Phase Dynamics of the Ferromagnetic Josephson …Phase Dynamics of the Ferromagnetic Josephson...
Transcript of Phase Dynamics of the Ferromagnetic Josephson …Phase Dynamics of the Ferromagnetic Josephson...
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.