Paul Scherrer Institut, CH-5232 Villigen, Switzerland≪ WIR SCHAFFEN WISSEN - HEUTE FÜR MORGEN ≫1

Non-Equilibrium Dynamics Studied by
Femtosecond Laser-Pump/X-Ray Probe Diffraction

G. Ingold
FEMTO GroupPaul Scherrer Institut
Laboratory for Synchrotron Radiation
Cheiron School 2011
SPring-8, JapanSep 25 - Oct 5, 20112

Motivation
Dynamics, Correlations and Couplingin Ultrafast Phase Transitions
in Condensed Matter:
Transition from microscopic tomacroscopic behaviour

3

Bibliography I• Non-resonant (grazing incidence) diffraction- S. L. Johnson et al., Non-equilibrium phonon dynamics studied by grazing-incidence femtosecond X-ray crystallography, Acta Cryst. A66 (2010) 157.
- I. K. Robinson and D. J. Tweet, Surface x-ray diffraction, Rep. Prog. Phys. 55 (1992) 599.

• Resonant diffraction- M. Altarelli, Resonant X-ray Scattering: A Theoretical Introduction, Lect. Notes Phys. 697 (2006) 201, Springer- S. W. Lovesey et al., Electronic properties of crystalline materials observed in X-ray diffraction, Physics Reports 411 (2005) 233.
- J. P. Hill and D.F. McMorrow, X-ray Resonant Exchange Scattering: Polarization Dependence and Correlation Functions, Acta Cryst. A52 (1996) 236.
- S. W. Lovesey and S. P. Collins, X-Ray Scattering and Absorption by Magnetic Materials, Clarendon Press, Oxford, (1996).

• Strongly correlated systems:- Y. Tokura, Critical features of colossal magnetoresistive manganites, Rep. Prog. Phys. 69 (2006) 797.
- E. Dagotto et al., Colossal Magnetoresistant Materials: The Key Role of Phase Separation, Physics Reports 344 (2001) 1.
- M. Imada, A. Fujimori and Y. Tokura Metal-insulator transitions, Rev. Mod. Phys. 70 (1998) 1039.

• Magnetization dynamics- A. Kirilyuk et al., Ultrafast optical manipulation of magnetic order, Rev. Mod. Phys. 82 (2010) 2731.

4Bibliography II• Inelastic X-ray scattering- P. Abbamonte et al., Ultrafast Imaging and the Phase Problem for Inelastic X-Ray Scattering, Adv. Mater. 22 (2010) 1141.
- J.P. Reed et al., The Effective Fine- Structure Constant of Freestanding Graphene Measured in Graphite, Science 330 (2010) 805.
- P. Abbamonte et al., Implicit spatial averaging in inversion of inelastic x-ray scattering data, Phys. Rev. B 80 (2009) 054302.

• Multiferroics- K. W. Wang et al., Multiferroicity: the coupling between magnetic and polarization orders, Advances in Physics 5 (2009) 321.
- D. Khomskii, Classifying multiferroics: Mechanisms and effects, Physics 2 (2009)- J. van den Bring and D. Khomskii, Review Article: Multiferroicity due to charge ordering, J. Phys.: Condens. Matter 20 (2008) 434217.
- S.-W. Cheong and M. Mostovoy, Multiferroics: a magnetic twist for ferroelectricity, Nature Materials 6 (2007) 13.
- H.C. Walker et al., Femtoscale Magnetically Induced Lattice Distortions in Multiferroic TbMnO3 , Science 333 (2007) 1273.

5

Ballet dancing: choreography of complex motion[ photos: www.staatsballett-berlin.de ]... coordinated motion due to mutual vision and musical rhythm ...

6

Biology: the formation process vast oceanic fish shoals[figures: www.seatops.com][N. Markis et al., Science 323 (2009)]• In the beginning the fish are widely distributed in a diffuse low-density layer close to seafloor• Shoal formation is triggered by reduction in light level (external stimulus)• Shoals evolve from small, isolated catalyzing clusters to extensive, dense horizontal layers• Having reached a critical population density, coherent shoal-forming waves appear• Vast shoals migrate by synchronous swimming of hundreds of millions of individual fish
• Vast shoals remain stable in the night and dissipate as light levels increase with sunrise

