Interplay between spin, charge, lattice and orbital degrees of freedom

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Interplay between spin, charge, lattice and
orbital degrees of freedom

• Lecture notes Les Houches June 2006 lecture 3
• George Sawatzky

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Need multiband models to describe TM compounds

• However numerous studies have shown that this can
  sometimes be reduced to an effective single band
  Hubbard model at least for highTcs BUT ONLY FOR
  LOW ENERGY EXCITATIONS Elt0.5eV

Macridin et al Phys. Rev. B 71, 134527 (2005)
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Tpd(eg) 2x Tpd(t2g)
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Crystal and ligand field splittings
Often about 0.5 eV In Oh symmetry
Angular integrals Are different for t23g and eg
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Eg-O2p hoping is 2 times as large as T2g-O-2p
hoping
Often about 1-2eV In Oxides
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High Spin Low Spin transition very common
in Co(3)(d6), as in LaCoO3, not so common in
Fe(2)(d6) Because of the smaller hybridization
with O(2p)
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Mixed valent system could lead to strange effects
Such as spin blockade for charge transport and
high thermoelectric powers
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What would happen if 2Jh lt10Dqlt3Jh If we
remove one electron from d6 we would go from S0
in d6 to S5/2 in d5. The hole would carry a
spin Of 5/2 as it moves in the d6 lattice.
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If the charge transfer energy gets small we have
to Modify the superexchange theory
Anderson 1961
New term
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Khomskii et al S S Comm.102,87, 1997
tij t cos (Oij/2) Oij angle between
neighbouring spins
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This orbital ordering yields a large internal
Antiferromagnetic exchange and a weak external
ferromagnetic exchange .
dxy
dxz
dyz
Orbital ordering removes frustration
Pen et al PRL 78,1323
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YVO3 Pervoskite structure V(3) 2 electrons in
T2g Orbitals S1. Note the tilted and Rotated
octahedra
Tsvetkov et al PRB 69, 075110 (2004)
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YVO3 Perovskite V(d2 S1) O not In inversion
symmetry DM canting competing With staggered
magnetic Anisotropy . See Aharonis lectures
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Without the high field Applied in the
downward trajectroy
After applying a high field Just above above
trans On the downward tragectory
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All V have one electron in a dxy orbital
O between the V ions are not in inversion
center Tilted Octahedra D.SxS interactions
compete With local staggered anisotropy
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Three ways to get ferromagnets with High Tc
without using 3ds or 4fs

• Use electronic reconstruction of polar surfaces
• Use defects and topology and symmetry
• 3. Use doping and large Hunds rule coupling of
  O,N

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Electronic reconstruction at surfaces and
interfaces
By moving 1 electr. Per O From 2- side to 2
side the Potential becomes flat.
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Example of two particles in U? limit
Energy level diagram for holes (tgt0)
for singlet - for triplet
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One electron spectral function in a magnetically
and orbitally Ordered system
Balla et al
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Resonant soft x ray scattering
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Doped holes in cuprate
Cu2 d9 S1/2
O 2- full shell
La2-xSrxCuO4 Sr ---doped holes
C. T. Chen et al. PRL 66, 104 (1991)
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Nature 431, 1078 (2004)
Chains with model of spin singlets
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CDW with Q0.2 is 5 cl modulation along the ladder
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Rushdy et al PRL in press
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Models mentioned in White , Affleck and Scalapino
PRB 65 165122 For ¼ modulation
NOTE WE DONT SEE A 4 FOLD MODULATION
RXS shows that ¼ does not exist but 1/3 and 1/5
do and more recent Results show the model with
paired holes along the rungs is most likely
Correct. This could be of great importance for
the understanding of High Tcs
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Pr0.6Ca0.4MnO3 CE type charge, orbital and
magnetic order
K.J. Thomas et al NSLS/BNL
Phys. Rev. Lett. 92, 237204 (2004)
Pr1-xCaxMnO3

• Charge ordering below TCO 240K
• Cooperative orbital ordering oxygen
  distortion at TOO TCO
• Magnetic ordering below TN 170K

Goodenough (1955)
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