Gross R., Sidorenko A., Tagirov L. Nanoscale Devices

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Superconducting/Ferromagnetic Nanostructures 229

thickness are measured with a quartz deposition controller with an accuracy

of 1 Å. The normal metal is either Ag, Pt, Pd or Pd

1-x

Pd is a highly paramagnetic metal and only few percents of Ni impurities

are necessary to drive it into the ferromagnetic state. We probe the onset of

ferromagnetism by Anomalous Hall Effect (AHE) on Pd

1-x

thin films

deposited on a bare substrate. The Hall resistance (i.e. V

Hall

/I) is reported in

Fig. 1a for diffrent Ni concentration ranging from 2.4 to 10%, an

anomalous component proportional to the magnetization appears for a Ni

concentration higher than 2.4%, as observed in bulk Pd

1-x

, while a

hysteresis in the Hall resistance appears for 7% (not shown). The Ni

concentration is determined by Rutherford Back Scattering spectrometry. In

Fig. 1b the magnetoresistance for the highest Ni concetration of Fig. 1a is

also reported. The magnetic field is oriented either in the film plane but

perpendicular to the current or perpendicular to the film plane. A strong

anisotrpy is observed, this anisotropy appears at concetration higher than

2.4% Ni together with the AHE. The hysteresis on the magnetoresistance is

not of magnetic origin, it results from fluctuations of the bath temperature.

Fig. 1. a) Hall resistance for different Ni concentrations. An anomalous Hall

component (AHE) appears at 2.5 % Ni. b) The anisotropy of magnetoresistance.

The paramagnetic regime

Figure 2 shows the tunnel conductance of CE/I/N/S junctions with pure Ag,

Pt, Pd and Pd

0.988

012

as a normal metal. The main feature of the

conductance is a minigap, E

. Note that the minigap decreases when the

susceptibility of the metal increases as expected by faster dephasing. In

Fig. 2 are also shown the fits (blue lines) of the conductance by the DOS

-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

(ž)

-0.4

0.0

0.4

(

)

T=1.3K

2.4 %

9.8 %

-0.4

-0.2

0.0

0.2

0.4

∆

-0.4

0.0

0.4

(

)

Field ⊥

Field //

230 M. Aprili, M. L. Della Rocca, T. Kontos

found solving the Usadel equations. We used a self consistent code to solve

equation (1) together with the usual boundary conditions [9]. It turns out

that a finite

∆ is unnecessary to account for the data and that an upper

bound for the coupling constant

is -0.1.

A finite interface resistance of about 5.10

-4

Ω

was used to account

for both the shape and the value of the energy gap for pure Pd. This value is

consistent with the one measured in Nb/Pd/Nb Josephson jutions [10]. This

finite resistance is supposed not varying when changing material and

remains also constant when adding Ni impurities in Pd. From the fits we

obtained

= 0.05, 2.05, 4.15, 5.3 for Ag, Pt, Pd and Pd

0.988

0.012

respectively. The electron-spin fluctuation coupling constant increases

between Ag and Pt and between Pt and Pd. It increases further when

increasing the Ni concentration as expected since the magnetic

susceptibility increases below the paramagnetic-ferromagnetic transition

consistently with specific heat data. Even though the precise relationship

between

and the Stoner enhancement is model dependent, a rough

estimate of it is given by

~2 (1-1/S)\lnS, where S is the Stoner factor.

This yields a Stoner factor of 10 for Pd, 3.3 for Pt and 1 for Ag, in

surprisingly good agreement with the known values for these metals.

Fig. 2. The superconducting density of states induced in a normal metal by the

proximity effect (red dots). The density of states of pure Nb is also shown. The fits

(blue lines) are obtained by solving the Usadel equations self consistently as

indicated in the text. In the inset the four probes cross geometry of the tunnel

junction is presented.

