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Periodic magnetization instabilities in a superconducting Nb film with a square lattice of Ni dots
Physica C 332 Ž2000. 5–11 www.elsevier.nlrlocaterphysc
Periodic magnetization instabilities in a superconducting Nb film with a square lattice of Ni dots A. Terentiev a , B. Watkins a , L.E. De Long a,) , L.D. Cooley b, D.J. Morgan c , J.B. Ketterson c a
Department of Physics and Astronomy, UniÕersity of Kentucky, CP 177, Lexington, KY 40506-0055, USA b Applied SuperconductiÕity Center, UniÕersity of Wisconsin, Madison, WI 53706-1687, USA c Department of Physics and Astronomy, Northwestern UniÕersity, EÕanston, IL 60208, USA
Abstract Isothermal magnetization curves of a superconducting Nb film perforated by a square lattice of Ni dots exhibit quasiperiodic instabilities below ; 4 K, with a field-dependent period equal to the first, second, or third matching fields. The instabilities are found in a range of applied fields well above the saturation matching value, and where a Nb film with the same dimensions and magnetization remained stable. The recovery of matching effects well below Tc ; 8.8 K is unexpected, because strong flux gradients generated by the geometric barrier and random pinning suppress the formation of large domains of matched flux lines and dots. The results suggest that terraces of matched flux density may exist at the border of a flux-free zone near the film edge. q 2000 Elsevier Science B.V. All rights reserved. PACS: 74.60.Ge; 74.60.Jg; 74.80.Dm; 75.70.Cn; 73.50.Jt Keywords: Periodic magnetization; Ni dots; Thermomagnetic instabilities
1. Introduction Thin film superconductors patterned with lattices of artificial pinning centers ŽAPC. exhibit a variety of interesting mesoscopic and quantum phenomena w1–4x. Lattices of antidots Žholes. w4–8x, or dots of normal w9x or magnetic w9–12x metals induce unique modifications of various physical properties that provide novel opportunities to precisely control flux pinning and flow, as desired in practical applications of superconducting films. )
Corresponding author. Fax: q1-606-323-2846. E-mail address: [email protected] ŽL.E. De Long..
In particular, magnetization and electrical resistivity data for patterned films exhibit ‘‘matching anomalies’’ at specific values of applied perpendicular field Hn , for which the number of flux lines ŽFL. is an integral multiple n of the number of APC w2–8x. Higher order Ž n ) 1. matching anomalies, corresponding to multiply quantized fluxoids resident at each APC, occur if the APC diameter D is large on the scale of the coherence length j . Close to Tc and at intermediate applied fields Hn - H Hnq 1 , the system of FL consists of a spatial mixture of fluxoids Ž nF 0 or w n q 1xF 0 . strongly localized at the APC. The magnetization curve M Ž H . is then similar to the logarithmic flux penetration above the
0921-4534r00r$ - see front matter q 2000 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 3 4 Ž 9 9 . 0 0 6 3 6 - X
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A. TerentieÕ et al.r Physica C 332 (2000) 5–11
lower critical field; however, irreversible hopping of singly quantized FL produces strong magnetic hysteresis and substantially enhanced critical current densities compared to unpatterned films w5–8x. When the number of flux quanta trapped by each APC reaches a saturation number n s , additional FL penetrating the film will be repelled into the interstitial region between the APC, where the much weaker pinning potential of random defects within the interstices leads to a sharp transition to high flux–flow rates and greatly reduced magnetization hysteresis w5–8,13x, a behavior desired for flux–flow device applications w14x. The saturation number n s s Dr4j ŽT . Žand therefore the overall pinning strength of the film. can be controlled by varying temperature. However, matching anomalies in APC systems previously have been found to exist only in a narrow temperature range very close to the transition temperature Tc ; at lower temperatures, matching anomalies were observed to be suppressed w15x. It is not fully understood why matching anomalies disappear at lower temperatures. Random pinning on interstitial pinning sites, which grows in strength with decreasing temperature, should permit the formation of metastable interstitial flux lines ŽIFL. even when H - HsŽ n s . w1,13,16,17x, and strongly irreversible motion of the IFL may then obscure matching anomalies in the magnetization. On the other hand, it was suggested w18x that the coordination of vortices to the pins might not be lost well below Tc , and instead the critical state might develop a terraced profile. In that case, since domains of matched FL have a length scale given by the magnetic penetration depth lŽT ., the number of terraces penetrating the sample increases as the temperature decreases. Magnetization anomalies, due to the formation of new terraces at the sample edge, then become small compared to the background magnetization. Alternatively, molecular dynamic simulations w19x of flux penetration into periodic pin arrays suggest that the domain walls around the terraces become zones where the FL lattice is plastically deformed. Matching then occurs only near the sample edge, whereas complex flux profiles are formed deep inside the film, and no magnetization peaks would be anticipated. In the present work, matching anomalies are reported to occur near and below 3 K, well below the
zero-field Tc f 8.8 K. The anomalies in this case are similar to flux jumps, but they are quasiperiodic in field; that is, the period of the jumps sometimes changes sharply from ; 14 Oe, to ; 28 Oe, to ; 42 Oe, as the external field is increased. The values of the observed periods are remarkably close to those for the first-through-third matching fields detected w10,12,20x very close to Tc . This indicates that the observed periodicity is an unexpected result of field matching at anomalously low temperatures.
