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Resonant (soft) x-ray scattering
SUCCESS-2014 : School on UV and X-ray spectroscopies of correlated electron systems
1-12 Sept. 2014
Peter AbbamonteUniversity of Illinois at Urbana-Champaign
[email protected]://users.mrl.illinois.edu/abbamonte/
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Resonant (elastic) scattering: main points
• Resonant x-ray scattering is a probe of the ground state valence electronic structure
• Optimized for studying phenomena that are electronically inhomogeneous:
• Antiferromagnetism, spin density waves, charge stripes, Wigner crystals, orbital order, toroidal order, electronic reconstruction of interfaces, etc.
• Closest sibling is STM
• Easier to interpret than RIXS. Has made a bigger impact in condensed matter physics.
• Still some subtleties to understand –this is a good thing
Core level
valence band
Ei
Es = Ei
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Origins: Resonant magnetic hard x-ray scattering
• Holmium metal• HCP crystal structure
• Spiral spin density wave (SDW) of FM aligned layers along c axis
• Ho L3 edge at 7.85 keV was accessible at CHESS and SSRL
• 2p 5d transition goes directly to the 4f / 5d valence band
• Lots of spin-orbit coupling large magnetic scattering cross section
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Origins: resonant magnetic scattering
• Peak only visible on resonance
• Exhibits expected polarization dependence
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Modern Era: Soft X-Rays
• The Gibbs experiment was possible because the Ho L3 edge is in the hard x-ray regime: Accessible with existing facilities at CHESS, SSRL
• Problem: Rare earth materials generally do not order. Mainly of interest in CMP for Kondo lattice and Heavy Fermion physics, which are spatially homogeneous phenomena (great for DMFT).
• Inhomogeneity most prevalent in 3d transition metals: HTSC in cuprates and Fe-based materials, manganites, nickelates, etc.
• These materials hand TM 3d – O 2p hybridized valence bands. Relevant edges are in the soft x-ray range:
Oxygen K edge (1s-2p): 540 eV 3d TM L edges: 480 – 950 eV (Ti through Cu)
• Requires scattering with soft x-rays. Everything has to be in UHV.
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Modern Era: Soft X-Rays
• Field was enabled by development of vacuum diffractometers
NSLS X1B Sector 29 at APS (new in 2014)
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Soft x-ray scattering from iron foil
• Specular reflectance from an iron film.
• Ferromagnetism contributes to scattering at q=0
• Line shape at Fe L3 edge indicates interference between Thomson and resonant scattering
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Measure the orbital state in manganites?
• Prediction for LaMnO3
• Used atomic multiplet approach for computing f()
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Cuprate holes: Stripes?
• Use XAS and Kramers-Kronig to compute form factors for La2CuO4+y
• Scattering from doped holes enhanced by more than 104 at O Kedge.
• Direct detection of valence band order in cuprates possible: Stripes, checkerboards, etc.
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Magnetic scattering: bilayer manganite
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Orbital Scattering
• Could never get good enough agreement with theory to deduce orbital shape.
• Too much nonlocality?
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Focus on Polarization / Symmetry
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Wigner crystal in Spin Ladders
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Stripes in cuprates
• Calibrated f() with x-ray absorption
• Deduced charge amplitude ~ 0.5 holes: “stripes are charged”
• Close to expectation for half-filled stripes
• Looked at YBCO and BSCCO. Never saw anything. Gave up.
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Heterostructures
• Deduced existence of Fermi surface at Mott-Band insulator interface• In retrospect, it may have been magnetic scattering
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Heterostructures
• Measured orbital disproportionation between inner and outer NiO2 layers
• “Orbital engineering” with oxide MBE
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Loop currents (“anapoles”) in CuO
Toroidal moment
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Charge order in YBCO
Explains mysterious periodicities observed in quantum oscillation experiments as change in Luttinger volume due to folding of the Fermi surface.
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Work in Progress: nonlocality?
In the extreme nonlocal limit:
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Rapid Developments: nonlocality?
• Charge amplitude may be small after all. Uh oh!
• If I was wrong all this time, at least I can claim to have helped show it.
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Rapid Developments: Better detectors
• 1 eV resolution with no spectrometer
• Eliminate fluorescence background study glassy order
• Credit: Joel Ullom, Dan Swetz, Randy Doriese, NIST, Boulder, CO