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Spin transfer torque and magnetization dynamics inin-plane and out-of-plane magnetized spin valves
Pavel Baláž
Institute of Molecular Physics in PoznanPolish Academy of Sciences
andFaculty of Physics
A. Mickiewicz University in Poznan
Univerzita Karlova, 5 December 2013
P. Baláž (AMU, Poznan) Spin transfer torque and magnetization dynamics Prague, December 2013 1 / 35
Nanoscale spin torque devices for spin electronicsJoint research project under the framework of Polish-Swiss research programme
nanospin.agh.edu.pl
Partners
• AGH University of Science and Technology in KrakówT. Stobiecki – coordinator
• Institute of Molecular Physics in Poznan, Polish Academy of SciencesJ. Dubowik – experiment, J. Barnas – theory
• Ecolé Polytechnique Fédérale in LausanneJ.-Ph. Ansermet
Objectives
jointly developing novel nanoscale spintronic devices based on the spin transfer torqueeffect, which promises unrivaled future scaling, flexibility and low power consumption
P. Baláž (AMU, Poznan) Spin transfer torque and magnetization dynamics Prague, December 2013 2 / 35
1 Introduction
2 Spin-torque in metallic spin valves
3 Dual spin valve
4 Nonlinear magnetoresistance in dual spin vales
5 Current-induced switching in metallic spin valves with perpendicular polarizers
P. Baláž (AMU, Poznan) Spin transfer torque and magnetization dynamics Prague, December 2013 3 / 35
Introduction
Outline
1 Introduction
2 Spin-torque in metallic spin valves
3 Dual spin valve
4 Nonlinear magnetoresistance in dual spin vales
5 Current-induced switching in metallic spin valves with perpendicular polarizers
P. Baláž (AMU, Poznan) Spin transfer torque and magnetization dynamics Prague, December 2013 4 / 35
Introduction
Spin valves and Giant magnetoresistance
spin
spin
M. N. Baibich, J. M. Broto, A. Fert, F. Nguyen Van Dau, F. Petroff, P. Etienne, G. Creuzet, A. Friederich, and J. Chazelas
Giant Magnetoresistance of (001)Fe/(001)Cr Magnetic Superlattices
Phys. Rev. Lett. 61, 2472–2475 (1988)
G. Binasch, P. Grünberg, F. Saurenbach, and W. Zinn
Enhanced magnetoresistance in layered magnetic structures with antiferromagnetic interlayer exchange
Phys. Rev. B 39, 4828–4830 (1989)
R. E. Camley and J. Barnas
Theory of giant magnetoresistance effects in magnetic layered structures with antiferromagnetic couplingPhys. Rev. Lett. 63, 664–667 (1989)
T. Valet and A. Fert
Theory of the perpendicular magnetoresistance in magnetic multilayersPhys. Rev. B 48, 7099–7113 (1993)
P. Baláž (AMU, Poznan) Spin transfer torque and magnetization dynamics Prague, December 2013 5 / 35
Introduction
Current-induced dynamics and magnetization switching
Magnetization can be switched by electric current without need of magnetic field
Slonczewski’s model (ballistic)
J. Magn. Magn. Mater. 159, L1-L7 (1996)
0.0
0.1
0.2
0.3
0 0.25 0.5 0.75 1
g(θ)
si
n(θ)
θ/p
0.2
0.3 (Py)
0.35 (Co)
0.4
τSloncz =Ig(θ )
es×
(
s× S)
where
g(θ ) =
[
−4+(1+P)3 3+cos θ
4P3/2
]−1
P. Baláž (AMU, Poznan) Spin transfer torque and magnetization dynamics Prague, December 2013 6 / 35
Introduction
Current-induced dynamics and magnetization switching
Magnetization can be switched by electric current without need of magnetic field
Slonczewski’s model (ballistic)
J. Magn. Magn. Mater. 159, L1-L7 (1996)
0.0
0.1
0.2
0.3
0 0.25 0.5 0.75 1
g(θ)
si
n(θ)
