Ferromagnetic π-junctions

Physica C 408–410 (2004) 606–609 www.elsevier.com/locate/physc

Ferromagnetic p-junctions M. Aprili

a,* a

, T. Kontos a, W. Guichard b, J. Lesueur c, P. Gandit

b

CSNSM-CNRS, Universit
e Paris-Sud, B^at 108, 91405 Orsay Cedex, France b CRTBT-CNRS, 25 Avenue des Martyrs, 38000 Grenoble, France c ESPCI, 10, rue Vauquelin, 75005 Paris, France

Abstract Phase sensitive experiments have shown that the gap function of HTC superconductors changes of sign in the way expected for a condensate wave function with dx2
y 2 symmetry suggesting unconventional pairing. We present tunneling spectroscopy, Josephson effect and quantum interference measurements on superconducting/ferromagnetic (S/F) nanostructures based on a conventional superconductor: Nb. We observe a change sign oscillating order parameter induced into the ferromagnet by the proximity effect. This new inhomogeneous superconducting state indicates that a negative order parameter and hence p-coupling does not necessarily require unconventional pairing. More generally, it suggests that S/F hybrid nanostructures are an interesting alternative to investigate the interplay between magnetic order and superconductivity.
2004 Elsevier B.V. All rights reserved. Keywords: S/F hybrid structures; Josephson effect; Tunneling spectroscopy; SQUID

1. Introduction A series of experiments have shown that the ground state of a Josephson junction separating two superconductors can be defined by a negative energy. Josephson junctions with such a negative coupling are commonly called p-junctions as negative coupling is obtained introducing a p-phase shift in the current-phase relationship of the junction. p-coupling was first observed in high temperature superconductors ðHTc SÞ [1] and attributed to a sign change of the superconducting gap function on the Fermi surface suggesting unconventional pairing. It has been also reported in 3 He and related to the p-wave symmetry of the superfluid condensate in the B-phase [2]. But does p-coupling necessarily require unconventional supraconductivity? The answer is not. In fact, as pointed out by Buzdin et al. [3], the critical current, Ic , of ballistic superconductor/ferromagnet/superconductor weak links (S/F/S),

*

Corresponding author. E-mail address: [email protected] (M. Aprili).

displays damped oscillations around zero as a function of /F ¼ 2Eex dF = hvF leading to p-coupling when Ic is negative. Eex is the exchange energy, vF the Fermi velocity and dF the ferromagnetic layer thickness. Physically, this is a consequence of the phase change of the pair function induced in F by the proximity effect [4]. Energy conservation requires that a Cooper pair, in the singlet state, entering into the ferromagnet receives a finite momentum, Dp ¼  hvF =2Eex , from the spin splitting of the up and down bands. By quantum mechanics, Dp modifies the phase, / ¼ Dp  x, of the pair wave function that increases linearly with the distance, x, from the S/F interface generating an oscillating order parameter in F. As the Josephson critical current is proportional to the pair amplitude, Ic follows the sign of the order parameter in F [5]. It is either positive or negative depending on the phase hF . An oscillating order parameter has been predicted more than 30 years ago, by Fulde and Ferrel [6] and Larkin and Ovchinnikov [7] (FFLO) in ferromagnetic superconductors. However, as pairing and coherence occurs together in bulk superconductors, the FFLO state occupies a tiny part of the phase diagram and it is fragile to atomic disorder. Instead, it is much more

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2004 Elsevier B.V. All rights reserved. doi:10.1016/j.physc.2004.03.047

M. Aprili et al. / Physica C 408–410 (2004) 606–609 1.010

7 75 Å

Normalized conductance

5 1.000

4 50 Å

3

0.995

2

Nb

0.990

1 0.985 -4

-2

0

(a)

-1 -1

ρHall/ρHallo

50 0

4

0

0.8

TCurie 0.4

-50 0.0 -4

(b)

2

Energy (meV)

2

2. Planar tunnel junctions We have measured the superconducting density of states in F and the Josephson critical current, Ic , as function of the ferromagnetic layer thickness using superconductor insulator–ferromagnetic–superconductor (SIFS) and normal–insulator–ferromagnetic–superconductor (NIFS) planar junctions, respectively. The junctions were fabricated [4] by e-gun evaporation on a Si wafer in a typical base pressure of 10
9 Torr, with film thicknesses being monitored during growth to  by a quartz balance. The insulating layer better than 1 A  was obtained by oxidizing a thin Al layer (1500 A). Tunnel junction areas (500 lm · 500 lm) were defined  of SiO through shadow masks just by evaporating 500 A  after oxidation. A Pd1
x Nix thin layer (50–150 A; x  10–12%) was then deposited, hereafter called PdNi,  layer of Nb (Tc ¼ 8:8 K). The Nb and backed by a 500 A and the PdNi respectively provide the Cooper pair reservoir and the ferromagnetic thin film. The four terminal cross-junction geometry is reported in the inset of Fig. 1a. The Ni concentration is measured by Rutherfordbackscattering (RBS). The PdNi Curie temperature 100 K was measured by Anomalous Hall Effect on a bare substrate. The temperature dependence of the  thick PdNi thin Anomalous Hall resistivity for a 50 A film is shown in Fig. 1c. The Hall resistivity at T ¼ 1:5 K normalized by the square of the film resistivity is presented in Fig. 1b. For the Josephson measurements, the  was evaporated on a Nb buffer (1500 A;  Al (500 A) Tc ¼ 9:15 K).

