Mesoscopic Spintronics - Université Paris-Saclay · Spin-dependent transport is a key phenomenon...
Transcript of Mesoscopic Spintronics - Université Paris-Saclay · Spin-dependent transport is a key phenomenon...
Mesoscopic Spintronics
Taro WAKAMURA (Université Paris-Sud)
Lecture 1
Today’s Topics
• 1.1 History of Spintronics
• 1.2 Fudamentals in Spintronics
Spin-dependent transport
GMR and TMR effect
Spin injection into diverse materials
Spin current and spin relaxation
Spin transfer torque
First of all... What is “spintronics”?
Electronics and Spintronics
Electron has: charge e Electronics
Electron has: spin 1/2 Spintronics
Spintronics in our daily lives
Magnetoresistive Random Access Memory
(MRAM)
Hard Disc Drive
(HDD)
How was spintronics born?
Spin polarized current
Ie ( = I↑ + I↓) ≠ 0
IS ( = I↑-I↓) ≠ 0
=
Flow of charge and spin
Pure spin current
=IS ( = I↑-I↓) ≠ 0
Flow of spin only
I↑: ↑spin current
I↓: ↓spin current
:Charge :Spin
Spin-dependent transport
Currents
in ferromagnets
?
Birth of Spintronics
Giant Magneto-Resistance (GMR) effect
Peter Grunberg
Albert Fert
Nobel Prize in Physics in 2007
Nonmagnetic metal
Birth of Spintronics
Giant Magneto-Resistance (GMR) effect
Fert’s experiments
Fe/Cr/Fe structure Antiferromagnetic coupling depending on the thickness of Cr
Magnetoresistance (MR) ratio
Parallel ParallelAntiparallel
Inplane magnetization curves
MR(%) =𝑅𝐴𝑃 − 𝑅𝑃
𝑅𝑃x 100 ~ 50 % @ 4.2 K
M.N. Baibich et al., Phys. Rev. Lett. 61, 2472 (1988).
Birth of Spintronics
Giant Magneto-Resistance (GMR) effect
Grunberg’s experiments
Similar Fe/Cr/Fe structure, but measurements are at room temperature.
Small MR ratio: ~1.5 %
Fe/Cr/Fe trilayer structure
G. Binasch et al., Phys. Rev. B 39, 4828 (R) (1989).
Birth of Spintronics
Giant Magneto-Resistance (GMR) effect
How can we explain the gigantic magnetoresistance effect?
Electrical currents in ferromagnets are spin-polarized via s-d interaction
Most of carries can pass through in the parallel alignment of the ferromagnets
(= low R)
Most of carries are scattered at the interface in the antiparallel alignment
of the ferromagnets (= high R)
Birth of SpintronicsNote: Exchange coupling between ferromagnetic layers
Stuart Parkin (left)
Co/Ru/Co structure Fe/Cr/Fe structure
Coupling between
ferromagnetic layers
oscillates!
S. S. P. Parikin et al., Phys. Rev. Lett.
64, 2304 (1990).
Birth of SpintronicsNote: Exchange coupling between ferromagnetic layers
Rudermann, Kittel, Kasuya, Yoshida (RKKY) interaction between magnetic
moments via nonmagnetic layer can induce oscillating interaction.
S1S2
Conduction electron
Spin density wave of Cr might play a role as well (Wang, Levy and Fry, PRL 1990).
Birth of Spintronics
Tunneling Magneto-Resistance (TMR) effect
Breakthrough by magnetic tunnel junction (MTJ)
TMR in Fe/Al2O3/Fe multilayers MR ratio 18 % at room temperature
Thanks to high-quality amorphous Al2O3 tunnel barrier!
T. Miyazaki and N. Tezuka, J. Magn. Magn. Mater. 139, L231 (1995).
Birth of Spintronics
Giant Magneto-Resistance (GMR) effect
Julière’s model
Birth of Spintronics
Tunneling in a simple picture
Birth of SpintronicsTunneling in real materials
Importance of symmetries
of crystals
Birth of SpintronicsTunnel Magneto-Resistance (TMR) effect
There are many Bloch states in Fe, and they
have different spin polarization.
e.g. D1 state has high positive spin polarization,
and D2 state has negative spin polarization.
Amorphous Al2O3 mixes these states, thus
decrease of net spin polarization.
Decrease of MR ratio
Incoherent tunneling
Birth of SpintronicsTunnel Magneto-Resistance (TMR) effect
D1 state with high spin polarization coherently
couples D1 evanescent wave in MgO tunnel barrier.
High MR ratio is expected.
Coherent tunneling
Birth of SpintronicsTunnel Magneto-Resistance (GMR) effect
High tunneling probability of the D1 state for parallel alignment
High MR ratio
Tunnel Magneto-Resistance (GMR) effect
Birth of Spintronics
Tunnel Magneto-Resistance (GMR) effect
Birth of Spintronics
Small lattice mismatch (3%) between Fe and MgO
MgO with high crystallinity can be grown on Fe(001).