Superconducting/Ferromagnetic Nanostructures 231

The ferromagnetic regime

For Ni concentrations higher than 5.5%, the tunnel conductance displays

only one characteristic energy,

∆

, of about 1.35 meV, while the shape of

the spectra remains roughly the same. This is shown in Fig. 3, where all the

spectra have been scaled to the DOS corresponding to 5.5% of Ni. As finite

size effects vanished altogether, the proximity bilayer becomes similar to

that of a semi-infinite mesoscopic system

> . The overall amplitude is

smaller than 5% of the background conductance and therefore it is possible

to find an analytical expression for the DOS and extract directly the value

of the exchange field in the Pd

1-x

layer. Linearizing eq. (2) we find the

following DOS:

[]

( ) 1 ( ) 1 exp( 2 / )cos(2 / )

ex th ex th

NE NE EE EE=+ − − ,

(3)

where N

(E) is the DOS at the Nb/Pd

1-x

boundary. We found

E = 0.1,

0.5, 2.8, 3.3, 3.9 for 5.5%, 6%, 7%, 9.8%, 11.5% Ni, respectively.

Fig. 3. The proximity effect tunneling spectroscopy in a weak ferromagnet (PdNi)

is presented. The spectra are normalized by the PdNi exchange energy. The red line

is the best fit using the analytical expression.

232 M. Aprili, M. L. Della Rocca, T. Kontos

Therefore superconductivity is a very sensitive probe of

E provided that

the size of the magnetic domains is larger than the superproduction

coherence length. On other words, the spatial resolution of a «Cooper pair

E sensor» is given by

Spontaneous Vortices in Ferromagnetic Josephson

Junctions

In the ferromagnetic regime for a Ni concentration of about 10% the

superconducting wave function oscillates in F on a length scale given by

≈20 Å. A negative critical current occurs when the ferromagnetic thin

layer is coupled with a second superconductor and the superconducting

wave function is negative, originating

-coupling [11]. By shorting a

ferromagnetic

-junction with a 0-junction, a spontaneous supercurrent

sustaining half a quantum vortex occurs. We have detected such a current

by measuring the related phase gradient. The ground state of the 0-

junction is doubly degenerate, so that either half a quantum vortex or half

a quantum antivortex appears. As no coupling is observed at low

temperature between the two levels, the junction can be seen as the classical

limit of a two level system. It behaves macroscopically as a magnetic

nanoparticle of quantized flux, the magnetic anisotropy axis being defined

by the junction plane.

Device Design

The

-junction in a superconducting loop behaves as a phase bias

generator producing a spontaneous current and hence a magnetic flux. In

the limit 2

Φ , the system gains energy by minimizing its magnetic

energy against the junction energy. The system maintains a constant phase

everywhere and a shift of

/2 in the current-phase relationship of the

junction is expected. On the other hand, when 2

the system's

minimum energy corresponds to that of the junction while maximizing its

magnetic energy. A phase gradient is maintained by generating a

spontaneous superconducting current, which sustains exactly half a

quantum flux. The ground state is degenerate as, the spontaneous

supercurrent

can circulate clockwise and counterclockwise with exactly

the same probability. Applying a small magnetic field can lift the

degeneracy and define an easy magnetization direction. The existence of a

Superconducting/Ferromagnetic Nanostructures 233

spontaneous supercurrent sustaining half a quantum flux in

-rings has

been recently shown in Nb loops interrupted by a ferromagnetic (PdNi)

junction [12]. Analogously, in a highly damped single Josephson junction

fabricated with a 0 and a

-region in parallel, a spontaneous half quantum

vortex is expected at the 0-

boundary.

The way we detect such a spontaneous supercurrent is by measuring the

phase gradient by a phase sensitive device, a second Josephson junction.

The ferromagnetic 0-

junction (source) and the detection junction

(detector) are coupled, as schematized in Fig. 4a, by sharing an electrode.

I.e., the top electrode of the detector Josephson junction is simultaneously

the bottom electrode of the ferromagnetic one. If half a quantum vortex is

spontaneously generated in the ferromagnetic junction, the spontaneous

supercurrent sustaining it circulates in the common electrode [Nb2, Fig. 4a]

producing a phase variation equal to

/2. A

/4-shift of the detection

junction's magnetic diffraction pattern is thus produced.

Fig. 4. a) Device geometry b) I-V characteristic of the detector junction.