2. Experimental and discussion An Ni dot lattice of spacing 1.2 mm was patterned by electron beam lithography Žwith PMMA photoresist. using a block size of 90 = 90 mm2 , with an overall film area of 1 = 1 mm2 . Nickel was then deposited by electron beam evaporation followed by lift-off in acetone. No effort was made to remove any oxide barrier on the Ni dots prior to Nb deposition. The resulting samples consist of square lattices of Ni dots Ž120 nm diameter by 110 nm tall. covered by a film of Nb of 95 nm thickness, such that the Ni dots completely perforate the Nb layer. The superconducting transition temperature was Tc s 8.8 K in zero magnetic field for all samples, with and without Ni dots, which implies that there was no macroscopic reduction of Tc due to magnetic depairing or proximity effects. More detailed descriptions of the fabrication of sample films and their magnetic and electrical properties were given elsewhere w10,12,20x. DC magnetization and AC magnetic susceptibility measurements were done using a Quantum Design MPMS5 SQUID Magnetometer. In this paper, we present results for demagnetized Ni dots with the external magnetic field aligned perpendicular to the plane of the film. Demagnetization of dots was accomplished by oscillating the field of the superconducting magnet with a gradual decrease of field amplitude, starting at 1 T, while the sample was held at room temperature. In several experiments, the sample was taken out of the magnetometer and warmed up to 1008C after field cycling for better demagnetization. The superconducting magnet was then reset Žquenched to eliminate trapped flux. while the sample was held out of the magnetometer. After demagnetization, the sample was cooled in zero-field
A. TerentieÕ et al.r Physica C 332 (2000) 5–11
and isothermal field dependencies of DC magnetization were taken at several temperatures. Additional magnetization measurements were conducted using a 1 T electromagnet fitted with a cryostat insert that accommodated a Hall-probe ŽHP. sensor so that sample motion in the applied magnetic field was eliminated. The applied magnetic field was measured by a separate HP; by calibrating the sample HP voltage vs. field at 77 and at 4 K with an empty sample holder Žthe temperature variation of the sample HP was less than 0.01%., most of the signal due to the applied field could be nulled out. Thus, the magnetization M s Ž4p .y1 Ž B y H . s Žsample HP voltage. = Žcalibration constant. y Žmagnet HP reading.. The sample HP had an active area of about 10 mm2 and was mounted in the center of a round rod that fit snugly into a hole in the sample holder. The sample was mounted on a second rod of equal diameter and carefully inserted into the same hole until the film surface contacted the HP substrate. Both rods contained a millimeter-size notch to admit helium liquid into the sample space. Separate calibration runs showed that the measured magnetization was about 10% of the expected value due to the 0.3-mm separation Žthickness of the HP substrate. between the HP and the sample. The polarity of the magnet was not reversible; all runs should be considered as typical of a fully penetrated sample subsequently returned from high field. Initial DC magnetic measurements using the SQUID magnetometer were performed on patterned and unpatterned Ži.e., without dot lattice. Nb films at a temperature of 8.7 K, as shown in Fig. 1a. Matching anomalies were observed at the first Ž H1 ; 13 Oe., second Ž H2 ; 26 Oe., and third Ž H3 ; 39 Oe. matching fields for the perforated film Žsee Fig. 1a.. These matching anomalies previously were found w10,12x to be strongly asymmetric with respect to a reversal of the applied magnetic field with respect to the direction of polarized Ni moments. The magnetization curve shown in Fig. 1a is essentially symmetric and consistent with a very low remanent magnetization of Ni dots in demagnetized samples. The magnetization data for the unpatterned film at 8.7 K are smooth, and the hysteresis width for unperforated films is lower than that of patterned films at low fields, indicating that Ni dots act to enhance FL pinning in the matching regime H F H3 ,
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Fig. 1. Ža. Magnetization curves for the perforated Nb film and for an unperforated Nb film at a temperature of 8.7 K ŽTc s8.8 K.. First and second matching fields of ;13 and 26 Oe are clearly seen, as well as a weak matching field near 39 Oe. Žb. Magnetization curves for a perforated film and an unperforated Nb film taken at a temperature of 8.5 K. Matching anomalies are not well-defined in these data.
but exhibit no significant enhancement of magnetic hysteresis at higher fields. Matching anomalies have been observed in a number of systems with APC only when the temperature is held very near to Tc w5–13x; as the temperature is reduced, the matching features become less pronounced w15x. A similar effect is apparent in Fig. 1b, which shows that by 8.5 K, the matching anomalies are almost completely smeared out. Further decrease of the temperature below 8.3 K caused the magnetization curve to break up into irregular, discontinuous jumps, as briefly reported elsewhere and interpreted as due to the onset thermomagnetic instabilities w12x. Moshchalkov et al. argued w21x that at temperatures close to Tc , where matching anomalies are commonly observed, only a ‘‘single-terrace state’’ is
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realized, where the fluxoid density is constant over the entire sample, except possibly in a thin surface layer. On the other hand, a substantial field gradient across a sample is required for the development of a true terraced critical state. The critical current and the field gradient increase as the temperature decreases, but it seems apparent that as the tendency toward formation of the Bean critical state becomes stronger, large-scale terraces are destroyed by strong random pinning and instabilities w12,21x, which consistent with our observations in the temperature range below 8.5 K. The unexpected and primary result of this study is shown in Fig. 2. At the lowest experimental temperature of ; 2.5 K, the magnetization curve underwent a remarkable change; the magnetization jumps became more regular and some segments of the curve exhibited a ‘‘quasiperiodic’’ saw-tooth structure, which is emphasized in Fig. 3. Moreover, the sawtooth oscillations first exhibited a 14–15 Oe period at fields above ; 70 Oe f 5H1 , then as the field passed 140 Oe f 5H2 , the period abruptly switched to ; 27–29 Oe, followed by another switch to ; 41 Oe as the field crossed 205 Oe f 5H3 . These periods approximate the first-through-third matching fields obtained at high temperatures Žsee Fig. 1a.. There is a sudden ‘‘turn-off’’ of the quasiperiodic instabilities above a reproducible field Hf f 800 Oe at T s 3 K, as shown in Fig. 4; lower-level flux noise persists above this field, but without any periodic structure. Unperforated Nb films having similar area and thickness Žand therefore similar magnetization and critical
Fig. 2. Development of a saw-tooth structure in the magnetization curve of a perforated film at a temperature of 2.5 K.
