1. Phase Dynamics of the Ferromagnetic Josephson Junctions
I. Petković and M. Aprili
Laboratoire de Physique des Solides
In collaboration with:
François Beuneu, LSI
Hervé Hurdequint, LPS
Sadamichi Maekawa, Tohoku University
Stewart Barnes, University of Miami
GDR Physique Mesoscopique, Decembre , Aussois.

2. Spin Physics in Superconductors
Y = Y0 ei 
How j couples to the spin degrees of freedom ?
-kF +dkF
kF +dkF
-kF kF
SF: S:
Cooper pair
Spin splitting - FFLO
j = 2 dk x = x
Eex
ћvF
Fulde Ferrell Larkin Ovchinnikov
Aharonov-Bohm phase
j =
A·dl 2е ћ ∫
M(t)
in hybrid structures: S F
(t)
Magnetic Flux
Required small junctions
2. Adiabatic phase transformation

3. Junction Fabrication Nb SEM photo of the mask 1 2 3 Nb PdNi PES Si3N4
2mm
SEM photo of the mask 1 2 3 Nb
PdNi
PES
Si3N4
500x500nm
500nm
1mm
SEM photos
Nb(50nm)
PdNi(20nm)
NbO IJ
cross section:
SIFS
T=1.2 K
T=5.7 K
IV curve

4. Magnetostatics and the Josephson phase
j = jo -
A·dl 2p Fo ∫
Analogy with Fraunhofer
diffraction
I=Icsin j
(pF/Fo)
Ic (F)
Ic (0) =
sin
F = B·S = j 2p Fo A B C
time-reversal
t -t
B -B
We measure a shift in the Fraunhofer pattern due to magnetization.

5. Magnetization Dynamics and the Josephson effect
VDC
= VDC = wJ dj dt 2e ћ
Josephson
frequnency
j(t) = jo -
A(t)·dl 2p Fo ∫
M(t)
spin wave resonance wS
Resonant coupling
wJ ≈ wS
10 mV ~ 5 GHz I V
I = R – k IC2 c’’(wJ)
VDC R
IC2 2V
susceptibility of
the ferromagnet JJ X R
Z(w) ~ c’’(ws)
equivalent circuit :

6. Josephson spectroscopy of the
magnetic modes
mm trilayer
same cross-section
Josephson
Resonant cavity
non-ferro
ferro
9.3 GHz
FMR:
ws = g (Hk – 4pMs)2 – H2
Hk anisotropy field
Ms saturation magnetization
900 G
ws= wJ ~ VDC = 23 mV
no fitting parameters !

7. Coupling with external RF – Shapiro step side bands
Vac
= VDC + Vac(Wt) dj dt 2e ћ
cos(Wt)
VDC = wJ = nW 2e ћ
resonances :
n-integer
Shapiro steps
VDC
-50dBm
20dBm
with ferromagnetic modes: 2W W
W-ws
sideband resonances at
wJ = nW  ws

8. Pump probe measurement
Phase Dynamics
Is there a contribution of magnetization dynamics to the phase noise? I JJ X R C
P(I)
37Hz
350mK IS Ir
Current-biased
Josephson junction
j + b j + w02 sin j = hb sin wbt
damping RC
plasma
freq.
ramp Ib V
SIFS
Pump probe measurement
pump
probe
Dt<tj
phase relaxation time

9. Phase Dynamics in the Stationary Regime
slow ramp
Kramers escape
kBT
0.5 K
4.2 K
3 K
2 K
0.8 K
1.1 K
Effective temperature equal to bath temperature.
No additional temperature due to ferromagnet.

10. Non-stationary regime - Bifurcation
fast ramp
ramp freq. wb
wb<<tj
Kinetic Phase Transition
wb≈tj ts tr
wb>>tj
P(I) I Ir Is
Bifurcation timescale is damping time, due to KPT.

11. Phase Relaxation Time - tj
nb=4 kHz
nb=6 kHz
nb=12 kHz Is Ir
N1 – number of events at Ir
T=350 mK
ramp freq. wb=2pnr
N1=1 - A exp (- tj wb )
direct measurement of the phase
relaxation time
T=350 mK
tj ~ 50 ms

12. Numerical Simulations
numerically fitted formula
N1=1 – 1.8 exp ( )
hb wb b
3/2
b=(RqpC w0) -1
range of parameters:
b, wb = w0
T=1.5 K
T=0.67 K
n* - frequency at which
bifurcation starts
The phase relaxation is set by the
quasiparticle resistance.

13. Electromagnetic waves inside the ferromagnetic barrier – Fiske steps
Fiske step – resonance between em
cavity mode and Josephson phase. I
Insulator
j(x) due to B L
non-ferro
kn = n p/L
ferro
wn = Vn = c k 2e h B
FERRO
NON-FERRO
first
second
Offset in dispersion relation
due to ferromagnet.

14. Fiske resonances and bifurcation
To augment sensitivity in bifurcation measurement,
we trigger at the Fiske resonance, not Ir
bifurcation DC
measurement

15. Conclusions Time reversal symmetry of Josephson coupling.
Diffraction pattern with “wedge phase plate” :
Fraunhofer pattern with finite Magnetization
Spectroscopy of Ferromagnetic modes
NanoFMR (105 Ni atoms )
High sensitivity to domain wall dynamics
Kinetic phase transition allows to probe the
phase relaxation time of strongly underdamped
Josephson Junctions.
Coupling to EM modes (Fiskes steps)