θ/p
0.2
0.3 (Py)
0.35 (Co)
0.4
τSloncz =Ig(θ )
es×
(
s× S)
where
g(θ ) =
[
−4+(1+P)3 3+cos θ
4P3/2
]−1
Unified description (diffusive)
Description of spin-transfer torque
should be consistent with description
of giant magnetoresistance (Valet-Fert
model)
J. Barnas, A. Fert, M. Gmitra, I. Weymann, V.K. Dugaev
From giant magnetoresistance to current-inducedswitching by spin transferPhys. Rev. B 72, 024426 (2005)
Spin-transfer torque
τθ = a(θ ) I s×(
s× S)
τφ = b(θ ) I s× S
P. Baláž (AMU, Poznan) Spin transfer torque and magnetization dynamics Prague, December 2013 6 / 35
Introduction
Equation of motion
Landau-Lifshitz-Gilbert equation
ds
dt=−|γg|µ0 s×Heff −α s×
ds
dt+
|γg|
Msd
(
τθ + τφ
)
Effective magnetic field
Heff =−Hextez −Hani (s · ez) ez +Hdemag
Spin-transfer torque
τθ = a(θ ) I s×(
s× S)
τφ = b(θ ) I s× S
P. Baláž (AMU, Poznan) Spin transfer torque and magnetization dynamics Prague, December 2013 7 / 35
Spin-torque in metallic spin valves
Outline
1 Introduction
2 Spin-torque in metallic spin valves
3 Dual spin valve
4 Nonlinear magnetoresistance in dual spin vales
5 Current-induced switching in metallic spin valves with perpendicular polarizers
P. Baláž (AMU, Poznan) Spin transfer torque and magnetization dynamics Prague, December 2013 8 / 35
Spin-torque in metallic spin valves
Mathematical description
Two channels model
bulk resistivities
ρ↑(↓) = 2ρ∗ (1∓β )
interface resistances
R↑(↓) = 2R∗ (1∓ γ)
β bulk asymmetry paramters
γ interfacial asymmetry parameter
Diffusive transport
∂ 2(µ↑− µ↓)
∂x2=
1
l2sf
(µ↑− µ↓)
∂ 2(µ↑+ µ↓)
∂x2= η
∂ 2(µ↑− µ↓)
∂x2
J. Barnas, A. Fert, M. Gmitra, I. Weymann, V.K. Dugaev
From giant magnetoresistance to current-inducedswitching by spin transferPhys. Rev. B 72, 024426 (2005)
P. Baláž (AMU, Poznan) Spin transfer torque and magnetization dynamics Prague, December 2013 9 / 35
Spin-torque in metallic spin valves
Mathematical description
Two channels model
bulk resistivities
ρ↑(↓) = 2ρ∗ (1∓β )
interface resistances
R↑(↓) = 2R∗ (1∓ γ)
β bulk asymmetry paramters
γ interfacial asymmetry parameter
Diffusive transport
∂ 2(µ↑− µ↓)
∂x2=
1
l2sf
(µ↑− µ↓)
∂ 2(µ↑+ µ↓)
∂x2= η
∂ 2(µ↑− µ↓)
∂x2
for electrochemical potentials we get
µ↑ = (1+η)[
Aex/lsf +Be−x/lsf
]
+Cx+G
µ↓ = (η −1)[
Aex/lsf +Be−x/lsf
]
+Cx+G
J. Barnas, A. Fert, M. Gmitra, I. Weymann, V.K. Dugaev
From giant magnetoresistance to current-inducedswitching by spin transferPhys. Rev. B 72, 024426 (2005)
P. Baláž (AMU, Poznan) Spin transfer torque and magnetization dynamics Prague, December 2013 9 / 35
Spin-torque in metallic spin valves
Mathematical description
Magnetic layer
ˇµ = µ01+gσz
µ0 =µ↑+ µ↓
2, g =
µ↑− µ↓
2
with g being spin accumulation
j =−ρ(EF)D∂ ˇµ
∂x
j =1
2
(
j01+ jzσz
)
with jz being spin current
Diffusive transport
∂ 2(µ↑− µ↓)
∂x2=
1
l2sf
(µ↑− µ↓)
∂ 2(µ↑+ µ↓)
∂x2= η
∂ 2(µ↑− µ↓)
∂x2
for electrochemical potentials we get
µ↑ = (1+η)[
Aex/lsf +Be−x/lsf
]
+Cx+G
µ↓ = (η −1)[
Aex/lsf +Be−x/lsf
]
+Cx+G
J. Barnas, A. Fert, M. Gmitra, I. Weymann, V.K. Dugaev
From giant magnetoresistance to current-inducedswitching by spin transferPhys. Rev. B 72, 024426 (2005)
P. Baláž (AMU, Poznan) Spin transfer torque and magnetization dynamics Prague, December 2013 9 / 35
Spin-torque in metallic spin valves
Mathematical description
Nonmagnetic layer
has no natural quantization axis
ˇµ = µ01+g.σ
j =1
2
(
j01+ j.σ)
where
