introduction to spintronics - physik to spintronics. jaroslav fabian. ... • above room-temperature...

15.6.2011, Lecture at the Graduate School Nanoscience

Regensburg

Introduction to Spintronics Jaroslav

Fabian

I. Zutic, J. Fabian, and S. Das Sarma, Spintronics: Fundamentals and applications, Rev. Mod. Phys. 76, 323 (2004)

J. Fabian, A. Matos-Abiague, C. Ertler, P. Stano, and I. Zutic,Semiconductor spintronics, Acta

Phys. Slovaca, 57, 566 (2007)

J. Fabian and I. Zutic, The standard model of spin injection, arXiv:0903.2500

my group’s web site:www.physik.uni-regensburg.de/forschung/fabian/index_lecturenotes.html

http://lanl.arxiv.org/abs/0903.2500

http://www.physik.uni-regensburg.de/forschung/fabian/index_lecturenotes.html

WHAT IS SPINTRONICS?

what’s in the name?

Attempts to label fields rarely succeed, because names have a life of their own. ‘Nanotechnology’, when coined in 1974, had nothing like the meaning it has today —

it referred to rather conventional micromechanical engineering. ‘Spintronics’, the field of quantum electronics that lies behind this year’s physics Nobel, is arguably a slightly ugly

and brutal

amalgam (of ‘electronics’

and the electron’s quantum property of ‘spin’), yet somehow it works.

P. Ball in Nature News 19.10.2007, doi:10.1038/news.2007.171

what

is

spintronics?

narrow (device): electronics

with spin

broad: umbrella for electron spin

phenomena in solids

spintronics drive

technology fundamental discoveries

The Royal Swedish Academy of Sciences has decided to award the Nobel Prize in Physics for 2007 jointly to

Albert Fert

Unité

Mixte

de Physique CNRS/THALES, Université

Paris-Sud, Orsay, France

Peter Grünberg

Forschungszentrum

Jülich, Germany,

"for the discovery of Giant Magnetoresistance".

The Nobel Prize in Physics 2007

Giant MagnetoResistance P. Grunberg et al. (1988), A. Fert et al. (1988)

multilayers

30 -

40% at RT

small resistance large resistance

GMR hard

disk

read

heads

From: IBM web site

Tunneling Magneto Resistance TMR non-volatile MRAM

bit line (top)

free layer, bittunnel barrier AlOfixed (pinned) layerbase electrode

digit line (bottom)

isolation transistor

sense current

large current

small current

SPINTRONICS GOALS

spin

control

of electrical

properties(I-V characteristics)

electrical

control

of spin(magnetization)


Phys. Slov, 57, 566 (2007):

I.

B. 1 Can the spin magnetic moment of a free electron be detected?I. B. 2 Can Stern-Gerlach experiments be used to polarize electron beams?

SPINTRONICS’

3 REQUIREMENTS

•

EFFICIENT SPIN INJECTION

•

SLOW SPIN RELAXATION @ SPIN CONTROL

•

RELIABLE SPIN DETECTION

Silsbee-Johnson spin-charge coupling

F N

spin accumulation

:materials issues:room temperature ferromagnetic semiconductors?

• 1-15 % Mn• p-doped (Mn

replaces Ga) • degenerate: p = 1020

- 1021/cm3

• Tc

up to 180 K• fm and p-density coupled• impurity band or not?

T. Jungwirth et al., Rev. Mod. Phys. 78, 809 (2006)

(Ga,Mn)As Fe Au

• above room-temperature fm• a few nm of GaMnAs

involved• bias control?• anisotropies?

GaMnAs Fe/GaMnAs

F. Maccherozzi et al., Phys. Rev. Lett. 101, 267201 (2008)See also poster 234 for related work S. Mark et al.

There is no Si-based ferromagnetic semiconductor!

spin-orbit coupling in zincblende

systems what happens when inversion symmetry is broken?

(Bychkov-Rashba

Hamiltonian)

Yu. A. Bychkov

and E. I. Rashba, J. Phys. C 17, 6039 (1984); JETP Lett. 39, 78 (1984)

J. Fabian, A. Matos-Abiague, C. Ertler, P. Stano, and I. Zutic, Semiconductor spintronics, Acta

Phys. Slov, 57, 566 (2007)

:spin transistors:

Datta-Das

Sugahara-Tanaka

Johnson

Magnetic bipolar transistor

hot-electron spin transistors

Spin current basis for confusions

N. Mott (1936) : as long as spin-orbit coupling is week, current is carried by spin up and spin down channels

Charge Spin

Spin current is not conserved: no unique way of defining it microscopically

Electrical Spin Injection

Silsbee: emf

appears in the proximity of a ferromagnetic metal and spin-

polarized nonmagnetic metal (inverse of spin injection)

R. Silsbee, Bull. Mag. Reson. 2, 284 (1980)M. Johnson and R. H. Silsbee, Phys. Rev. Lett. 55, 1790 (1985).

spin injection spin detection

Johnson-Silsbee spin injection experiment

δMμ0μ0

E E

N (E) N (E) N (E) N (E)

contactferromagnet nonmagnet

Q: How much spin accumulates in N if there is a charge current j

flowing?

