Momentum Resolved Spectroscopy/Scattering Facility at LCLS

Greg Boebinger – National High Field Magnet Lab and Florida State UniversityThomas Devereaux – University of Waterloo

Zahid Hasan – Princeton UniversityZahid Hussain – Lawrence Berkeley National Laboratory

Eric Isaacs – Argonne National Laboratory and The University of ChicagoGeorge Sawatzky – University of British Colombia

Z.X. Shen (Coordinator) and Steve Kivelson – Stanford University

Outline

• Introduction to Strongly Correlated Electron Systems– Rich and novel physical properties– Correlated electrons with quantum tuning parameters: quantum criticality and

magnetic field

• Overview of Inelastic X-ray Scattering– Why momentum resolved spectroscopies are so important?– Why inelastic x-ray scattering has not made an impact yet, unlike neutron and

photoemission?– Why LCLS presents an unprecedented opportunity for this field?– Why timing is right?– Why soft x-ray?

• Examples for the Science Case– Exotic modes– Quantum criticality– Probing the strong correlation: k-, r-, and q-space perspectives.

• Technical Considerations– Approach and methods– Technical specifications and implementation plan

Strongly Correlated Electron SystemsStrongly Correlated Electron Systems

Controlparameters

Bandwidth (U/W)Band filling

Dimensionality

Degrees offreedom

Charge / SpinOrbital Lattice

d - fopen shells

materials

U<<WCharge fluct.

U>>WSpin fluct.

• High-Tc SC• Colossal MR• Heavy Fermions• Mott-Hubbard• Kondo• Spin-charge order• Unconventional SC

Nd2-xCexCuO4 La2-xSrxCuO4

0.3 0.2 0.10

100

200

300

SC

AFTem

pera

ture

(K

)

Dopant Concentration x0.0 0.1 0.2 0.3

SC

AF

Pseudogap

'Normal'Metal

Tc

I II IIIb IVb Vb VIb VIIb VIIIb Ib IIb III IV V VI VII 0H HeLi Be B C N O F NeNa Mg Al Si P S Cl Ar

Rb Sr Y Zr Nb Mo Rh Pd Ag Cd In Sn Sb Te I XeCs Ba La* Hf Ta W Re Os Ir Pt Au Hg Tl Pb Bi Po At RnFr Ra Ac** Rf Db Sg Bh Hs Mt

Lanthanides*Actinides** Th Pa U Np Pu Am Cm Bk Cf Es Fm Md No Lr

K Ca Sc Ti V Cr Fe Co Ni Cu Zn Ga Ge As Se Br Kr

Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu

MnRu

Ca2-xSrxRuO4

““ Materials with Materials with extreme propertiesextreme properties””

Strongly Correlated Electronic Systems

Unconventional Superconductivity

Electronic Phase separation and Charge order Phenomena

Magnetism

Non-S-wave

Broken T-Reversal Symmetry

Antiferromagnetism

Spin liquid

Ferromagnetism

Negative - U centers

Stripes/Checkerboard order

Charge density waves

Kondo effectsRole of Bosonic Excitations

Coupled charge/Spin orderSuperconductivity and magnetism

Superconductivity and charge/spin ordered states

Rich and Novel Electronic Phenomena

Gap Inhomogeneities

Magnetic Field: “Quantum” Tuning ParameterQuantum phase transition and quantum critical point in

strongly correlated Materials

Science 294, 329 (2001)

Phys. Rev. Lett., 91, 256401 (2003).

•Angle Resolved Photoemission (ARPES) :

Single-particle spectrum A(k,ω)

•Inelastic Neutron Scattering (INS) :

Spin fluctuation spectrum Ss(q,ω)

•Inelastic X-ray Scattering (IXS) :

Coupled excitation in the charge channel Sc(q,ω)

Spectroscopies of Correlated Electrons

?

Momentum Distribution of Spectral WeightImpact of Momentum Resolved Neutron and

Photoelectron Spectroscopy has been very significant

Both neutron and ARPES are vast fields by their own right

Do we have an opportunity to elevate IXS to the same league as ARPES and Neutron, to be one of the three main pillars for fundamental physics in condensed matter?

IXS measures the density response function of valence charge [~ S(q,ω)], critical to understand the charge dynamics and charge collective modes.

Do we have an opportunity to gain important information that cannot be obtained by other means?