g = (gx,gy,gz) , j = (jx, jy, jz)
are 3D vectors written in the
coordinate system of one of the
adjacent magnetic layers
Diffusive transport
∂ 2(µ↑− µ↓)
∂x2=
1
l2sf
(µ↑− µ↓)
∂ 2(µ↑+ µ↓)
∂x2= η
∂ 2(µ↑− µ↓)
∂x2
for electrochemical potentials we get
µ↑ = (1+η)[
Aex/lsf +Be−x/lsf
]
+Cx+G
µ↓ = (η −1)[
Aex/lsf +Be−x/lsf
]
+Cx+G
J. Barnas, A. Fert, M. Gmitra, I. Weymann, V.K. Dugaev
From giant magnetoresistance to current-inducedswitching by spin transferPhys. Rev. B 72, 024426 (2005)
P. Baláž (AMU, Poznan) Spin transfer torque and magnetization dynamics Prague, December 2013 9 / 35
Spin-torque in metallic spin valves
Boundary conditions at N/F interface
• particle current is continuous across all interfaces
e2j0 = (G↑+G↓)(µF0 − µN
0 )+(G↑−G↓)(gFz −gN
z )
• spin current component parallel to the magnetization is continuous across the
interface
e2jz = (G↑−G↓)(µF0 − µN
0 )+(G↑+G↓)(gFz −gN
z )
• transversal component of the spin current vanishes in the magnetic layer – jump at
the interface
e2jx =−2ReG↑↓gNx +2ImG↑↓gN
y
e2jy =−2ReG↑↓gNy −2ImG↑↓gN
x
A. Brataas, Yu.V. Nazarov, G.E.W. Bauer
Spin-transport in multi-terminal normal metal-ferromagnet systems with non-collinear magnetizationsEur. Phys. J. B 22, 99 (2001)
P. Baláž (AMU, Poznan) Spin transfer torque and magnetization dynamics Prague, December 2013 10 / 35
Spin-torque in metallic spin valves
Boundary conditions at N/F interface
• particle current is continuous across all interfaces
e2j0 = (G↑+G↓)(µF0 − µN
0 )+(G↑−G↓)(gFz −gN
z )
• spin current component parallel to the magnetization is continuous across the
interface
e2jz = (G↑−G↓)(µF0 − µN
0 )+(G↑+G↓)(gFz −gN
z )
• transversal component of the spin current vanishes in the magnetic layer – jump at
the interface
e2jx =−2ReG↑↓gNx +2ImG↑↓gN
y
e2jy =−2ReG↑↓gNy −2ImG↑↓gN
x
Spin-transfer torque
τ =h
2(j⊥L − j⊥R)
P. Baláž (AMU, Poznan) Spin transfer torque and magnetization dynamics Prague, December 2013 10 / 35
Spin-torque in metallic spin valves
Boundary conditions at N/F interface
• particle current is continuous across all interfaces
e2j0 = (G↑+G↓)(µF0 − µN
0 )+(G↑−G↓)(gFz −gN
z )
• spin current component parallel to the magnetization is continuous across the
interface
e2jz = (G↑−G↓)(µF0 − µN
0 )+(G↑+G↓)(gFz −gN
z )
• transversal component of the spin current vanishes in the magnetic layer – jump at
the interface
e2jx =−2ReG↑↓gNx +2ImG↑↓gN
y
e2jy =−2ReG↑↓gNy −2ImG↑↓gN
x
Components
in-plane τθ =−h
2j′y|N/F
out-of-plane τφ =h
2j′x|N/F
P. Baláž (AMU, Poznan) Spin transfer torque and magnetization dynamics Prague, December 2013 10 / 35
Spin-torque in metallic spin valves
ResultsCalculations for real structures
Standard spin valve
Py(20)/Cu(10)/Py(8)
-0.04
0
0.04
0.08
0.12
0.16
0 p/4 p/2 3p/4 p
ST
T /
(h I
/ |e
|)
θ
τθ
102 τφ
Nonstandard spin valve
Co(8)/Cu(10)/Py(8)
-0.16
-0.12
-0.08
-0.04
0
0.04
0.08
0.12
0 p/4 p/2 3p/4 pS
TT
/ (
h I
/ |e
|)
θ
τθ
-102 τφ
P. Baláž (AMU, Poznan) Spin transfer torque and magnetization dynamics Prague, December 2013 11 / 35
Dual spin valve
Outline
1 Introduction
2 Spin-torque in metallic spin valves
3 Dual spin valve
4 Nonlinear magnetoresistance in dual spin vales
5 Current-induced switching in metallic spin valves with perpendicular polarizers
P. Baláž (AMU, Poznan) Spin transfer torque and magnetization dynamics Prague, December 2013 12 / 35
What is a dual spin valve?
Dual spin valve
Spin accumulation in dual spin valve
spin accumulation in single spin valve
10 20 30 40x
-0.2
-0.1
0.1
0.2spin accumulation
P. Baláž (AMU, Poznan) Spin transfer torque and magnetization dynamics Prague, December 2013 14 / 35
Dual spin valve
Spin accumulation in dual spin valve
spin accumulation in single spin valve
10 20 30 40x
-0.2
-0.1
0.1
0.2spin accumulation
spin accumulation in dual spin valve
20 40 60 80x
-0.2
-0.1
0.1
0.2
0.3
spin accumulation
L. Berger
Multilayer Configuration for Experiments of Spin Precession Induced by a DC CurrentJ. Appl. Phys. 93, 7683 (2003)
P. Baláž (AMU, Poznan) Spin transfer torque and magnetization dynamics Prague, December 2013 14 / 35
Dual spin valve
Enhancement of switchingsingle vs. dual spin valve
Co(20)/Cu(10)/Co(8) vs. Co(20)/Cu(10)/Co(8)/Cu(10)/Co(20)
Spin-transfer torque
0
0.04
0.08
0.12
0.16
0.2
0 0.25 0.5 0.75 1
ST
T /
(h
I /
|e|)
θ / p
Dual SV
Single SV
P. Baláž (AMU, Poznan) Spin transfer torque and magnetization dynamics Prague, December 2013 15 / 35
Dual spin valve
Enhancement of switchingsingle vs. dual spin valve
Co(20)/Cu(10)/Co(8) vs. Co(20)/Cu(10)/Co(8)/Cu(10)/Co(20)
Spin-transfer torque
0
0.04
0.08
0.12
0.16
0.2
0 0.25 0.5 0.75 1
ST
T /
(h
I /
|e|)
θ / p
Dual SV
Single SV
Switching time
0 1 2 3 4 5 6 7
8 9
0.5 1 1.5 2 2.5 3 3.5 4sw
itch
ing
tim
e [n
s]I / (108 A cm-2)
Dual SV
Single SV
P. Baláž (AMU, Poznan) Spin transfer torque and magnetization dynamics Prague, December 2013 15 / 35
Dual spin valve
Enhancement of switchingsingle vs. dual spin valve
Co(20)/Cu(10)/Co(8) vs. Co(20)/Cu(10)/Co(8)/Cu(10)/Co(20)
Spin-transfer torque
0
0.04
0.08
0.12
0.16
0.2
0 0.25 0.5 0.75 1
ST
T /
(h
I /
|e|)
θ / p
Dual SV
Single SV
Switching time
0 1 2 3 4 5 6 7
8 9
0.5 1 1.5 2 2.5 3 3.5 4sw
itch
ing
tim
e [n
s]I / (108 A cm-2)
Dual SV
Single SV
Is this all?
P. Baláž (AMU, Poznan) Spin transfer torque and magnetization dynamics Prague, December 2013 15 / 35
Question: How torque changes in non-collinear configurations?
