Quantum Hall Ferromagnets-I Les Houches June 2006 University

Quantum Hall Ferromagnets-I Les Houches June 2006 University of Texas at Austin 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

A Few Remarks About `Ordinary’ Magnetism

Magnetism in Atomic Physics Electrons are Fermions Magnetism due to Fermi Statistics and spin-independent interactions Make 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 Doubles - Interaction Energy Cost U Empties Simple model – Sophisticated QF Theory Possible

Itinerant Electron Ferromagnetism Bloch-Stoner Picture E = E 0 + M 2/D(EF) - Δ M 2 xc E Singly Occupied Orbitals

DOS d s E μ μ

Itinerant Electron Ferromagnetism Spin-Density Functional Theory One very successful picture of transition metal ferromagnetism is Density Functional Theory. Hohenberg-Kohn Theorem Kohn-Sham Trick E= E[n, m]= Es[n, m]+Exc[n, m] v = ves + vxc B = D[n, m] m/m Local Spin-Density Approx.

Stoner Criterion - Elements Δ

Itinerant Electron Ferromagnetism Spin-Density Functional Theory of Itinerant Electron Magnetism JÜRGEN KÜBLER, Institute of Solid State Physics Darmstadt University of Technology

Itinerant Electron Ferromagnetism Quasiparticle and Collective Aspects Majority Spins Minority Spins Q Fermi Surface Singly Occupied Orbitals ph spin flip Spin Wave Collective Q E

Micromagnetics Dipole-Dipole Interactions Direction of Magnetization

Micromagnetics

A Few Remarks About Spintronics

SPIN (Elec)TRONICS = Spin-Torques + Spin-Orbit (AHE+Spin-Galvanic) + Magnetic Semiconductors

GMR TMR and Spin Torques Dan Ralph – KITP Spintronics Program Talk www. kitp. ucsb. edu

Hard-disk Technology 10 GByte/(person. year)

A Few Remarks About the Quantum Hall Effect

Quantum Wells Al. Ga. As Al. Ga. As - e- Ga energy As Si 100 A Quantum Well Double Quantum Well

Landau Levels Cyclotron Orbit

Integer Quantum Hall Effect xx xy/(h/e 2)

Incompressible States & Streda Formula Compressibility Edge Current Conductance and LL degeneracy

Integer Quantum Hall Effect xx xy/(h/e 2)

QHF- Stoner-Criterion Landau Band 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