Key assumptions:

• degenerate Fermi gases• charge neutrality (no space charges)• spin conservation at the contact

Spin-polarized transport key conceptes

key concepts: electric transportQuasichemical potentials

f0(²) = [exp(²− η)/kBT ) + 1]−1 → f(², x) = f0 [²− eφ(x)− η − eμ(x)]

n(x) =Rd²g(²)f(², x) = n0 =

Rd²g(²)f0(²)

Local charge neutrality

μ(x) = −φ(x)

j = σE + eD∇n =³−σ + e2D ∂n0

∂η

´∇φ+ e2D ∂n0

∂η ∇μ =

Electric current

= 0

Einstein‘s relation

σ∇μ

Contact resistance

j = Σc∆μ Rc = 1/Σc

g

emf (electromotive force)

key concepts: spin accumulation

Spin density and spin polarization

n = n↑ + n↓

n↑(x) = n↑0(η + eμ↑ + eφ) ≈ n0↑ + g↑(eμ↑ + eφ)Spin accumulation

s = n↑ − n↓

n↓(x) = n↓0(η + eμ↓ + eφ) ≈ n0↓ + g↓(eμ↓ + eφ)

s = s0 + δs

δs = 4eg↑g↓g μs

μ = (μ↑ + μ↓)/2 μs = (μ↑ − μ↓)/2

spin accumulation

key concepts: spin-polarized transport

Charge and spin currents

j = j↑ + j↓ j↑ = σ↑∇μ↑

j = j↑ − j↓j = σ∇μ+ σs∇μs

spin-charge coupling

j↓ = σ↓∇μ↓ js = σs∇μ+ σ∇μs

Current spin polarization

Spin-polarized currents in contacts

j↑ = Σ↑∆μ↑

j↓ = Σ↓∆μ↓

j = Σ∆μ+ Σs∆μs

js = Σs∆μ+ Σ∆μs

Pj = PΣ +∆μs/jRc Rc = Σ/4Σ↑Σ↓ 6= Rc = 1/Σ

key concepts: spin diffusion

Diffusion of spin accumulation

∇j = 0 ∇js = ?∇js = eδs/τs = ... = 4e2μsg↑g↓g

1τs

∇js = ∇³Pσj +∇μs

4σ↑σ↓σ

´= 4

σ↑σ↓σ ∇2μs

Also,

Compare,

∇2μs = μs/L2s

Ls = (Dτs)1/2

case study: spin injection in FN junctions

Strategy:

1.

study spin-polarized transport in each region2.

connect different regions by continuity equations

3.

calculate spin injection efficiency

F region

μsF = μsF (0)ex/LsF

Spin diffusion

PjF (0) = PσF +1jμsF (0)RF


RF =σF

4σF↑σF↓LsF 6= RF

N region

μsN = μsN (0)e−x/LsN

Spin diffusion

PjN (0) = − 1jμsN (0)RN


RN =LsNσN

6= RN

Effective resistance

Contact

Pjc = PΣ +1jμsN (0)−μsF (0)

Rc


Algebraic system

PjF (0) = PσF +1jμsF (0)RF

PjN (0) = − 1jμsN (0)RN

Pjc = PΣ +1jμsN (0)−μsF (0)

Rc

Pj ≡ PjF (0) = PjN (0) = PjcContinuity of spin current at C:

Spin injection efficiency

central result of the standard model of spin injection:

Equivalent electrical circuit model of spin injection

ferromagnetic electrode contact nonmagnetic conductor

Transparent junctionRc ¿ RN , RF

Pj =RF

RF+RNPσF

Spin injection efficiency is due to the spin-polarization of the ferromagnet

Q: What happens if we would inject spin into a semiconductor from aferromagnetic metal?

Pj ≈ RF

RNPσF ¿ PσF

the conductivity mismatch problem!

Tunnel junctionRc À RN , RF

Pj ≈ PΣSpin injection efficiency is due to the spin-polarization of the contact

Q: Is there is the conductivity mismatch problem now?

No! Spin injection into semiconductors can be done through

tunnel junctions

Nonequilibrium resistance & spin bottleneckμN (∞)− μF (−∞) = (RF +RN +Rc + δR)j

δR = RN (P2ΣRc+P

2σFRF )+RFRc(PσF−PΣ)2RF+Rc+RN

> 0

Spin bottleneckQ: Why is the extra resistance positive?

