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TRANSCRIPT
SpinelektronikChapter 12
Spin Transfer Processes
http://www.fz-juelich.de/iff/staff/Schneider_C_M/Lectures/Vorlesungen_WS_2005.html
Winter 05/06 Spinelektronik
Half-metallic ferromagnets (HFM)
2
• HFM: gap in D↑(E) or D↓(E) around EF
• intermetallic compounds
• oxides
• perovskites
• double-perovskites
Winter 05/06 Spinelektronik
Classes of ferromagnets
3
• (a) weak ferromagnet
• (b) strong ferromagnet
• (c) half-metallic ferromagnet (gap in the minority spin bands)
• (d) half-metallic ferromagnet (gap in the majority spin bands)
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Simple oxides
4
• CrO2: simple oxide
• ferromagnetic metal
• ferromagnetic superexchange + double exchange
• other simple oxides: Fe3O4
CrO2
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Perovskites
5
• different types of half-metallicity
LSMO
Sr2FeMoO6
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Heusler alloys
6
• original Heusler: ferromagnetism without ferromagnetic elements
• half-metallicity in the minority spin bands
half HeuslerNiMnSb
full HeuslerCo2MnSi
Winter 05/06 Spinelektronik
Slater-Pauling curve for full-Heusler
7
• full-Heusler alloys follow a Slater-Pauling dependence (magnetic moment varies with number of valence electrons)
• large variety of compounds
• many have low ordering temperatures
Full Heusler Alloys: Slater-Pauling Curvetotal moment Mt versus total valence charge Zt: Mt=Zt-24
20 21 22 23 24 25 26 27 28 29 30 31 32
Number of valence electrons: Zt
−3
−2
−1
0
1
2
3
4
5
6
7
To
tal
spin
mo
men
t: M
t (µΒ)
Mn2VAl
Fe2VAl
Fe2CrAl
Co2VAl
Fe2MnAl
Rh2MnGe
Co2FeAl
Co2MnSi
Co2MnGe
Co2MnAl
Co2MnGa
Rh2MnAl
Rh2MnGa
Ru2MnSb
Co2CrAl
Fe2MnSi
Ru2MnSi
Ru2MnGe
Ru2MnSn
Co2TiAl
Ni2MnAl
Co2MnAs
Co2FeSi
Rh2MnTl
Rh2MnSn
Rh2MnPb
Mt=Z t
−24
Rh2MnIn
Co2TiSn
Mn2VGe
Co2MnSn
Co2MnSb
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Full-Heusler alloy
8
• characteristic feature is a gap in the minority band structures half-metallic behavior
• similar electronic structure for all 4 systems
• holds for bulk crystals with perfect chemical order
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Full-Heusler alloys: surface properties
9
• surface termination is important for the surface-electronic structure
• formation of gap states half-metallic behavior is destroyed
Winter 05/06 Spinelektronik
Half-metallic spin-valve
10
• Use zinc-blende compounds separated by semiconductors for decoupling
• No interface states at EF
• Tune FM-AF coupling by choice of spacer material & thickness
AP: DOS at EF
P (17 meV)(Conducting)
AP(Insulating)
Mn
Cr
Cr
Mn
Cd
Te
Te
Te
Mn
Cr
Cr
Mn
Te
Te
Te
Te
Te
P: DOS
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Rashba effect
11
• electric field in the quantum well transforms into magnetic field acting on the spin in the rest frame of the electron
• precession of electrons along their path
Rashba Hamiltonian
€
⇓
Hso =αr σ ×
r k [ ]r e z
z
Winter 05/06 Spinelektronik
Spin transfer effects
12
• 1996 Theoretically predicted by Slonczewski and Berger
• 1999 First experimental observation of CIMS at Cornell
• 2003 Current-driven microwave oscillations
• originates from the interaction of spin-polarized electrons with the magnetization
• transfer of spin angular momentum to the magnetization of the ferromagnet
• induces the motion of domain walls
• may initiate entire magnetization reversal process
• applications in MRAM and magnetic logics
“History”
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Current-induced magnetization switching
13
electron flux
ø 10
0 nm
Consider a FM / NM / FM structure with FM layers of different thickness:
NM
thickFM
thinFM
electron flux
NM
thickFM
thinFM
Current-induced magnetization switching (CIMS):• the alignment of the FM layers depends on the current direction• non-equilibrium effect requires high current densities: 108 A/cm2 or 10 mA per (100 nm)2
