Introduction to Spintronics - Physik to Spintronics. Jaroslav Fabian. ... • above room-temperature...
Transcript of 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
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)
J. Fabian, A. Matos-Abiague, C. Ertler, P. Stano, and I. Zutic,Semiconductor spintronics, Acta
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
Current spin polarization
RF =σF
4σF↑σF↓LsF 6= RF
N region
μsN = μsN (0)e−x/LsN
Spin diffusion
PjN (0) = − 1jμsN (0)RN
Current spin polarization
RN =LsNσN
6= RN
Effective resistance
Contact
Pjc = PΣ +1jμsN (0)−μsF (0)
Rc
Current spin polarization
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)
spin injectorcircuit
spin detectorcircuit
e-
flow
spin flow
Non-local spin injection geometry Johnson-Silsbee experiment
spin injectorcircuit
spin detectorcircuit
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
J. Fabian, A. Matos-Abiague, C. Ertler, P. Stano, and I. Zutic,Semiconductor spintronics, Acta
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)
J. Fabian, A. Matos-Abiague, C. Ertler, P. Stano, and I. Zutic,Semiconductor spintronics, Acta
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).