Fig. 3. Expanded view of the magnetization curve of Fig. 2, exhibiting pronounced periodicity with period switching from ;14 Oe at fields below 140 Oe, to ; 28 Oe period at higher fields. The ; 42 Oe period observed at 200 Oe corresponds to the third matching field.
current densities. to the patterned samples also exhibited instabilities at 2.5 K only on field-decreasing branches of the magnetization loops close to zerofield, and they did not exhibit any field periodicity, as shown in Fig. 5. These observations strongly
Fig. 4. DC magnetic moment vs. applied magnetic field for a patterned Nb film at a temperature T s 3.0 K. Note the abrupt turnoff of the quasiperiodic magnetization instabilities at Hf f800 Oe.
A. TerentieÕ et al.r Physica C 332 (2000) 5–11
Fig. 5. DC magnetic moment vs. applied magnetic field for an unpatterned Nb film held at a temperature of 2.5 K. Note the narrow interval of unstable magnetization as the last flux exits the film.
suggest that the Ni dot lattice exerts a crucial influence on the appearance and nature of the instabilities. The HP magnetometer data confirmed the general features of the SQUID experiments. Magnetization instabilities were observed in field sweeps from approximately 15–160 Oe Žascending. and 210–0 Oe Ždescending. at 4.2 K. The hysteresis width D H f aJc is about 5 Oe, in agreement with the loop turnaround field Ž50 Oe. and the HP loss factor Ž10%.. A value of critical current density Jc f 10 9 – 10 10 Arm2 was estimated from the turnaround field Žtaking into account the strong demagnetization factor f 10 3 –10 4 of the fieldrfilm geometry. and the sample width a f 1 mm, and is in agreement with the DC SQUID data. Lower temperature HP data were obtained by pumping on liquid helium in which the sample holder was immersed. The HP data shown in Fig. 6 were obtained while slowly cooling over the range 3.0–2.9 K, and are in qualitative agreement with the DC SQUID results in Figs. 3 and 4. Although there is no reproducibility of the magnetization jumps at a given applied magnetic field, there seems to be a roughly consistent field separation between successive jumps that may reflect a periodic buildup in the screening current density D J A D M s Mmax y Mmin , the discontinuity in magnetization at the jumps. The sample exhibits frequent small jumps at low fields Ž- 120 Oe., then the jumps become larger and less frequent as better thermomagnetic stability sets in at higher
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fields Ži.e., lower Jc .. It is interesting that even the largest jumps are partial; M does not fall to zero. Standard stability arguments w22x predict stable flux fronts for m 0 Jc2 a 2rr C ŽTc y T . - 3, assuming that Jc has a linear temperature dependence, where r is the density Ž8550 kgrm3 for Nb., and C is the specific heat Žabout 0.8 Jrkg K.. Inserting Jc s 10 9 Arm2 yields the condition a - 0.3 mm Žclose to the actual sample size. for adiabatic stability. The reproducible shutoff field Hf , above which quasiperiodic flux jumps cease to occur, is observed to increase with decreasing temperature Že.g., Hf f 200 Oe at T s 4.0 K; 230 Oe at 3.5 K; 800 Oe at 3.0 K., and further indicates thermomagnetic instabilities initiate the magnetization jumps. The saw-tooth structure of the magnetization curve for Nb films perforated with Ni dots is qualitatively very similar to the metastable flux distributions predicted for a multi-terrace critical state by Cooley and Grishin w18x. A 14–15 Oe period of oscillation is observed clearly over limited field ranges at T s 2.5 K Že.g., between 80 and 140 Oe, and between y250 and y190 Oe in Fig. 3.. A period near 14 Oe is in an excellent agreement with the calculated first matching field of H1 s 14.4 Oe for a square lattice of APC with our spacing of 1.2 mm, and in agreement with our observations at 8.7 K Žsee Fig. 1.. The magnetization has a clear saw-tooth shape with an abrupt collapse of magnetization Žsee Fig. 4., and between the instabilities, the magnetization exhibits a slope quite similar to the one seen in the initial ramp
Fig. 6. Magnetization ŽHP data. vs. applied magnetic field for a patterned film held at a temperature between 2.9 and 3.0 K. ŽAn ; 40 G instrumental offset should be subtracted to recover the true film magnetization..
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away from zero-field in the diamagnetic state, indicating that the anomalies reflect unstable currents circulating near the film edge. The observed features lead us to conclude that we have observed the first evidence of a multi-terrace critical state, albeit modified by considerable disorder and thermomagnetic instabilities. The observation of quasiperiodic oscillations of magnetization in a field much above the saturation matching field Hs f 42 Oe is an unexpected result. Recall that at high temperatures near Tc f 8.8 K, the film under study exhibits single-terrace matching effects only for applied fields below ; 42 Oe. On the other hand, at temperatures near and below 3 K, quasiperiodic jump instabilities are observed at applied fields as high as ; 1200 Oe, which is well above both the first matching field H1 s 14 G and the saturation field HsŽ n s f 3., as verified at high temperature w10,12x. It is extremely unlikely that single-terrace matching can be observed when the total number of vortices exceeds the number of the periodic pins by factors of 20–100 and the overall pinning contributed by the Ni dots is rather weak w13x. Alternatively, the FL density is probably very non-uniform due to the relatively strong pinning developed in the interstices between the APC at low temperatures. It is also unlikely that the anomalies are related to a conventional lack of adiabatic stability of the film, since a duplicate Nb film with no artificial pins and the same magnetization was relatively stable Žsee Fig. 5..