I>0
Dual spin valve
Noncollinear configurations in dual spin valvesCo(20)/Cu(10)/Py(4)/Cu(4)/Co(10)/IrMn(8)
I>0
P.B., M. Gmitra, J. Barnas
Current-induced dynamics in non-collinear dualspin-valvesPhys. Rev. B 80, 174404 (2009)
P. Baláž (AMU, Poznan) Spin transfer torque and magnetization dynamics Prague, December 2013 17 / 35
Dual spin valve
Noncollinear configurations in dual spin valvesCo(20)/Cu(10)/Py(4)/Cu(4)/Co(10)/IrMn(8)
I>0
P.B., M. Gmitra, J. Barnas
Current-induced dynamics in non-collinear dualspin-valvesPhys. Rev. B 80, 174404 (2009)
P. Baláž (AMU, Poznan) Spin transfer torque and magnetization dynamics Prague, December 2013 17 / 35
Dual spin valve
Noncollinear configurations in dual spin valvesCo(20)/Cu(10)/Py(4)/Cu(4)/Co(10)/IrMn(8)
I>0
P.B., M. Gmitra, J. Barnas
Current-induced dynamics in non-collinear dualspin-valvesPhys. Rev. B 80, 174404 (2009)
Current-induced dynamics
We calculated average
〈sz〉=1
tend − teq
∫ tend
teqsz dt
and dispersion
D(sz) =
√
⟨
s2z
⟩
−〈sz〉2
for each couple of I and Ω to map the dynamicbehaviour.
P. Baláž (AMU, Poznan) Spin transfer torque and magnetization dynamics Prague, December 2013 17 / 35
Dual spin valve
Noncollinear configurations in dual spin valvesCo(20)/Cu(10)/Py(4)/Cu(4)/Co(10)/IrMn(8)
I>0
P. Baláž (AMU, Poznan) Spin transfer torque and magnetization dynamics Prague, December 2013 17 / 35
Nonlinear magnetoresistance in dual spin vales
Outline
1 Introduction
2 Spin-torque in metallic spin valves
3 Dual spin valve
4 Nonlinear magnetoresistance in dual spin vales
5 Current-induced switching in metallic spin valves with perpendicular polarizers
P. Baláž (AMU, Poznan) Spin transfer torque and magnetization dynamics Prague, December 2013 18 / 35
Nonlinear magnetoresistance in dual spin vales
Nonlinear magnetoresistance in dual spin vales
Experimental works
A. Aziz, O. P. Wessely, M. Ali, D. M. Edwards, C. H. Marrows,
B. J. Hickey, and M. G. BlamireNonlinear giant magnetoresistance in dual spin valves
Phys. Rev. Lett. 103, 237203 (2009)
N. Banerjee, A. Aziz, M. Ali, J. W. A. Robinson, B. J. Hickey,
and M. G. Blamire
Thickness dependence and the role of spin transfer torque in
nonlinear giant magnetoresistance of permalloy dual spin
valves
Phys. Rev. B 82, 224402 (2010)
N. Banerjee, J. W. A. Robinson, A. Aziz, M. Ali, B. J. Hickey,
and M. G. BlamireNonlocal Magnetization Dynamics in Ferromagnetic Hybrid
Nanostructure
Phys. Rev. B 86, 134423 (2012)
Experimental results [Aziz et al, PRL (2009)]: (b) minor loops for
Co90Fe10 (6)/Cu(4)/Py(1)/Cu(2)/Co90Fe10 (6)/IrMn(10) (c) Py thickness: 1 nm
(blue), 2 nm (red), and 8 nm (magenta)
P. Baláž (AMU, Poznan) Spin transfer torque and magnetization dynamics Prague, December 2013 19 / 35
Nonlinear magnetoresistance in dual spin vales
Nonlinear magnetoresistance in dual spin valesModel’s assumptions
• Spin accumulation in the central layer changes density of states on Fermi level
• This may change bulk/interfacial material parameters in the central layer
We extended the diffusion transport model
J. Barnas, A. Fert, M. Gmitra, I. Weymann, V.K. Dugaev
From giant magnetoresistance to current-induced switching by spin transferPhys. Rev. B 72, 024426 (2005)
Bulk contribution
ρ∗ = ρ∗0 +q〈g〉
β = β0 +ξ 〈g〉
Interfacial contribution
R∗ = R∗0 +q′ g(xi)
γ = γ0 +ξ ′g(xi)
where