7

Choreography: timescale of coherent motion

Ballet dancing: ∼ 10−2 - 101 s

Spin wave (magnon) excitation: ∼ 10−13 - 1012 s

8Correlated Structural and Electronic Dynamics in Complex Materials
Goal: Resolve correlated dynamics: lattice, charge, orbital and spin orderreal time & atomic resolution• Lattice dynamics: (time domain & atomic resolution): τvib ≃ 100 fs (vibrational period)• Electron dynamics: (charge-, orbital-, spin-order): τe−ph ≃ 1 ps (e-phonon);τe−e ≃ 10 fs (e-e scattering); τe−corr ≃ 0.1 fs (e-correlation)9

... warning: even simple mechanical systems exhibit complex behaviour depending on the boundary
conditions ...

Coupled Pendula
regular motion

Double Pendula
chaotic motion

10This lecture is mainly about our R & D work
- work in progress -Laser-pump / X-ray-probe Experiments
Femtosecond Probing ofLong-Range Orderin Solids with
Non-resonant and Resonant
X-Ray Scattering
11Outline of the lecture- Motivation- Why study strongly correlated systems & perovskite structure ?
- Short remark: stimulated non-equilibrium phase transition- All optical pump-probe: reflectivity & TR-MOKE- Femtosecond X-rays generated with undulators & relativistic electron beams( generation at slicing sources & XFELs, synchronization, timing )- Femtosecond grazing incidence X-ray diffraction( experimental set-up & technique, coherent phonon dynamics )- Laser-pump / X-ray-probe: hard X-rays( Slicing source: non-resonant diffraction on manganites )- Laser-pump / X-ray-probe: soft X-rays( Free electron laser : resonant diffraction on multiferroics )- Summary & conclusions

12

Why strongly correlated systems& perovskite structure ?

13

Effective One-Particle Approach ⇔ Electronic Correlations
Dynamics is becoming accessible by DMFT theories

delocalizing effects
kinetic energy: T
FM metal⇔⇔

localizing effects
Coulomb repulsion: U
AFM CO-OO insulator

Tuning between these two phases: chemical substitution (doping), lattice strain,
magnetic field, electrical field, . . .

14

Transition Metal Oxides with Perovskite Structure ...
... display a broad range of interesting phenomena, including ...

Electrical

High-Tc Superconductivity (HTSC)
Cuprates ( Bednorz & Müller, Nobel Prize 1987 )Magnetic

Colossal Magnetoresistance (CMR)
Manganites ( → GMR: Fert & Grünberg, Nobel Prize 2007 )Electrical & Magnetic

Multiferroicity
15

Manganites: Insulator-Metal Phase Control - Pr0.7 Ca0.3 MnO3

[Y. Tokura, Rep. Prog. Phys. 69 (2006) 797]

MIT control by ”photo doping”: possible on the femtosecond time scale ?

16High-Tc Superconductivity[ D. Fausti et al., Science 331 (2011) 189. ]- this topic will not further be discussed in this lecture -17

Phase Control in Multiferroics[ N. Spaldin and M. Fiebig, Science 309 (2005) ]strain σ ↔ stress ǫ / electric field E ↔ polarization P / magnetic field H ↔ magnetization M

Magnetoelectric multiferroicity:
coexistence of spontaneous ferroelectricity and ferromagnetism
18

Phase Control in Multiferroics
Thermodynamic expansion of the free energy:

Derivatives provide polarization P and magnetization M:

Linear magnetoelectric effect: components αij of tensor α for P and M[ M. Fiebig, J. Phys. D: Appl. Phys. 38 (2005) ]⇔ Recent demonstration of magneto-electric coupling in TbMnO3 (static):[ H.C. Walker et al., Science 333 (2011) ]19

Motivation
The essence of Turning
Physics into Technology
Relies on Control:
electricity with magnetism
magnetism with electricity
elasticity with magnetism
etc.

