8 High-Temperature SQUID Magnetometer Neeraj Khare National Physical Laboratory, New Delhi, India 8.1 INTRODUCTION The superconducting quantum interference device (SQUID) is the most sensitive detector of the magnetic flux. This feature makes the SQUID an attractive device for a range of applications. The SQUIDs based on low-T c superconductors have shown unsurpassed sensitivity for the measurement of current, voltage, magnetic field, and magnetic field gradient (1). Potentiality of the applications of these SQUID magnetometers in measuring the biomagnetic field (2), nondestructive testing (2), and geological prospecting (3) have been demonstrated much earlier. In spite of the commercial availability of low-T c SQUID for several years, the SQUID-based applications did not gain widespread acceptability. This has been mainly due to the inconvenience of its operation at liquid-helium temperature. The feasibility of the fabrication of high-T c SQUID operating at 77 K was soon demonstrated after the discovery of high-T c superconductors (HTS). Since then, there has been continuous progress in this area (4–6). Several novel ap- proaches have been conceived and applied for improving the performance of the high-T c SQUIDs. HTS SQUID magnetometers exhibiting magnetic field sensitiv- ity ϳ 10–50 fT/Hz 1/2 in the white-noise region at 77K have been demonstrated (5). Several companies have started commercializing high-T c SQUIDs (7). HTS Copyright © 2003 by Marcel Dekker, Inc. All Rights Reserved. SQUID magnetometers and gradiometers have been successfully used in the de- tection of biomagnetic signals from the heart and brain (8,9), nondestructive test- ing of deep buried flaws in metallic specimens (10), geophysical applications (11), and several other novel applications such as in biological immunoassays (12), sen- tinels-lymph node biopsy (13), and so forth. This chapter presents a review of the developments of high-T c SQUID mag- netometers and discusses their applications in different areas. 8.2 SUPERCONDUCTING QUANTUM INTERFERENCE DEVICE The SQUID is an ultrasensitive magnetic flux sensor that converts magnetic flux into voltage. There are two types of SQUIDs: dc-SQUID and rf-SQUID (1). A dc- SQUID consists of a superconducting loop interrupted by two Josephson junc- 234 Khare FIGURE 8.1 (a) Schematic of a dc-SQUID. Two Josephson junctions are shown by ϫ in the superconducting ring, (b) Variation of voltage of the dc- SQUID with the applied flux (⌽) for a constant bias current, (c) Schematic of an rf-SQUID and (d) variation of peak amplitude of V rf with the applied flux (⌽) for a fixed rf bias current. Copyright © 2003 by Marcel Dekker, Inc. All Rights Reserved. tions, as shown in Figure 8.1a. The prefix dc implies that it is biased with a direct current. Both Josephson junctions in the dc-SQUID have identical characteristics. Critical current of the dc-SQUID is an oscillatory function of the applied flux with a period of one flux quantum, ⌽ 0 . The value of one flux quantum, ⌽ 0 (ϭh/2e), is 2 ϫ 10 Ϫ7 G/cm 2 . When the dc-SQUID is biased with a dc current I B Ϸ I c , where I c is the critical current of the Josephson junction, the voltage across the SQUID shows an oscillatory function of applied magnetic flux with the periodicity of ⌽ 0 (Fig. 8.1b). The rf-SQUID consists of one Josephson junction in the superconducting ring as shown in Figure 8.1c. The rf-SQUID is biased with an rf current applied to the SQUID through a inductively coupled tank circuit. Here also for an appropri- ate biasing, the rf voltage across the SQUID oscillates as a function of magnetic flux having a periodicity of ⌽ 0 (Fig 8.1d). 8.2.1 Designing of SQUID The performance of a SQUID depends on the characteristics of the Josephson junction and inductance of the SQUID loop, L SQ . For the Josephson junction, im- portant parameters are the critical current (I c ), the capacitance (C), and the shunt resistance (R). Designing of a highly sensitive SQUID requires careful selection of the appropriate values of L SQ , I c , R, and C (14,15). Noise due to thermal fluctuation puts an upper limit on the selection of the value of L SQ . The thermal noise power in the SQUID is ᎏ 1 2 ᎏ k B T/Hz and the mean en- ergy per Hertz in an inductor is ᎏ 1 2 ᎏ L SQ I n 2 ; thus I n 2 ϭ k B T/L SQ . The corresponding equivalent flux noise is ⌽ 2 n ϭ L 2 SQ I n 2 ϭ L SQ k B T (1) where k B is the Boltzman constant and T is the operating temperature of the SQUID. Due to this constraint of the thermal fluctuation noise, the SQUID effect can be observed only if ⌽ n is less than ⌽ 0 /2, where ⌽ 0 is the flux quantum. Thus, the condition for observing the SQUID response is L SQ Ͻ ᎏ 4 ⌽ k B 2 0 T ᎏ (2) which imposes a condition that L SQ Ͻ 1 nH for operating the SQUID at 77 K. Similar to L SQ , the choice of the critical current (I c ) of the junction is also very crucial. In order to observe the quantum interference effect, the junction coupling strength I c ⌽ 0 /2 must be significantly greater than the thermal energy, the (k B T). For taking into account Josephson coupling strength and thermal energy, the ⌫ parameter for the SQUID is defined as ⌫ ϭ ᎏ 2 I c ⌽ k B 0 T ᎏ (3) High-T c SQUID Magnetometer 235 Copyright © 2003 by Marcel Dekker, Inc. All Rights Reserved. For observing the SQUID effect, the value of the ⌫ parameter should be Ͻ1 (preferably Ϸ 0.1). This puts a condition that I c Ϸ 10–50 A for operating the SQUID at 77 K. Other important parameters for the SQUID design are  c ϭ ᎏ 2 ⌽ I c R 0 2 C ᎏ (4) and  L ϭ ᎏ 2L ⌽ SQ 0 I c ᎏ (5) To ensure nonhysteretic characteristics of the junction, the McCumber parameter  c Ͻ1 and for the optimum SQUID performance  L Ϸ 1. For a optimum bias current, the SQUID transfer function V ⌽ ഠ ␦V/␦⌽ is given as V ⌽ ഠ ᎏ L R SQ ᎏ (6) The value of spectral density of thermal noise (S v ) is S v (ƒ) ഠ 16k B TR (7) and the thermal flux noise density is given by S ⌽ ϭ ᎏ (V S ⌽ v ) 2 ᎏ (8) S ⌽ ഠ ᎏ 16k B R TL 2 SQ ᎏ (9) Thus, for reducing the thermal flux noise, the value of R should be large and C should be kept small to satisfy the condition for  c . Typically, ͙ S ෆ ⌽ ෆ (ƒ ෆ ) ෆ is frequency independent down to a frequency below which it scales approximately as 1/ƒ. In order to compare different SQUIDs, a figure of merit (energy resolution of the SQUID) is defined as (ƒ) ϭ ᎏ S 2 ⌽ L ( S ƒ Q ) ᎏ (10) Substitution of S ⌽ from Eq. (9) gives (ƒ) ഠ ᎏ 8k B T R L SQ ᎏ (11) thus, one should reduce T and L SQ and increase R in order to improve the energy resolution of the SQUID. 236 Khare Copyright © 2003 by Marcel Dekker, Inc. All Rights Reserved. 8.2.2 SQUID Magnetometer The dependence of SQUID voltage on the applied flux suggests that it can be used as a flux meter. Figure 8.1b shows that the SQUID voltage varies periodically with the applied flux. However, for several applications, one requires that the output of the SQUID should vary linearly with the applied flux even when the flux is much greater than ⌽ 0 . This linear response is obtained by means of a feedback circuit, as shown in Figure 8.2. The dc-SQUID is biased with a constant current I B Ϸ I c , and an ac magnetic field (ƒ ac ϳ 10–100 kHz) is applied to the SQUID with a peak- to-peak amplitude Յ⌽ 0 /2. The ac signal developed across the SQUID is detected with a lock-in at the fundamental frequency. When the external field is equal to exactly n⌽ 0 /2, the signal from the SQUID is at twice the fundamental frequency and the lock-in output is zero. For an external flux corresponding to (n ϩ ᎏ 1 4 ᎏ )⌽ 0 and (n ϩ ᎏ 3 4 ᎏ )⌽ 0 , the output from the lock-in is maximum and minimum, respectively. Therefore, the lock-in output is also oscillatory and the period of the oscillation is one flux quantum. To obtain a linear response to the external flux, the lock-in out- put is amplified and is fed back to the SQUID through a feedback resistor and a coil coupled to the SQUID. A flux change (␦⌽) produces a voltage across the SQUID which is fed back through the coil coupled to the SQUID, thereby gener- ating a flux (Ϫ␦⌽) exactly equal but opposite to the applied flux. Thus, the SQUID will experience no flux and it will always be “locked” at the minima of High-T c SQUID Magnetometer 237 FIGURE 8.2 Arrangement for a feedback circuit to operate the dc-SQUID in flux locked loop mode. Copyright © 2003 by Marcel Dekker, Inc. All Rights Reserved. the V–⌽ characteristics. Any increase in the applied flux increases the feedback current linearly and the voltage across the feedback resistance is proportional to the applied flux. In the flux-locked loop mode, one can detect flux much less than ⌽ 0 as well as flux corresponding to several ⌽ 0 ’s with the same sensitivity. The overall performance of the SQUID magnetometer is also determined by the readout electronics. In recent years, there has been considerable advancement in SQUID electronics (16–18). Direct-coupled SQUID electronics with large bandwidth and high slew rate at a very low noise level have been developed. These electronics have features like automatic bias voltage tuning, background field cancellation, and bias reversal scheme. The SQUID can also be used to measure the magnetic field in the digital mode by counting the number of oscillations that occur when the field is applied. The digital SQUID electronics uses the SQUID itself as an integral part of the ana- log-to-digital conversion. Digital SQUID electronics have been developed to per- form software gradiometry with SQUID magnetometers (19) for measurements in an unshielded environment or in a moving platform. 