SUPERCONDUCTOR-FERROMAGNET NANOSTRUCTURES

Transcription

1 SUPERCONDUCTOR-FERROMAGNET NANOSTRUCTURES A. Buzdin Institut Universitaire de France, Paris and Condensed Matter Theory Group, University of Bordeaux 1

2 OUTLINE Mechanisms of magnetism and superconductivity interaction. Electromagnetic interaction in S/F heterostructures. Proximity effect in superconductor-ferromagnet systems. Josephson π-junction. Spin-valve effet. Domain wall superconductivity. Coupling between magnetic moment and Josephson current in φ 0 -junctions. The way to superconducting spintronics. Possible applications.

3 Supraconductivity Since the discovery by Heike Kamerlingh Onnes 6 Nobel Prizes. Many important applications Magnetism 4 Nobel Prizes. Recent Nobel Prize : A. Fert and P.Grunberg Spintronics 007 3

4 Is it possible to couple magnetism and superconductivity? Superconducting Cooper pairs 4

5 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~ ~T c I r r ( ) S s Tc S z =+1/ S z =-1/ Exchange interaction 5

6 FERROMAGNETIC UNCONVENTIONAL (TRIPLET) SUPERCONDUCTORS Triplet pairing UGe (Saxena et al., 000) and URhGe (Aoki et al., 001) Very low T c < 1 K, clean limit UGe 6

7 The coexistence of singlet superconductivity and ferromagnetism is basically impossible in the same compound but may be easily achieved in artificially fabricated superconductor/ferromagnet heterostructures. S S F S F S Due to the proximity effect, the Cooper pairs penetrate into the F layer and we have the unique possibility to study T the properties of superconducting electrons under the influence of the huge exchange field. h>>t c The Josephson junctions with ferromagnetic layers reveal many unusual properties quite interesting for applications, in particular the so-called π- Josephson junction (with the π-phase difference in the ground state). 7

8 Varying in the controllable manner the thicknesses of the ferromagnetic and superconducting layers it is possible to change the relative strength of two competing ordering. Interesting effects at the nanoscopic scale. 8

9 Domain wall superconductivity in hybrid S/F systems or ferromagnetic superconductors S/F bilayer with domain structure (Buzdin, Melnikov, PRB, 00) 3 Phase diagrams of S/F systems with periodic domain structures H /B orb (T T )/ T 1 0 c c0 c This domain wall superconductivity has been observed on experiment by Moschalkov et al. (Nature Material, 005). 9

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15 Superconducting order parameter behavior in ferromagnet Standard Ginzburg-Landau functional: F = a Ψ + 1 4m Ψ b + 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 = a Ψ γ Ψ + η Ψ +... The non-uniform state Ψ~exp(iqr) will correspond to minimum energy and higher transition temperature 15

16 F F = γ η 4 ( a q + q ) Ψq q 0 q Ψ~exp(iqr) - Fulde-Ferrell-Larkin-Ovchinnikov state (1964). Only in pure superconductors and in the very narrow region. 16

17 E k F -δk F k k F +δk F The total momentum of the Cooper pair is -(k F -δk F )+ (k F -δk F )= δk F 17

18 aψ Proximity effect in a ferromagnet? In the usual case (normal metal): 1 4m Ψ = 0, and solution for T > T c is Ψ qx e, where q = 4ma In ferromagnet ( in presence of exchange field) the equation for superconducting order parameter is different aψ + γ Ψ η 4 Ψ = 0 Ψ Its solution corresponds to the order parameter which decays with oscillations! Ψ~exp[-(q 1 ±iq )x] Wave-vectors are complex! They are complex conjugate and we can have a real Ψ. Order parameter changes its sign! x 18

19 Proximity effect as Andreev reflection Classical Andreev reflection (September, 008, Miraflores, Spain) Quantum Andreev reflection F S h>>t c p p F F 19

20 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) S F S S F S «π phase» «0 phase» S F S/F bilayer ξ f = D f / h (1 10) nm h-exchange field, D f -diffusion constant 0

21 The oscillations of the critical temperature as a function of the thickness of the ferromagnetic layer in S/F multilayers has been predicted in 1990 and later observed on experiment by Jiang et al. PRL, 1995, in Nb/Gd multilayers F S F S F 1

