Periodic table

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Periodic table
Transition-metal elements
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Why manganites? Colossal Magnetoresistance (CMR)

• Drastic reduction of resistivity with small
  magnetic fields.

FM metal
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Why materials with large MR are important?

• Using magnetic technology, the most significant
  market is recording.
• Projected aerial density for 2005 is 10Gbits/in2
  (rapidly growing). 1 bit size 1000 Angstroms.

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Basic-science motivation

• Understand the complex phase diagram that
  experiments are unveiling.

T
Fraction of holes
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Structure of the Manganites
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Models for Manganites
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Main couplings in models for manganites and
Double-Exchange mechanism for ferromagnetism
Mn 3
Mn 4

WARNING SOME COUPLINGS ARE LARGE!
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Computational Techniques

• Partition Function

• Monte Carlo simulation over classical spins.
  Quantum itinerant electrons treated exactly.
• All temperatures and densities are accessible.
• Dynamical properties can be calculated
  straightforwardly.

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Typical results
As observed experimentally (see later)

• FM, AF , Phase Separation and Spin
  Incommensuration observed.

T0
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Monte Carlo and DMFT evidence of phase separation
in 1-orbital model
Phase separation manifests as a discontinuity in
density vs. chemical potential. It appears in all
dimensions investigated .
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Influence of 1/r Coulomb interaction

• Droplets, stripes or other nanometer size
  patterns may form.

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Pseudogap in simulations
At intermediate temperatures dynamical clusters
are found near the phase-separation critical
temperature. The clusters are metallic
or insulating, inducing a Pseudogap. ?
similarities with cuprates!
No disorder
With disorder
A.Moreo et al., PRL 83, 2773 (1999)
First reported by Dessau et al. ARPES,
bilayers PG observed..
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Two Orbitals plus Jahn-Teller phonons
g electron-phonon coupling
k phonon stiffness
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Orbital and Spin order at x0
Hotta et al. PRB 60, R15009 (1999)
Spin and orbital order at x0
Many states close in energy gt JAF is much
relevant.
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2 Orbitals and J-T Phonons

• All the stable phases observed experimentally are
  obtained.
• PS very prominent as in 1 orbital model.

T 0
Yunoki et al., PRL 81, 5612 (1998)
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Stripes exist as the ground state at large e-JT
coupling
Hotta et al. PRL86, 4922 (2001)
Pi-shift in orbital order. 1/r not needed.
Ferromagnetic phase.
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Nanoscale phase coexistence in manganites
Renner et al., Nature 02 BiCaMnO STM
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Polarons or Larger Clusters?
FM Polaron
Lattice polaron
One carrier surrounded by a distortion.
Mn oxide experiments reveal far larger
clusters, with many carriers inside. Polaron
picture not suitable.
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Quenched disorder plays an important role
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Phase Competition in the Presence of Quenched
Disorder
Double Exchange
n1
nlt1
(phase separation)
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Global Phase Diagram
T
FM
W
SG
T
quenched disorder
quenched disorder
FM
CO
W
SG
T
FM
CO
bandwidth W
W
Courtesy Prof. Yoshi Tokura, Tokyo.
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Disorder effects are very important near a
first-order transition
Disorder due to chemical doping gt random hopping
and Coulomb centers.
large clusters equal density disorder-induced phas
e separation
Imry-Ma Wortis
Warning Cluster size is disorder strength
dependent!
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Random Resistor Network
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CMR effect in inhomogeneous states
Field is small, but effective spin is large!
T
Tc
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Evidence of T
Thermal expansion
LCMO
From De Teresa, Ibarra et al.
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State of the art simulations Sen et al., PRL
2007
Resistance vs. temperature via transmission
(Landauer).
Large magneto-resistance observed.
Summary CMR appears in a tiny cluster! Now we
can ask questions to the computer, as in an
experiment.