• depends on symmetry of the system• relates to GMR like “actio = reactio”
Winter 05/06 Spinelektronik
First observation of CIMS
14
• electric field in the quantum well transforms into magnetic field acting on the spin in the rest frame of the electron
• precession of electrons along their path
z
Si3N4 membrane with holes coveredfrom two sides with metallic films:
Hole diameter : 5 - 10 nm
2-4 nm Co / 4 nm Cu / 100 nm Co
Current density: ~ 109 A/cm2
CPP-GMR
E.B. Myers et al., Science 285, 867 (1999)
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Observation of CIMS
15
dV/d
I (Ω
)
J.A. Katine et al., Phys. Rev. Lett. 84, 3149 (2000)
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Spin-transfer-torque acts like interlayer coupling
16
•
Coercive fields:Co1: 400 OeCo2: 200 Oe
“AF-coupled”
“FM-coupled”
GMR at high current (±50 mA):
Sample area:200 x 600 nm2
Current density:4 x 107 A/cm2
GMR at low current (±50 µA):“decoupled”
J. Grollier et al., Appl. Phys. Lett. 78, 3663 (2001)
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Switching by Oersted field ?
17
•
The current gives rise to a circular magnetic field, which favors a vortex-like magnetization state in the small magnetic elements: required current density: 107 - 108 A/cm2
the maximum field at the edge scales like (for spin-transfer )B ∝ Ir
[23 Å NiFeCo / 40 Å Cu / 12 Å NiFe / 40 Å Cu]5
with a pillar diameter of 0.3 µm
Ir2
K. Bussmann et al., Appl. Phys. Lett. 75, 2477 (1999)
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Mechanism of spin transfer effects (I)
18
• electric field in the quantum well transforms into magn
after X. Waintal et al., Phys. Rev. B 62, 12317 (2000)
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Quantum-mechanic spin filtering
19
ψ in =cosθ
2
sinθ2
⇒
ψ in σ x ψ in = sinθ
ψ in σ y ψ in = 0
ψ in σ z ψ in = cosθ
ψ in ψ in = 1ψ R =
0
sinθ2
⇒
ψ R σ x ψ R = 0
ψ R σ y ψ R = 0
ψ R σ z ψ R = − sin2 θ2
ψ R ψ R = sin2 θ2
ψ T =cosθ
20
⇒
ψ T σ x ψ T = 0
ψ T σ y ψ T = 0
ψ T σ z ψ T = cos2 θ2
ψ T ψ T = cos2 θ2
Spin transfer: ψ in σ→
ψ in − ψ R σ→
ψ R + ψ T σ→
ψ T
=
sinθ − (0 + 0)0 − (0 + 0_
cosθ − (− sin2 θ2+ cos2 θ
2)
=
sinθ00
x
z
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Mechanism of spin transfer effects (II)
20
• after X. Waintal et al., Phys. Rev. B 62, 12317 (2000)
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Influence of spacer thickness
21
•
Spin-flip scattering (spin relaxation length λs) in the spacer leads to an asymmetric thickness dependence of the critical currents for CIMS:
Jc+: P → APJc
- : AP → P
GMR: ΔR A ∝ exp(-d/λs) ⇒ λs = 190 ± 20 nm
AP → P: Jc- ∝ exp(d/λs) ⇒ λs = 170 ± 40 nm
P → AP: Jc- ∝ exp(2d/λs) ⇒ λs = 140 ± 30 nm (70 ± 20 nm without factor 2)
Reflected electron must cross the spacer layer twice!F.J. Albert et al., Phys. Rev. Lett. 89, 226802 (2002)
Winter 05/06 Spinelektronik
A microscopic picture: Spin-transfer at interface
22
•
Consider perpendicular Fermi wave vectors for spin-up and spin-down: k↑,↓
k↑ = k↓ for a non-magnetic metal N k↑ ≠ k↓ for a magnetic metal F
An incident electron is in general a superposition of spin-up and spin-down. In N thephase angle ϕ is constant, but in F ϕ varies because of “different propagation speeds”
of spin-up and spin-down components:ϕ(ζ) = ϕ(0) + (k↑ - k↓) ζ
Different states on the Fermi surfacehave different k↑ - k↓
⇒ Loss of coherence within about 10 monolayers from interface
⇒ Transfer of spin momentum
after J.C. Slonczewski (1999)
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Absorbed spin momentum is a torque
23
τ =α I IM
M × (M × MP )
αI describes the strength of the spin-transfer (must be determined from a microscopic picture that takes material properties into account)M is the magnetization of the free layerMP is the magnetization of the pinned layerI is the current density. Its sign depends on the current direction!
