interplay between spin, charge, lattice and orbital degrees of freedom lecture notes les houches...
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Interplay between spin, charge, lattice and orbital degrees of
freedom
Lecture notes Les Houches June 2006
George Sawatzky
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Rough content of 3 lectures
• Basics of the electronic structure of correlated systems
• Some theoretical and experimental methods
• Towards real materials involving charge, orbital, spin and lattice degrees of freedom
• Some new experimental methods and new ideas for magnetic materials
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Content Lecture 1
• Electronic structure of correlated electron systems– Why are TM compounds and rare earths
special– Quasi atomic vs band structure approaches– Hund’s rule, spin orbit interactions– DFT, LDA+U, DMFT, Model H exact
diagonalization – Spectral weight transfer
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Some Historical notes
• 1929-1931 Bloch Wilson theory of solids • 1937 De Boer and Verwey ( NiO-CoO
breakdown of band theory• 1937 Peierls 3d electrons avoid each other
( basically the Hubbard model)• 1950 Jonker van Zanten - Zener Pervoskites
double exchange • 1959 Anderson superexchange (U>>W)• 1964 Hubbard model- Hohenberg Kohn DFT-
Goodenough Transition metal compounds
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Wide diversity of properties
• Metals: CrO2, Fe3O4 T>120K• Insulators: Cr2O3, SrTiO3,CoO• Semiconductors: Cu2O• Semiconductor –metal: VO2,V2O3, Ti4O7• Superconductors: La(Sr)2CuO4, LiTiO4• Piezo and Ferroelectric: BaTiO3• Catalysts: Fe,Co,Ni Oxides• Ferro and Ferri magnets: CrO2, gammaFe2O3• Antiferromagnets: alfa Fe2O3, MnO,NiO ---
Properties depend in detail on composition and structure
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Phase Diagram of La1-xCaxMnO3
Uehara, Kim and Cheong
R: Rombohedral
O: Orthorhombic(Jahn-Teller distorted)
O*: Orthorhombic(Octahedron rotated)
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Model for Charge, Spin and Orbital Correlations in Manganites
Mizokawa et al (2001)
Mn4+ , d3, S=3/2 ,No quadrupole ; Mn3+, S=2, orbital degeneracy
S=27/2
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Ordering in strongly correlated systemsStripes in Nd-LSCO
QC ~ 1 eQO ~ 0
Q < 0.5 e
Charge inhomogeneity in Bi2212
Pan, Nature, 413, 282 (2001); Hoffman, Science, 295, 466 (2002)
Q ~ 0.1 e
Quadrupole moment ordering
rivers of Charge—Antiferro/Antiphase
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Coexistance-----HybridizationKondo, Mixed valent, Valence fluctuation, local moments, Semicond.-metal transitions, Heavy Fermions, High Tc’s, Colossal magneto resistance, Spin tronics, orbitronics
Two extremes for atomic valence states in solids
Where is the interesting physics?
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Special place for transition metal and rare earths
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Why are 3d and 4f orbitals special
• Lowest principle q.n. for that l value• Large centrifugal barrier l=2,3• Small radial extent, no radial nodes
orthogonal to all other core orbitals via angular nodes
• High kinetic energy ( angular nodes)• Relativistic effects• Look like core orb. But have high energy
and form open shells like valence orb.
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HubbardFor 4f
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ARPES Cu
3d bands
4s,4p,band
Cu is d10 so one d holeHas no other d holes to Correlate with so 1 part.Theory works
Points –exp.Lines - DFT
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Two hole state with Auger spectroscopy
3d
2p 932eV
Photon
Photoelectron
Auger electron
E(photon)-E(photoelectr) = E(2p) , E (2-d holes)= E(2p)-E(3d)-E(Auger)
U = E( 2-d holes) -2xE(1-d hole)
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Auger spectroscopy of Cu metalAtomic multipletsLooks like gas phase U>W
Hund’s ruleTriplet F is Lowest
Two hole bound state
Phys. Rev. B15, 1669 (1977)Antonides
SawatzkyPRL. 39, 504 (1977).
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Photoelectron spectroscopy of the rare earths