JOSEPHSON EFFECTS IN CERAMIC SUPERCONDUCTORS AND THEIR APPLICATION TO SQUID MAGNETOMETRY

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JOSEPHSON EFFECTS IN CERAMIC

SUPERCONDUCTORS AND THEIR APPLICATION

TO SQUID MAGNETOMETRY

C. Gough

To cite this version:

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JOURNAL DE PHYSIQUE

Colloque C8, Supplkment au no 12, Tome 49, d6cembre 1988

JOSEPHSON EFFECTS IN CERAMIC SUPERCONDUCTORS AND THEIR

APPLICATION TO SQUID MAGNETOMETRY

C. E. Gough

University of Birmingham Superconductivity Research Group, Birmingham, B15 ZTT, G.B.

Abstract. - A brief review is given of Josephson Effects in high-Tc superconductors with specific reference to ceramic material properties and device applications. The development of liquid-nitrogen cooled rf and dc SQUIDS for ultrasensitive magnetometry will be described. Field sensitivities of better than have already been achieved but l/f -noise becomes important at low frequencies.

1. Introduction

The discovery of high temperature superconductivity in cuprate perovskite compounds has enabled quantum physics on a macroscopic scale to be demonstrated at liquid nitrogen temperatures for the first time. In- deed, it was the Saclay measurements of photon- as- sisted superconducting electron-pair tunnelling [I] and the Birmingham determination of the flux quantum [2] that established the newly discovered materials as superconductors in a truly quantum mechagical sense rather than simply being conductors with a vanishingly small electrical resistance.

These measurements were manifestations of the ac and dc Josephson effects [3], which describe the tunnelling of pairs of superconducting electrons across an insulating or non-superconducting barrier. Such barri- ers are assumed to exist between the grains of ceramic superconductors and even within the grains themselves

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across internal crystallographic domain walls and twin boundaries.

The maximum supercurrent that a ceramic superconductor can support is limited by Josephson tunnelling across these internal weak-links. At present, no way has been found to eliminate such weal-links from ceramic superconductors. Understanding the properties of weal-links and their relation to the microstruc- ture is therefore central to the control and optimisation of critical currents in high Tc superconductors.

2. T h e Josephson effect

Consider two superconducting grains separated by a thin non-superconducting barrier across which pairs of superconducting electrons can quantum mechanically tunnel. In practice this might be a non-superconducting region of amorphous, non- stoichiometric or second-phase material between two ceramic grains, or a twin-boundary or crystallographic domain wall within a grain. The coherence length in superconducting ceramic materials is so short (for YBCO

<

5

A

in the c-direction and 30 in the

ab-plane [4]) that any lattice defect or change in stoi- chiometry, even on an atomic scale, may give rise to a significant local depression of superconductivity.

On either side of the tunnel junction, the superconducting state can be described by a macroscopic wave-function of the form

f i

exp

(is),

where N is the number density of superconducting electrons and

S is a phase factor. When superconducting electrons tunnel across the barrier, I = I, sin 0, and dO/dt =

4reV/h, where 0 is the phase difference and V the voltage across the junction [3, 51. These are known as the Josephson current and voltage phase relations.

Provided I < I,, a supercurrent can tunnel across the insulating barrier with no voltage appearing across it. This is the dc Josephson effect. For an ideal junction, the maximum supercurrent I,= (7r/2) A/eR ( 6 ) , where R is the resistance across the junction in the normal state and A the superconducting energy gap. From this expression an estimate for the maximum critical current density in a ceramic superconductor, J , ~ e A / p a , can be made, where p is the bulk resistivity and a the average intergrain spacing. If A/e is taken to be 20 mV, a resistivity of 100 p0cm and a grain size of 10 pm, a maximum ~ , - 2

x

10' A cm-2 is obtained. This is somewhat larger than has yet been achieved in sintered material because the critical current of a junction is often, in practice, considerably less than that given by the theoretical expression, even for conventional superconductors.

