1 Ferromagnetic Josephson Junction and 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.

2 Outline 1. 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

3 DC Josephson Effect I or NM x SC LL RR d I; Insulator Cooper pair NM; Normal metal Thickness dependence of I c IcIc d Penetration depth of order parameter to barrier NM ; I ; 0 Current flow without voltage drop Phase difference between superconductors dc Josephson effect I J = I c sin(  ) Josephson current V I Current-Voltage characteristic B.D.Josephson Phys. Lett. 1, 251 (1962) Josephson critical current IcIc 0

4 Properties of superconducting phase difference Fraunhofer pattern ・ Gauge invariant phase Magnetic field B LL RR Vector potential ； ・ Josephson current density z  ∝  Flux    Magnetic flux quantum y x

5 Dynamics of SC phase difference B.D.Josephson Phys. Lett. 1, 251 (1962) W. C. Stewart, APL. 12, 277 (1968) D. E. McCumber, JAP. 39, 3113 (1968) SC X SC : superconductor Dynamics of superconducting phase LL RR Cooper pair Josephson current R RSJ model V I Phase dynamics Current equation ・ Phase difference ・ AC Josephson current DC voltage AC current :Josephson frequency t IJIJ

6 Josephson Effect in ferromagnetic Josephson junction (FJJ) ・ Josephson current  Phase difference between SC’s d IcIc 0 A. I. Budzin, Rev. Mod. Phys. 76, 411 (2004)  Current-phase relation 0-state SC/NM/SC junction FJJ junction SC NM k FM E I J = I c sin(  )  -state I J = I c sin(  )

7 Josephson Coupling SFS I+ V+ d F1 d F2 V- I- Kontos et al. PRL 89, (2002) I (mA) V (mV) x10 SIS SIFS I-V characteristics IcRn(µV) d F (Å) experiment at 1.5K theory R Interface =   F = 46 Å Nb Pd 1-x Ni x 0 state  state

8 Diffraction Pattern d F (Å) +- I=-I c sin  I=I c sin  0-junction  -junction I c (  /o/o I c (  /o/o

9 SC/F/SC junction Ryazanov et al., PRL 86, 2427 (2001) S/F/S junction S/N/S π-state 0-state S F FSS θ θ＋πθ＋π FSS θθ

10 Magnetization dynamics in FM Landau-Lifshitz-Gilbert (LLG) equation Ferromagnetic resonance (FMR) x y z Ferromagnetic thin film DC magnetic field RF-magnetic field M : Magnetization M H eff

11 Phase dynamics Magnetization dynamics  t  MtMt SC FM Coupling

12 Model x y M SC FM M is parallel to x axis. d is thickness of FM L is width of junction SC z Josephson current density Phase difference d L Vector potential coupled with M dynamics M z x y B i : Dynamical flux density i=y,zi=y,z Josephson frequency RSJ model : FJJ i ; Current density i c ; Critical current density

13 Procedure of calculation ・ First step : ・ Second step Using the solution of Maxwell’s and LLG equations Phase difference Magnetic field Ampere’s law Ac magnetic field due to ac Josephson current M Precessional M Magnetic flux density B Ac Josephson current Dynamical flux coupled with M dynamics i=y,zi=y,z

14 Analytic formula of dc Josephson current i=y,zi=y,z Magnetic susceptibility H K : anisotropic field Josephson frequency Self-induced ferromagnetic Josephson resonance FMR induced by ac Josephson current SC FM SC M z x y

15 Voltage dependence of dV/dI V [  V] FJJ CJJ FMR CJJ : Conventional Josephson junction W. C. Stewart, APL. 12, 277 (1968) D. E. McCumber, JAP. 39, 3113 (1968) RSJ model dV/dI [  ] V [  V] dV/dI [  ]

16 In conclusion : SC/FM/SC Josephson junction. Dynamical coupling between SC phase and magnetization. Ferromagnetic Josephson resonance on 10 7 Ni atoms.