Phase Dynamics of the Ferromagnetic Josephson Junctions

I. Petković and M. Aprili

Laboratoire de Physique des Solides

GDR Physique Mesoscopique, Decembre 8-11 2008, Aussois.

In collaboration with:François Beuneu, LSIHervé Hurdequint, LPSSadamichi Maekawa, Tohoku UniversityStewart Barnes, University of Miami

Spin Physics in Superconductors

Aharonov-Bohm phase ϕ = A·dl2ећ ∫

M(t)

Ψ = Ψ0 ei ϕ

How ϕ couples to the spin degrees of freedom ?

S SF

Φ(t)Magnetic Flux

1. Required small junctions2. Adiabatic phase transformation

-kF kF -kF +δkF kF +δkF

S: SF:

Spin splitting - FFLO ϕ = 2 δk x = x EexћvFFulde Ferrell Larkin Ovchinnikov

in hybrid structures:

Cooper pair

Junction Fabrication

500x500nm

500nm1μm

SEM photos

Nb(50nm)

PdNi(20nm)Nb(50nm) NbONbO

IJ

cross section: SIFS

IV curve

T=5.7 K

T=1.2 K

Nb

2μm

SEM photo of the mask

1

23

Nb

PdNi

PESSi3N4

Magnetostatics and the Josephson phase

ϕ = ϕo - A·dl2πΦo∫

Φ = B·S = ϕ2πΦo

A

B

C

B

C

A

(πΦ/Φo)Ic (Φ)

Ic (0)=

sin (πΦ/Φo)

Analogy with Fraunhoferdiffraction

We measure a shift in the Fraunhofer pattern due to magnetization.

I=Icsin ϕ

time-reversalt -tB -B

Magnetization Dynamics and the Josephson effect

ϕ(t) = ϕo - A(t)·dl2πΦo∫

M(t)spin wave resonance ωS

Resonant coupling ωJ ≈ ωS 10 μV ~ 5 GHz

= VDC = ωJdϕdt

2eћ

Josephsonfrequnency

IV

I = + R – κ IC2 χ’’(ωJ)VDC

RIC2

2Vsusceptibility of the ferromagnet

JJ X R Z(ω) ~ χ’’(ωs)equivalent circuit :

VDC

Josephson spectroscopy of the magnetic modes

non-ferro

ferro

Josephson Resonant cavity

FMR: ωs = γ (Hk – 4πMs)2 – H2

Hk anisotropy fieldMs saturation magnetization

ωs= ωJ ∼ VDC = 23 μVno fitting parameters !

mm trilayersame cross-section

9.3 GHz

900 G

Coupling with external RF – Shapiro step side bands

cos(Ωt)

VDC

= VDC + Vac(Ωt)dϕdt

2eћ

Vac

resonances : VDC = ωJ = nΩ2eћ

Shapiro stepsn-integer

-50dBm 20dBm

with ferromagnetic modes:

sideband resonances at

ωJ = nΩ ωs

2Ω

Ω

Ω-ωs

Phase Dynamics

Ib

V

SIFS

P(I)

37Hz350mK

IS

Ir

Is there a contribution of magnetization dynamics to the phase noise?

Pump probe measurement

Current-biasedJosephson junction

I

JJ X R C

pump

probe

Δτ<τϕ

phase relaxation time

ϕ + β ϕ + ω02 sin ϕ = ηb sin ωbt

dampingRC

plasmafreq.

ramp

Phase Dynamics in the Stationary Regimeslow ramp

Kramers escape

Effective temperature equal to bath temperature.No additional temperature due to ferromagnet.

0.5 K

4.2 K 3 K 2 K

0.8 K1.1 K

kBT

Non-stationary regime - Bifurcation

Kinetic Phase Transition

fast ramp

ts tr

P(I)

IIr Is

ramp freq. ωb

ωb<<τϕ

ωb≈τϕ

ωb>>τϕ

Bifurcation timescale is damping time, due to KPT.

Phase Relaxation Time - τϕ

νb=4 kHz

νb=6 kHz

νb=12 kHz

IsIr

N1=1 - A exp (- τϕ ωb )

N1 – number of events at Ir

ramp freq. ωb=2πνr

direct measurement of the phase relaxation time

τϕ ~ 50 μsT=350 mK

T=350 mK

Numerical Simulations

numerically fitted formula

N1=1 – 1.8 exp (- 0.76 )ηb ωb

β 3/2

β=(RqpC ω0)-1

ν* - frequency at whichbifurcation starts

The phase relaxation is set by thequasiparticle resistance.

range of parameters: β, ωb = 0.0001 - 0.1 ω0

T=1.5 K

T=0.67 K

Electromagnetic waves inside the ferromagnetic barrier – Fiske steps

FERRO

NON-FERRO

Fiske step – resonance between emcavity mode and Josephson phase.

kn = n π/LI

Insulator

ϕ(x) due to B

Lωn = Vn = c k

2eh

non-ferroferro

first

second

Offset in dispersion relationdue to ferromagnet.

B

Fiske resonances and bifurcation

To augment sensitivity in bifurcation measurement,we trigger at the Fiske resonance, not Ir

bifurcation

DCmeasurement

Conclusions

Coupling to EM modes (Fiskes steps)

Time reversal symmetry of Josephson coupling.Diffraction pattern with “wedge phase plate” : Fraunhofer pattern with finite Magnetization

Spectroscopy of Ferromagnetic modesNanoFMR (105 Ni atoms )High sensitivity to domain wall dynamics

Kinetic phase transition allows to probe the phase relaxation time of strongly underdampedJosephson Junctions.