• Complement ARPES• Matter under extreme conduction:

magnetic field, pressure• Bulk sensitivity• Unoccupied state information

• Complement Neutron•Direct coupling to charge•Element specific (resonance)•Smaller, more uniform samples

Why IXS has limited Impact so far?

Superconducting gap ~ 1 – 35meVOptical Phonons: ~ 40 - 70 meVMagnons: ~ 10 meV - 40 meVPseudogap ~ 30-300 meV

Multiphonons and multimagnons ~ 50-500 meV

Orbital fluctuations (originated from optically forbidden d-d excitations): ~ 100 meV - 1.5 eV

Limited resolution and low throughput are the problemsLimited resolution and low throughput are the problems

Superconducting gap

Multiphonons/Multimagnons/pseudogaps

0

100meV

X

3 eV

1 eV

Mott Gap,C-T Gap

dd excitations,Orbital Waves

Optical Phonons,Magnons,Local Spin -flips

Energy Scale of Important ExcitationsEnergy Scale of Important Excitations

Why IXS has limited Impact so far?

Superconducting gap ~ 1 – 35meVOptical Phonons: ~ 40 - 70 meVMagnons: ~ 10 meV - 40 meVPseudogap ~ 30-300 meV

Multiphonons and multimagnons ~ 50-500 meV

Orbital fluctuations (originated from optically forbidden d-d excitations): ~ 100 meV - 1.5 eV

LCLS can change the situationLCLS can change the situation

Superconducting gap

Multiphonons/Multimagnons/pseudogaps

0

100meV

X

3 eV

1 eV

Mott Gap,C-T Gap

dd excitations,Orbital Waves

Optical Phonons,Magnons,Local Spin -flips

Energy Scale of Important ExcitationsEnergy Scale of Important Excitations

Why LCLS provides such an opportunity?

• Brightness (present) – About 1-2 orders of magnitude more photon than 3rd Generation

light sources better resolution/efficiency.

• Magnetic Field Tuning– The low rep rate of the LCLS pulse makes it easier to match the

pulsed extreme magnetic field (also pressure field: shock waves generated by laser).

• Brightness (future)– About 4-5 orders of magnitude more photon if LCLS pulse becomes

fully transform limited revolutionary improvement in resolution/efficiency.

• The short pulsed nature of LCLS makes it possible to study dynamics in the time domain below 100 femto-seconds.

Why Timing is Right?

• Important Scientific Need– A sizable scientific community with ideas and interest.– Theoretical predictions and support (Stanford, Waterloo, UBC).– Experience with materials (ALS, Princeton, Argonne, UBC,

Stanford).

• Maturing Technologies– Spectrograph development (ALS/Princeton)– Magnets for scattering experiments (NHFML/ALS)

• Accumulated Experience– Resonant inelastic x-ray scattering (Princeton/Argonne/Stanford)– Soft x-ray scattering (UBC)

Essential Ingredients for a Successful Program are in Place

Why soft x-ray ?• Direct coupling – e.g., 3d state of transition metal probed via

resonance process.• Non-dipole transitions – e.g., d-d transitions via resonance

process.• Better relative q-resolution with respect to Brillouin zone. • Better detection efficiency – spectrograph mode • Intrinsic energy calibration

– very important for the current stage of LCLS operation where the pulse shape is not well controlled.

• Disadvantage: – Limited q transfer (by almost a BZ forcomplex materials)

Tc

I II IIIb IVb Vb VIb VIIb VIIIb Ib IIb III IV V VI VII 0H HeLi Be B C N O F NeNa Mg Al Si P S Cl Ar

Rb Sr Y Zr Nb Mo Rh Pd Ag Cd In Sn Sb Te I XeCs Ba La* Hf Ta W Re Os Ir Pt Au Hg Tl Pb Bi Po At RnFr Ra Ac** Rf Db Sg Bh Hs Mt

Lanthanides*Actinides** Th Pa U Np Pu Am Cm Bk Cf Es Fm Md No Lr

K Ca Sc Ti V Cr Fe Co Ni Cu Zn Ga Ge As Se Br Kr

Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu

MnRud - f

open shells

materials

U<<WCharge fluct.

U>>WSpin fluct.