3. Conclusion Taking these observations into account, we postulate that strong magnetization anomalies exhibiting Žlow-field. matching periodicities reflect magnetization processes in edge regions of the film that experience local magnetic fields on the order of the lowest matching fields Hn Ž n s 1,2,3.. This conjecture can be supported by special features of perpendicular field penetration into thin slabs or films w23–25x. In a recent study, Zeldov et al. w23x have reported a geometrical barrier that leads to an altered depth profile for the external field and Meissner current present in thin slabs. The Lorentz force between the FL and Meissner current results in a concentration of
FL in the center of the sample Ž‘‘flux compression effect’’., and the flux profile tapers steeply into a ‘‘flux-free region’’ near the sample edge w24x. Thus, it is expected that, depending upon the external field level and temperature, the local magnetic field B L in the ‘‘flux-free region’’ will be much lower than the external magnetic field or the average field in the compression region, and conditions for appearance of matching effects Ži.e., BL - m 0 Hs . can be favorable near the two edges of the flux-free region. Therefore, both steep macroscopic flux gradients and flux densities that are close to matching values can exist near the edge region, and it is plausible that the flux profile has uniform terraces which consist solely of strongly pinned fluxoids Ži.e., no IFL. at the sample edge. The matching anomalies then arise due to the competition between the steep flux gradient and these matched domains. We speculate that the vortices pile up in roughly terraced domains in the edge area until the saturation number is achieved, then the pinning is greatly reduced and the flux distribution abruptly rearranges with a heat release, which leads to the partial collapse of the magnetization observed. This interpretation suggests that the geometrical barrier remains important at all temperatures, and must be considered in developing an understanding of the magnetic behavior of patterned superconducting films. Acknowledgements Research at the University of Kentucky was supported by the U.S. Dept. Energy Office of Basic Energy Science, Division of Materials Science, Grant aDE-FG02-97ER45653. Research at Northwestern University was supported by the National Science Foundation under the Materials Research Center Grant aDMR-9309061. Research at the University of Wisconsin was supported by the U.S. Dept. Energy Division of High-Energy Physics, Grant aDEFG02-96ER40961 and the NSF MRSEC for Nanostructured Materials. References w1x K. Harada, O. Kamimura, H. Kasai, F. Matsuda, A. Tonomura, V.V. Moshchalkov, Science 274 Ž1996. 1167. w2x P. Martinoli, Phys. Rev. 17 Ž1978. 1175.
A. TerentieÕ et al.r Physica C 332 (2000) 5–11 w3x P. Martinoli, M. Nsabimana, G.A. Racine, H. Beck, J.R. Clem, Helv. Phys. Acta 55 Ž1982. 655. w4x A.T. Hebard, A.T. Fiory, S. Somekh, IEEE Trans. Magn. 13 Ž1977. 589. w5 x V.V. Metlushko, M. Baert, R. Jonckheere, V.V. Moshchalkov, Y. Bruynseraede, Solid State Commun. 91 Ž1994. 331. w6x M. Baert, V.V. Metlushko, R. Jonckheere, V.V. Moshchalkov, Y. Bruynseraede, Phys. Rev. Lett. 74 Ž1995. 3269. w7x M. Baert, V.V. Metlushko, R. Jonckheere, V.V. Moshchalkov, Y. Bruynseraede, Europhys. Lett. 29 Ž2. Ž1995. 157. w8x Y. Bruynseraede, V.V. Metlushko, K. Temst, M. Baert, E. Rosseel, M.J. Van Bael, V.V. Moshchalkov, Proc. SPIESoc. Opt. Eng. 2697 Ž1996. 328. w9x Y. Jaccard, J.I. Martin, M.C. Cyrille, M. Velez, J.L. Vicent, I.K. Schuller, Phys. Rev. B 58 Ž1998. 8232. w10x D.J. Morgan, J.B. Ketterson, Phys. Rev. Lett. 80 Ž1998. 3614. w11x J.I. Martin, M. Velez, J. Nogues, I.K. Schuller, Phys. Rev. Lett. 79 Ž1997. 1929. w12x A. Terentiev, D.B. Watkins, L.E. De Long, D.J. Morgan, J.B. Ketterson, Physica C 324 Ž1999. 1. w13x V.V. Metlushko, L.E. De Long, M. Baert, E. Rosseel, M.J. Van Bael, K. Temst, V.V. Moshchalkov, Y. Bruynseraede, Europhys. Lett. 41 Ž1998. 333.
