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 8-11 2008, Aussois.

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

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

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.

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 :

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 !

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

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

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.

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.

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

Numerical Simulations numerically fitted formula N1=1 – 1.8 exp (- 0.76 ) hb wb b 3/2 b=(RqpC w0) -1 range of parameters: b, wb = 0.0001 - 0.1 w0 T=1.5 K T=0.67 K n* - frequency at which bifurcation starts The phase relaxation is set by the quasiparticle resistance.

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.

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

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)