20

Multiferroic ErMn2 O5 : Manipulating Magnetic Moments with Electric Fields[Bodenthin PRL 100 (2008)][Cheong & Mostovoy Nat Mat 2007]

Spontaneous electric polarization P // b-axis at TC1 = 39.1 K induced by non-collinear magnetic moments(a) Static RESOXS on magnetic (1/2 0 1/4) reflection at Mn L3 -edge: temperature dependence(b) Intensity difference due to (static) electric field

Future plans: use half cycle THz E-fields for ultrafast switching21

Short remark: stimulated
non-equilibrium phase transtition22

Non-equilibrium phase transitions

Thermal equilibrium:
Idealized state where all the memory about the initial state is lost due to relaxation processes
Microstates A, B, C: Dynamics obeys detailed balancemNonequilibrium:
Dynamic, involving flow of time, on equal footing with spatial coordinates
Microstates A, B, C: transitions occur only clockwise, stationary state out of equilibrium[ H. Hinrichsen, University Würzburg ]23

Stimulated (Photoinduced) Non-Equilibrium Phase Transitions
equilibrium⇔?

m
Lattice(heat bath)24

Fingerprint of a nonthermal effect• pump - pulse: polarization dependence• double - pump: ultrafast coherent control- We have demonstrated this for coherent phonon excitation (see later) - Later it has also been shown for coherent spin wave excitation -25

Double-Pump: Ultrafast Coherent Control of Spin Waves
IR induced spin waves in DyFeO3[ Kirilyuk et al., Rev. Mod. Phys. 82 (2010) ]THz induced spin waves in AFM NiO[ Kampfrath et al., Nat. Photonics 5 (2011) ]26

pump-probe→ all optical: reflectivity & TR-MOKE→ laser-pump / X-ray probe27

Pump-Probe Measurements- pump- or probe-pulse: laser, X-ray, electrons, E-field, H-field, ...
(... choose any combination ... depending on the experiment ... )”Start - Stop” type of experiment( reminds us of time-of-flight measurements, but we don’t use TAC conversion )- trick: convert time-measurement ∆ t → distance-measurement ∆ d( ↔ use optical delay line: c ∼ 0.3 µm / fs )- pump-probe time delay ∆ t → ∆ d = c · ∆ t / 2( ∆ t = 3 fs ∼ ∆ d = 1 µm )28

Pump-Probe Measurements
laser-pump / laser-probe[ Uni Konstanz ]laser-pump / X-ray probe[ FEMTO / PSI ]- Time-resolved data are recorded as a function of delay time ∆ t between pump and probe- Stroboscopic measurement over millions of shots: sample recovery time τrecov << 1 / frep−rate- Time resolution: ∆ τ = τpump + τprobe + ∆ τsyn−jitter + ∆ τsyn−drift- Task: measure pulse lengths τp and the uncertainty ∆ τs due to synchronization jitter and drift- In the IR/optical regime, non-linear effects can be employed- But: cross sections for non-linear effects (i.e. parametric conversion) in the x-ray regime are very small[ P. Eisenberger et. al., PRL 23 (1969); PRL 26 (1971) ]29

Example 1: All Optical Reflectivity Measurements- Coherent Phonons in Charge Density Wave System TiSe2 -[ Vorobeva et al., Phys. Rev. Lett. 107 (2010) ]- Optical reflectivity measures the variation of the dielectric function in the material- Microscopic mechanism ⇒ timeresolved X-ray diffraction (TR-XRD) to track the atomic positions

30

Example 2: All Optical MOKE Measurements- Demagnetization Dynamics in Ferromagnetic Ni time-resolved magneto optical Kerr measurement (TR-MOKE)[ http://www.physik.uni-kl.de ]magnetization Ni[ Koopmans et al., Nat Mat 9 (2008) ]- The Kerr rotation and ellipticity depend in first oder linearly on the sample magnetization- Different transition probabilities of spin-up and spin-down electrons for left & right polarized light- Microscopic mechanism ⇒ timeresolved resonant X-ray diffraction (TR-RXRD) to track the electronicand spin states in an element specific manner⇒ timeresolved X-ray circular dichroism (TR-XMCD) to track the orbitaland spin states separately in an element specific manner

31

Example 3: All optical measurement on Phonon-Magnon Coupling- Coherent Optical Phonons and Parametrically Coupled Magnons -[A. Melnikov et al., PRL 91 (2003)]- Optical phonons as driving mechanism to coherently excite the spin system in Gd at 3 THz- Even (odd) reflected SH intensity measures the pump-induced spin (magnetization) dynamics- Finite transfer time between lattice and spin system below time resolution ≤ 100 fs

32

Femtosecond X-rays generated with
undulators & relativistic e-beams→ laser sliced or compressed e-beams→ femtosecond polarized x-rays