Birth of SpintronicsApplication of TMR to hard disk drives
Birth of SpintronicsApplication of TMR to hard disk drives
Brief Summary
Spin-dependent transport is a key phenomenon for the birth of spintronics.
One representative example is the giant magnetoresistance effect with metallic
insertion layer between two ferromagnets.
Giant magnetoresistance effect provoked intensive studies for systems
with higher MR ratio, and replacing metallic layer with tunnel barrier (insulator)
enables dramatically gigantic MR (TMR)
Then, is it possible to transfer spin angular momentum without charge
flow? If it is possible, Joule heating effects can be suppressed!
Spin polarized current
Ie ( = I↑ + I↓) ≠ 0
IS ( = I↑-I↓) ≠ 0
=
Flow of charge and spin
Pure spin current
=IS ( = I↑-I↓) ≠ 0
Flow of spin only
I↑: ↑spin current
I↓: ↓spin current
:Charge :Spin
Pure spin currents
Currents
in ferromagnets
?
Nonlocal spin injection and detectionEasiest way: lateral spin valves
charge current
+ spin current
spin accumulation
spin current
F side N side
Spin Polarized CurrentPure Spin Current
Spin Current
Lateral Spin Valve (LSV) structure
↑
↓
N F
VP
VAP
DV
-500 0 500
-1
0
Magnetic field [Oe]
DV
/I [
m
]
DR
V
Nonlocal spin injection and detection
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-500 0 500
-1
0
Magnetic field [Oe]
DV
/I [
m
]
DR
Fitting equation
where
PI: spin polarization of tunneling
junction
lX: spin diffusion length of X
T. Wakamura et al., Appl. Phys. Exp. 4, 063002 (2011).
Nonlocal spin injection and detectionData evaluation
L eB B
S
Larmor precession
NM
a 0 rotation
NM
B
b
B = 0
p/2 rotation
NM
B
c p rotation
V/I
B
0
0
VI
Hanle effectAnother way to estimate tsf and D: the Hanle effect
N
B=0V
Time t
t=0
44 46 48
P (
arb
.)
Time (ps)
DN
= 500 cm2/s
t = 40 ps
0
( )cosPV
dt tI
t
21( ) exp e p
4x
4 sfNN
LP t
D t
t
D t
p t
Diffusion Spin-flip
( )P t
F. J. Jedema et al, Nature 416, 713 (2002).
Hanle effectEstimation of tp and D by the Hanle effect
F. J. Jedema et al., Nature 416, 713 (2002).
B (G)
First experimental report
Information we can derive from the fitting of the Hanle curve:
Diffusion coefficient (D), Spin polarization of Co (P),
Spin diffusion length (lsf)
Many examples of the Hanle measurement for different materials:
n-GaAs (e.g. Lou et al., 2007), LaAlO3/SrTiO3 2DEG (Reyren et al., 2013).
Hanle effect
Key points of spin transport
Spin can transfer information
Spin transport in a long distance is preferable
However
Spins (to a certain quantized axis) are not conserved
Charges are conserved on the contrary.
Therefore, it is important to choose materials with long spin relaxation length or
spin relaxation time.
Then how does spin relaxation occur in materials?
Spin relaxation mechanismSpin relaxation mechanism
A: Elliot-Yafet mechanism
Periodic ion scattering containing
phonon contribution
B: D’yakonov-Perel’ mechanism
Spin precesses along an effective
magnetic field during momentum
scattering.J. Fabian and S. Das Sarma, J. Vac. Sci. Technol. B 17, 1708 (1999).
e.g. Metals, Graphene…
e.g. Semiconductors, Graphene…
Two mechanisms show different dependence of ts on tp.
ts: spin relaxation time, tp: momentum relaxation time
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A: Elliot-Yafet mechanism
Basic idea: impurity or phonon scattering + spin-orbit interaction
B: D’yakonov-Perel mechanism
Spin tilts a little every time the electron
experiences momentum scattering.
ps tt
Basic idea: spin precession by random magnetic fields
The system lack of inversion symmetry:
kkEE
Kramer’s theorem: if Hamiltonian is time-reversal symmetric
J. Fabian and S. Das Sarma, J. Vac. Sci. Technol. B 17, 1708 (1999).
kkEE
Spin relaxation mechanism
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From two equations
kkEE
This can be regarded as a spin split caused by an effective
k-dependent magnetic field (k):
)(2
1)( kΩk Η
J. Fabian and S. Das Sarma, J. Vac. Sci. Technol. B 17, 1708 (1999).
Electrons change their momentum after
each momentum scattering process
Random magnetic field between
the scattering processes
The smaller tp, the smaller the net magnetic field for spin becomes.