Chaudari et al. [7] a t IBM have recently succeeded in measuring Josephson junction tunnelling characteristics across single intergrain boundaries and within single grains in a 100 pm grain size polycrystalline thin film of YBCO. The measured critical current across grain boundaries was always significantly less than that of the grains on either side. This supports the view that it is largely the weak intergrain coupling that limits the supercurrent in ceramic materials.

As soon as I, is exceeded, a voltage is developed across the junction resulting in a sinusoidal variation of current through the junction, I = I, sin (27r (2eVlh) t)

,

with frequency f = 2eVlh =

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2076 JOURNAL DE PHYSIQUE

484 MHz/pV. This corresponds to the radiation of photons of energy hf when pairs of electrons lose energy 2 eV on crossing the barrier and is known as the ac Josephson effect. In principle, it can be used t o prG vide a voltage-tunable, low-power source of microwave radiation.

With suitable external biasing, it is possible to switch very rapidly between the superconducting and voltage states. The possibility of ultra-fast switching circuits using LN2 cooled high-Tc materials has rekin- dled interest in a Josephson junction based computer technology.

If a Josephson junction is exposed to electro- magnetic radiation of frequency f (equivalent t o the in- jection of an ac current), steps appear in the I / V characteristics at voltages which are multiples of hf/2e. This is known as the inverse ac Josephson effect and provided the first experimental evidence for the pairing of electrons in high-Tc ceramic superconductors [I]. The observed I / V characteristics in these experiments suggested that the ac Josephson effects were associ- ated with weak-links between the ceramic grains rather

than between the ceramic and the sharp niobium point used to form the junction. Similar microwave steps have subsequently been observed on ceramic samples with weakened superconducting properties produced by crack junctions [81 or thinned down to form narrow constricted regions [9] where the Josephson junctions are clearly those of the intergrain boundaries.

3. Superconducting weak-link rings

When a superconducting ring contains a weak-link across which Josephson tunnelling can occur, the re- quirement that the phase S should everywhere be single-valued results in a direct relationship between

8, the phase difference across the junction, and the magnetic flux contained within the ring, 6 = 2~cp/cpo, where cpo = h/2e = 2.07 x 10-l6 ~m~ is the flux quantum. The 2e in the denominator follows from the assumed pairing of electrons in the superconducting state. The current flowing round the ring is therefore

I = Ic sin (2x(p/cpo)

.

When an external flux, cpext, is applied - for exam- ple, by a current-carrying coil placed inside the ring - a shielding supercurrent is induced resulting in the following relation between the applied and net flux, cpext=cp+LIc sin 2xp/,, where L is the inductance of the ring.

The magnetic behaviour of the ring then depends on the value of ,B = 2nLIc/cp,,. If ,6

<

1, the magnetic properties of the ring are completely reversible. However, if ,f3

>

1, the magnetic properties become irreversible and energy is dissipated on cycling the external field around a magnetic hysteretic loop. This

energy loss is periodic in any additional externally applied dc field with the periodicity of the flux quantum. This is the basis of operation of the rf SQUID (see van Duzer j10] for a more detailed discussion of weak-link rings and of rf and dc SQUIDS).

When ,B >> 1, for any value of applied magnetic field, many metastable flux states of the ring exist separated by cpo. It was the observation of transitions between such states within a hollow ring of multi-phase YBCO material by the Birmingham group [2], that first established the magnitude of the flux quantum as h/2e, proving that electrons were paired in ceramic superconductors, just as they are in conventional BCS superconductors.

An additional feature of the above measurements was the demonstration of long-range order of the superconducting order-parameter around paths involv- ing many thousands of superconducting grains weakly coupled together across grain boundaries. For the particular multi-phase YBCO ring studied, the superconducting loop appeared fortuitously to be broken by a single, thermally recyclable, Josephson Junction, pre- sumably the weakest point on a particular percolating superconducting path between two grains.