33

Femtosecond (fs) X-rays: fs electron bunch ⇒ fs X-ray pulse- Generation of a fs electron pulse: copressing or slicing a long bunch- Method: manipulation of relativistic electrons in phase space- Step 1: energy modulation of the e-bunch with oscillating E-fieldcompressing: E-field = rf cavity fieldslicing:
E-field = optical laser field(correlated energy transfer)(resonant energy transfer)- Step 2: energy-momentum dispersion in a static B-fieldcompressing: B-field ↔ magnetic compressor
slicing:
B-field ↔ slicing spectrometer- Generation of a fs X-ray pulse: undulator radiation- Step 3: energy-momentum dispersion in a static oscillating B-fieldcompressing: XFEL facility ↔ ampl., coh., lin & circ pol., fs X-rays
slicing:
slicing facility ↔ spon., incoh., lin & circ pol., fs X-rays

34

Femtosecond Slicing Source FEMTO at SLS: 5 - 12 keVResonant laser-electron interaction in a static undulator magnetic field:
1. step: modulator
2. step: dispersion
3. step: radiatorlaser energy modulation

pulse separation[ R. Schoenlein et al., Science 287 (2000);
10

fs X-ray generation

S. Khan et al., PRL 97 (2006);

P. Beaud et al., PRL 99 (2007) ]- Only the laser electric field (∼ 10 V/m) couples to the electrons- Highly relativistic electrons: laser magnetic field (∼ 30 T) does not affect the electron trajectory35

Femtosecond Soft X-Rays & Flexlibe Polarization: 0.5 - 2.5 keV
BESSY slicing facility[ S. Khan et al., PRL 97 (2006) ]APPLE II undulators: lin / circ pol

measured Stokes parameters[ J. Bahrdt et al., NIM A 467 (2001) ]Example TR-XMCD: fs demagnetization in ferromagnetic Ni - spin & orbital momentum dynamics[ Ch. Stamm et al., Nat Mat 6 (2007); Phys. Rev. B 81 (2010); I. Radu et al., Nature 472 (2011) ]36

FEMTO Slicing Source: Laser-Pump/X-Ray-Probe Experiments (200 fs)

Laser-synchronization: cavity feedback

Electron orbit: position feedback & top operation
ID

Feedback systems ⇔ Spatiotemporal stability[G. Ingold, AIP Conf. Proc. 879 (2007)]

37

Pump-Probe Experiments - Laser Slicing Source - Synchronization

38

FEMTO Slicing Source: Laser-Pump /X-Ray-Probe Experiments- Inherent Synchronization fs-laser system: oscillator → Amplifier-I (pump)→ Amplifier-II (slicing/probe)

Slicing spectrometer: modulator - dispersion - refocussing - radiator
Beamline: mirror - mono (Si 111) - KB-optics (refocussing) - mono (multilayer ML)
Diagnostics: laser/e-beam timing & overlap (CSR)
Detectors (gated): APD, [⇒ µStrip-, Pixel-detector (PSI detector group)]
Measured sliced flux: 4·105 (2·105 ) ph/s/0.1% bw at 5 (8) keV (rep rate 2 kHz)
Upgrade (proposed): x 20 flux increase39Bismuth: Peierls System - Coherent Phonon excitation
Bi unit cellpossible mechanism for charge denstiy wave (CDW) formation (see slide 30)

40

FEMTO: Sub-ps Pulse Length Measurement of Electrons and X-Rays
Electrons: Interferometry

X-Rays: Optical Phonon Oscillations

3
Turn 4

2.5

Intensity [a.u.]Turn 3

2
Turn 2

1.5
Turn 1

1Turn 0

0.5
0
-10

-5

0
5
Delay Time [ps]10Electrons: autocorrelation spectra ∼ 200 fs FWHM (assuming Gaussian sliced bunches)
X-rays (7.1 keV; laser fluence: 2 mJ/cm2 ):Oscillation frequency:
2.60 ± 0.05 THz
Fitted x-ray pulse width: 140 ± 30 fs [FWHM]
Time resolution ∆ τ :195 ± 25 fs [FWHM]

41

Grazing Incidence TR-XRD & 2-Pulse Excitation ↔ Spatiotemporal Stability
spatial stability

coherent control: phonon

timing jitter & drift[ P. Beaud et al., PRL 99 (2007) & PRL 100 (2008) ]- Double pulse excitation: coherent control of A1g optical phonon in Bi at 2.6 THz.
- Temporal stabiliy ∆ τsyn−jitter + ∆ τsyn−drift : 30 fs (rms) ⇔ spatial stability on sample: ≤ 5 µm
- Longterm temporal stability for hours (days) allows data accumulation over millions of shots.