Correlated Electron Systems

Soft X-Ray Inelastic Scattering

ener

gy

core level

valence band

conduction band

p

d

Resonant Inelastic Soft X-ray Scattering(Raman spectroscopy with finite q)

Energy loss: ω=ω2-ω1Momentum transfer: q=k2-k1Resonance: ω1~ ωedge

hω1,k1,ε1

Photon-in hω2,k2,ε2

Photon-out Optically forbidden d-d excitationOptically forbidden d-d excitation

Finite q transfer allows one to study indirect Mott gap

Finite q transfer allows one to study indirect Mott gap

Couples to charge density directly (Neutrons couples to spin).

Couples to charge density directly (Neutrons couples to spin).

Energy Resolution not limited by the core hole lifetime: achieve kBT resolution

Energy Resolution not limited by the core hole lifetime: achieve kBT resolution

Can be applied in the presence of magnetic/electric field

Bulk sensitive probe for studying unoccupied electronic states

Can be applied in the presence of magnetic/electric field

Bulk sensitive probe for studying unoccupied electronic states

Why???Why???

Why soft x-ray ?• Direct coupling …

– Soft x-ray resonance (2p 3d) provides the most sensitive channels to study ordering and excitations.

Nature 431, 1078 (2004)

Example I: Symmetry and Exotic Modes

• Starting point to understand novel physics in a quantum matter is often the reduction of a complex situation to a simple effectiveHamiltonian.

• Determination of exotic modes has far reaching implications on the symmetry of the effective Hamiltonian– ETA mode in negative U Hubbard model [SU(2)]

• S.C. Zhang – unpublished– Φ mode of pairing amplitude fluctuation in gauge theory and t-J

model [SU(2)]• P.A. Lee and N. Nagaosa, PRB 68, 024516 (2003)

– θ mode of current fluctuation in guage theory and t-J mode [SU(2)]• P.A. Lee and N. Nagaosa, PRB 68, 024516 (2003)

– D-exciton: 3 band model t-J model?• Y.Y. Wang, F.C. Zhang et al., PRL 77, 1809 (1996)

– Spin mode in SO(5) theory• S.C. Zhang – Science, 1999

Zoology of exotic modes that coupled to charge

D Exciton

D

Φ Mode

• Modes couple to x-ray• Dispersion reveals their nature• Magnetic field suppresses ETA

mode• Important discovery if one of

them is found

S(q=

π, ω

)

ωU-2µ

ETA Mode

Classical transitionClassical transition Quantum phase transitionQuantum phase transition

Sparta Sparta et alet al., ., ActaActa CrystCryst. B 60, 491 (2004). B 60, 491 (2004)

Driven by temperature T.Driven by temperature T.

The singularity of The singularity of SS((QQcc))::

divergent!Strongly,1~~)()(

γχ γ−−= ccc TTQTQS

Detectable by elastic xDetectable by elastic x--ray scattering.ray scattering.

Driven by some tuning parameter.Driven by some tuning parameter.

00~~)(~)(

>−

− −

or γνωχ γν

zllQQS zcCC

S(Q )c

QCP

Tuning parameter, l

cl

The singularity of The singularity of S(QS(Qcc)) is weakly is weakly divergent, or even not divergent.divergent, or even not divergent.Can We probe Can We probe χχ((QQcc ), which is still ), which is still strongly divergent near strongly divergent near llcc??

Example II: quantum phase transitionExample II: quantum phase transition

NbSe3

Classical transitionClassical transition Quantum phase transitionQuantum phase transition

Sparta Sparta et alet al., ., ActaActa CrystCryst. B 60, 491 (2004). B 60, 491 (2004)

Driven by temperature T.Driven by temperature T.

The singularity of The singularity of SS((QQcc))::

divergent!Strongly,1~~)()(

γχ γ−−= ccc TTQTQS

Detectable by elastic xDetectable by elastic x--ray scattering.ray scattering.

At T ~ 0, At T ~ 0,

Better hope is to probe S(qS(q,ω,ω)) by inelastic x-ray scattering, especially at the low frequency range, such that we can calculate χ(q,ω).

