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
A Few Remarks About
`Ordinary’ Magnetism
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
Magnetism in Insulators
A playground for strongly-correlated electron physics
Magnetism in Metals – Hubbard Picture
Simple model – Sophisticated QF Theory Possible
Doubles - Interaction Energy Cost U
Empties
Itinerant Electron Ferromagnetism
Bloch-Stoner Picture
Singly Occupied Orbitals
E
xc
E = E0 + M2/D(EF) - Δ M2
E
DO
Sd s
DO
S
μ
μ
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.
Stoner Criterion - Elements
Δ
Theory of Itinerant Electron MagnetismJÜRGEN KÜBLER, Institute of Solid State PhysicsDarmstadt University of Technology
Itinerant Electron Ferromagnetism
Spin-Density Functional Theory
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
Micromagnetics
Direction of Magnetizatio
n
Dipole-Dipole
Interactions
Micromagnetics
A Few Remarks About
Spintronics
SPIN (Elec)TRONICS =
Spin-Torques +
Spin-Orbit (AHE+SHE+Spin-Galvanic) +
Magnetic Semiconductors
Dan Ralph – KITP Spintronics Program Talkwww.kitp.ucsb.edu
GMR TMR and Spin Torques
Hard-disk Technology
10 GByte/(person.year)
A Few Remarks About
the
Quantum Hall Effect
AlGaAs AlGaAsGaAs
100 A
Quantum Well
e-
energ
y
Ga
As
Si
AlGaAs
GaAs
100 A
AlGaAs
Double Quantum Well
-
Quantum Wells
Landau Levels
Cyclotron
Orbit
Integer Quantum Hall Effect
xy/(h/e2)
xx
Incompressible States & Streda Formula
Compressibility
Edge Current
Conductance and
LL degeneracy
Integer Quantum Hall Effect
xy/(h/e2)
xx
QHF- Stoner-Criterion
LandauBand Landau-Level
Exchange Energy
QHF- Stoner-Criterion
Maude et al. PRB (2005)
Landau Levels - Really! (Ashoori – MIT)
Next Time:
• Skyrmions
• QHF Anistropy – Ising or XY
• QHF in Graphene
• Pseudo-spin Transfer Torques