• g(x) is spin accumulation
• ρ∗0 and R∗
0 are zero-current bulk resistivity and interfacial resistance
• β0 and γ0 are zero-current bulk/interfacial asymmetry parameters
• q, ξ , q′, ξ ′ are phenomenological parameters
P. Baláž, and J. Barnas
Nonlinear magnetotransport in dual spin valvesPhys. Rev. B 82, 104430 (2010)
P. Baláž (AMU, Poznan) Spin transfer torque and magnetization dynamics Prague, December 2013 20 / 35
Nonlinear magnetoresistance in dual spin vales
Nonlinear magnetoresistance in dual spin valesCalculations for Cu - Co(6) / Cu(4) / Py(2) / Cu(2) / Co(6) / IrMn(10) - Cu
Bulk parameters
22.76
22.78
22.8
22.82
22.84
0 0.25 0.5 0.75 1
R [
fΩ m
2 ]
θ / p
i = 3i = -3
-0.06
-0.04
-0.02
0
0.02
0.04
-5 -4 -3 -2 -1 0 1 2 3 4 5
∆R [
fΩ m
2 ]
Reduced current density
(1)only ρ*
only β
P. Baláž, and J. Barnas
Nonlinear magnetotransport in dual spin valvesPhys. Rev. B 82, 104430 (2010)
Interfacial parameters
23.04
23.08
23.12
23.16
23.2
23.24
0 0.25 0.5 0.75 1
R [
fΩ m
2 ]
θ/p
i = 3i = -3
-0.15
-0.1
-0.05
0
0.05
0.1
-5 -4 -3 -2 -1 0 1 2 3 4 5∆R
[fΩ
m2 ]
Reduced current density
d = 2 nmd = 8 nmd = 16 nm
for q = 0.1, ξ = 0.1, I0 = 108Acm−2
P. Baláž (AMU, Poznan) Spin transfer torque and magnetization dynamics Prague, December 2013 21 / 35
Nonlinear magnetoresistance in dual spin vales
Nonlinear magnetoresistance in dual spin valesCalculations for Cu - Co(6) / Cu(4) / Py(2) / Cu(2) / Co(6) / IrMn(10) - Cu
Bulk parameters
-0.45 -0.3 -0.15 0 0.15 0.3 0.45iq~
-0.45
-0.3
-0.15
0
0.15
0.3
0.45
iξ~
-0.06-0.05-0.04-0.03-0.02-0.01 0 0.01 0.02 0.03 0.04
∆R
[f
Ω m
2]
∆R > 0 ∆R < 0
-0.45 -0.3 -0.15 0 0.15 0.3 0.45iq~
-0.45
-0.3
-0.15
0
0.15
0.3
0.45
iξ~
∆R > 0 ∆R < 0
Interfacial parameters
-0.45 -0.3 -0.15 0 0.15 0.3 0.45iq~¢
-0.45
-0.3
-0.15
0
0.15
0.3
0.45
iξ~ ¢
-0.4-0.3-0.2-0.1 0 0.1 0.2 0.3 0.4 0.5
∆R
[f
Ω m
2]
∆R > 0
∆R < 0
-0.45 -0.3 -0.15 0 0.15 0.3 0.45iq~¢
-0.45
-0.3
-0.15
0
0.15
0.3
0.45
iξ~ ¢
∆R > 0
∆R < 0
for interfaces ∆R is symmetric with current density
P. Baláž, and J. Barnas
Nonlinear magnetotransport in dual spin valvesPhys. Rev. B 82, 104430 (2010)
P. Baláž (AMU, Poznan) Spin transfer torque and magnetization dynamics Prague, December 2013 22 / 35
Perpendicular polarizer
Outline
1 Introduction
2 Spin-torque in metallic spin valves
3 Dual spin valve
4 Nonlinear magnetoresistance in dual spin vales
5 Current-induced switching in metallic spin valves with perpendicular polarizers
P. Baláž (AMU, Poznan) Spin transfer torque and magnetization dynamics Prague, December 2013 23 / 35
Perpendicular polarizer
Model of the polarizer
I>0
PP FL IPNL NR
(a)
P. Baláž, M. Zwierzycki, J. Barnas
Spin-transfer torque and current-induced switching in metallic spin valves with perpendicular polarizersPhys. Rev. B 88, 094422 (2013)
P. Baláž (AMU, Poznan) Spin transfer torque and magnetization dynamics Prague, December 2013 24 / 35
Perpendicular polarizer
Transport through the polarizer
• We considered the perpendicular polarizer as amagnetized ballistic scaterrer in frame ofcoherent transport regime
• To calculate the transport properties of thepolarizer we used Ab initio wave functionmatching method
M. Zwierzycki et al
Calculating scattering matrices by wave functionmatchingPhys. Stat. Sol. (b) 245, 623 – 640 (2008)
• In our formalism the scaterrer coresponds to asingle interface.