8.2.2.1 Flux Transformer and Gradiometer The magnetic field sensitivity of a SQUID depends on its effective area. The in- trinsic magnetic field sensitivity of the SQUID is less due to its small geometric area. Due to the design constraints, the area of the SQUID loop cannot be made very large. For an applied field B a , the flux coupled to the SQUID is ⌽ SQ ϭ B a A S , where A S is the area. Using a superconducting flux transformer, one can increase the magnetic field sensitivity of the SQUID. The configuration of such a super- conducting transformer is shown in Figure 8.3. It is a closed superconducting loop consisting of a large pickup coil connected in series with a small area input coil that is inductively coupled to the SQUID. When a magnetic field is applied to the pickup coil, fluxoid quantization requires that the total flux in the superconducting loop remain fixed in the multiples of flux quantum. As a result, a supercurrent is gener- 238 Khare FIGURE 8.3 Superconducting flux transformer inductively coupled to a SQUID. L p , L i , and L SQ are inductance of pickup loop, the input coil, and the SQUID loop respectively, and M i is the mutual inductance between the input coil and the SQUID loop. Copyright © 2003 by Marcel Dekker, Inc. All Rights Reserved. ated in the transformer with the appropriate direction and magnitude so as to counter any change in the magnetic flux within the loop. As this supercurrent flows through the input coil, it couples a magnetic field on the SQUID. The small loop that couples flux to the SQUID is magnetically shielded from the external field. For a field B a applied to the pickup loop, flux quantization in the flux trans- former requires that (15) B a A p Ϫ (L p ϩ L i )I ϭ 0 (12) where A p is the area of the pickup loop, L p and L i are the inductance of pickup loop and input coil of the transformer, respectively, and I is the supercurrent in the loop. The flux coupled to the SQUID is ⌽ ϭ ᎏ M L p i A ϩ p B L a i ᎏ (13) where M i is the mutual inductance between input coil and the SQUID inductance. It is evident that flux coupled to the SQUID through the flux transformer is much larger than the flux coupled to the SQUID without a transformer. For an efficient flux transformer, inductance of the pickup loop, L p , should be nearly equal to the inductance of the input coil, L i . An important extension of flux transformer is a gradiometer that is used to measure the magnetic field gradient. Figure 8.4 shows schematic configurations High-T c SQUID Magnetometer 239 FIGURE 8.4 (a) Superconducting first-order gradiometer and (b) second-order gradiometer. Copyright © 2003 by Marcel Dekker, Inc. All Rights Reserved. of first–order and second–order gradiometers that enables one to measure minute localized magnetic signals even in the presence of large uniform background mag- netic field. In the first-order gradiometer, the two superconducting pickup loops are wound in the opposite sense so that an uniform magnetic field produces no su- percurrent in the flux transformer, whereas a gradient ѨH z /Ѩz generates a net su- percurrent that is proportional to the difference in the flux threading the two loops. In the second-order gradiometer, two first-derivative gradiometers are wound end to end (Fig. 8.4b). This configuration measures the double derivative Ѩ 2 Hz/Ѩz 2 . In the design of the gradiometer, considerable care is taken to ensure that the loops are of the same size and exactly parallel to each other. In the low-T c SQUID, a wire-wound gradiometer (20) or thin-film gradiometer (21) is used. For the high-T c superconductor, wires of adequate quality are still not available and, thus, planar thin-film HTS flux transformers and gradiometers are used. 8.3 HIGH-T C JOSEPHSON JUNCTIONS AND SQUIDS In the low-T c SQUID, S-I-S (superconductor–insulator–superconductor) tunnel junctions are usually used for the fabrication of the SQUID. In high-T c supercon- ductors, it is extremely difficult to prepare S-I-S-type tunnel junctions because of the short coherence length along the c axis and various other novel approaches have been followed. Figure 8.5 shows the schematics of some of the high-T c junc- tions that have been used in the fabrication of HTS SQUIDs. Soon after the discovery of high-T c superconductors, it was established that natural grain boundaries (NGBs) in polycrystalline HTS samples behave as Josephson junctions. Several groups have reported the fabrication of rf- and dc- high T c SQUIDs using NGB junctions (references cited in Ref. 6). The