22 SF-bilayer T c -oscillations Ryazanov et al. JETP Lett. 77, 39 (003) Nb-Cu 0.43 Ni 0.57 V. Zdravkov, A. Sidorenko et al PRL (007) Nb-Cu 0.41 Ni 0.59 d F min =(1/4) λ ex largest T c -suppression

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24 S-F-S Josephson junction in the clean/dirty limit 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. (Buzdin, Bulaevskii and Panjukov, JETP Lett. 81) h- exchange field in the ferromagnet, d F - its thickness I c E(φ)=- I c (Φ 0 /πc) cosφ J(φ)=I c sinφ α 4

25 5 Theory of S/F/S systems in dirty limit Analysis on the basis of the Usadel equations. ( ) ( ) ( ) ( ) ( ) ( ) 1,,,,,, 0,,,, * = + = + + h x h F x F h x G h x ih F 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. (Buzdin and Kuprianov, 1991)

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. 000, PRL S S F layer is CuNi alloys F Later more S/F/S junctions has been observed, see for example a transition as a thickness of a ferromagnetic (NiPt) layer by Kontos et al. 00, PRL 6

27 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 πli c > Φ 0 / φ = π = (π / Φ 0 ) Adl E E = π 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 / 7

28 Current-phase experiment. Two-cell interferometer I c 8

29 30µm Cluster Designs (Ryazanov et al.) x unfrustrated fully-frustrated checkerboard-frustrated 6 x 6 fully-frustrated checkerboard-frustrated 9

30 x arrays: spontaneous vortices Fully frustrated Checkerboard frustrated 30

31 Scanning SQUID Microscope images (Ryazanov et al.) I c Tπ T= 1.7K T =.75K T= 4.K T 31

32 Critical current density vs. F- layer thickness (V.A.Oboznov et al., PRL, 006) I c =I c0 exp(-d F /ξ F1 ) cos (d F /ξ F ) + sin (d F /ξ F ) d F >> ξ F1 0 -state π-state Spin-flip scattering decreases the decaying length and increases the oscillation period. ξ F >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) 3

33 Critical current vs. temperature (0-π- and π-0- transitions) Nb-Cu 0.47 Ni Nb d F1 =10-11 nm d F = nm (V.A.Oboznov et al., PRL, 006) 33

34 S angle θ L θ R S (+ small term) 34

35 Ic ΠG 4eTc Φ L Π Φ R Π Π 3 Π 4 Π 6 Π 1 0 Φ R Π 1 Π 6 Π 4 Π 3 Π d L Ξ f d R Ξ f 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,

36 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 d 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 36

37 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 : = 0 1 x L with L>>d S Buzdin, Vedyaev, Ryazhanova, Europhys Lett. 000, 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 D s 4πT * * T 1 = Ψ Ψ 1 d Tc ln Re + * Tc dstc c 1 c 0. Phase ( + i) T c ln T * d / c * d s = Ψ 1 Ψ 1 + d d T * c * stc 37

38 Recent experimental verifications AF F1 S F F layer with fixed magnetization «free» F layer F (Ni) S (Nb) F (Ni) P state AP state CuNi/Nb/CuNi Gu, You, Jiang, Pearson, Bazaliy, Bader, 00 Ni/Nb/Ni Moraru, Pratt Jr, Birge,

39 39 Evolution of the difference between the critical temperatures as a function of interfaces transparency ( ) n B n c s D h i D h T D d γ γ γ π + + = ~ T c T c T c T c = 0 B γ Infinite transparency 5 B γ Finite transparency d s d / ~ ( ) + Ψ = Ψ + + Ψ = Ψ * * * * ~ 1 1 ln 1 ~ 1 Re 1 ln c s c c c c s c c c T d dt T T i T d dt T T

40 Similar physics in F/S bilayers In practice, magnetic domains appear quite easily in ferromagnets Ni 0.80 Fe 0.0 /Nb (0nm) Thin films : Néel domains Rusanov et al., PRL, 004 w: width of the domain wall H=0 mt H=4. mt Localized (domain wall) superconducting phase. Theory - Houzet and Buzdin, Phys. Rev. B (006). 40

