Domain Walls and Long-Range Triplet Correlations in SFS Josephson Junctions. A. Buzdin

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1 Domain Walls and Long-Range Triplet Correlations in SFS Josephson Junctions A. Buzdin University of Bordeaux I and Institut Universitaire de France in collaboration with A. Melnikov, N. Pugach 1 "Superconducting hybrids: from conventional to exotic", September 7-10, Villard de Lans (France).

2 Outline Ø I. Introduction. Main mechanisms of the interaction between superconductivity and ferromagnetism Domain walls and superconductivity in S/F bilayer systems Ø II. SFS Josephson junctions! junctions. Experimental realization. Junctions with composite F interlayer Ø III. Long range proximity effect Experimental evidences Long range triplet correlations in SF systems with inhomogeneous exchange field. Ø IV. Clean SFS junctions with sharp domain walls Collinear magnetic moments Ø V. Dirty SFS junctions with sharp domain walls Collinear magnetic moments Noncollinear magnetic moments

3 Antagonism of magnetism (ferromagnetism) and superconductivity Orbital effect (Lorentz force) F L p -p B F L Electromagnetic mechanism (breakdown of Cooper pairs by magnetic field induced by magnetic moment) Paramagnetic effect (singlet pair) ( ) µ B H~Δ~T c I S s Tc S z =+1/2 S z =-1/2 Exchange interaction 3

4 Domain walls and superconductivity in S/F bilayer systems + Domain wall superconductivity in purely electromagnetic model 2πi A( r) Φ 2 Ψ = 1 2 ξ ( 0 T ) Ψ Ferromagnetic layer Superconducting film w>>d M w w<<d D? E.B.Sonin (1988) H c3 Pb-Co/Pt 4

5 Superconducting nucleus in a periodic domain structure in an external field H 0 πb w Φ 2 0 = 0 1 Domain wall superconductivity πb w Φ 2 0 = 0 5 5

6 Nb/BaFe 12 O 19 Z. YANG et al, Nature Materials,

7 DOMAINS IN SUPERCONDUCTOR-FERROMAGNET BILAYERS D x Superconductor It has been demonstrated by Bulaevskii et al. ( ) and Sonin (2002), that the maximum contraction of the domain width due to the superconductivity is around 20% only.

8 Brandt 2000 SC Vortex/ FM Domain Coupling Domain Wall Pinning Bulaevskii-Chudnovsky , Bulaevskii 2003 Sonin 2002, Laiho-Sonin 2003 Combined Domain Structures U VM =-MΦ o d F Genkin 1994, Lyuksyutov-Pokrovsky E v =d s Φ 0 H c1 /4π 8

9 SC Nb / FM garnet bilayers RE 3 (Fe,Al,Ga) 5 O nm Experiments at ANL -Vlasko-Vlasov et al. PRB (2010) 1 Wide domains D>d F D=6.6 µm d f =3.9 µm Q= Film with in-plane M(290K) Compensation T 2 Narrow domains D<d F D=1.1 µm d f =1.6 µm Q=3.8 8K Go to Insert (View) Header and Footer" to add your organization, sponsor, meeting name here; 9

10 Experiments at ANL -Vlasko-Vlasov et al Practically 3 times shrinking!

11 Different character of the field penetration -> coupled ferromagnet +vortex structure

12 F/S/F trilayers, spin-valve effect If d s is of the order of magnitude of ξ s, the critical temperature is controlled by the proximity effect. φ -φ F S F R R d f 2d s d f Firstly the FI/S/FI trilayers has been studied experimentally in 1968 by Deutscher et Meunier. In this special case, we see that the critical temperature of the superconducting layers is reduced when the ferromagnets are polarized in the same direction 12

13 In the dirty limit, we used the quasiclassical Usadel equations to find the new critical temperature T * c. We solved it self-consistently supposing that the order parameter can be taken as : x = Δ 0 1 L 2 Δ 2 with L>>d S Buzdin, Vedyaev, Ryazhanova, Europhys Lett. 2000, Tagirov, Phys. Rev. Let In the case of a perfect transparency of both interfaces * 0.4 Phase T c / T c d * = γ h D n * * T 1 = Ψ Ψ 1 d Tc ln Re + * Tc 2 2 dstc D s 4πT c 1 c 0.2 Phase ( + i) T c ln T * d / c * d s = Ψ 1 2 Ψ d d T * c * stc 13