4. Influence of Josephson Tunnelling o n bulk properties

Many authors have observed electrical properties, such as electrical resistance 191, rf absorption [ l l , 121 and microwave absorption [13], to fluctuate markedly as a function of small applied field. These fluctuations are assumed t o arise from flux quantisation in the superconducting loops between individual grains of the ceramic superconductor [ l l ]

.

The magnetic properties of such loops will be periodic in the flux quantum with a typical field periodicity cpo/a2. Although the net effect of averaging over many different sized loops tends t o destroy evidence for the underlying periodicity, the characteristic spectrum still reflects the average periodicity.

The existence of microscopic current loops between grains also affects the bulk magnetic properties. For

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C. E. Gough C8

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Fig. 1. - Temperature dependence of resistance and ac- susceptibility of a typical sintered YBCO sample with modest Jc.

temperature T* below Tc by an amount that depends on both Jc and the typical grain size.

It is a common observation that bulk superconductivity does indeed set in a little way below the onset of superconductivity in individual grains, as illustrated in figure 1. This shows superimposed measurements of electrical resistance and ac susceptibility for a sintered material with a relatively modest Jc of around 100 A cm-2 and N 10 pm grain size. The onset of

bulk superconductivity a t T* is indicated by the drop in electrical resistance to zero and the onset of a peak in the imaginary component of the susceptibility.

Between Tc and T* the measured properties are ef- fectively independent of the magnitude of the measuring current and the value of any small applied field. However, below T*, where flux can be trapped within individual intergrain-loops, the magnetic and theoretical properties become highly hysteretic, as expected for material in which the intergrain-loop ,O exceeds unity.

Between Tc and T*, Clem [14] has predicted that the magnetic properties arising from weak Josephson tunnelling between grains will be slightly diamagnetic with magnetic properties analogous to those of a type- I1 superconductor. However, the effective superconducting penetration depth and coherence length are determined by the ceramic properties rather than by those of the bulk superconductor. Alternative models to describe the transition between the reversible and hysteretic regions, based on the concept of a superconducting glass phase have also been proposed [15]. Thermal fluctuations and sample inhomogeneities will also affect the magnetic and superconducting properties near Tc.

5. SQUID magnetometry using ceramic su- perconductors

Under laboratory conditions a liquid-helium cooled SQUID can have a sensitivity approacbing the quantum limit, --h (see the recent review by Clark

2L

[16])

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many orders of magnitude better than the best available flux-gate magnetometer. There is therefore considerable interest in developing SQUIDS which might operate at LN2 temperatures with a similar sensitivity using Ceramic materials.

Evidence for rfSQUID behaviour arising from rf- coupling to weak-link current loops between individual grains of a ceramic ring was first reported in the original determination of the magnitude of the flux quantum by the Birmingham group [2]. Subsequently, it was shown that quasi-periodic rf SQUID field dependences could be observed within mm-sized ceramic samples placed inside an rf-coil [ l l , 121. The scale of the quasi-periodicity of the field dependence suggested SQUID action in intergranular loops of typical 10-50 pm size.

Using an electronic feedback system, it is straight- forward to "lock" to a local minimum of the magnetic behaviour and produce a sensitive magnetometer. the sensitivity, however, is relatively low because of the small effective area of the loops - the field sensitivity being proportional to cpo/(area of loop).

Conventional liquid helium-cooled rf SQUIDs in- volve superconducting loops of mm size. The first such device incorporating a YBCO ceramic superconductor was developed at NBS by Zimmerman et al. [17]. It incorporated a single hole in a disc with a slit containing a Josephson junction formed by cracking the ceramic material under liquid helium or nitrogen, cre- ating what is known as a crack junction. Although such a device is potentially unstable and cannot be thermally cycled with any reliability, an ideally periodic field dependence, corresponding 'to quantized flux

in the hole, was observed at LN2 temperature. A flux

sensitivity of order 5 x cpo/& was quoted as an unspecified frequency, corresponding to a field sensitivity comparable to the best flux-gate magnetometers avaiable (18).

