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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

15

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.