χ(Q )c

QCP

Tuning parameter, l

cl

Example II: quantum phase transitionExample II: quantum phase transition

∫= ωωπωωχ ),(2~)0,( qSdq

NbSe3

QQF F : nesting vector of the Fermi surface (by ARPES): nesting vector of the Fermi surface (by ARPES)QQcc : charge ordering vector (by x: charge ordering vector (by x--ray scattering)ray scattering)QQss : spin ordering vector (by neutron scattering): spin ordering vector (by neutron scattering)

The relation between QThe relation between QFF, Q, Qcc, and Q, and Qss is reflecting the correlation effect of the system, is reflecting the correlation effect of the system, which is a very fundamental issue of correlated materials.which is a very fundamental issue of correlated materials.

Fermi surface (ARPES)Fermi surface (ARPES) Density wave (scattering experiment)Density wave (scattering experiment)

Examples III: probe on strong correlation effectExamples III: probe on strong correlation effect

Weak coupling Weak coupling Strong couplingStrong coupling

Instability is driven by QInstability is driven by QF.F.

QQc c ~ Q~ Qss ~ Q~ QFF

Long range order developed.Long range order developed.

SS((qq) has peak around Q) has peak around QFF

Detectable by elastic xDetectable by elastic x--ray scattering.ray scattering.

Instability is not necessary driven by QInstability is not necessary driven by QFF

QQcc ≠≠ QQss ≠≠ QQFF

Generally short range ordering developed.Generally short range ordering developed.

SS((qq, , ωω)) has structure around Qhas structure around Qcc

Detectable by inelastic xDetectable by inelastic x--ray scattering.ray scattering.

1,0' <<= tUt

Examples II: probe on strong correlation effectExamples II: probe on strong correlation effect

1,0' >>≠ tUt

QQss

Momentum Distribution of Spectral Weight

Spectral Weight Map (+/- 10 meV)

Nature of Charge Ordered State- k-space, r-space and q-space perspective

K.M. Shen et al., Science 05ARPES (k-space)

STM (r-space)T. Hanaguri et al., Nature 05

Scattering (q-space)

FT?

Highly non-trivial relationships are found, direct probe of S(q,ω) (and comparison with k and r space derived result) would be very informative

Similar Effects in Manganites

N. Mannella et al., Nature 05

La1.2Sr1.8Mn2O7 (x = 0.4)

Strategy to Advance the Field

• Phased approach to advance the field– Phase I: Experiments with

moderately high resolution (30-40 meV, ~ an order of magnitude improvement).

– Phase II and III: Experiments with even higher resolution

Some examples for phase IGap opening – high energy manifestations

(simulation by Hasan et al.)

Momentum transfer q

Ene

rgy

2

1

0

-1

ky (p

i/a u

nits

)

3210-1kx (p i/a units)

100806040200 Some CDW gaps are big: e.g. up to 400 meV in CeTe3(Brouet et al. PRL 2004)

D Exciton

Technical Approach/Method

Use variable line spacing (VLS) grating → high spectral resolution

Use pre-mirror → large solid angle

Make instrument slitless → higher throughput

Detector normal to photon beam → maximize efficiency

How ?How ?

Build ultra-high resolution and high throughput emission spectrographs.

2400 l/mm grating, 200 mm long, -1 order, r1=2.913 m5.5 m total, spot 4 µm, pixel 13.5 µm. 0.04” RMS slope error in grating.Plane elliptical 500 m from sample collecting horizontally .Area enclosed is the pixel size.Same contribution to energy resolution from source and pixel size

Spectrograph

Magnets for Scattering

NHFML Dipole Magnet

Wang Multipole Magnet

Needs and Execution Plan

• Monochromator: up to 30,000 RP– (we could help design it)

• Phase I– One spectragraph with 30-40 meV energy resolution

• Phase II– Adapt magnetic field– Additional spectrographs to cover the entire Brillouin zone– Develop spectrographs with 20 meV resolution (also

implementing new grating for the mono)

• Phase III(Assume LCLS will become a transform limited source)

– Spectrograph with better than 10 meV resolution– Pulsed extreme magnetic field

Scientific Justifications: Manganite as Model System for Complexity

Novel electronic phase diagram

CO: charge-orderingFM: ferromagnetic metallicCAF: canted anti-ferromagnetic insulatingPI: paramagnetic insulating

Competition/cooperation between various degrees of freedom: spin, charge, lattice and orbital

10

5

0

-5

-10

50-5

electronic

e

orbital lattice

spinS

Strong interplay between these degrees of freedom could result in real-space phase separation… critical for manganite physics

Ins

Met

Y.-D.Chuang et al., Science 292, 1509 (2001).B. Campbell et al., PRB 65, 014427 (2002).S. Mori et al., Nature 392, 473 (1998).M. Uehara et al., Nature 399, 560 (1999).M. Fath et al., Science 285, 1540 (1999).