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w14x J.E. Nordman, Supercond. Sci. Technol. 8 Ž1995. 681. w15x V.V. Moshchalkov, L. Gielen, M. Baert, V. Metlushko, G. Neuttiens, C. Strunk, V. Bruydoncx, X. Qiu, M. Dhalle, K. Temst, C. Potter, R. Jonckheere, L. Stockman, M. Van Bael, C. Van Haesendonck, Y. Bruynseraede, Physica Scripta T55 Ž1994. 168. w16x I.B. Khalfin, B.Ya. Shapiro, Physica C 207 Ž1993. 359. w17x I.K. Marmorkos, A. Matulis, F.M. Peeters, Phys. Rev. B 53 Ž1996. 2677. w18x L.D. Cooley, A.M. Grishin, Phys. Rev. Lett. 74 Ž1995. 2788. w19x C. Reichhardt, J. Groth, C.J. Olson, S.B. Field, F. Nori, Phys. Rev. B 54 Ž1996. 16108. w20x D.J. Morgan, PhD Thesis, Northwestern University, 1998 Žunpublished.. w21x V.V. Moshchalkov, M. Baert, V.V. Metlushko, E. Rosseel, M.J. Van Bael, K. Temst, Y. Bruynseraede, R. Jonckheere, Phys. Rev. B 57 Ž1998. 3615. w22x Wilson, in: Superconducting Magnets, New York, Oxford Univ. Press, 1983, chapt. 7, pp. 131–158. w23x E. Zeldov, A.I. Larkin, V.B. Geshkenbein, M. Konczykowski, D. Majer, B. Khaykovich, V.M. Vinokur, H. Shrtrikman, Phys. Rev. Lett. 73 Ž1994. 1428. w24x M. Benkraouda, J.R. Clem, Phys. Rev. B 53 Ž1996. 5716. w25x M. Benkraouda, J.R. Clem, Phys. Rev. B 58 Ž1998. 15103.
Periodic magnetization instabilities in a superconducting Nb film with a square lattice of Ni dots A. Terentiev a , B. Watkins a , L.E. De Long a,) , L.D. Cooley b, D.J. Morgan c , J.B. Ketterson c a
Department of Physics and Astronomy, UniÕersity of Kentucky, CP 177, Lexington, KY 40506-0055, USA b Applied SuperconductiÕity Center, UniÕersity of Wisconsin, Madison, WI 53706-1687, USA c Department of Physics and Astronomy, Northwestern UniÕersity, EÕanston, IL 60208, USA
Abstract Isothermal magnetization curves of a superconducting Nb film perforated by a square lattice of Ni dots exhibit quasiperiodic instabilities below ; 4 K, with a field-dependent period equal to the first, second, or third matching fields. The instabilities are found in a range of applied fields well above the saturation matching value, and where a Nb film with the same dimensions and magnetization remained stable. The recovery of matching effects well below Tc ; 8.8 K is unexpected, because strong flux gradients generated by the geometric barrier and random pinning suppress the formation of large domains of matched flux lines and dots. The results suggest that terraces of matched flux density may exist at the border of a flux-free zone near the film edge. q 2000 Elsevier Science B.V. All rights reserved. PACS: 74.60.Ge; 74.60.Jg; 74.80.Dm; 75.70.Cn; 73.50.Jt Keywords: Periodic magnetization; Ni dots; Thermomagnetic instabilities
1. Introduction Thin film superconductors patterned with lattices of artificial pinning centers ŽAPC. exhibit a variety of interesting mesoscopic and quantum phenomena w1–4x. Lattices of antidots Žholes. w4–8x, or dots of normal w9x or magnetic w9–12x metals induce unique modifications of various physical properties that provide novel opportunities to precisely control flux pinning and flow, as desired in practical applications of superconducting films. )
Corresponding author. Fax: q1-606-323-2846. E-mail address: [email protected] ŽL.E. De Long..
In particular, magnetization and electrical resistivity data for patterned films exhibit ‘‘matching anomalies’’ at specific values of applied perpendicular field Hn , for which the number of flux lines ŽFL. is an integral multiple n of the number of APC w2–8x. Higher order Ž n ) 1. matching anomalies, corresponding to multiply quantized fluxoids resident at each APC, occur if the APC diameter D is large on the scale of the coherence length j . Close to Tc and at intermediate applied fields Hn - H Hnq 1 , the system of FL consists of a spatial mixture of fluxoids Ž nF 0 or w n q 1xF 0 . strongly localized at the APC. The magnetization curve M Ž H . is then similar to the logarithmic flux penetration above the
0921-4534r00r$ - see front matter q 2000 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 3 4 Ž 9 9 . 0 0 6 3 6 - X
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A. TerentieÕ et al.r Physica C 332 (2000) 5–11
lower critical field; however, irreversible hopping of singly quantized FL produces strong magnetic hysteresis and substantially enhanced critical current densities compared to unpatterned films w5–8x. When the number of flux quanta trapped by each APC reaches a saturation number n s , additional FL penetrating the film will be repelled into the interstitial region between the APC, where the much weaker pinning potential of random defects within the interstices leads to a sharp transition to high flux–flow rates and greatly reduced magnetization hysteresis w5–8,13x, a behavior desired for flux–flow device applications w14x. The saturation number n s s Dr4j ŽT . Žand therefore the overall pinning strength of the film. can be controlled by varying temperature. However, matching anomalies in APC systems previously have been found to exist only in a narrow temperature range very close to the transition temperature Tc ; at lower temperatures, matching anomalies were observed to be suppressed w15x. It is not fully understood why matching anomalies disappear at lower temperatures. Random pinning on interstitial pinning sites, which grows in strength with decreasing temperature, should permit the formation of metastable interstitial flux lines ŽIFL. even when H - HsŽ n s . w1,13,16,17x, and strongly irreversible motion of the IFL may then obscure matching anomalies in the magnetization. On the other hand, it was suggested w18x that the coordination of vortices to the pins might not be lost well below Tc , and instead the critical state might develop a terraced profile. In that case, since domains of matched FL have a length scale given by the magnetic penetration depth lŽT ., the number of terraces penetrating the sample increases as the temperature decreases. Magnetization anomalies, due to the formation of new terraces at the sample edge, then become small compared to the background magnetization. Alternatively, molecular dynamic simulations w19x of flux penetration into periodic pin arrays suggest that the domain walls around the terraces become zones where the FL lattice is plastically deformed. Matching then occurs only near the sample edge, whereas complex flux profiles are formed deep inside the film, and no magnetization peaks would be anticipated. In the present work, matching anomalies are reported to occur near and below 3 K, well below the
zero-field Tc f 8.8 K. The anomalies in this case are similar to flux jumps, but they are quasiperiodic in field; that is, the period of the jumps sometimes changes sharply from ; 14 Oe, to ; 28 Oe, to ; 42 Oe, as the external field is increased. The values of the observed periods are remarkably close to those for the first-through-third matching fields detected w10,12,20x very close to Tc . This indicates that the observed periodicity is an unexpected result of field matching at anomalously low temperatures.
