1. Chern-09 Supercurrents in ferromagnets J. Aarts, M. S. Anwar Kamerlingh Onnes Laboratory, Leiden. II.The experimental scene : - Experiments with CrO 2. I.The theoretical scene : - from LOFF state to odd-frequency triplets. + discussions / experiments with T. Klapwijk (Delft), S. Goennenwein, F. Cheska (HMI- München) Schegolev Memorial Conference 2009

2. Chern-09 S/F hybrids – some history, proximity effect S/F multilayers, oscillation of T c (d F ) Theory : Radovic,.., Buzdin PRB 1991 Experiment : Nb / Gd multilayer Jiang, PRL 1995

3. Chern-09 I. F / S hybrids; inhomogeneous superconductivity in ‘weak F’ The 'LOFF' - state : pairing in presence of exchange field : not between +k ↑ and -k ↓. Larkin & Ovchinnikov, Sov. Phys. JETP '65; Fulde & Ferrell, Phys. Rev. '64 Characteristic : inhomogeneous pair density; e.g C-pair from S to F. In F (exchange field h), pair gains momentum or oscillates : cos(Qx) So, S induces in F : oscillatory damped pair density.

4. Chern-09 Oscillations : length scale ξ F E ex >> k B T, E ex  1 eV (Ni)  ξ F  1 nm E ex  k B T ξ F1 : decay ξ F2 : period Need weak magnets for large ξ F : Cu 50 Ni 50, Pd 90 Ni 10, etc. ξ F → 10 nm and can change phase – by π S / F / S π - junction

5. Chern-09 Consequences : oscillations Nb / Co multilayer Obi, Phys C ‘99 note small d F Nb / CuNi junction Oboznov – Ryazanov, PRL ‘06 in T c (d F ) and I c (T) / I c (d F )

6. Chern-09 New development : odd-frequency triplets attractive interaction + exchange : spin singlet + spin triplet Pauli : singlet : spin odd, orbit even  s, (d) ‘ = ‘ Nb, YBCO triplet : spin even, orbit odd  p, (f) ‘ = ‘ Sr 2 RuO 4 but, ‘Pauli’ = ‘equal times’ only. Using negative times / frequencies allows to circumvent this : triplet : spin even, ω odd, orbit even  s : isotropic, (d) Matsubara :  n    n with f 0 (  n ) = f 0 (-  n ) and f 1 (  n ) = -f 0 (-  n ) The receipe for triplets : Spin mixing by different spin scattering at interface singlet |  > - |  > → m=0 triplet |  > + |  > Spin rotation by exchange field then also yields m=1 triplet |  > and |  >

7. Chern-09 Volkov / Bergeret / Evetov mix at interface, rotate in domain wall end with |  > Triplet is not broken in F : Long range proximity ! triplet singlet Possibly observed : Ho bridge in Al loop (Sosnin – Petrashov, PRL ’06) Super- current

8. Chern-09 Halfmetallic ferromagnet – mix and rotate at interface Eschrig, N Phys ‘ 08 weak magnet does not introduce much m = 0 component. rotation is by disordered interface moments. Effect is long range, no spin flip in HFM.

9. Chern-09 Special feature : π / 2 shift at each interface π – junction without thickness dependence Braude ’07, Asano ‘07 Possible to measure ? ½ Φ 0 by scanning SQUID Hilgenkamp / Kirtley 2006 LDOS by low-T STM SS F zero-bias conductance peak Δ0Δ0

10. Chern-09 Zero-bias conductance peak ? As in d-wave HTS Surface Andreev Bound State has zero-energy solution - ZBPC Leiden LT-UHV-STM, 300 mK, 8 T operational since fall ’08 (Federica Galli) YBCO (110) sample Maarten v.Zalk Twente data Simon Kelly Leiden

11. Chern-09 Found in CrO 2 / NbTiN ? Keizer, Klapwijk, Gupta et al, Nature 2006 F - films from Alabama ; S - contacts in Delft Note the biaxial anisotropy 100 nm Candidates for the triplet supercurrents : (La,Sr)MnO 3, CrO 2 revisited in Leiden

12. Chern-09 CrO 2 – difficult as thin film not by sputtering, PLD, MBEonly CVD, and only on TiO 2 S contacts are not grown in-situ surface cleaning issue intermediate thickness has biaxial anisotropy modified with extra precursor heater

13. Chern-09 Basic properties reproduce well Morphology is subtle – depends on pretreatment TiO 2 (HF etch) TiO 2, Untreated [001] TiO 2, Treated roughness of order 2 nm Basis for biaxial anisotropy. easy axis Bulk CrO 2 : c Strained (TiO 2 ) : b Relax : bi-axial (100 nm) c (200 nm

14. Chern-09 2008 – new expts on Alabama and Leiden samples contacts by lift-off after Ar-etching the surface. CrO 2 + (Nb,Ti)N and CrO 2 + a-MoGe no supercurrent Problem is interface and / or magnetic stuff and / or something else. Try something different, grow on sapphire ….. CrO 2 Cr 2 O 3 Al 2 O 3

15. Chern-09 60 o [001] a 3c CrO 2 on Al 2 O 3 AFM

16. Chern-09 HREM Rabe – Güntherodt J.Phys.Cond.Mat ‘02 Note the Cr 2 O 3 layer, and the columnar growth of the CrO 2

17. Chern-09 Use different structure (larger) zero-bias resistance I-V, current-biased film disordered and rough lift-off

18. Chern-09 I c (T) - 1 μm slit; two samples 10 4 A/cm 2 compare Nb / CuNi Dev. A : 1 mA  5  10 5 A/cm 2 d CrO2 = 100 nm

19. Chern-09 I c (H a ) at 3 K, field in-plane,  bridge 80 mT compare CrO 2 on TiO 2 increase with H a Φ 0 / 2 = 80 mT junction area : 1 μm  d CrO2 d CrO2 = 10 nm - smallish 45 mT junction area : 0.3 μm  d CrO2 d CrO2 = 70 nm - nominally 100 nm

20. Chern-09 I c max = 4 mA (d = 10 nm) or I c max = 40 mA (d = 100 nm) Thouless-energy analysis S/N : I c ~ T 3/2 exp(-2πk B T / E th ) 1/2 ; eR N I c = 10.82 E th  E Th  80 μeV  = 2 μΩcm R N = 0.2 Ω (d = 10 nm) or R N = 20 mΩ (d = 100 nm)  I c (too) small - grain boundaries ?

21. Chern-09 Conclusion and outlook : looks like confirmation of the 1 st report promise of (very) long range effects (1 μm at 4 K) promise of a novel π – junction (no thickness dependence) Main questions still not answered …. what constitutes a magnetically active interface what is the role (if any) of the magnetic anisotropy ? In progress smaller gaps (increase I c ) contact CrO 2 strips instead of film → rings I c to 300 mK → Eschrig 2008

22. Chern-09 Alabama – Delft sample