Subsequently Zavaritski et al. [I91 in Moscow and

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2078 JOURNAL DE PHYSIQUE

Fig. 2.

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Quantum field periodicity of 2-hole rf-SQUID shown in inset. The single hole is to determine rf-properties of the material alone.

apply the external flux [20]. Unlike the field dependences observed in bulk rf SQUIDs, the observed field fluctuations are magneticaily reversible for applied flux

changes of many hundreds of flux quanta.

In many applications, the performance of a SQUID is determined by its low-frequency noise. The noise spectrum of the Birmingham 2-hole SQUID shown in figure 3, illustrates the dominance of an approximately l / f source of noise a t low frequencies (see also Refs. [21 and 271). Detailed measurements of the sample and temperature dependence of this l/ f noise should lead t o an understanding of its origin and will, hopefully, suggest ways in which it might be reduced. Above about 100 Hz the sensitivity is limited largely by the room temperature electronics. Improvements in the performance will undoubtedly be obtained by the use of LNZcooled amplifiers, LN2-cooled superconducting tank-circuits and by optimised coupling. Such measurements already demonstrate the viability of the LN2 rf SQUID as a potential competitor to conventional magnetometers and su est an ultimate sensitivity approaching cpo/ Hz may be achievable at audio-frequencies.

J=

01 0.1 1 lo

roo

law

Fig. 3.

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Noise measurements for 2-hole &-SQUID at 77 K

and above T, to determine electronic noise done.

6. D C SQUIDs using ceramic materials A dc SQUID is based on the periodic field variations of the voltage across a ring containing a matched pair of resistivity damped Josephson-Junctions [lo].

Evidence for dc SQUID-like periodicities were again first observed in bulk material [22], where the loops between grains act as elemental dc SQUIDs in series and parallel, affecting the flow of supercurrent through the bulk. In measurements of the I / V characteristics of two pieces of ceramic materials pushed together, de Waele et al. [22] observed a near perfect field periodicity at 4.2 K with quasi-periodic features persisting to about 68 K. The observed periodicity corresponded to flux quantisation within intergranular loops of t y p ical 10 pm size. Periodic field fluctuations, similar to those observed in the rf rulk SQUID measurements, have been observed [23] in sintered material that has been purposely thinned down t o form a constriction region. The sensitivity of such devices as magnetometers is again limited by the small size of the intergranular current loops involved.

There have been a number of attempts to devise DC SQUIDs using thin-films of YBCO. The earliest such SQUID was reported by IBM [23], who lithographi- cally patterned a 40 pm square central hole and two 10 pm weak-link regions in a thin polycrystalline film of 5 pm typical grain size. The strength of the Joseph- son tunnelling in the weak-link regions was adjusted by ion implantation.

At liquid helium temperatures the I / V charac-

teristics exhibited the anticipated field periodicity but on increasing the temperature the field dependence became increasingly aperiodic, reminiscent of the field dependences observed for current loops between grains. All evidence of SQUID operation disap- peared a t 68 K, almost certainly because the thin film after processing was no longer sufficiently strongly superconducting.

Similar devices have been reported by other groups [7, 24, 251 but, t o date, it has proved difficult to es- tablish satisfactory LN2 temperature dc SQUID o p eration using YBCO thin films. However, the use of higher temperature superconductors with completed transitions greater than 100 K 1271 is likely to rem- edy this situation. One remaining problem is likely to be l / f -noise, which, if caused by thermal fluctuations of trapped flux, could be appreciably worse in thin-film devices than in the bulk rf SQUID geometries described earlier.

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outweigh the slight loss in sensitivity with increased temperature.

Acknowledgements

I should like t o acknowledge the assistance of F. Wellhofer, C. M. Muirhead and S. Harrop in preparing this review. The work is supported by the SERC.

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