(motional narrowing)
Thusps tt 1
Spin relaxation mechanism
Spin relaxation from Hanle measurement
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Example: single-layer graphene case
ts∝ D∝ tp
Single layer graphene
EY mechanism
Bilayer graphene
ts∝ D-1∝ tp-1
DP mechanism
H. Wei and R. K. Kawakami, Phys. Rev. Lett. 107, 047207 (2011).
Spin Transport in Materials
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Spin Transport in Various Materials
Y. Fukuma et al., Nat. Mater. 10, 527 (2011).
Important issues in spintronics: efficient spin injection and detection
(spin impedance mismatch problem)
Search for materials with which long-range spin transport is possible
Examples in metals: Ag, Al, Cu etc.
(low spin-orbit materials)
B (Oe)S. P. Dash et al., Nature. 462, 491 (2009).
Spin Transport in MaterialsSpin Transport in Various Materials
Spin currents can also be transferred through semiconductors
(e.g. silicon, GaAs, LAO/STO)
Gate control of spin transport is possible
N. Reyren et al., Phys. Rev. Lett. 108, 186802 (2012).
N. Tombros et al., Nature 448, 571(2007).
Spin Transport in MaterialsSpin Transport in Various Materials
New materials
Carbon-based materials (graphene)
Graphene Small spin-orbit interaction
Good materials for transferring spin currents for a long distance (lsf ~ a few mm)
Brief summary
Spin angular momentum can be transferred with out any charge flow by means
of spin currents.
Spin currents can be easily generated by using ferromagnet-nonmagnet lateral
spin-valve structures.
The biggest difference between spin currents and charge currents is that spin
currents are not conserved.
Spin relaxation occurs by magnetic impurities or spin-orbit interaction. For the
latter, the EY and DP mechanisms can be considered.
Spin currents can be generated from ferromagnets. Then can spin currents
affect magnetization of ferromagnets?
Spin transfer torque (STT)
Concept of STT
When a current is passed
through magnetic junction as
shown in the right figure, spin-
polarized current is injected into
FM2 from FM1. If S1 and S2 is
not parallel, a net torque is
exerted on S2 by injected spin-
polarized current.
Magnetization can be
controlled by flowing a current.
Spin(-polarized) currents flow of spin angular momentum
Basics of spin dynamics
Landau-Lifsitz Equation
0: gyromagnetic constant
When a magnetic field is applied to a magnetic moment,
the magnetic field exerts a magnetic torque –0M x Heff
Magnetic moment continuously precesses around H
In real systems, there is relaxation, thus
phenomenological damping term
Basics of spin dynamics
phenomenological damping term
This equation implicitly assumes small damping (namely, the direction of M for
the second term does not depend on t).
Precisely speaking, damping is the force to prevent dM/dt. Gilbert
proposes the following equation:
Landau-Lifsitz-Gilbert (LLG) equation
These equations are equivalent by substituting
Basics of spin dynamics
For electrons from FM1 to FM2, three
situations can be considered.
(a) Reflection or spin scattering
at the interface
(b) Transmission (with
presession)
(c) Absorption of spin angular
momentum by FM2
Basics of spin dynamics
A spin points to (q ,f) can be expressed as
For example, in the case of (b), the phase shift for upspin and down spin
electrons is and , respectively.
Thus the spin function for the transmitted spin can be written as
Basics of spin dynamics
If , the electron’s spin
completely flips. This angular
momentum lost during the transmission
transfers to FM2.
In real materials, the phase shift should be random and averaged out for all
electrons. Therefore the net angular momentum change becomes
Spin-transfer-torque term proposed by Slonczewski
John Slonczewski
Spin transfer torque (STT)Theory of STT
Slonczewski’s STT term
Spin transfer torque (STT)
Magnetic domain wall motion driven by STT
Spin transfer from electrons to magnetic
moments move magnetic domail walls.
Magnetic force microscope images
A. Yamaguchi et al., Phys. Rev. Lett. 92, 077205 (2004).
Spin transfer torque (STT)
Magnetization switching by STT
AP
P
AP
P
Electrons with minority spin carrier from
nanomagnet scattered at the interface with Cu
Exert torque on magnetization of nanomagnet
A
B
A: Magnetic field driven magnetization switching
B: STT driven magnetization switching
F. J. Albert et al., Appl. Phys. Lett. 77, 3809 (2000).
Above the critical current, minor spin electrons
reflected back from the thick Co layer transfer
sufficient spin-angular momentum to the
nanomagnet to force it into antiparallel
alignment with the Co layer.P
AP
Brief summary
Spin(-polarized) currents are a flow of spin angular momentum, thus can
exert a torque on magnetization (spin-transfer torque, STT).
Magnetization dynamics can be described by Landau-Lifsitz-Gilbert (LLG)
equation, and STT is expressed as a Sloczewski term.
One can move magnetic domain walls by using STT with currents, and also
switch magnetization with STT larger than Gilbert damping.