42

Femtosecond X-Ray Diffraction: Mapping the Int eratomic Potential- Laser/X-Ray Pump-Probe: Comparison of Different Timing Methods SPPS/Linac: Arrival Time Stamping
pulse compression
28 Gev, data acquisition: 0.3 h[D.M. Fritz et al., Science 315 (2007)]FEMTO/SLS: Inherent Synchronization
pulse slicing
2.4 GeV, data acquisition: 2-4 h[S. Johnson et al., PRL 100 (2008)]

Arrival time of electron bunches measured with EO-sampling[A.L. Cavalieri et al., PRL 94, (2005)]

43

SwissFEL (proposed): hard & soft X-ray FEL

SwissFEL: soft & hard X-ryas[ http://www.psi.ch/swissfel ]44

Femtosecond grazing incidence
X-ray diffraction→ experimental setup→ phonon dynamics in semimetals→ phonon-phonon coupling→ hot carrier & phonon dynamics

45

Laser-pump / X-ray-probe experimental station
Pump-probe setup (2-pulse excitation)

Pixel detector (gateble)(PSI Detector Group)46

Grazing Incidence X-Ray Diffraction
asymmetric cut crystal

Bi: normalized diffraction from (ijk) planes[ S.L. Johnson et al., Acta Cryst. A66 (2010)]

Diffracted intensity: I ∼ | F |2 , structure factor: F =P−iG·rj −Wj
f
e
e
j
j

(fj : scatt. form factor, G: recipr. lattice vector, rj : atom lattice position, e−Wj : Debye-Waller factor)⇒ Homogenous (optical) phonon excitations: modify structure factor within the unit cell
⇒ Measure time-dependent diffraction efficiency as a function of sample rotation angle φ47

Grazing incidence: matching of pump- and probe volume

Bi: depth profile (7 keV)

• X-ray absorption length Labs depends only on the wavelength and the incident angle48

Mechanisms of Coherent Phonon Excitation[ figures: K. Ishioka, NIMS, Japan ]Phonon amplitude at t0 :Time dependence:at maximum
cos-function

at minimum
sin-function- Displacive excitation: excited carriers push the atomic potential V(z) much faster than the vibrational period that forces the atoms to oscillate
around the new minimum of V(z).
- Raman scattering:inelastic photon scattering via an intermediate vibrational state having a virtual energy level; the process must involve
the polarizability of the material.

49

Application 1: Bismuth - Search for Ag -Eg Phonon-Phonon Coupling- Potential energy surface for Bi: Ag & Eg mode coupling predicted by DFT theory- No change of Eg (1-21) diffraction signal by coherent control of Ag (111) motion(double pulse excitation)50

Application 2: Eg Mode in Bi - Direct Observation via Polarization Control

Laser wavefront tilting allows excitation with two polarizations rotated by 90◦ (at 170 K)

51

Application 3: fs XRD - Nanoscale Depth-Resolved Lattice Dynamics in Bi
zeq = 0.2334 ( in units c = 1.18 nm)

A1g optical phonon[S.L. Johnson et al., PRL 100 (2008)]- information on hot carrier dynamics: timescales of e - h, e - ph interactions & carrier diffusion- nm depth resolution required to separate effects

52

Application 3: fs XRD - Nanoscale Depth-Resolved Lattice Dynamics in Bi
Grazing incidence angle: 0.50

- Time scale for thermal equilibration of the carriers with the lattice: τ 1 = 7.6 ± 0.6 ps- Time scale for thermal equilibration between electrons and holes: τ 2 = 260 ± 20 fs- Coherent phonon damping rate: γ = 1.01 ± 0.11 ps−1
- X-ray absorption length: L0 = 26 ± 2 nm

53

Related Topic: Hot Carrier & Phonon Dynamics in Solar Cell Materials
Increase efficiency 31% (Si) → > 66% ? Problem: hot electrons are lost as heat (→ phonons)⇔ transfer demonstrated in PbSe nanocrystals (pump-probe at 810 nm) [ W.S. Tisdale et al., Science 328 (2010) ]competition e-transfer ↔ relaxation

peak: e-transfer < 500 fs / tail: relaxation

phonon dynamics 2 - 4 THz→ use fs grazing incidence diffraction to study nanoscale depth-resolved carrier & atom dynamics