14 Recent experimental verifications AF F1 S F2 F layer with fixed magnetization «free» F layer CuNi/Nb/CuNi Gu, You, Jiang, Pearson, Bazaliy, Bader, 2002 Ni/Nb/Ni Moraru, Pratt Jr, Birge,

15 Inhomogeneous exchange field near domain walls provides better conditions for Cooper pair survival Cooper pair

16 Similar physics in F/S bilayers In practice, magnetic domains appear quite easily in ferromagnets Ni 0.80 Fe 0.20 /Nb (20nm) Thin films : Néel domains Rusanov et al., PRL, 2004 w: width of the domain wall H=0 mt H=4.2 mt Localized (domain wall) superconducting phase. Theory - Houzet and Buzdin, Phys. Rev. B (2006). 16

17 II. SFS Josephson junctions Superconducting order parameter behavior in a ferromagnet Standard Ginzburg-Landau functional: F = a Ψ m Ψ 2 b + 2 Ψ 4 The minimum energy corresponds to Ψ=const The coefficients of GL functional are functions of internal exchange field h! Modified Ginzburg-Landau functional! : F 2 = a Ψ γ Ψ + η 2 2 Ψ The non-uniform state Ψ~exp(iqr) will correspond to minimum energy and higher transition temperature 17

18 F F = γ η 2 4 ( a q + q ) Ψq 2 q 0 q Ψ~exp(iqr) - Fulde-Ferrell-Larkin-Ovchinnikov state (1964). Only in pure superconductors and in the very narrow region. 18

19 E k F -δk F k F +δk F k The total momentum of the Cooper pair is -(k F -δk F )+ (k F -δk F )=2 δk F 19

20 aψ Proximity effect in a ferromagnet? In the usual case (normal metal): 1 4m 2 Ψ = 0, and solution for T > T 4ma In ferromagnet ( in presence of exchange field) the equation for superconducting order parameter is different c is Ψ qx e, where q = aψ + γ 2 Ψ η 4 Ψ = 0 Ψ Its solution corresponds to the order parameter which decays with oscillations! Ψ~exp[-(q 1 ± iq 2 )x] Wave-vectors are complex! They are complex conjugate and we can have a real Ψ. Order parameter changes its sign! x 20

21 Proximity effect in FS structures. δ ˆ H = h ˆ σ Inhomogeneous superconductivity induced by the exchange field: 1. FFLO state Ψ 2. Interference effects for Cooper pairs in FS layered structures Damped oscillatory S N dependence of pair S F x wave function in ferromagnets Ψ x ξ n ~(D n /T) 1/2 h= exchange energy ξ f in dirty limit:

22 Proximity effect as Andreev reflection p F Classical Andreev reflection Quantum Andreev reflection F S h>>t c p p F F 22

23 23 Theory of S-F systems in dirty limit Analysis on the basis of the Usadel equations. ( ) ( ) ( ) ( ) ( ) ( ) 1,,,,,, 0,,,, 2 * 2 2 = + = + + h x F h x F h x G h x F ih h x F D f f f f f f ω ω ω ω ω ω leads to the prediction of the oscillatory - like dependence of the critical current on the exchange field h and/or thickness of ferromagnetic layer.

24 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) Δ S F S Δ S F S Δ «π phase» Δ «0 phase» Δ S F S/F bilayer ξ = D / f f h Δ h-exchange field, D f -diffusion constant 24

25 S-F-S Josephson junction in the clean limit (Buzdin, Bulaevskii and Panjukov, JETP Lett. 81) S F S Damping oscillating dependence of the critical current I c as the function of the parameter α=hd F /v F has been predicted. h- exchange field in the ferromagnet, d F - its thickness I c E(φ)=- I c (Φ 0 /2πc) cosφ J(φ)=I c sinφ α 25

26 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 S S F and as a function of a ferromagnetic layer thickness by Kontos et al. 2002, PRL 26

27 Critical current density vs. F-layer thickness (V.A.Oboznov et al., PRL, 2006) I c =I c0 exp(-d F /ξ F1 ) cos (d F /ξ F2 ) + sin (d F /ξ F2 ) d F >> ξ F1 0 -state π-state Spin-flip scattering decreases the decaying length and increases the oscillation period. ξ F2 >ξ F1 0 -state I=I c sinϕ 0 Nb-Cu 0.47 Ni Nb π-state I=I c sin(ϕ+ π)= - I c sin(ϕ) 27

