNL

Zahid Hussain Yi-De Chuang Jonathan Denlinger Shih-Wen Huang Wanli Yang Ruimin Qiao Elke Arenholz

UC Berkeley

Z. Q. Qiu Jia Li R. Ramesh Jian Liu

Princeton University

M. Zahid Hasan Yuqi Xia Su-Yang Xu Nasser Alidoust Madhab Neupane

SPring-8

K. Ishii K. Ikeuchi

BNL

Ignace Jarrige Jinsheng Wen Zhijun Xu Genda Gu

APS

Yuri Shvyd’ko

Harvard University

Charles Mathy

AIST

Hiroshi Eisaki

Special thanks to

Takami Tohyama Kenji Tsutsui R. Eder K. Wohlfeld Dung-Hai Lee Ronny Thomale Suman Hossain Sujoy Roy Padraic Shafer IXS 2013 2

Talk outline

1. Introduction 2. RIXS at high resolution: dd modes in CoO • “pseudo-anti-Stokes” radiation • beyond the atomic multiplet

How does high resolution change what you can study with RIXS?

3. Quantum interference in RIXS spectra • 2-slit interference in cuprates • transforming into the time domain • interference in arbitrary experimental spectra

Where does quantum interference fit into RIXS analysis and simulation?

4. Future directions: into the time domain!

• A non-Kramers-Heisenberg calculation • New physics with ultrashort pulses • A momentum-resolved thermometer 8/14/2013 IXS 2013 3

ALS MERLIN beamline (4.0.3)  RIXS at hv~40-120eV  >~10meV RIXS resolution  Polarization control  ARPES at hv~14-120eV 8/14/2013 IXS 2013 4

2 SrCuO RIXS at the M-edge M 2,3 : 3p ½  3d (Mn 47eV to Cu 77eV) 8/14/2013 IXS 2013 5

RIXS at high resolution

dd modes in CoO

2 e g t 2g -e g dd mode t 2g 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 8/14/2013 Inter-site ZRS in quasi-0D

The observation of effects like this is of existential importance for future pump probe 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

IXS 2013

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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Quantum interference in RIXS spectra

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When a particle follows two different paths that arrive at the same place, at the same time

Cuprate orbitons (SrCuO 2 ) 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!

RIXS with a 100as X-ray pulse: 8/14/2013 IXS 2013 13

Direct, indirect and elastic scattering SIAM Charge Transfer (NiO) ~0.2fs~1/E SOC

See definitions in L. Ament review [RMP 83, 705 (2011)]

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Quantum interference in complex spectra 8/14/2013 IXS 2013 15

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 4

Wenceslas Hollar, 17 th century

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

L-edge 2.5

2 Γ t 1.5

1 A 0 SCLC(∞) B KH 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

IXS 2013

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!

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

Now Near Future

Resolution similar to k B T!

Resolution similar to ARPES

• resolving electronic superstructure and susceptibility features Flux δE~5meV Laser coherence ?

A cleaner elastic tail?

Summary

RIXS at high resolution: •

Observed temperature dependence in a simple orbiton

•

First observation of “pseudo-anti-Stokes” radiation

•

Identified many-body spectral structure in simple orbitons

Color code black: M only blue: M, L and K!

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 24

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 8/14/2013 IXS 2013 27

8/14/2013 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.

IXS 2013 Kramers-Heisenberg equation 28

When is a core hole not a core hole?

Ni orbitals in NiO 9 8 3 2 1 0 0 7 6 5 4 2p 3s 3p 3d 0.5

1 Radial distance (Angstroms) 1.5

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