τ is the absorbed moment and thus a torque on M
The spin-transfer (absorbed momentum) can be written as
Winter 05/06 Spinelektronik
Magnetization dynamics and spin-transfer (I)
24
The equation of motion for a magnetization M is the Landau-Lifshitz-Gilbert (LLG) equation:
∂M∂t
= −γM × Heff
Hef
f
MxHe
ff
M
stable precession with frequency γHeff/(2π)γ: gyromagnetic ratio
∂M∂t
= −γM × Heff +αM(M ×
∂M∂t)
damped precession with frequency γHeff/(2π)
α: Gilbert damping coefficient
Winter 05/06 Spinelektronik
Magnetization dynamics and spin-transfer (II)
25
Spin-transfer fro the pinned layer with magnetization MP acts as a torque on the free layer (magnetization M) and gives rise to a further term in its LLG equation:∂M∂t
= −γM × Heff +αM(M ×
∂M∂t) + α I I
MM × (M × MP )
Depending on the sign of the current density I, the additional term acts as a positive damping or a negative damping. In the latter case, it can (over-) compensate the Gilbert damping and leads to a destabilized precession that eventually switches M.
At the compensation point M rapidly jumps (thermally excited) between AP and P alignment.
For larger fields the describes small or large angle oscillatory motions with typical frequencies of GHz.
Winter 05/06 Spinelektronik
Example of simulated oscillatory motion of M
26
• The opening angles of these motions are large compared to FMR precessions
Rashba Hamiltonian
z
Hext is applied along the x-axis
Z. Li and S. Zhang, Phys. Rev. B 68, 024404 (2003)
Winter 05/06 Spinelektronik
Microwave oscillations driven by spin-pol. currents
27
•S.I. Kiselev et al., Nature 425, 380 (2003)
The phase diagram and the types of motion can be understood by solutions of the LLG equation when the spin torque term is included:
0.5
kOe
field
step
s
LLG simulation experiment
Winter 05/06 Spinelektronik
Electron beam lithography for CPP-GMR and CIMS
28
For CPP: RA ≈ 10-4 - 10-3 Ω µm2 ⇒ sub-µm structures are required
Winter 05/06 Spinelektronik
Lithographic procedure in detail
29
Winter 05/06 Spinelektronik
Realization of nanocontacts at FZJ
30
200 nm
AFM
Optical microscopy
Winter 05/06 Spinelektronik
Inverted CIMS in Fe(Cr)/Cr/Fe(Cr) nanopillars
31
•M. AlHajDarwish et al., J. Appl. Phys. 95, 6771 (2004)
Py/Cu/Py:• Stronger minority scattering (β>0)
• Normal GMR• Normal CIMS
Fe(5% Cr)/Cr/Fe(5% Cr): • Stronger majority scattering (β<0)
• Normal GMR • Inverse CIMS
⇒ Spin scattering asymmetries determine CIMS
So far, all experiments are performed with Co, Co alloys, and Py. Other materials?
