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Quantum Hall Ferromagnets-I
Ramin Abolfath Luis Brey Anton Burkov Rene Cote Jim Eisenstein Herb Fertig Steve Girvin Charles Hanna Tomas Jungwirth Kentaro
Nomura Leo Radzihovksy (Doug) Rajaraman Mark Rasolt Jairo Sinova Kun
Yang
Les Houches June 2006
University of Texas at Austin
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A Few Remarks About
`Ordinary’ Magnetism
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Magnetism in Atomic Physics
Electrons are Fermions
Magnetism due to Fermi Statistics and spin-independent interactionsMake all orbitals in an open shell as similar to each other as possible
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Magnetism in Insulators
A playground for strongly-correlated electron physics
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Magnetism in Metals – Hubbard Picture
Simple model – Sophisticated QF Theory Possible
Doubles - Interaction Energy Cost U
Empties
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Itinerant Electron Ferromagnetism
Bloch-Stoner Picture
Singly Occupied Orbitals
E
xc
E = E0 + M2/D(EF) - Δ M2
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E
DO
Sd s
DO
S
μ
μ
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Itinerant Electron Ferromagnetism
Spin-Density Functional Theory One very successful picture of transition metal ferromagnetism is Density Functional Theory.
E= E[n,m]= Es[n,m]+Exc[n,m]
v = ves + vxc
B = n,m] m/m
Hohenberg-Kohn TheoremKohn-Sham Trick
Local Spin-Density Approx.
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Stoner Criterion - Elements
Δ
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Theory of Itinerant Electron MagnetismJÜRGEN KÜBLER, Institute of Solid State PhysicsDarmstadt University of Technology
Itinerant Electron Ferromagnetism
Spin-Density Functional Theory
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Itinerant Electron Ferromagnetism
Quasiparticle and Collective Aspects
Q
ph spin flip
Spin Wave Collective
Majority Spins Minority Spins
Fermi Surface
Q
Singly Occupied Orbitals
E
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Micromagnetics
Direction of Magnetizatio
n
Dipole-Dipole
Interactions
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Micromagnetics
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A Few Remarks About
Spintronics
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SPIN (Elec)TRONICS =
Spin-Torques +
Spin-Orbit (AHE+SHE+Spin-Galvanic) +
Magnetic Semiconductors
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Dan Ralph – KITP Spintronics Program Talkwww.kitp.ucsb.edu
GMR TMR and Spin Torques
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Hard-disk Technology
10 GByte/(person.year)
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A Few Remarks About
the
Quantum Hall Effect
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AlGaAs AlGaAsGaAs
100 A
Quantum Well
e-
energ
y
Ga
As
Si
AlGaAs
GaAs
100 A
AlGaAs
Double Quantum Well
-
Quantum Wells
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Landau Levels
Cyclotron
Orbit
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Integer Quantum Hall Effect
xy/(h/e2)
xx
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Incompressible States & Streda Formula
Compressibility
Edge Current
Conductance and
LL degeneracy
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Integer Quantum Hall Effect
xy/(h/e2)
xx
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QHF- Stoner-Criterion
LandauBand Landau-Level
Exchange Energy
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QHF- Stoner-Criterion
Maude et al. PRB (2005)
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Landau Levels - Really! (Ashoori – MIT)
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Next Time:
• Skyrmions
• QHF Anistropy – Ising or XY
• QHF in Graphene
• Pseudo-spin Transfer Torques