54laser-pump / X-ray-probe
non-resonant hard x-ray
diffraction on manganites( FEMTO slicing source )55

Transition Metal Oxides: Complicated Phase Diagrams - Manganites
Complex phase diagrams reveal the existence of several competing states[ J.W. Lynn et al., Phys. Rev. B 76 (2007) ]spin: CE-type & charge/orbital: stripe pattern[ H.Y. Hwang & S.-W. Cheong, Monographs in Condensed Matter Science (1999) ]Two competing states (x ∼ 0.5)
High T:

Ferromagnetic (FM) Metallicm
Low T:

Charge-Ordered (CO) & Antiferromagnetic (AFM) Insulating (AFI)

56

Complexity in Strongly Correlated Electronic Systems - Manganites
Complexity: generation of properties that do not preexist in a systems constituent
clean limit: two competing phases

Transition
Metal-to-Insulator (MIT)Magnetic

HT phasefirst order transition
insulating⇔
paramagnetic (PM)⇔LT phase
metallic
ferromagnetic (FM)quenched disorder: both states are nearly degenerate and coexistmlocal: PM or FM short-distance correlations ↔ global: neither of the two state dominates

Generic phase diagram of two competing states: FM metal vs. CO/AF insulator (g is a variable to move from one phase to the other)
Sketch of CMR state: FM clusters with randomly oriented moments separated by regions with where a competing CO/AF phase is stabilized[ E. Dagotto, Science 309 (2005) ]57

Percolation in a Manganite La0.33 Pr0.34 Ca0.33 MnO3 Thin Film

[ L. Zhang et al., Science 298 (2002) ]Local magnetic microstructure using low temperature (LT) magnetic force microscope (MFM)
Direct observation of inhomogeneity and AFM-FM phase separation upon heating/cooling
CMR effect: ground state is a nanoscale mixture of insulating regions and metallic FM domains ?
[ E. Dagotto, Science 309 (2005) ]58

Manganites: spin-, charge-, orbital- & lattice coupling[ E. Dagotto, Phys. Rep. 344 (2001) ][ Y. Tokura, Rep. Prog. Phys. 69 (2006) ]double exchange mechanism
FM - orbital

Jahn-Teller distortion
orbital - latticeeg - electron hopping
hopping enhanced in FM statespin directions preserved

local distortions at Mn3+ site
orbital ordering to be consideredelectron-phonon coupling59

Orbital-lattice coupling: Jahn-Teller (J-T) distortion of MnO6 octahedron

Crystal-field splitting of the five-fold degenerate 3d levels: 10 Dq ∼ 4-5 meVJ-T distortion (∼ 1-2 meV) lifts t2g and eg degeneracy causing MnO6 deformation

Local structure of La0.5 Ca0.5 MnO3 [E.E. Rodriquez et al., PRB 71 (2005)]
The active J-T modes of the oxygen octhedra, couple with the eg orbitals

60

Photoinduced J-T Release at Mn3+ Site ⇒ Change of Crystal Symmetry
20 K : cell doubling(55̄2) superlattice reflection

laser excitation: 1.55 eV

300 K[P. Beaud et al., Phys. Rev. Lett. 103 (2009)][J.H. Jung et al., PRB 57 (1998)]1
Mn 3d - O 2p hybridization allows (dipole forbidden) intra-atomic transition eg (Mn3+ ) → e1g (Mn3+ )61

La1−x Cax MnO3 : Dynamics at Short (fs) & Long (ps - ns) Time Scales- Short time scale: SL peak drops 80% after 200 fs (= time resolution) and ∼ 100% after 1 ps
- At 1 mJ/cm2 displacive excitation of 2 THz coherent optical phonon (due to La/Ca atom motion)- Coherent phonon modes of oxygen octahedra drive structural phase transition(time scale of structural phase transition set by quarter period of phonon mode)- Octahedra phonon modes (50 - 70 fs) require time resolution < 10 fs (→ XFEL)- Melting of charge & orbital order on time scale << 100 fs: soft X-ray resonant diffraction (→ XFEL)(52̄2)