Coexistence of metallic and insulating phases

Complex phase diagram in 3d TMO

High Energy Manifestations of Low Energy Phenomena– some hidden benefits of q resolution

• Low energy gap opening with high energy consequence

• d-excitons: – Determining the

effective Hamiltonian. (ZR singlet)

d - excitonY.Y. Wang et al., PRL 77, 1809 (1996)

M.Z. Hasan et al., 2006

Soft x-ray inelastic scattering with high resolution and “inherently” high throughput is expected to become a technique of choice for the study of low energy coupled excitations in complex materials.

LCLS represents a special opportunity to advance this important field. The timing is right for an inelastic x-ray scattering facility – a combined outcome of LCLS characteristics, accumulated instrumentation development world wide, and advancement in ideas and materials.

The proposed facility will help push the frontier of condensed matter physics, with a strong user base and rich science programs for the next decade to come.

Outlook

Theoretical prediction of the eta modeTheoretical prediction of the eta mode

Shoucheng ZhangS(

q=π,

ω)

ω

High Energy Manifestations of Low Energy Phenomena– some hidden benefits of q resolution

• Low energy gap opening with high energy consequence

• d-excitons: – Determining the

effective Hamiltonian. (ZR singlet)

d - excitonY.Y. Wang et al., PRL 77, 1809 (1996)

M.Z. Hasan et al., 2006

Weak coupling Weak coupling Strong couplingStrong coupling

Instability is driven by QInstability is driven by QF.F.

QQc c ~ Q~ Qss ~ Q~ QFF

Long range order developed.Long range order developed.

S(qS(q)) has peak around Qhas peak around QFF

Detectable by elastic xDetectable by elastic x--ray scattering.ray scattering.

Instability is not necessary driven by QInstability is not necessary driven by QFF

QQcc ≠≠ QQss ≠≠ QQFF

Generally short range ordering developed.Generally short range ordering developed.

S(qS(q, , ω)ω) has structure around Qhas structure around Qcc

Detectable by inelastic xDetectable by inelastic x--ray scattering.ray scattering.

1,0' <<= tUt

Examples III: probe on strong correlation effectExamples III: probe on strong correlation effect

1,0' >>≠ tUt

QQss

ETA mode of the Hubbard U<0 model

• U<0 Hubbard model describes the competition between CDW and s-wave SC.• The collective mode which rotates between these two forms of order is the

eta mode: sharp collective mode with S=0 singlet, momentum=(pi,pi), charge=2, energy=chemical potential shift from half-filling.

• So far, inelastic charge probe with momentum=(pi,pi) has not been available. The inelastic X-ray provides an ideal probe, in the channel of S=0, momentum=(pi,pi), charge=0.

• The superconducting condensate violates charge conservation by 2.• Therefore, inelastic X-ray scattering can detect the eta mode only below

the Tc transition. The intensity is directly proportional to the square of the s-wave SC order parameter. This provides a clean way to distinguish from other modes.

• The energy of the eta mode can be determined INDEPENDENTLY in Arpesexperiment, which can measure the shift of the chemical potential away from half-filling.

S.C. Zhang, Stanford Univ.

- Hidden order of URu2Si2 near a quantum critical point.- Fundamental issues in the metal-insulator transition: energy gap in single –particle excitation; plasmonic to excitonic collective mode.- Quantum critical behavior of spin and charge order in model systems such as chromium and complex oxides as the quantum critical point is approached with high magnetic fields (>10 tesla).- Novel collective modes in unconventional superconductors. Charge in vortex core of novel superconductors.- Investigation of high energy vibronic, libronic and rotational excitations in strongly correlated materials and molecular complexes. - The general mapping of phonons with much higher resolution than achieved by neutrons with the added polarization selection rules enabling the characterization of phonons in complex materials with many atoms in the unit cell – an advantage over neutrons is also that small samples may be used. - Two magnon or multiple spin-flip excitations under magnetic field.- Superconductors under magnetic field – how does the electronic continuum evolve (without KK and surface issues), spectral weight gets transferred, and how do the phonon lineshapes evolve with magnetic field.- Investigation of orbital ordering and “orbitons” with magnetic field in manganites.- Investigation of fractional excitations in magnetically frustrated systems such as the pyrochlores where spin and charge are coupled.- 1D materials and spin-charge separation with magnetic field. Quantum collective excitation and fractional statistics.