28 Phase-sensitive experiments π-junction in one-contact interferometer 0-junction minimum energy at 0 I π-junction minimum energy at π I I=I c sin(π+φ)=-i c sinφ E= E J [1-cos(π+φ)]=E J [1+cosφ] φ φ I L 2πLI c > Φ 0 /2 φ = π = (2π / Φ 0 ) Adl E E = 2π Φ/Φ 0 φ Bulaevsky, Kuzii, Sobyanin, JETP Lett φ Spontaneous circulating current in a closed superconducting loop when β L >1 with NO applied flux β L = Φ 0 /(4 π LI c ) Φ = Φ 0 /2 28

29 30µm Cluster Designs (Ryazanov et al.) 2 x 2 unfrustrated fully-frustrated checkerboard-frustrated 6 x 6 fully-frustrated checkerboard-frustrated 29

30 Scanning SQUID Microscope images (Ryazanov et al.) I c Tπ T T = 1.7K T = 2.75K T = 4.2K 30

31 Complementary Josephson logic RSFQ-logic using π-shifters A.V.Ustinov, V.K.Kaplunenko. Journ. Appl. Phys. 94, 5405 (2003) RSFQ- logic: Rapid Single Quantum logic Conventional RSFQ-cell LI c >Φ 0 Fluxon memorizing cell RSFQ -π cell Là 0 L J = Φ 0 /(2π I c ) τ ~ 1/(I c R) To operate at 20 GHz clock rate I c R~50 µv has to be We have I c R > 0.1 µv for the present π -RSFQ Toggle Flip-Flop 31

32 Superconducting phase qubit 32

33 July

34 July

35 Junctions with composite F interlayer S S S Clean limit antiparallel orientation, Blanter, Hekking PRB (2004) Diffusive limit arbitrary orientation, Crouzy et al. PRB (2007) 35

36 III. Long range proximity effect Experimental evidences for long range proximity effect in some SF systems Supercurrent measured in NbTiN/CrO2/NbTiN junctions Klapwijk s group in Delft, S. Keizer et al, Nature (2006) Long junctions with «large» I c CrO 2 is half-metallic! 36

37 W-Co-W junctions

38 The most direct evidences of the long range proximity effect T. S. Khaire et al., PRL (2010) talk of N. Birge at this workshop J. W. A. Robinson et al., Science (2010) talk of J. Robinson at this workshop 38

39 Triplet correlations Bergeret, Volkov Efetov -as a review see Bergeret et al., Rev. Mod. Phys. (2005). 39

40 Triplet proximity effect may substantially increase the decaying length in the dirty limit. The same, but larger amplitude No oscillations 40

41 Some source of triplet correlations? ξ f = D f / h Why difficult to observe? Magnetic scattering and spin-orbit scattering are harmful for long ranged triplet component. Magnetic disorder, spin-waves 41

42 S angle θ L θ R S (+ small term) More details - M. Houzet and A. Buzdin «Long range triplet Josephson effect through a ferromagnetic trilayer», PRB,

43 Rather sharp maximum of the critical current at d L =d R =ξ f More details - M. Houzet and A. Buzdin «Long range triplet Josephson effect through a ferromagnetic trilayer», PRB,

44 SFS junction with of domains Different types of domains 44

45 IV. Clean SFS junctions with sharp domain walls Domain walls with collinear and non-collinear magnetic moments S S S S

46 Clean SFS junctions, BdG equations g= (u,v), u and v are the electronlike and holelike parts of the quasiparticle wave function 2D : 3D : I~ I~ δi ( α) = sin 2 α δi ( π ) 2

47 Long range triplet proximity effect in dirty SF systems Bergeret Volkov Efetov (2001) Ψ S F ξ N Long range triplet component ξ f x T. Champel et al. PRL (2008)

48 V. Dirty SFS junctions with sharp domain walls. Usadel equations.

49 Dirty SFS junctions with sharp domain walls. Collinear magnetic moments No change in the length of decay of superconducting correlations No long range triplet component In accordance with the result of Crouzy et al. PRB 76 (2007) Dirty SFS junctions with sharp domain walls. Noncollinear magnetic moments d < ξ N

50 Clean SFS junctions with domain walls Dirty SFS junctions with domain walls Maximum contribution to the critical current: Domain walls with antiparallel magnetic moments Maximum contribution to the critical current: Domain walls with non-collinear magnetic moments

51 Conclusions Magnetic domains may strongly influence the properties of superconductor-ferromagnet bilayers: a) Superconductivity localized on the domain walls b) Coupled vortex-domain structures. Noncollinear domains in SFS junctions are sources of the long range triplet correlation. The domain walls connecting superconducting leads can be considered as the channels for triplet current. 51