2. Experimental and discussion An Ni dot lattice of spacing 1.2 mm was patterned by electron beam lithography Žwith PMMA photoresist. using a block size of 90 = 90 mm2 , with an overall film area of 1 = 1 mm2 . Nickel was then deposited by electron beam evaporation followed by lift-off in acetone. No effort was made to remove any oxide barrier on the Ni dots prior to Nb deposition. The resulting samples consist of square lattices of Ni dots Ž120 nm diameter by 110 nm tall. covered by a film of Nb of 95 nm thickness, such that the Ni dots completely perforate the Nb layer. The superconducting transition temperature was Tc s 8.8 K in zero magnetic field for all samples, with and without Ni dots, which implies that there was no macroscopic reduction of Tc due to magnetic depairing or proximity effects. More detailed descriptions of the fabrication of sample films and their magnetic and electrical properties were given elsewhere w10,12,20x. DC magnetization and AC magnetic susceptibility measurements were done using a Quantum Design MPMS5 SQUID Magnetometer. In this paper, we present results for demagnetized Ni dots with the external magnetic field aligned perpendicular to the plane of the film. Demagnetization of dots was accomplished by oscillating the field of the superconducting magnet with a gradual decrease of field amplitude, starting at 1 T, while the sample was held at room temperature. In several experiments, the sample was taken out of the magnetometer and warmed up to 1008C after field cycling for better demagnetization. The superconducting magnet was then reset Žquenched to eliminate trapped flux. while the sample was held out of the magnetometer. After demagnetization, the sample was cooled in zero-field
A. TerentieÕ et al.r Physica C 332 (2000) 5–11
and isothermal field dependencies of DC magnetization were taken at several temperatures. Additional magnetization measurements were conducted using a 1 T electromagnet fitted with a cryostat insert that accommodated a Hall-probe ŽHP. sensor so that sample motion in the applied magnetic field was eliminated. The applied magnetic field was measured by a separate HP; by calibrating the sample HP voltage vs. field at 77 and at 4 K with an empty sample holder Žthe temperature variation of the sample HP was less than 0.01%., most of the signal due to the applied field could be nulled out. Thus, the magnetization M s Ž4p .y1 Ž B y H . s Žsample HP voltage. = Žcalibration constant. y Žmagnet HP reading.. The sample HP had an active area of about 10 mm2 and was mounted in the center of a round rod that fit snugly into a hole in the sample holder. The sample was mounted on a second rod of equal diameter and carefully inserted into the same hole until the film surface contacted the HP substrate. Both rods contained a millimeter-size notch to admit helium liquid into the sample space. Separate calibration runs showed that the measured magnetization was about 10% of the expected value due to the 0.3-mm separation Žthickness of the HP substrate. between the HP and the sample. The polarity of the magnet was not reversible; all runs should be considered as typical of a fully penetrated sample subsequently returned from high field. Initial DC magnetic measurements using the SQUID magnetometer were performed on patterned and unpatterned Ži.e., without dot lattice. Nb films at a temperature of 8.7 K, as shown in Fig. 1a. Matching anomalies were observed at the first Ž H1 ; 13 Oe., second Ž H2 ; 26 Oe., and third Ž H3 ; 39 Oe. matching fields for the perforated film Žsee Fig. 1a.. These matching anomalies previously were found w10,12x to be strongly asymmetric with respect to a reversal of the applied magnetic field with respect to the direction of polarized Ni moments. The magnetization curve shown in Fig. 1a is essentially symmetric and consistent with a very low remanent magnetization of Ni dots in demagnetized samples. The magnetization data for the unpatterned film at 8.7 K are smooth, and the hysteresis width for unperforated films is lower than that of patterned films at low fields, indicating that Ni dots act to enhance FL pinning in the matching regime H F H3 ,
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Fig. 1. Ža. Magnetization curves for the perforated Nb film and for an unperforated Nb film at a temperature of 8.7 K ŽTc s8.8 K.. First and second matching fields of ;13 and 26 Oe are clearly seen, as well as a weak matching field near 39 Oe. Žb. Magnetization curves for a perforated film and an unperforated Nb film taken at a temperature of 8.5 K. Matching anomalies are not well-defined in these data.