7.1 mJ/cm2- Long time scale: ground state recovers completely after 100 ns allowing stroboscopic measurements
Drop from 70% (200 fs) → 50% (50 ps) at 1 mJ/cm2 indicates ’thermal’ formation of coexisting ordered & disordered domains on a ps time scale62

laser-pump / X-ray-probe
resonant soft x-ray
diffraction on multiferroic( LCLS free electron laser )63

Resonant X-Ray Diffraction (RXRD): Charge-, Orbital- & Magnetic Order

Tunability: energy tuned to absorption edges

Resonant process: intermediate states

Coherent summation: interference

Flexible polarization: multipole decomposition

64

CuO Resonant Soft X-Ray Scattering: LCLS Collaboration

65

CuO: A High-T Induced Multiferroic [ Kimura et al., Nat. Mat. 7 (2008) ]Low T: collinear antiferromagnetic orderHigh T: spiral magnetic ordernon-multiferroic, commensurate, qCM =(0.5 0 -0.5)

multiferroic, incommensurate, qICM =(0.506 0 -0.483)

spontaneous electric polarization

66

CuO: Resonant Soft X-ray Magnetic Scattering (Static)( RESOXS station at SLS )Temperature dependence: ICM rises as magnetic
structure factor decreases ↔ thermal disorder increases

67

LCLS Endstation: Resonant Soft X-Ray Scattering (RSXS)[ constructed by consortium: LBL - DESY - SLAC ]68

Femtosecond Magnetic Order Dynamics in Multiferroic CuO
Pump-probe RXRD experiment at Cu L3 edge 930 eV (SXR instrument at LCLS)

Magnetic phase transition: CM collinear AFM ⇒ ICM spiral AFM magnetic ordering[ S.L. Johnson et al., arXIV:1106.6128v1 (2011) ](collaboration: PSI - U Stanford - LBL - SLAC - XFEL - U Oxford)

69Magnetic Order Dynamics in CuO: Time-Dependence of Ratio ICM /IICM- Sudden drop for both peaks, difference after time tp due to shift in population of the CM andICM domains- Limiting time scale of tp ∼ 400 fs corresponding to 1/4 coherent oscillation of a low momentum
q ∼ 0 spin wave

70

Antiferromagnetic Phase Transition Driven by Disorder: CuO chain[ D.A. Yablonskii, Physica C 171 (1990) ]Exchange interactions:spins:

J1 < 0: nearest neighbor FM;

J2 > 0: next-nearest neighbor AFM;

Sn : spin of Cu atom along the c-axis;

I > 0: biquadratic term

S: spatially averaged value of spin magnitude

S 2 > J 2 /8IJ2 : ECM < EICM , but S decreases with temperature → S 2 < J 2 /8IJ2 and EICM < ECM
1
1

71

Summary & conclusions (1): fs laser-pump / X-ray-probe- Coherent modes can launch non-equilibrium phase transition in solids on a fs time scale→ Structural phase transition: coherent phonon excitation (experiment at Slicing Source)→ Magnetic phase transition: coherent spin wave (magnon) excitation (experiment at XFEL)- Fundamental time scale: quarter/half period of coherent phonon/magnon oscillation- Laser slicing sources provide valuable proof-of-principle experiments prior to XFELs- Time resolution achieved in experiments: 100 - 200 fs (slicing sources) & 250 - 350 fs (XFELs)- But: we need time resolution < 10 fs !
- Pump-probe experiments on correlated systems are feasible at XFELs- fs probing of long-range electronic-, spin- and atomic order in solids:→ fs non-resonant and resonant X-ray scattering in soft & hard X-ray regime demonstrated- XFEL experiments need careful preparation→ all optical pump-probe & static x-ray experiments (i.e. reflectivity, MOKE, static RESOXS, etc.)- We just started ... much work lies ahead:→ short pulses, timing, flexible pumping schemes, flexible polarization, flexible sample environment, fully coherent beams, coherent diffraction, ...

72

Summary & conclusion (2): fs laser-pump / X-ray-probe
To resolve the correlated dynamics between lattice, charge, orbital and spinin complex materials in real time with femtosecond x-ray diffraction, we need . . .

. . . 10 - 100 fs FWHM soft ⊕ hard x-rays & flux on sample ∼ 108 ph/pulse/0.1% bw(focus 10 x 10 µm2 ) & lin ⊕ circ polarization & pump-probe timing jitter ≤ 10 fs FWHM

73