Transcript Slide 1
Topics in Condensed Matter Physics
Lecture Course for graduate students
CFIF/Dep. Física
Spin-dependent transport theory
Vitalii Dugaev
Winter semester: 2004/2005
Dates and time: Thursdays, 14:00, starting December 2, 2004
Location: 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 Mikrostrukturphysik
Halle, 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
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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
(S.A. Wolf, DARPA Initiative, 1996)
spintronics
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:
Co
Cu
Co
without H
H
How to explain GMR?
Conductivity in a non-magnetic metal or semiconductor:
ne2
m
Both spin up and down electrons are involved in conductivity
Separate contributions:
(Mott, 1936)
ne 2 ne 2
m
m
In magnetic materials the contributions are different
Why τ↑ and τ↓ are different?
Main reason – scattering is energy dependent
Simple explanation: spin-valve effect:
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
EF
V=0
V≠0
2e
2
j
1 ( eV ) 2 ( ) T ( ) f ( eV ) f ( )d
2. Tunneling in magnetic structures
EF
EF
V=0
V≠0,
H=0
EF
V≠0,
H ≠0
“Half-metals”:
EF
V≠0,
H=0
EF
V≠0,
H ≠0
Applications
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Advantages:
magnetic memory
read/write heads
MRAM
spin transistor
spin filters
spin diodes
spin quibits for quantum computing
What about other particles?
spintronics + photonics
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multifunctionality
nonvolatility
increased integration density
increased data processing speed
low power consumption
(dissipationless currents?)