character- istics of NGB junctions varies from one grain boundary to the other. It has been possible to fabricate a NGB junction rf-SQUID with reasonable characteristics be- cause only one junction is required for the rf-SQUID (22–25). However, fabrica- tion of a NGB dc-SQUID has not been very reproducible (26). Moreover, it has also been found that the trapping of flux in the body of the SQUID causes large 1/ƒ noise resulting into a poor sensitivity of the SQUID. Soon it was realized that the flux noise in an in situ grown epitaxial HTS film is much smaller as compared to the polycrystalline films (27) and many ef- forts have been directed toward the fabrication of HTS Josephson junctions using epitaxial films. Figure 8.5 shows the step-edge junction, the bicrystal junction, the ramp-edge junction, and the biepitaxial junction that have been fabricated using epitaxial films. The fabrication of the step-edge junction and the bicrystal junction involves the preparation of single-layer HTS film, whereas for the biepitaxial junction and the ramp-edge junction, deposition of multilayers of HTS films are required. For the HTS bicrystal grain-boundary junction, the HTS film is epitaxi- ally grown on a bicrystal substrate (28). The critical current density across the 240 Khare Copyright © 2003 by Marcel Dekker, Inc. All Rights Reserved. grain boundary depends on the misorientation angle of the grain boundary (29). For the HTS step-edge junction, a sharp step is created on a single-crystal sub- strate using lithography and the ion-beam-milling technique (30–32). The thick- ness of the film is kept smaller than the step height. In the ramp-edge junction, first a layer of HTS film is deposited on a substrate and the ramp edge is created using lithography and an etching process. In the second step, a thin insulating layer and HTS film are deposited on the ramp edge (33). For the biepitaxial junction, a seed epitaxial layer of MgO is deposited on an r-plane sapphire and then an epitaxial buffer layer of SrTiO 3 is deposited. The SrTiO 3 film grows on MgO and sapphire High-T c SQUID Magnetometer 241 FIGURE 8.5 Various types of the high-T c Josephson junction: (a) natural grain boundary, (b) bicrystal junction, (c) step-edge junction, (d) multilayer ramp- edge junction, and (e) biepitaxial junction. Copyright © 2003 by Marcel Dekker, Inc. All Rights Reserved. in two different orientations separated by a 45° grain boundary. The epitaxial YBCO film deposited on the SrTiO 3 film also has a 45° grain boundary (34,35). In all of the above cases, a HTS junction exhibiting Josephson junction char- acteristics can be fabricated by patterning a microbridge across the bicrystal grain boundary, the biepitaxial boundary, a step edge, or a ramp edge. The characteris- tics of these artificial HTS Josephson junctions fabricated using HTS epitaxial films can be easily controlled and the reproducibility of the junction is very high. Several groups have reported on the fabrication of high-T c SQUIDs using these ar- tificial junctions (references cited in Refs 5 and 6). Figures 8.6a and 8.6b show the geometry of step-edge junction and bicrys- tal junction dc-SQUIDs, respectively. Figure 8.6c shows typical voltage-flux characteristics for the YBCO thin-film bicrystal junction dc-SQUID (36). The SQUID characteristics depends on the geometry of the SQUID and characteristics 242 Khare FIGURE 8.6 (a) Step-edge junction high-T c SQUID, (b) bicrystal junction high- T c SQUID, and (c) voltage-flux characteristics of YBCO bicrystal junction dc- SQUID at different biasing current. (Adapted from Ref. 36). Copyright © 2003 by Marcel Dekker, Inc. All Rights Reserved. [...]... R Kleiner, F Ludwig, E Dantsker, J Clarke High- transition -temperature superconducting quantum interference devices Rev Mod Phys 71:631–686, 199 9 AK Gupta, N Khare High Tc SQUIDs : a review In: AV Narlikar, ed Studies of High Temperature Superconductors, Vol 12 New York: Nova Science Publishers, 199 4, pp 43 94 H Itozaki Development and commercialization of high Tc SQUID Physica C 357–360:7–10, 2001... 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The feasibility of the fabrication of high- T c SQUID operating at 77 K was soon demonstrated after the discovery of high- T c superconductors (HTS). Since then,. function of magnetic flux having a periodicity of ⌽ 0 (Fig 8.1d). 8.2.1 Designing of SQUID The performance of a SQUID depends on the characteristics of the Josephson junction and inductance of the. focuser of diameter 13.4 mm (47). Figures 8.9b and 8.9c show schematics of a single-layer flux transformer and multiturn input coil transformer. The first one is fabricated using a single layer of high- T c thin