Rich and Novel Physics of Interest …

VLS Emission Spectrometer

Gauss fit on elastic peak of samples: y=y0 + (A/(σ*sqrt(2π)))*exp(-2*((x-xc)2/(2σ2)) y0 3.06482 ± 1.8993E-12 (counts)xc 0.00009 ± 1.4312E-16 (eV)σ 0.04630 ± 2.9804E-16 (eV)A 21.7319 ± 2.6039E-13 (counts*eV)

Photon Energy: 68eVSample: NiObeamline resolution: ~28meVbeamspot size: ~15µmCCD Pixel Size: 13.5x13.5µm2

-0.1 0.0 0.1

0

400

800

coun

ts (H

z)

experiment Gauss fit

Energy Loss(eV)

FWHM = 30meV

hv=68eV

Spectrometer Optics Resolution

60 65 70 75 80

1.8

2.0

Inte

nsity

(a. u

.)

Photon Energy (eV)

Absorption (M edge)

-3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0.0

0

20

40

60

collection time: 1 hourInelastic excitations

65.7eV

68.0eV

cou

nts

Energy Loss (eV)

dd-excitations in NiO : Combined Resolution ~ 75 meV

Width of sharpest inelastic features ~ 80 meV

-3.0 -2.5 -2.0 -1.5 -1.0 -0.5

0

20

40 collection time: 1 hourInelastic excitations

65.7eV

68.0eV

cou

nts

Energy Loss (eV)

Spin-flip dd scattering (side-band)

Experiment

Theory

This spin scattering is resolved for the first time

-2.0 -1.5 -1.0 -0.5 0.0

with exchange interaction without exchange interaction

Energy Loss(eV)

S.G. Chiuzbaian et. al, PRL 95 (2005)

LCLS VLS Spectrograph Ray Traces-Summary

Tables

Table 1 : To tal reso lution and total effi ciency (geo me trica l efficiency tim es gratingeffic iency ) for differen t op tions for system 2. The distance mi rror grating is 300 m m. T hedistance grating-sou rce is the “v irtua l distance” f rom the grating to the image of theellipso ida l.

Case Distance Samp le-El lipsoid (m)

DistanceGrating-source(m )

Acce ptance Hor_Ve r(m rad2)

Acce p_GratingEffic.

SourceHeight(_m)

El lipsoid RMSSE

(ArcSec)

Centrallinedensity(l/mm)

TotalResolution(m eV )

1 1200 -4000 17.4_11.0 14.9 4 0.7 2400 762 1200 -4000 17.4_11.0 14.9 2 0.7 2400 483 900 -4300 23.3_12.4 24.7 2 0.7 2400 564 1500 -3700 14.0_9.2 9.9 2 0.7 2400 455 1500 -3700 14.0_9.2 9.9 2 0.5 2400 426 1500 -2500 14.0_9.2 9.9 2 0.7 2400 467 1800 -3400 11.6_7.9 7.1 2 0.7 2400 448 1200 -4000 17.4_13.1 3.9 2 0.7 3600 349 1800 -3400 11.6_9.3 1.8 2 0.7 3600 28

Overal length of the spectrograph = 5.5mResolution Range = 28meV - 76 meV

(tradeoff between resolution and throughput)

Backup figure of AF ordering cartoonBackup figure of AF ordering cartoon

Backup figure of Density wave cartoonBackup figure of Density wave cartoon

Why inelastic x-ray scattering?• Importance of density response function, or

approximately S(q,ω) and S(q,t)) for valence charge with sufficient resolution.

– Critical to understand the charge dynamics and charge collectivemodes

– Enrich the information from neutron: extend the information fromspin channel, with the additional advantages of element and chemical specificity, and photon polarization control.

– Enrich the information from Raman: incorporate q resolution and core-hole resonance: investigation of phonons, orbital transitions, excitons, spin-orbit effects and selection rules, as well as mapping energy gaps.

Ray traces at 930 eV (+- 40 meV) showing expected resolution of the Spectrograph with 5.5m of total length.