P. Baláž (AMU, Poznan) Spin transfer torque and magnetization dynamics Prague, December 2013 25 / 35
Perpendicular polarizer
Transport through the polarizer
• We considered the perpendicular polarizer as amagnetized ballistic scaterrer in frame ofcoherent transport regime
• To calculate the transport properties of thepolarizer we used Ab initio wave functionmatching method
M. Zwierzycki et al
Calculating scattering matrices by wave functionmatchingPhys. Stat. Sol. (b) 245, 623 – 640 (2008)
• In our formalism the scaterrer coresponds to asingle interface.
P. Baláž (AMU, Poznan) Spin transfer torque and magnetization dynamics Prague, December 2013 25 / 35
Perpendicular polarizer
Transport through the polarizer
• We considered the perpendicular polarizer as amagnetized ballistic scaterrer in frame ofcoherent transport regime
• To calculate the transport properties of thepolarizer we used Ab initio wave functionmatching method
M. Zwierzycki et al
Calculating scattering matrices by wave functionmatchingPhys. Stat. Sol. (b) 245, 623 – 640 (2008)
• In our formalism the scaterrer coresponds to asingle interface.
Outputs of the calculation:
• channel conductances G↑, G↓
• mixing conductance
G↑↓ = g↑↓r + ig
↑↓i
• mixing transmission conductance
T↑↓ = t↑↓r + i t
↑↓i
Differences in definitions
Gσσ ′ = ∑nn′
[
δnn′ − rσnn′
(
rσ ′
nn′
)∗]
Tσσ ′ = ∑nn′
tσnn′
(
tσ′
nn′
)∗
P. Baláž (AMU, Poznan) Spin transfer torque and magnetization dynamics Prague, December 2013 25 / 35
Perpendicular polarizer
Boundary conditions
Longitudinal components
e2
j0
jz
=
G↑+ G↓ G↑− G↓
G↑− G↓ G↑+ G↓
µR0 −µL
0
µRz −µL
z
Transverse components
e2
jR⊥
jL⊥
=
G T′
T G′
µµµR⊥
µµµL⊥
where
jR/L⊥ =
jR/Lx
jR/Ly
µµµR/L⊥ =
µR/Lx
µR/Ly
and
G = 2
−g↑↓r g
↑↓i
−g↑↓i −g
↑↓i
T = 2
t↑↓r −t
↑↓i
t↑↓i t
↑↓r
Y. Tserkovnyak, A. Brataas, G. E. W. Bauer, and B. I. Halperin
Nonlocal Magnetization Dynamics in Ferromagnetic Hybrid NanostructureRev. Mod. Phys 77, 1375 (2005)
P. Baláž (AMU, Poznan) Spin transfer torque and magnetization dynamics Prague, December 2013 26 / 35
Perpendicular polarizer
Spin transfer torque
Spin torque acting on the free layer
τ⊥ = Is×[
SOP ×(
aOPSOP +aIPSIP
)]
τ‖ = Is×(
bOPSOP +bIPSIP
)
aOP =−h
2
j′1y |N1/F1
I sinθOPbOP =
h
2
j′1x |N1/F1
I sinθOP
aIP =−h
2
j′′2y |F1/N2
I sinθIPbIP =
h
2
j′′2x |F1/N2
I sinθIP
where cosθOP = s · SOP and cosθIP = s · SIP
P. Baláž (AMU, Poznan) Spin transfer torque and magnetization dynamics Prague, December 2013 27 / 35
Perpendicular polarizer
Studied structures
Cu - PP / Cu(6) / Py(5) / Cu(12) / Py(20) - Cu
Perpendicular polarizer
PP1 = Co(2 ML) / [Cu(2 ML)/Co(2 ML)]L−1
PP2 = Pt(6 ML) / [Co(2 ML)/Pt(3 ML)]L / Co(3 ML) / Cu(2 ML) / Co(3 ML)
P. Baláž (AMU, Poznan) Spin transfer torque and magnetization dynamics Prague, December 2013 28 / 35
Perpendicular polarizer
Results for PP1Spin transfer torque
Co(2 ML) / [Cu(2 ML)/Co(2 ML)]L−1
-0.10
-0.05