6

1.005

ρHall/ ρ ( Ω cm )

robust in S/F hybrid structures as only phase coherence is required for the propagation of superconducting correlations in F. However, this state vanishes on a scale given by the coherence length in F, nF ¼ hvF =2Eex ¼ 1=Q [8], which is typically of the order of a few nm. Progress in the thin film deposition technology has made possible controlling the layer thickness and homogeneity down to this scale. We have investigated this proximity effect induced FFLO-state in a weak ferromagnetic alloy by tunneling spectroscopy, Josephson effect and macroscopic quantum interference. We observe that a sign change of the order parameter produces capsized tunneling spectra in F as suggested theoretically. When F is coupled with a second superconductor, the Josephson critical current also oscillates as a function of the ferromagnetic layer thickness going from 0 to p depending on the sign of the induced order parameter in F. Finally, the diffraction pattern of a dc-superconducting-quantum-interference-device (SQUID) made with a p-junction is observed to be shifted of a half quantum flux as expected [1].

607

0

4

H(KG)

0

(c)

40

80

120

T (K)

Fig. 1. (a) Differential conductance vs. bias for two NIFS  of PdNi. A capsized tunnel junctions containing 50 and 75 A tunneling spectrum for the thicker ferromagnetic layer evidences a negative induced superconducting order parameter. The normalized conductance for a tunnel junction without PdNi is reported on the r.h.s. The four terminal geometry of the junctions is also sketched. (b) Temperature dependence of  thick NiPd thin film. the Anomalous Hall effect for a 50 A (c) The field dependence of the normalized Hall resistivity at T ¼ 1:5 K for the same PdNi film as in (b).

3. Tunneling spectroscopy In Fig. 1 the superconducting density of states (DOS) at T ¼ 300 mK is presented for two different thickness of PdNi corresponding to a positive and a negative induced order parameter [4]. The Al counter-electrode is driven into the normal state by applying a magnetic field of 100 Gauss perpendicular to the film. The tunneling conductance is normalized by the background conductance obtained by raising the applied field up to 25 kg to quench the Nb superconductivity. The Nb BSC DOS measured without the ferromagnetic layer is also reported in Fig. 1a. For the thinner ferromagnetic layer  the DOS displays a maximum at the Nb gap edge (50 A) and a minimum at the Fermi level set to zero in our spectra. As a result of the finite interface resistance

M. Aprili et al. / Physica C 408–410 (2004) 606–609

between PdNi and Nb (10
10 X cm2 ), the pair amplitude is small, corresponding to a few per cent difference from the background conductance. Increasing the  the superthickness of the ferromagnetic layer (75 A), conducting order parameter becomes negative and the DOS is flipped with respect to the normal state.

10 8 6

Ic (mA)

608

dF = 0 Å

4 x 50

dF = 60 Å

x 100

dF = 90 Å

x 40

dF = 110 Å

2

4. Josephson effect 0

SIS junctions without a ferromagnetic layer showed high quality tunneling. The I–V characteristic is hysteretic as expected [9]. The subgap conductance at 1.5 K is less than 10
2 of the high energy conductance corresponding to negligible current leakage as shown in the inset of Fig. 2. The inset of Fig. 2 also shows the I–V characteristics of a SIFS junction with a thin layer of  The critical current is strongly rePdNi (dF ¼ 50 A). duced while the subgap conductance is enhanced. Both effects result from the suppression of the order parameter in F by the exchange field. The superconducting correlations are so efficiently reduced at the I/F interface [4] that the dissipative branch of the I–V curve reflects the energy dependence of the density of states in the Nb/ Al bilayer. The Josephson coupling, Ic Rn , as a function of the thickness of the ferromagnetic layer is presented in the main body of Fig. 2 [10]. Rn is the junction resistance, typically 0.2–0.3 X. For each value of dF , the Ic Rn product of two different junctions is reported. The Josephson coupling is of the order of 20 lV, i.e. 50 times lower than that measured on junctions without PdNi. The sign of Ic cannot be determined from the I–V 80 20 x10

10 I (mA)

IcRn (µV)

60

SIS

-2

-1

0 V (mV)

1

2

3

20

60

-2

0

2

4

Φ /Φo

Fig. 3. Critical current at T ¼ 1:5 K as a function of magnetic flux for four different junctions, three with and one without PdNi. The data are shifted vertically for clarity. The full line is the Fraunhofer pattern expected for a square junction with homogeneous current density and a misalignment of 7 between the field and the junction edge.

characteristics and the transition from ‘‘0’’ to ‘‘p’’ coupling is revealed as a zero of the Ic Rn product. The latter  consistent with the measurements occurs at dF ’ 65 A, of the density of states presented above. Fig. 2 also shows the best fit to the theory in which the Ic Rn product is obtained by integrating the spectral current density found solving the Usadel equations for a SIFS junction. In Fig. 3, the critical current, Ic , as a function of the magnetic flux is presented for (i) a junction without PdNi and (ii) three junctions with different thickness of PdNi but roughly the same Ic Rn product. One of the  and two ‘‘p’’ coupling latter gives ’’0’’ coupling (60 A)  The diffraction patterns are those ex(90 and 110 A). pected for a square junction with homogeneous current density provided a small misorientation of 7 between the field direction and one edge of the junction is included [9] (see fit in Fig. 3).