2400 l/mm grating, 200 mm long, -1 order, Total acceptance angle = 10 microrad x 40 microrad (relatively large)Required spot size at sample = 2microns, Detector pixel 13.5 microns (smaller size will imrove the resolution). Plane elliptical mirror 500 mm from sample collecting horizontally .Area enclosed is the pixel sizeSame contribution to energy resolution from source and pixel size

ReferencesS. C. Zhang, ``Pseudospin symmetry and new collective modes in the Hubbard model", Phys. Rev. Lett. 65, 120 (1990).

C. N. Yang and S. C. Zhang, ``SO(4) symmetry in the Hubbard model", Mod. Phys. Lett. B4, 759 (1990).

S. C. Zhang, ``SO(4) symmetry of the Hubbard model and its experimental consequences", Int. J. Mod. Phys. B5, 153 (1991).

E. Demler, S. C. Zhang, N. Bulut and D. Scalapino, ``A class of collective excitations of the Hubbard model: eta excitation of the negative U model", Int. J. Mod. Phys. {\bf B10}, 2137 (1996).

pi mode of the t-J or the Hubbard U>0 model

• Pi mode: sharp collective mode with S=1 triplet, momentum=(pi,pi), charge=2, energy=fraction of J.

• Neutron scattering only couples to spin excitations with S=1 triplet, momentum=(pi,pi), charge=0.

• The superconducting condensate violates charge conservation by 2.

• Therefore, neutron scattering can detect the pi mode only below the Tctransition. The intensity is directly proportional to the square of the SC order parameter.

eta mode of the Hubbard U<0 model

• U<0 Hubbard model describes the competition between CDW and s-wave SC.

• The collective mode which rotates between these two forms of order is the eta mode: sharp collective mode with S=0 singlet, momentum=(pi,pi), charge=2, energy=chemical potential shift from half-filling.

• So far, inelastic charge probe with momentum=(pi,pi) has not been available. The inelastic X-ray provides an ideal probe, in the channel of S=0, momentum=(pi,pi), charge=0.

• The superconducting condensate violates charge conservation by 2.• Therefore, inelastic X-ray scattering can detect the eta mode only below

the Tc transition. The intensity is directly proportional to the square of the s-wave SC order parameter. This provides a clean way to distinguish from other modes.

• The energy of the eta mode can be determined INDEPENDENTLY in Arpes experiment, which can measure the shift of the chemical potential away from half-filling.

BaKBiO superconductor• BaKBiO has a CDW state at half-filling. O

breathing mode has a static distortion. Superconductivity is obtained upon K doping with Tc=20K?

• Superconductivity is mediated by the O breathing mode phonon. However, effectively, the system can be described as a U<0 Hubbard model with on-site interaction.

• Therefore, inelastic X ray scattering can detect the eta mode below the Tc transition. The intensity is directly proportional to the square of the SC order parameter.

meV Resolution Beamline and VLS Spectrograph:Engineering Design

Sample

Mirror

Grating

CCD Detector

Progress:•Optical design and Mechanical design - completed•All optics and CCD detector – received and characterized•Fabrication of spectrograph- assembly in progress•meV resolution beamline – under construction(completion date: fall 2005)

Orbital Physics

Photon-in/photon-out technique to probe orbital excitation

E. Saitoh et al, Nature 410, 180 (2001).

Photon-in Photon-out

dd excitations (~1eV)

Site i

Site j

time

Localized picture

inout

inout

ppqEEE

rrr−=

−=∆

Provides information about dispersion of orbiton

Raman data

Strong orbital-electron-lattice coupling is expected

Long-range strain field could favor orbital excitations: orbital wave

Crystal Mono vs Grating Mono

Parameters for the existing Wang device

“A novel superconducting octupole magnet for photon scattering experiments”, C. S. Wang et al., JMMM

Temperature dependence of Jc at 8T

-500

0

500

1000

1500

2000

2500

3000

3500

4000

4500

4 4.5 5 5.5 6 6.5 7 7.5 8

Tem perature [K]

Jc[A

/mm

2]

NbTiNb3Sn

ALS proposed material (5T)

Material used by Wang

•Eight-magnets NbTi design (in vacuum)

• 210° slit for scattering ; Five access ports

•~3.6T center field with 19mm center chamber

• Quenching and stability problems!!

Sup rcon uct ng Magnet:

Designed by Wang