Topics in Condensed Matter Physics Lecture Course for graduate students

CFIF/Dep. Física

Spin-dependent transport theory

Vitalii Dugaev

Winter semester: 2004/2005Dates and time: Thursdays, 14:00, starting December 2, 2004Location: Edifício de Pós-Graduação, Sala P1

About myself

From Ukraine: Frantsevich Institute for Problems of Materials Science, National Academy of Sciences of Ukraine, Chernovtsy Branch(Chernovtsy, Ukraine)

Max-Planck-Institut für MikrostrukturphysikHalle, Germany (Patrick Bruno)

ISEL, Lisbon (Manuela Vieira)

Lecture 1. Introduction into physics of spin-dependent phenomena in nanostructures. Giant magnetoresistance (GMR) and tunneling magnetoresistance (TMR) effects. Spintronics.

Lecture 2. Transport theories of metals and semiconductors. Classical theory of Drude-Lorentz. Boltzman kinetic equation. Magnetoresistance of metals and semiconductors. Hall effect.

Lecture 3. Transport theories of metals and semiconductors (cont). Formalism of Green functions and Feynman diagrams. Kubo formula for conductivity. Charge and spin currents. Spin Hall effect.

Lecture 4. Scattering from magnetic impurities. Kondo effect on magnetic impurities and Abrikosov-Suhl resonance. Spin-orbit interaction. Spin relaxation.

Lecture 5. Transport in low-dimensional systems: size-quantization effects. Two-dimensional electron gas. Semiconductor quantum wells. Quantum wires. Quantum dots. Spin-orbit interaction in low-dimensional systems.

Lecture 6. Transport in low-dimensional systems: size-quantization effects (cont). Ballistic transport in nanoconstrictions. Aharonov-Bohm effect in nanorings. Quantization of Hall conductivity in 2D systems.

Lecture 7. Transport in magnetic systems. Spin-dependent scattering. GMR effect. Anomalous Hall effect: mechanisms of side-jump and skew scattering.

Lecture 8. Localization and mesoscopic effects. Anderson localization. Theory of weak localization. Negative magnetoresistance effect. Localization in magnetic systems.

Lecture 9. Coulomb interaction and theories of strongly correlated systems. Landau theory of the Fermi liquid. Coulomb interaction in 1D system. Bosonization method.

Lecture 10. Coulomb interaction and theories of strongly correlated systems (cont). Stoner mechanism of ferromagnetism in metals. Effect of Coulomb blockade.

Lecture 11. Kondo effect in conductivity through the quantum dot. Splitting of the Kondo resonance in magnetic structures with quantum dots and nanoparticles. Spin transistor.

Lecture 12. Spin-dependent tunnelling in magnetic nanostructures. Effect TMR. Spin quantum well. Transport in ferromagnetic wires with domain walls. Negative resistance of the domain wall.

Literature

Review articles:

1. G.A. Prinz. Magnetoelectronics. Science, 282, 1660 (1998)2. S.A. Wolf, D.D. Awschalom et al. Spintronics: a spin-based electronics Vision for the Future. Science 294, 1488 (2001).3. I. Żutić, J. Fabian, S. Das Sarma. Spintronics: fundamentals and applications. Rev. Mod. Phys. 76, 323 (2004).

Books:

1. G.D. Mahan. Many-particle physics (Kluwer, 2000).2. A.A. Abrikosov. Fundamentals of the theory of metals (North-Holland, 1988).3. D.D. Awschalom, D. Loss, N. Samarth (Eds.) Semiconductor spintronics and quantum computation (Springer, 2002).4. Spin dependent transport in magnetic nanostructures. Ed. by S. Maekawa, T. Shinjo (Taylor and Francis, 2002).

Lecture 1

Introduction into physics of spin-dependent phenomena in nanostructures

• Introduction into physics of spin-dependent phenomena in nanostructures. • Giant magnetoresistance (GMR)• Tunneling magnetoresistance (TMR) effects. • Spintronics• Applications

What we know from physics?

Electron = spin + charge

In electronics – charge (-e)In magnetism – spin (½) and, correspondigly, magnetic moment (μB)

In electronics we control electron motion using charge –by electric field (voltage, gate control) and also by magnetic field

In magnetism we control electron using its spin –by magnetic field and – also by electric field (relativistic effect)

Spin-dependent physical phenomena spintronics(S.A. Wolf, DARPA Initiative, 1996)

How to realize?

• Magnetic materials (metals and semiconductors) as spin injectors

• “Working elements” to manipulate spin – spin control

• Detecting spin

nanostructures (all-semiconductor, hybrid structures)

Giant magnetoresistance (GMR) effect

Experiments of A. Fert et al (1988) and P. Grünberg et al (1989)

First theory: J. Barnaś et al (1990)

Magnetic multilayers:

without H

How to explain GMR?

Conductivity in a non-magnetic metal or semiconductor:

CoCuCo

H

m

ne 2

Both spin up and down electrons are involved in conductivity

Separate contributions: (Mott, 1936)

In magnetic materials the contributions are different

Why τ↑ and τ↓ are different?

Main reason – scattering is energy dependent

Simple explanation: spin-valve effect:

m

en

m

en

22

Tunnel magnetoresistance (TMR)

M. Julliere (1975) J.S. Moodera et al (1995)

Two magnetic metals separated by tunneling barrier

1. Tunneling in monmagnetic metals or semiconductors

EF

V=0 V≠0

EF

dfeVfTeV

ej )()()()()(

2 2

21

V=0 V≠0,H=0

2. Tunneling in magnetic structures

V≠0,H ≠0

EF

EF EF

V≠0,H=0

V≠0,H ≠0

EF EF

“Half-metals”:

Applications

• magnetic memory• read/write heads• MRAM• spin transistor• spin filters• spin diodes• spin quibits for quantum computing• What about other particles? spintronics + photonics

Advantages:

• multifunctionality• nonvolatility• increased integration density• increased data processing speed• low power consumption (dissipationless currents?)