5. p-SQUIDs

SIFS

-20 -3

0 40

-4

0

-10

40

-2

80

100

120

140

dF (Å)

Fig. 2. Josephson coupling at T ¼ 1:5 K as a function of thickness of the PdNi layer (full circles). The critical current  indicating the transition from ‘‘0’’ to cancels out at dF ’ 65 A ‘‘p’’-coupling. The full line is the best fit obtained from the theory. Inset shows typical I–V characteristics of two junctions with (full circles), and without (empty circles) PdNi layer.

The transition from 0 to p coupling can be detected using a dc-SQUID. For a dc-SQUID with negligable loop inductance (LIc /0 , /0 is the quantum flux and L the loop inductance) and equal junction critical currents, i.e. Ica ¼ Icb ¼ I0 , the critical current modulates with applied flux from a maximum of 2I0 to zero current according to Ic ð/ext Þ ¼ 2I0 j cos½p //ext0 þ dab =2 j [9]. Thus, for conventional superconductors, if one of the two junctions is a p-junction the diffraction pattern is shifted of half a quantum flux as dab ¼ p. If both junctions are p-junctions, dab ¼ 2p, the diffraction pattern is shifted by a flux quantum and it is identical to the diffraction pattern of a SQUID with two 0 junctions.

M. Aprili et al. / Physica C 408–410 (2004) 606–609

The SQUIDs were obtained by lift-off after angle evaporation through resin masks. The mask was fabricated by e-lithography from a trilayer, PES(0.8 lm)/ Ge(45 nm)/PMMA(110 nm), where the poly phenyleneethersulfone (PES) is a thermostable polymer. The arrows in Fig. 4a indicate the direction of the evaporations. (1) Evaporation of the first Nb layer (25 nm). (2) Evaporation of the first PdNi layer (dF1 ). (3) Evaporation of the second PdNi layer (dF2 ). (4) Evaporation of the Nb counter electrode (25 nm). The first Nb layer is oxidized just after deposition. As the Ni-concentration is higher (18%) than that used in the planar junctions, the transition from 0- to p-coupling is expected at about dF ¼ 4:6 nm. The evaporated ferromagnetic layer thickness for a 0-junction is 4.2 nm and for a p-junction it is 8 nm. The outer dimensions of the superconducting rectangle are 8 · 12 lm2 , the junction size is 0.5

609

lm · 0.7lm. The geometrical inductance of the loop is about LG  40 pH so that the SQUID is in the linear limit for critical currents of some microamperes (LIC ¼ 0:1/0 < /0 =2). On the same substrate, we prepared four types of masks corresponding to 0–0, 0–p and p–p SQUIDs with ferromagnetic layers in each junction and to a 0–0 SQUID without a ferromagnetic layer. For 0–0 and p–p SQUIDs, both junctions are obtained from the same PdNi evaporation. The SQUID critical current Ic as a function of the magnetic flux in the loop is presented in Fig. 4b for SQUIDs made with either 0 or p junctions [11]. The diffraction pattern for a 0–0, a 0–p and a p–p SQUID show no-shift between a 0–0 SQUID and a p–p SQUID, whereas a shift of /0 =2 is observed between a 0–p SQUID and a 0–0 SQUID or p–p SQUID. We have reproduced these results on five samples per SQUID type. For each of them we have also checked that there are no changes when warming up above the Tc of Nb and cooling down several times. This rules out aging effects due to a vortex distribution. We always observed the expected /0 =2-shift for small critical currents (a few lA). Note that the flux quantum of 20 lT is the same for SQUIDs containing ferromagnetic junctions or not and corresponds to the outer dimensions of the SQUID. This is probably due to the phase gradient produced by the finite supercurrents in the loop.

Acknowledgements We acknowledge P. Monod, J. Ferr
e, D. Esteve, H. Pothier, W. Belzig, Yu. Nazarov, A. Buzdin, P. Feautrier, M. Salez, V. Ryazanov and J. Aarts for useful discussions.

References

Fig. 4. (a) Picture of a 0–p SQUID. The arrows corresponds to the different evaporations as described in the text. (b) Critical current modulations showing the expected no-shift between a 0–0 SQUID (solid line) and a p–p SQUID (dashed line) and of /=2 between a 0–p SQUID (dotted line) and a 0–0 SQUID or p–p SQUID. Each couple of the SQUIDs has been measured at the same time.

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