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