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Ferromagnetic Josephson Junction Ferromagnetic Josephson Junction and Spin Wave Resonanceand Spin Wave Resonance
Nagoya University on September 5,2009
Sadamichi Maekawa(IMR, Tohoku University)
Co-workers:
S. Hikino, M. Mori, S. Takahasi (IMR, Tohoku University)
I. Petkovic, M. Aprili (Univeriste Paris-Sud)S. E. Barnes (University of Miami)
Reference:I. Petkovic, M. Aprili, S.E.Barnes, F.Beuneu and S.Maekawa: to be published.
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OutlineOutline1. Superconducting phase difference
Josephson effect, Phase difference coupled with magnetic field,
Resistively shunted junction (RSJ) model, I-V characteristic,
Ferromagnetic Josephson junction (SC/FM/SC junction)
2. Magnetization dynamics in ferromagnet (FM)
Ferromagnetic resonance (FMR)
3. Coupled superconducting phase and magnetization dynamics
Ferromagnetic Josephson junction
Differential resistance
4. Model
RSJ model + Maxwell’s equation + LLG equation
5. Differential resistance
FMR signal
6. Summary
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DC Josephson EffectDC Josephson Effect
I or NM
x
xSC SC
LR
dI; Insulator
Cooper pair
NM; Normal metal
Thickness dependence of Ic
Ic
d
Penetration depth of order parameter to barrier
NM A few m NM ;
I ; I Several tens A
0
Current flow without voltage drop
Phase difference between superconductors
dc Josephson effect
IJ = Ic sin()
Josephson current
V
I
Current-Voltage characteristic
B.D.Josephson Phys. Lett. 1, 251 (1962)
Josephson critical current
Ic
0
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Properties of superconducting phase differenceProperties of superconducting phase difference
Fraunhofer pattern
・ Gauge invariant phase
Magnetic field B
L R
a b
0
2 b
ay d
r A r
Vector potential;
・ Josephson current density
J c sini i y
JI0B
0B
z
xA By
∝Flux
Magnetic flux quantum
y
x
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Dynamics of SC phase differenceDynamics of SC phase differenceB.D.Josephson Phys. Lett. 1, 251 (1962)
W. C. Stewart, APL. 12, 277 (1968)
D. E. McCumber, JAP. 39, 3113 (1968)
SC SCX
SC : superconductor
Dynamics of superconducting phase
L R
Cooper pair Josephson current
R
c sinI
IRSJ model
V
I
c sinV
I IR
2d eV
dt
Phase dynamics
Current equation
0J t
J c 0sin JI I t
・ Phase difference
・ AC Josephson current
DC voltageDC voltage AC currentAC current2
J
eV
:Josephson frequency
t
IJ
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Josephson Effect in ferromagnetic Josephson junction (FJJ)Josephson Effect in ferromagnetic Josephson junction (FJJ)
・ Josephson current
R L Phase difference between SC’s
d
Ic
0
A. I. Budzin, Rev. Mod. Phys. 76, 411 (2004)
Current-phase relation
0-stateSC/NM/SC junction
FJJ junction
SC SCNMk
ex2h
FM
E
FF
exh
vk
FF
exhk
v
F F( / ) ( / )
FM
Fcos /
e e .ex exi k h v x i k h
x
v x
eh x
c c
v
IJ = Ic sin()
-state-state
IJ = Ic sin()
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Josephson Coupling
S F S
I+
V+dF1 dF2
V-
I- Kontos et al. PRL 89, 137007 (2002)
-20
-10
0
10
20
I (m
A)
-3 -2 -1 0 1 2 3V (mV)
x10
SIS
SIFS
I-V characteristics
80
60
40
20
0
IcR
n(µ
V)
180160140120100806040
dF (Å)
experiment at 1.5K
theory
RInterface = 10-6
F = 46 Å
Nb NbPd1-xNix
0 state
state
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Diffraction Pattern
dF (Å)
+ -
I=-IcsinI=Icsin0-junction -junction
60
50
40
30
20
10
0
I c (
/o
140
120
100
80
60
40
20
0
I c (
/o
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SC/F/SC junctionSC/F/SC junction
Ryazanov et al., PRL 86, 2427 (2001)
S/F/S junction
S/N/S
π-state0-state
SF
FS S
θ θ+ π
FS S
θ θ
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Magnetization dynamics in FMMagnetization dynamics in FM
Landau-Lifshitz-Gilbert (LLG) equation
effd
dt M
d
d t
MMH MM
; Total Magnetization, ;Gyromagnetic ratio
; Effective field, ;Gilbert dampingeff
M
H
Ferromagnetic resonance (FMR)
x
y
z
Ferromagnetic thin film
DC magnetic field
RF-magnetic fieldM : Magnetization
M
Heff
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Phase dynamicsPhase dynamics Magnetization Magnetization dynamicsdynamics
t
Mt
SC FM
Coupling
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ModelModel x
y
MSC
FM
M is parallel to x axis.
d is thickness of FM
L is width of junction
SC zJosephson current density
c sin ,J xi i r t e
/ 2
/ 20
2, ,
d
J xd
r t t dxA r t
Phase difference
d
L
,x zyBA r t z B y
Vector potential coupled with M dynamics
M
z
x
y yBzB Bi : Dynamical flux density
i=y,z
2J
eV
Josephson frequency
c sin ,V
i i r tR
RSJ model : FJJ
i ; Current density
ic ; Critical current density
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Procedure of calculationProcedure of calculation・ First step :
・ Second stepUsing the solution of Maxwell’s and LLG equations
0 0
22,
yzJ
y zr t t
L L
Phase difference
Magnetic field
crot , sin J xH r t i t e
Ampere’s law
,H r t
Ac magnetic field due to ac Josephson current
M
Precessional M
Magnetic flux density B
0, , ,MHB r r tt r t
Ac Josephson current
Dynamical flux coupled with M dynamics
, ,i ir t B r t dL
i=y,z
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Im Imdc cJ
effz Jyy zJ
II
Analytic formula of dc Josephson currentAnalytic formula of dc Josephson current
0
1
16c
eff
d I
2 2Im 0
2 22 20 02
Jii J
J J
M
0 0/KH M
i=y,z
Magnetic susceptibility
HK : anisotropic field
2J
eV
Josephson frequency
Self-induced ferromagnetic Josephson resonanceSelf-induced ferromagnetic Josephson resonance
FMR induced by ac Josephson current
SC
FM
SC
M
z
x
yyB
zB
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10 20 300.9
1
1.1
1.2
Voltage dependence of Voltage dependence of dVdV//dIdI
V [V]
FJJCJJ
FMR
23 VV
CJJ : Conventional Josephson junction
221, 1
2c cc cd
JII R I R I RV
IR V V V
W. C. Stewart, APL. 12, 277 (1968)D. E. McCumber, JAP. 39, 3113 (1968)RSJ model
Im ImdcJ yy J zz JI
dV/d
I [
]
00.6 T, / 0.2 TKH M
FMR
FMR 70 GHz
Resonance frequency
FMR 11f
V [V]
dV/d
I [
]
23 VV
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In conclusion :
SC/FM/SC Josephson junction.
Dynamical coupling between SC phase and magnetization.
Ferromagnetic Josephson resonance on 107 Ni atoms.