Non-uniform superconductivity in superconductor/ferromagnet nanostructures

1. Non-uniform superconductivity in superconductor/ferromagnet nanostructures A. Buzdin Institut Universitaire de France, Paris and Condensed Matter Theory Group, University of Bordeaux in collaboration with M. Daumens, J. Cayssol, S. Tollis University of Bordeaux A. Koshelev, Argonne National Laboratory

2. Antagonism of magnetism (ferromagnetism) and superconductivity • Orbital effect (Lorentz force) p B FL FL -p • Paramagnetic effect (singlet pair) μBH~Δ~Tc Sz=+1/2 Sz=-1/2

3. Superconducting order parameter behavior in ferromagnet Standard Ginzburg-Landau functional: The minimum energy corresponds to Ψ=const The coefficients of GL functional are functions of internal exchange field! Modified Ginzburg-Landau functional: The non-uniform state Ψ~exp(iqr) will correspond to minimum energy and higher transition temperature

4. F q q0 Proximity effect in ferromagnet ? Ψ~exp(iqr) - Fulde-Ferrell-Larkin-Ovchinnikovstate (1964) In the usual case (normal metal):

5. In ferromagnet ( in presence of exchange field) the equation for superconducting order parameter is different Its solution corresponds to the order parameter which decays with oscillations!Ψ~exp[-(q1 + iq2 )x] Ψ Order parameter changes its sign! x

6. S F S S F S Remarkable effects come from the possible shift of sign of the wave function in the ferromagnet, allowing the possibility of a « π-coupling » between the two superconductors (π-phase difference instead of the usual zero-phase difference) «  phase » « 0 phase » F S S/F bilayer

7. F S F S F The oscillations of the critical temperature as a function of the thickness of the ferromagnetic layer in S/F multilayers has been predicted by Buzdin and Kuprianov, JETPL, 1990 and observed on experiment by Jiang et al. PRL, 1995, in Nb/Gd multilayers

8. S-F-S Josephson junction in the clean limit(Buzdin, Bulaevskii and Panjukov, JETP Lett. 81) Damping oscillating dependence of the critical current Ic as the function of the parameter =hdF /vF has been predicted. h- exchange field in the ferromagnet, dF - its thickness S F S Ic 

9. S S The oscillations of the critical current as a function of temperature (for different thickness of the ferromagnet) in S/F/S trilayers have been observed on experiment by Ryazanov et al 2000 PRL F and as a function of a ferromagnetic layer thickness by Kontos et al 2002 PRL

10. Critical current density vs. F-layer thickness (Ryazanov et al. 2005) Ic=Ic0exp(-dF/F1) |cos (dF /F2) + sin (dF /F2)| dF>> F1 F2 >F1 “0”-state dF,1 =(3/4)F2=(3/8)ex -state dF,2 =(7/4)F2=(7/8)ex 0 Nb-Cu0.47Ni0.53-Nb “0”-state -state I=Icsin I=Icsin(+ )= - Icsin()

11. Density of states at Fermi level 2.1 2.1 2.08 2.06 2.05 2.04 2.02 1 2 3 4 0 1 2 3 4 5 6 1.98 1.95 1.96 In the dirty limit (h<<1), we find oscillations of period oscillating like exp(-x)/x 1.9 In the clean limit (h>>1), we find oscillations of period vf/h, oscillating like sin(x)/x2 Density of states T/Tc variation

12. Density of statesmeasured by Kontos et al (PRL 2001) on Nb/PdNi bilayers

13. Atomic layer S-F systems (Andreev et al, PRB 1991, Houzet et al, PRB 2001, Europhys. Lett. 2002) Magnetic layered superconductors like RuSr2GdCu2O8 F exchange field h « 0 » BCS coupling S F « π » S t F « 0 » S Also even for the quite small exchange field (h>Tc) the π-phase must appear.

14. Hamiltonianof the system BCS coupling Exchange field It is possible to obtain the exact solution of this model and to find all Green functions.

15. T/Tco 1 0-phase p-phase h/Tco 2 The limit t<<Tco Ic p-phase 0-phase h/Tco

16. Superconducting multilayered systems (Buzdin, Cayssol and Tollis, to be published, PRL 2005 ) layered superconductors with a structure like high-Tc Zeeman effect, i.e. the exchange field μBH « 0 » BCS coupling S t1 « π » S t2<<t1 « 0 » BCS coupling S t1 « π » S At low temperature the paramagnetic limit may be strongly exceed μBH~t1. π-phase with FFLO modulation in plane.

17. S S The mechanism of the p -junction realization due to the tunneling through thin ferromagnetic layer(Buzdin, 2003) -d/2 d/2 The largeand small

18. S S At T=0, and γB>>h/Tc F(x)

19. J(φ)=Icsinφ ; Ic>0 in the0- state and Ic<0 in the p – state How the transition from 0- to p – state occurs? J(φ)=I1sinφ +I2sin2φ Energy E(φ)=(Φ0/2πc)[-I1cosφ –(I2/2)sin2φ] E I2>0 Ic=|I2| φ p 0

20. J(φ)=I2sin2φ I2<0 The realization of the equilibrium phase difference 0<φ0<π E φ p 0

21. Grain boundaries in YBaCuO (Manhnhart, van-Harlingen et al. 1995-1996) YBaCuO-Nb Josephson junctions of zig-zag geometry (Hilgenkamp, Smilde et al. 2002) Possibility to fabricate different alternating 0- and π- junctions S YBaCuO 0 F π S 0 Nb π 0 Arbitrary equilibrium phase difference: φ- junction (Buzdin, Koshelev, 2003) Nb π

22. We will study the properties of long Josephson junctions with lengths d0 of 0-junctions and dπ of π-junctions in the limit d0 , dπ <<λJ, λJis the Josephson length of individual junction (for simplicity we assume that it is the same for 0- and π-junctions) φ(x) π π π 0 0 0 dπ d0 The energy per period of our system is: x is the coordinate along the zig-zag boundary

23. The current-phase relation for φ - junction : The current-phase relation is quite peculiar, the current has two maxima and two minima at

24. New kinds of solitons in φ - junctions Besides 2π degeneracy, there is ±φ0 degeneracy! New solitons - φ0→+φ0 or φ0 → 2π -φ0, The flux of the first type of solitons is Φ0(φ0 /π). The flux of the second type of solitons is Φ0((π-φ0) /π).

25. Conclusions • The p-junction realization in S/F/S structures is quite a general phenomenon, and it exists even for thin F-layers (d<ξf), in the case of low interface transparency. • New non-uniform superconducting phases in superconducting layered structures with alternating electron transfer integrals • Transition to the φ- junction state can be observed by decreasing the temperature from Tc. For review see - A. Buzdin, Rev. Mod. Phys. (July 2005)