Winter 05/06 Spinelektronik
GMR in CPP Geometry
32
• Easy axis / hard axis behavior confirms epitaxy of nanopillar
Fe (001) easy axis: Fe (011) hard axis:
I- V-
I+ V+
variable B
small I
Winter 05/06 Spinelektronik
Spin-Torque Induced Switching
33
• W-shaped background due to contamination layer in pillar
• Hysteretic switching of free layer with γFe/Ag > 0 as expected
variable I
fixed B
Fe (001) easy axis: Fe (011) hard axis: 50 K
Winter 05/06 Spinelektronik
Current-Induced Microwave Emission
34
• Quality factor f/Δf of up to 90
• Microwave power per line is estimated to be of the order of 1 nW
fixed I
variable B
50 K
DC
curre
nt
Winter 05/06 Spinelektronik
R-I Loops vs. Microwave Excitations
35
• Microwave excitations appear close to switching processes and go along with peaks and dips in R-I curves
Winter 05/06 Spinelektronik
Interfacial dependence of CIMS
36
• Spin torque transfer depends on the electronic matching
M
Winter 05/06 Spinelektronik
Precession of transmitted spins
37
• Calculation of a single spin response
• transmitted electron precesses around the magnetization in the ferromagnet
• precession amplitude decays into the ferromagnet
• spin torque decays too
M
M.D. Stiles et al., Phys. Rev. B 66, 014407 (2002)
Winter 05/06 Spinelektronik
Explanation for inverse CIMS
38
Consider spin scattering asymmetries (similar to the case of the inverse GMR).Slater-Pauling curve gives an idea about volume and interface scattering
asymmetries as transition metal alloys XY and their interfaces X/Y
⇒ Py,Co, CoFe: stronger scattering of minority electrons (β > 0)⇒ BUT FeCr and Fe/Cr: stronger scattering of majority electrons (β < 0)
Winter 05/06 Spinelektronik
Mechanism of inverse CIMS (I)
39
New discussion for stronger scattering of the majority electrons:
β > 0β < 0
⇒ Polarization properties of a FM layer change with β
Winter 05/06 Spinelektronik
Mechanism of inverse CIMS (II)
40
both β > 0
both β < 0
antiparallel alignment
parallel alignment
⇒ CIMS is inverse when β of the thick (polarizer) layer or both β change sign⇒ Note: GMR is only inverse when βL βR < 0
Winter 05/06 Spinelektronik
Beyond the macrospin picture
41
• micromagnetic structures during the CIMS process
• very “chaotic” magnetization distribution during switching
• excitation of spin-wave modes
Winter 05/06 Spinelektronik
Current-driven domain wall motion
42
•A. Yamaguchi et al., Phys. Rev. Lett, 92, 077205 (2004)
Arrows indicate “technical” current.
The spin of the conduction electrons follow adiabatically the local magnetization, which varies slowly across the domain wall. Each conduction electron thus transfers a momentum to the domain wall.
Envisaged application:Switching of magnetic elements by reversibly pushing a domain wall across the elements
⇒ MRAM?
h
Winter 05/06 Spinelektronik
Application of CIMS in GMR-MRAM cells
43
•J.-G. Zhu et al., J. Appl. Phys. 87, 6668 (2000)
CIMS would simplify the chip layout because the paired word lines are not needed
VMRAM Memory cell:
Winter 05/06 Spinelektronik
CIMS in tunnel junctions
44
•Y. Huai, P.P. Nguyen, F. Albert, Grandis Inc., MMM/Intermag 2004
Low resistive TMR junctions: PtMn/CoFe/Al2O3/CoFe/NiFe • 0,5 - 10 Ωµm2
• 1 - 20 % TMR • 0,1 x 0,2 µm2
• critical current depends on external field • switching at low current densities of 1x107 A/cm2
• low current densities due to “hot spots”?
75.5
74 .5
73 .5
72 .5
71 .5-2.5 -1.5 -0.5 0.5 1.5 2.5
R (Ω
)
Current (mA)
75.5
74 .5
73 .5
72 .5
71 .5
-120 -70 -2 0 3 0 80 13 0 1 8 0
Field (Oe)
R (Ω
)
Field sweep: Current sweep:
Potential application: Simplified write-procedure of MRAM cells with less wiring!
Winter 05/06 Spinelektronik
Switching limitations
45
• Oersted field switching inefficient at small structures
• alternative: spin-transfer switching
0 200 400 600 800 1000
20
40
60
80
100
120
140
0 200 400 600 800 10000
2
4
6
8
10
12
14
16
18
20
22
Switc
hing
Fie
ld (O
e)
Lateral Dimension (nm)
Magnetic Dot Aspect Ratio = 2.0
Field Assist Switching
Sw
itchi
ng C
urre
nt (
mA
)
Lateral Dimension (nm)
Current Induced Switching