When an external magnetic field is applied, in the hypothesis that the

thickness of the common electrode, Nb2, is comparable to the penetration

depth, the diffraction pattern of the detection junction is given by:

I(B)

I(0)

sin((

)(

))

(

)(

+Φ

)

(4)

where

DtΦ= and

DtΦ= are the magnetic fluxes through the

ferromagnetic and detection junction respectively, with D the junction

width, t and t' the effective barrier thickness. J

is the spontaneous

supercurrent density, k

=0.5(

)D and k’=(

)/L(D/wd

Nb2

) with

the vacuum permittivity,

the penetration depth, L the ferromagnetic

junction inductance, w the junction length and d

Nb2

the thickness of the

common electrode. The term k

generates the shift due to the spontaneous

supercurrent contribution, while the term k’

reduces the diffraction

-5

I (mA)

-4 -2 0 2 4

V (mV)

T = 1.5K

B = 0

Detector

SiO

I+

I-

V-

V+

Nb2

Nb1

234 M. Aprili, M. L. Della Rocca, T. Kontos

pattern period as a result of the contribution due to the screening current in

the ferromagnetic junction.

Device Fabrication

Samples are fabricated as described above for the single tunnel junctions.

First the bottom planar Nb/Al/Al

/Nb detection junction is made. A

1000 Å thick Nb [Nb1, Fig. 4(a))] strip is evaporated and backed by 500 Å

of Al. Al

oxide layer is achieved by oxygen plasma oxydation during

12 min, completed in a 10 mbar O

partial pressure during 10 min. The

junction area is 0.6×0.8 mm

(D x w). Then, a 500 Å thick Nb [Nb2,

Fig. 4(a)] layer is evaporated perpendicular to the Nb/Al strip to close the

junction. This procedure results in a junction critical temperature, T

, equal

to 8.5 K. Typical junction normal state resistances are of the order of 0.1-

Ω and critical current values are of 1-10 mA at 4.2 K. The resulting

critical current density is 10

-1

A/cm

leading to a Josephson penetration

depth

~1 mm, i.e. larger than the size of the junction (small limit). The I-

V characteristic of a typical detector is shown in Fig. 4(b). The Nb2 layer

acts as both the counterelectrode of the bottom detection junction and the

base electrode of the top ferromagnetic 0-

junction. Its thickness is

comparable to the Nb penetration depth to insure good coupling between

the two junctions. The same procedure is used to prepare the top planar

Nb/PdNi/Nb/Al junction. Specifically, after defining the same junction area

by evaporating 500 Å thick SiO layers, a PdNi layer was evaporated

directly on the Nb layer, without any Al-oxide barrier. This results in a very

large critical current and very small junction resistance. An estimate of the

critical current density is 10

-10

A/cm

, so the Josephson penetration

depth,

< 10

-2

mm << D, is smaller than the size of the junction. Hence

the ferromagnetic junction is in the large limit, with a large screening

capability. The maximum degree of misalignment between the top and

bottom junction is 100

A detailed SEM and AFM analysis of devices where the fabrication

process has been stopped before closing the ferromagnetic junction with the

top Nb/Al bilayer, revealed the presence of inhomogeneities at the junction

window edges. SEM images (Fig. 5c) of the PdNi surface show such

inhomogeneities in the shape of black bubbles with 2-3

m diameter.

Fig. 5b shows an AFM picture of the same surface, the line cut indicates the

direction along which a thickness profile has been measured (Fig. 5a).

Apart from inhomogeneities, the roughness is lower then 100 Å, while

picks as high as 500 Å develop on the top of the inhomogeneity itself. This

indicates that the PdNi layer is not continuous, thus inducing 0-coupling in

Superconducting/Ferromagnetic Nanostructures 235

such zones. Therefore, 0-junction and 0-

junctions are obtained with

PdNi layer thickness coresponding to 0-coupling and

- coupling

respectively.

Fig. 5. a) Roughness profile along the black line in (b). b) AFM picture of an

inhomogeneity at the window edge. c) SEM image of one window edge.