0.00
0.05
0.10
0 0.5 1 1.5 2
Spin
torq
ue τ ||
PP polarizer
(a)
L=1L=3L=5
-0.15-0.10-0.050.000.05
0.100.15
0 0.5 1 1.5 2
IP polarizer
(b)
-0.25
-0.15
-0.05
0.05
0.15
0.25
0 0.5 1 1.5 2
Spin
torq
ue 1
0 ´ τ ^
angle θP / p
(c)
-0.01
0.00
0.01
0 0.5 1 1.5 2
angle θI / p
(d)
wavelike angular dependence for the perpendicular polarizer
P. Baláž (AMU, Poznan) Spin transfer torque and magnetization dynamics Prague, December 2013 29 / 35
Perpendicular polarizer
Results for PP1Current-induced switching from ⇑ to ⇓ at T = 300K
Co(2 ML) / [Cu(2 ML)/Co(2 ML)]L−1
0.0
0.2
0.4
0.6
0.8
1.0
-4 -2 0 2 4
P sw
tp = 50 ps
L=1L=3L=5
0.0
0.2
0.4
0.6
0.8
1.0
-4 -2 0 2 4
P sw
Im / 1012 [Am-2]
tp = 1 ns
0.0
0.2
0.4
0.6
0.8
1.0
-4 -2 0 2 4
tp = 100 ps
0.0
0.2
0.4
0.6
0.8
1.0
-4 -2 0 2 4
Im / 1012 [Am-2]
tp = 10 ns
P. Baláž (AMU, Poznan) Spin transfer torque and magnetization dynamics Prague, December 2013 30 / 35
Perpendicular polarizer
Switching mechanism
For I < 0 For I > 0
P. Baláž (AMU, Poznan) Spin transfer torque and magnetization dynamics Prague, December 2013 31 / 35
Perpendicular polarizer
Results for PP2Spin transfer torque
Pt(6 ML) / [Co(2 ML)/Pt(3 ML)]L / Co(3 ML) / Cu(2 ML) / Co(3 ML)
-0.20-0.15-0.10-0.050.000.050.100.150.20
0 0.5 1 1.5 2
Spin
torq
ue τ ||
Clean PP
(a)
L=1L=3L=5
-0.15
-0.10
-0.05
0.00
0.05
0.10
0.15
0 0.5 1 1.5 2
Disordered PP
(b)
L=3L=4L=6
-0.06-0.04-0.020.000.020.040.06
0 0.5 1 1.5 2
Spin
torq
ue 1
0 ´ τ ^
angle θP / p
(c) -0.08
-0.04
0.00
0.04
0.08
0 0.5 1 1.5 2
angle θP / p
(d)
P. Baláž (AMU, Poznan) Spin transfer torque and magnetization dynamics Prague, December 2013 32 / 35
Perpendicular polarizer
Results for PP2Current-induced switching from ⇑ to ⇓
Pt(6 ML) / [Co(2 ML)/Pt(3 ML)]L / Co(3 ML) / Cu(2 ML) / Co(3 ML)
0.0
0.2
0.4
0.6
0.8
1.0
-4 -3 -2 -1 0 1 2 3 4
P sw
tp = 50 ps
L=1L=3L=5
0.0
0.2
0.4
0.6
0.8
1.0
-4 -3 -2 -1 0 1 2 3 4
P sw
Im / 1012 [Am-2]
tp = 1 ns
0.0
0.2
0.4
0.6
0.8
1.0
-4 -3 -2 -1 0 1 2 3 4
tp = 100 ps
0.0
0.2
0.4
0.6
0.8
1.0
-4 -3 -2 -1 0 1 2 3 4
Im / 1012 [Am-2]
tp = 10 ns
P. Baláž (AMU, Poznan) Spin transfer torque and magnetization dynamics Prague, December 2013 33 / 35
Perpendicular polarizer
Summary
Noncollinear diffusive model is an useful and flexible framework for dealing
with spin dependent electronic transport in metalic multilayers
• spin tranfer torque and magnetoresistance in single and dual spin
valves
• nonlinear effects in magnetoresistance
• spin transfer torque due to a perpendicular polarizer
• also spin torque and dynamics in composite free layers (synthetic
ferro- or antiferromagnets)
P. Baláž (AMU, Poznan) Spin transfer torque and magnetization dynamics Prague, December 2013 34 / 35
Perpendicular polarizer
Thank you for your attention
P. Baláž (AMU, Poznan) Spin transfer torque and magnetization dynamics Prague, December 2013 35 / 35
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