41 Different mechanism for the φ 0 - Josephson junction realization. Recently the broken inversion symmetry (BIS) superconductors (like CePt 3 Si) have attracted a lot of interest. Very special situation is possible when the weak link in Josephson junction is a non-centrosymmetric magnetic metal with broken inversion symmetry! Suitable candidates : MnSi, FeGe. Josephson junctions with time reversal symmetry: j(-φ)= - j(φ); i.e. higher harmonics can be observed ~j n sin(nφ) the case the π junctions. Without this restriction a more general dependence is possible j(φ)= j 0 sin(φ+ φ 0 ). Rashba-type spin-orbit coupling α r r r ( σ p) n n r is the unit vector along the asymmetric potential gradient. 41

42 Geometry of the junction with BIS magnetic metal M r 4

43 43 ( ) ( ) ( ) [ ] i i i ea i D D D n h b D a F, * * 4 = Ψ + Ψ Ψ Ψ Ψ + Ψ + Ψ = r r r r r ε γ 0, = Ψ + Ψ Ψ x h i x a ε γ γ ε ε γ ε h where a a x x i c = Ψ ~ ), )exp( ~ exp( φ 0 - Josephson junction (A. Buzdin, PRL, 008).

44 Ψ exp( i ~ εx)exp( x a a γ c ), where ~ ε = εh γ In contrast with a π junction it is not possible to choose a real ψ function! 44

45 φ 0 Josephson junction j ( ϕ ) = sin( ϕ + ϕ ) j c o where ϕ o = εhl γ The phase shift φ 0 is proportional to the length and the strength of the BIS magnetic interaction. The φ 0 Junction is a natural phase shifter. Energy E J (φ)~-j c cos(φ +φ 0 ) 45

46 Spontaneous flux (current) in the superconducting ring with φ 0 - junction. L ϕ o E( ϕ) = j c e - cos( ϕ + ϕ0 ) k = c Φ 0 πlj c + kϕ In the k<<1 limit the junction generates the flux Φ=Φ 0 (φ 0 /π) ϕ o = εhl γ Very important : The φ 0 junction provides a mechanism of a direct coupling between supercurrent (superconducting phase) and magnetic moment (z component). 46

47 Let us consider the following geometry : voltage-biased Josephson junction 47

48 Magnetic anisotropy (easy z-axis) energy : Coupling parameter : Weak coupling regime : Γ<1. Srong coupling regime : Γ>1. Let us consider first the φ 0 - junction when a constant current I<I c is applied : I Minimum energy condition: 48

49 θ M I The current provokes rotation of the magnetic moment : For the case Γ>1 when I>I c / Γ the moment will be oriented along the y-axis. Applying to the φ 0 - junction a current (phase difference) we can generate the magnetic moment rotation. a.c. current -> moment s precession! 49

50 Magnetic moment precession voltage-biased φ 0 - junction M z M y (t) 50

51 Landau-Lifshitz equation : M Magnetic moment precession : 51

52 Complicated regime of the magnetic dynamics : For more details see ( F. KonschelIe and A. Buzdin, PRL, 009 ). 5

53 Complementary Josephson logic RSFQ-logic using π-shifters A.V.Ustinov, V.K.Kaplunenko. Journ. Appl. Phys. 94, 5405 (003) RSFQ- logic: Rapid Single Quantum logic Conventional RSFQ-cell LI c >Φ 0 Fluxon memorizing cell RSFQ -π cell L 0 L J = Φ 0 /(π I c ) τ ~ 1/(I c R) To operate at 0 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 53

54 Superconducting phase qubit 54

55 Conclusions Superconductor-ferromagnet heterostructures permit to study superconductivity under huge exchange field (h>>t c ). The π - junction realization in S/F/S structures is a quite general phenomenon. Domain wall superconductivity. Spin - valve effects. The BIS magnets provide a mechanism of the realization of the novel φ 0 -junctionswith the very special properties. In these φ 0 - junctions a direct (linear) coupling between superconductivity and magnetism is realized. Seems to be ideal for superconducting spintronics. Some Refs.: Magnetic superconductors- M. Kulic and A. Buzdin in Superconductivity, Springer, 008 (eds. Benneman and Ketterson). S/F proximity effect - A. Buzdin, Rev. Mod. Phys. (005). 55 φ 0 - junctions - A. Buzdin, PRL (008), F. Konschelle and A. Buzdin, PRL (009).