but exhibit no significant enhancement of magnetic hysteresis at higher fields. Matching anomalies have been observed in a number of systems with APC only when the temperature is held very near to Tc w5–13x; as the temperature is reduced, the matching features become less pronounced w15x. A similar effect is apparent in Fig. 1b, which shows that by 8.5 K, the matching anomalies are almost completely smeared out. Further decrease of the temperature below 8.3 K caused the magnetization curve to break up into irregular, discontinuous jumps, as briefly reported elsewhere and interpreted as due to the onset thermomagnetic instabilities w12x. Moshchalkov et al. argued w21x that at temperatures close to Tc , where matching anomalies are commonly observed, only a ‘‘single-terrace state’’ is
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realized, where the fluxoid density is constant over the entire sample, except possibly in a thin surface layer. On the other hand, a substantial field gradient across a sample is required for the development of a true terraced critical state. The critical current and the field gradient increase as the temperature decreases, but it seems apparent that as the tendency toward formation of the Bean critical state becomes stronger, large-scale terraces are destroyed by strong random pinning and instabilities w12,21x, which consistent with our observations in the temperature range below 8.5 K. The unexpected and primary result of this study is shown in Fig. 2. At the lowest experimental temperature of ; 2.5 K, the magnetization curve underwent a remarkable change; the magnetization jumps became more regular and some segments of the curve exhibited a ‘‘quasiperiodic’’ saw-tooth structure, which is emphasized in Fig. 3. Moreover, the sawtooth oscillations first exhibited a 14–15 Oe period at fields above ; 70 Oe f 5H1 , then as the field passed 140 Oe f 5H2 , the period abruptly switched to ; 27–29 Oe, followed by another switch to ; 41 Oe as the field crossed 205 Oe f 5H3 . These periods approximate the first-through-third matching fields obtained at high temperatures Žsee Fig. 1a.. There is a sudden ‘‘turn-off’’ of the quasiperiodic instabilities above a reproducible field Hf f 800 Oe at T s 3 K, as shown in Fig. 4; lower-level flux noise persists above this field, but without any periodic structure. Unperforated Nb films having similar area and thickness Žand therefore similar magnetization and critical
Fig. 2. Development of a saw-tooth structure in the magnetization curve of a perforated film at a temperature of 2.5 K.
Fig. 3. Expanded view of the magnetization curve of Fig. 2, exhibiting pronounced periodicity with period switching from ;14 Oe at fields below 140 Oe, to ; 28 Oe period at higher fields. The ; 42 Oe period observed at 200 Oe corresponds to the third matching field.
current densities. to the patterned samples also exhibited instabilities at 2.5 K only on field-decreasing branches of the magnetization loops close to zerofield, and they did not exhibit any field periodicity, as shown in Fig. 5. These observations strongly
Fig. 4. DC magnetic moment vs. applied magnetic field for a patterned Nb film at a temperature T s 3.0 K. Note the abrupt turnoff of the quasiperiodic magnetization instabilities at Hf f800 Oe.
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Fig. 5. DC magnetic moment vs. applied magnetic field for an unpatterned Nb film held at a temperature of 2.5 K. Note the narrow interval of unstable magnetization as the last flux exits the film.
suggest that the Ni dot lattice exerts a crucial influence on the appearance and nature of the instabilities. The HP magnetometer data confirmed the general features of the SQUID experiments. Magnetization instabilities were observed in field sweeps from approximately 15–160 Oe Žascending. and 210–0 Oe Ždescending. at 4.2 K. The hysteresis width D H f aJc is about 5 Oe, in agreement with the loop turnaround field Ž50 Oe. and the HP loss factor Ž10%.. A value of critical current density Jc f 10 9 – 10 10 Arm2 was estimated from the turnaround field Žtaking into account the strong demagnetization factor f 10 3 –10 4 of the fieldrfilm geometry. and the sample width a f 1 mm, and is in agreement with the DC SQUID data. Lower temperature HP data were obtained by pumping on liquid helium in which the sample holder was immersed. The HP data shown in Fig. 6 were obtained while slowly cooling over the range 3.0–2.9 K, and are in qualitative agreement with the DC SQUID results in Figs. 3 and 4. Although there is no reproducibility of the magnetization jumps at a given applied magnetic field, there seems to be a roughly consistent field separation between successive jumps that may reflect a periodic buildup in the screening current density D J A D M s Mmax y Mmin , the discontinuity in magnetization at the jumps. The sample exhibits frequent small jumps at low fields Ž- 120 Oe., then the jumps become larger and less frequent as better thermomagnetic stability sets in at higher
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fields Ži.e., lower Jc .. It is interesting that even the largest jumps are partial; M does not fall to zero. Standard stability arguments w22x predict stable flux fronts for m 0 Jc2 a 2rr C ŽTc y T . - 3, assuming that Jc has a linear temperature dependence, where r is the density Ž8550 kgrm3 for Nb., and C is the specific heat Žabout 0.8 Jrkg K.. Inserting Jc s 10 9 Arm2 yields the condition a - 0.3 mm Žclose to the actual sample size. for adiabatic stability. The reproducible shutoff field Hf , above which quasiperiodic flux jumps cease to occur, is observed to increase with decreasing temperature Že.g., Hf f 200 Oe at T s 4.0 K; 230 Oe at 3.5 K; 800 Oe at 3.0 K., and further indicates thermomagnetic instabilities initiate the magnetization jumps. The saw-tooth structure of the magnetization curve for Nb films perforated with Ni dots is qualitatively very similar to the metastable flux distributions predicted for a multi-terrace critical state by Cooley and Grishin w18x. A 14–15 Oe period of oscillation is observed clearly over limited field ranges at T s 2.5 K Že.g., between 80 and 140 Oe, and between y250 and y190 Oe in Fig. 3.. A period near 14 Oe is in an excellent agreement with the calculated first matching field of H1 s 14.4 Oe for a square lattice of APC with our spacing of 1.2 mm, and in agreement with our observations at 8.7 K Žsee Fig. 1.. The magnetization has a clear saw-tooth shape with an abrupt collapse of magnetization Žsee Fig. 4., and between the instabilities, the magnetization exhibits a slope quite similar to the one seen in the initial ramp
Fig. 6. Magnetization ŽHP data. vs. applied magnetic field for a patterned film held at a temperature between 2.9 and 3.0 K. ŽAn ; 40 G instrumental offset should be subtracted to recover the true film magnetization..