Silsbee-Johnson spin-charge coupling

Q: Suppose there is a source of nonequilibrium spin at the far right of N.What is the emf due to the proximity with equilibrium spin polarization F?

spin source

Spin injection in FNF junctions

Transparent contacts

Tunnel contacts

Maximum signal if

Non-local spin injection geometry Johnson-Silsbee experiment

spin injectorcircuit

spin detectorcircuit

M. Johnson and R. H. Silsbee, Phys. Rev. Lett. 55, 1790 (1985)



e-

flow

spin flow

Non-local spin injection geometry Johnson-Silsbee experiment



Q: Suppose electric current drives spin injection in the spin injector circuitF1/N as indicated below. What is the emf in the open detector F2/N junction?

nonlocal resistance

Tunnel contacts

Measurement of spin diffusion length

:experimental examples:

electrical spin injection into semiconductors•

Theoretically predicted byA. G. Aronov

and G. E. Pikus, Fiz. Tekh. Poluprovodn. 10, 1177 (1976) [Sov. Phys. Semicond. 10, 698-700 (1976)]

•

Experimental realization in semiconductors:

Fiederling

et al. Nature 402, 787 (1999).Ohno

et al. Nature 402, 790 (1999).

visualizing spin injection

S. A. Crooker et al., JAP, 101,081716 (2007)

S. A. Crooker at al., Science 309, 2191 (2005)

spin injection into silicon

I. Appelbaum et al, Nature 447, 295 (2007)I. Zutic and J. Fabian, Nature (NW) 447, 269 (2007)

spin injection into graphene

N. Tombros, C. Jozsa, M. Popinciuc, H. T. Jonkman, and B. J. van WeesElectronic spin transport and spin precession in single graphene

layers at room temperature, Nature 448, 571 (2007)

single-layer on a SiO2

substrate, room temperature

surprisingly small

Optical Spin Injection (usually called optical orientation)

Zincblende

band structure (GaAs) optical

orientation

transitions

σ+σ+

mj

Eg

Δ

CB

SO

E

LH

HH

0 k

(a)

3/2P

1/2P

1/2S (b)

HH,LH

σ− −σ

1/2−1/2

−1/2 1/2

−3/2 3/2

−1/2 1/2

SO

CB

3 1 1 3

22Γ7

Γ8

6Γ

so

From: I. Zutic, J. Fabian, S. Das Sarma, Rev. Mod. Phys. 76, 323 (2004)

Spin relaxation

t=0, spin imbalance t=T1

, spin balance

B Fe

Spin relaxation for pedestrians

impurity

phononSpin-orbit coupling

:key concepts: spin relaxation and dephasing

Bloch eqs

Spectral characteristics of magnetization depolarization•

CESR (resonant absorption of microwaves by Zeeman split electron

system)

•

Optical orientation

Time and space correlations of magnetization

•

Johnson-Silsbee spin injection•

Time-resolved photoluminescence•

Faraday and (magneto-optic) Kerr effects (rotation of polarization plane of linearly polarized light transmitted—Faraday—or reflected---

Kerr---by a magnetized sample; 100 fs

resolution)•

spin-to-charge conversion

Spin relaxation measurements

Time-resolved Faraday rotation

Source: web site of Awschalom’s

group

ZnCdSe

QW

mechanisms of spin relaxation


Physica

Slovaca, 57, 565 (2007)

Elliott-Yafet mechanismelemental metals and semiconductors

Dyakonov-Perel mechanismSemiconductors without center of inversion symmetry

Bir-Aronov-Pikus mechanismHeavily p-doped semiconductors

Hyperfine interactionElectrons bound on impurity sites or confinedIn quantum dots

:spin relaxation: GaAs, Si

J. L. Chang, M. W. Wu, and J. Fabian, Phys. Rev. Lett. 104, 016601 (2010)

Si (non-degenerate densities)GaAs

(low temperature)

spin relaxation time longest among semiconductors (+ graphene)

Elliott-Yafet

mechanism

simple model of spin relaxation and dephasing

spin in a random fluctuating magnetic field (almost Dyakonov-Perel

mechanism)


Physica

Slovaca, 57, 565-907 (2007)

Zeeman B=B0

z fluctuating

General strategy

Iterative solution

Ensemble averaging

Markov approximation(coarse graining)

:our system of fluctuating field:

after “some”

algebra …

effective correlation times

see: J. Fabian, A. Matos-Abiague, C. Ertler, P. Stano, and I. Zutic,Semiconductor spintronics, Acta

Physica

Slovaca, 57, 565-907 (2007)

discussion 1

I.

I.

Precession frequency fluctuations---motional narrowing (see later): 1/T2

’—secular broadening

II.

II.

Lifetime broadening: 1/2T1

discussion 2

motional narrowing why 1/Τ1,2

∼

τc

random spin walk

Spin as a qubit: quantum computing in quantum dots

:nanospintronics:spin-based quantum information processing

D. Loss and D. P. DiVincenzo, PRA 57, 120 (1998)

• single and few spins manipulation and detection• spin relaxation and decoherence• entanglement control (EDAP: Fabian, Hohenester, PRB 71, 201304 (2005))

A. Wild et al, Electrostatically

defined quantum dots in a Si/SiGe

heterostructure,NJP 12, 113019 (2010).

introduction to spintronics - physik to spintronics. jaroslav fabian. ... • above room-temperature...

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