Results

Residual fields were screened by cryoperm and

-metal shields. All

measurements showed comparable residual fields at 4.2 K of some tenths of

mG. Depending on the PdNi layer thickness, the ferromagnetic junction is

either 0 or

while a spontaneous half quantum vortex or antivortex is

expected only for

-coupling. In Fig. 6a we show the diffraction patterns

of a sample for a PdNi thickness of 100 Å corresponding to

-coupling at

T = 4.2 K (red data) and T = 2 K (blue data). The magnetic field

corresponding to a quantum flux is 300 mG. At T < T

period reduction is

accompanied

by a

Φ /4 shift in the detector, as expected for a

spontaneous half quantum vortex in the ferromagnetic junction. Similar

period reductions have been observed for PdNi thickness of 40 Å and

200 Å

corresponding to zero coupling together with not shift in the

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b) c)

236 M. Aprili, M. L. Della Rocca, T. Kontos

detector diffraction pattern [13]. The period reduction at the lowest

temperature (2 K) for all the samples was about 15%. This value results

from two competing effects: a smaller period is expected because of

screening in the ferromagnetic junction as shown in eq. 4, whereas the

decrease in the pénétration depth

(T), at lower temperatures should

increase the modulation period. Note that no period reduction or diffraction

pattern shift are measured when the source and the detector are decoupled

with a thin insulating layer. This indicates that inductive coupling between

the two junctions is negligible.

Might an external residual field or the magnetic layer itself affect the

spontaneous supercurrents? In this regard it is important to stress that the

shift is always about

Φ /4 for

-coupling and zero for 0 coupling. Since

this depends neither on the residual field nor, for 0-coupling, on the

thickness of the ferromagnetic layer, any effect of the PdNi magnetic

moment on the amplitude of the spontaneous supercurrents seems to be

ruled out. Instead, the PdNi magnetic structure breaks the degeneracy of the

ground state and polarizes the supercurrents. As a consequence, the sign

shift is always the same below the Curie temperature (100 K), indicating

the same spontaneous current polarization. When cooling down from room

temperature to 2 K, the shift, while reproducible in magnitude, becomes

random in sign. This is shown in fig. 3b for 26 cool-downs of two different

junctions.

Fig. 6. a)

/4 shift in the diffraction pattern of the detector junction above

(T = 4.2 K, red dots) and below (T = 1.5 K, blue dots) the ferromagnetic junction

critical temperature, T

. b) Statistics of the measured shift for 26 different cooling

down from room temperature. A positive shift correspond to half a quantum anti-

vortex, a negative shift to half a quantum vortex.

I (mA)

PdNi = 100A

ercentage (%)

(a)

a) b)

Superconducting/Ferromagnetic Nanostructures 237

Conclusion

In conclusion, the strong enhancement of the Stoner factor at the

paramagnetic/ferromagnetic transition is measured by proximity effect

tunneling spectroscopy (PETS). Ferromagnetic Josephson

-junctions

behaves as classical spins resulting from spontaneous supercurrents which

are revealed by measuring the shift in the magnetic diffraction pattern of a

Josephson junction directly coupled to a 0-

junction.

Acknowledgments

This work has been supported by the ESF through the “

-shift” program.

We are indebted with E. Reinwald of the University of Regensburg for

performing the AFM analysis.

References

1. Wolf (1986) Principles of electron tunneling spectroscopy. Wiley and sons,

New York

2. For a review see Buzdin AI (2005). Rev Mod Phys 77:935

3. Bulaevskii LN, Kuzii VV, Sobyanin AA (1978). Solid State Comm 25:1053

4. Kontos T, Aprili M, Lesueur J, Dumoulin L (2004). Phys Rev Lett 93:137001

5. Andreev AF (1964). Sov Phys-J Exp Theor Phys 19:1228

6. Belzig W, Bruder C, Schön G (1996). Phys Rev B 53:5727

7. Daams JM, Mitrovic B, Carbotte JP (1981). Phys Rev Lett 46:65

8. Kontos T, Aprili M, Lesueur J, Grison X (2001). Phys Rev Lett 86:304

9. Golubov AA, Kupriyanov Yu (1988). J Low Temp Phys 70:823

10. Guichard W (2003). Ph.D. thesis, Université Joseph Fourier, Grenoble

11. Kontos T, Aprili M, Lesueur J, Genêt F, Stephanidis B, Boursier R (2002).

Phys Rev Lett 89:137007-1

12. Bauer A, Bentner J, Aprili M, Della Rocca ML, Reinwald M, Wegscheider

W, Strunk C (2004). Phys Rev Lett 92:217001

13. Della Rocca ML et al cond-mat/0501459

COHERENCE EFFECTS IN F/S AND N/F

NANOSTRUCTURES

Gross R., Sidorenko A., Tagirov L. Nanoscale Devices - Fundamentals and Applications

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