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away from zero-field in the diamagnetic state, indicating that the anomalies reflect unstable currents circulating near the film edge. The observed features lead us to conclude that we have observed the first evidence of a multi-terrace critical state, albeit modified by considerable disorder and thermomagnetic instabilities. The observation of quasiperiodic oscillations of magnetization in a field much above the saturation matching field Hs f 42 Oe is an unexpected result. Recall that at high temperatures near Tc f 8.8 K, the film under study exhibits single-terrace matching effects only for applied fields below ; 42 Oe. On the other hand, at temperatures near and below 3 K, quasiperiodic jump instabilities are observed at applied fields as high as ; 1200 Oe, which is well above both the first matching field H1 s 14 G and the saturation field HsŽ n s f 3., as verified at high temperature w10,12x. It is extremely unlikely that single-terrace matching can be observed when the total number of vortices exceeds the number of the periodic pins by factors of 20–100 and the overall pinning contributed by the Ni dots is rather weak w13x. Alternatively, the FL density is probably very non-uniform due to the relatively strong pinning developed in the interstices between the APC at low temperatures. It is also unlikely that the anomalies are related to a conventional lack of adiabatic stability of the film, since a duplicate Nb film with no artificial pins and the same magnetization was relatively stable Žsee Fig. 5..
3. Conclusion Taking these observations into account, we postulate that strong magnetization anomalies exhibiting Žlow-field. matching periodicities reflect magnetization processes in edge regions of the film that experience local magnetic fields on the order of the lowest matching fields Hn Ž n s 1,2,3.. This conjecture can be supported by special features of perpendicular field penetration into thin slabs or films w23–25x. In a recent study, Zeldov et al. w23x have reported a geometrical barrier that leads to an altered depth profile for the external field and Meissner current present in thin slabs. The Lorentz force between the FL and Meissner current results in a concentration of
FL in the center of the sample Ž‘‘flux compression effect’’., and the flux profile tapers steeply into a ‘‘flux-free region’’ near the sample edge w24x. Thus, it is expected that, depending upon the external field level and temperature, the local magnetic field B L in the ‘‘flux-free region’’ will be much lower than the external magnetic field or the average field in the compression region, and conditions for appearance of matching effects Ži.e., BL - m 0 Hs . can be favorable near the two edges of the flux-free region. Therefore, both steep macroscopic flux gradients and flux densities that are close to matching values can exist near the edge region, and it is plausible that the flux profile has uniform terraces which consist solely of strongly pinned fluxoids Ži.e., no IFL. at the sample edge. The matching anomalies then arise due to the competition between the steep flux gradient and these matched domains. We speculate that the vortices pile up in roughly terraced domains in the edge area until the saturation number is achieved, then the pinning is greatly reduced and the flux distribution abruptly rearranges with a heat release, which leads to the partial collapse of the magnetization observed. This interpretation suggests that the geometrical barrier remains important at all temperatures, and must be considered in developing an understanding of the magnetic behavior of patterned superconducting films. Acknowledgements Research at the University of Kentucky was supported by the U.S. Dept. Energy Office of Basic Energy Science, Division of Materials Science, Grant aDE-FG02-97ER45653. Research at Northwestern University was supported by the National Science Foundation under the Materials Research Center Grant aDMR-9309061. Research at the University of Wisconsin was supported by the U.S. Dept. Energy Division of High-Energy Physics, Grant aDEFG02-96ER40961 and the NSF MRSEC for Nanostructured Materials. References w1x K. Harada, O. Kamimura, H. Kasai, F. Matsuda, A. Tonomura, V.V. Moshchalkov, Science 274 Ž1996. 1167. w2x P. Martinoli, Phys. Rev. 17 Ž1978. 1175.
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w14x J.E. Nordman, Supercond. Sci. Technol. 8 Ž1995. 681. w15x V.V. Moshchalkov, L. Gielen, M. Baert, V. Metlushko, G. Neuttiens, C. Strunk, V. Bruydoncx, X. Qiu, M. Dhalle, K. Temst, C. Potter, R. Jonckheere, L. Stockman, M. Van Bael, C. Van Haesendonck, Y. Bruynseraede, Physica Scripta T55 Ž1994. 168. w16x I.B. Khalfin, B.Ya. Shapiro, Physica C 207 Ž1993. 359. w17x I.K. Marmorkos, A. Matulis, F.M. Peeters, Phys. Rev. B 53 Ž1996. 2677. w18x L.D. Cooley, A.M. Grishin, Phys. Rev. Lett. 74 Ž1995. 2788. w19x C. Reichhardt, J. Groth, C.J. Olson, S.B. Field, F. Nori, Phys. Rev. B 54 Ž1996. 16108. w20x D.J. Morgan, PhD Thesis, Northwestern University, 1998 Žunpublished.. w21x V.V. Moshchalkov, M. Baert, V.V. Metlushko, E. Rosseel, M.J. Van Bael, K. Temst, Y. Bruynseraede, R. Jonckheere, Phys. Rev. B 57 Ž1998. 3615. w22x Wilson, in: Superconducting Magnets, New York, Oxford Univ. Press, 1983, chapt. 7, pp. 131–158. w23x E. Zeldov, A.I. Larkin, V.B. Geshkenbein, M. Konczykowski, D. Majer, B. Khaykovich, V.M. Vinokur, H. Shrtrikman, Phys. Rev. Lett. 73 Ž1994. 1428. w24x M. Benkraouda, J.R. Clem, Phys. Rev. B 53 Ž1996. 5716. w25x M. Benkraouda, J.R. Clem, Phys. Rev. B 58 Ž1998. 15103.