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Physica C 362 (2001) 251±255

www.elsevier.com/locate/physc

Collective motion of Josephson vortex lattice in long stacked junction fabricated from Bi-2212 whisker
Yu.I. Latyshev
b

a,b,c

, V.N. Pavlenko

a,b,* ,

S.-J. Kim

a,c

, T. Yamashita

a,c

a Research Institute of Electrical Communication, Tohoku University, 2-1-1, Katahira, Aoba-ku, Sendai 980-8577, Japan Institute of Radio-Engineering and Electronics, Russian Academy of Sciences, 11-7 Mokhovaya str., Moscow 101999, Russia c CREST, Japan Science and Technology Corporation (JST), Kawaguchi 305-0047, Japan

Received 23 August 2000

Abstract We study the I ±V characteristics of long Bi-2212 stacked junctions in the Josephson ¯ux-¯ow regime in parallel magnetic ®eld (Bkb). We measure both voltage position of the ¯ux-¯ow step, Vff , corresponding to the maximum velocity of Josephson vortex lattice, and the ¯ux-¯ow resistivity, qff , as a function of magnetic ®eld B 0:1±4 T. We found plateau-like features of constant Vff on dependence Vff B corresponding to washboard frequencies 600 GHz and 3 THz. We discuss these features as mode locking of washboard frequency with active intrinsic modes of the stack. We found also that ®eld dependence of ¯ux-¯ow resistivity can be well described by a recent model [A. Koshelev, Phys. Rev. B 62 (2000) R3616] which takes into account both out-of-plane and in-plane dissipation. ñ 2001 Elsevier Science B.V. All rights reserved.
PACS: 74.72.Hs; 74.60.Ge Keywords: Josephson ¯ux ¯ow; Intrinsic Josephson eects; Flux ¯ow resistivity; Dynamics of Josephson vortex lattice

1. Introduction Recently a great deal of interest aroused to the studies of Josephson ¯ux ¯ow in layered high-Tc materials [1±7]. As it was pointed out in Ref. [1], the sliding of the Josephson vortex lattice can generate high-frequency electromagnetic oscillations in THz region. The oscillation frequency in that case can be tuned by magnetic ®eld or by driving current. In Ref. [2] it was proposed that the
* Corresponding author. Address: Institute of Radio-Engineering and Electronics, Russian Academy of Sciences, 11-7 Mokhovaya str., Moscow 101999, Russia. Tel.: +7-095-2034976; fax: +7-095-203-8414. E-mail address: vit@iname.com (V.N. Pavlenko).

Josephson ¯ux ¯ow can excite transverse Josephson plasma oscillations in layered superconductors. Besides, ¯ux-¯ow resistivity can serve as important instrument for studies of out of plane and in-plane quasiparticle conductivity in superconducting state of high-temperature superconductors [3]. Experimentally the Josephson ¯ux ¯ow in high-Tc materials has not been studied yet so much [4±7]. There were only few papers on that matter at low-magnetic ®elds [4±6] and even less for the case of high ®elds [7]. Furthermore Josephson ¯ux-¯ow resistivity at high ®elds has not yet been experimentally studied at all. The present studies have been addressed to the studies of Josephson ¯ux-¯ow behavior in highquality Bi-2212 layered structures emphasizing on

0921-4534/01/$ - see front matter ñ 2001 Elsevier Science B.V. All rights reserved. PII: S 0 921 -453 4(01)00 681 -5


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detailed studies of the ®eld dependencies of ¯ux¯ow resonance step and ¯ux-¯ow resistivity at low temperatures. A wide range of magnetic ®elds has been covered starting from 0.1 T and up to ®elds 4 T above which the ¯ux-¯ow features become indistinguishable on the current voltage (I ±V ) characteristics. 2. Experimental The stacked structures have been fabricated by double-sided processing of high-quality Bi-2212 whiskers by focused ion beam (FIB). The stages of fabrications were similar to ones described in Ref. [8]. Fig. 1a shows schematically the geometry and orientation of the structure with respect to the crystallographic axes. The typical structure sizes L were La 10±30 lm, Lb 1±2 lm, Lc 0:03±0:05 lm. The measurements have been carried out in commercial cryostat of Quantum Design PPMS facility. The magnetic ®eld has been oriented parallel to the b-axis within accuracy 0.2°. Field has been changed in steps of 0.1 T. In each ®xed value of the ®eld the back and forth I ±V characteristics have been measured using fast oscilloscope. 3. Results and discussion 3.1. Flux-¯ow spectroscopy Fig. 1b±c shows a set of the I ±V characteristics illustrating a development of the ¯ux-¯ow step with increase of magnetic ®eld. In zero magnetic ®eld the I ±V characteristics are typical for mesatype junctions. They exhibit hysteresis and multibranched structure, corresponding to successive transition of the elementary junctions into a resistive state. The value of Jc was within 100±400 A=cm2 . Magnetic ®eld oriented parallel to the baxis (see Fig. 1a) suppresses critical current and at the same time leads to the appearance of resistive non-hysteretic branch, the so-called ¯ux-¯ow step (Fig. 1b). The step appears as a strong enhancement of current at ®xed voltage, Vff . We de®ne Vff as a maximum voltage of non-hysteretic branch. This step is associated with a resonance when Josephson vortex lattice achieves Swihart velocity c0 ,

Fig. 1. Schematic view of the junction in experimental setup (a) and I ±V characteristics of the long (La 30 lm, Lb 1 lm) Bi2212 stacked junction in magnetic ®eld parallel to b-axis, Bk , for the 0±0.7 T (b) and 0.8±3.6 T (c) ®eld ranges. The number of elementary layers N 30, T 4:2 K. Note: the multibranched structure is not shown in (c).


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the velocity of electromagnetic ®eld propagation in layered material. For one of the simplest mode of anti-phase-neighboring layers it can be expressed as follows [1]: p c0 cs=2kab ec 1 with c the light speed in vacuum, s the spacing between elementary superconducting layers, kab the in-plane London penetration depth, ec the interlayer dielectric constant. The frequency of electromagnetic radiation, m, generated by sliding lattice at the resonance condition (washboard frequency) can then be expressed as: m c0 sB 2U0 2
Fig. 2. Schematically shown Vff B dependence expected for the system with the two resonance frequences f1 and f2 (see text).

with U0 the magnetic ¯ux quantum. By sweeping magnetic ®eld one can tune a frequency of generated electromagnetic radiation. The generated frequency can be directly found by position of the ¯ux-¯ow step via Josephson relation: m 2eVff hN 3

with N, the number of elementary layers in the stack, h, Plank constant. If the radiation generated by Josephson ¯ux-¯ow excites some active modes in the system with some particular frequency fi (like plasma frequency [2] or optical phonon modes [9]) one can expect to observe resonance features on Vff B dependence when m fi , or Vff hN fi : 2e 4

The resonance is usually accompanied by mode locking regime. Therefore one could expect to observe some plateau like features on Vff B dependence near Vff values given by relation (4) (Fig. 2). We undertook experimental search for the resonance plateaus on Vff B dependence. Fig. 3a shows experimental dependence of Vff B measured at T 4:2 K for Bi-2212 stack 30 á 1 lm2 and containing 30 elementary junctions. Generally Vff B dependence has a quasi-linear form. The plateau features, however, are clearly seen at Vff equal to 35 and 180 mV. More distinctly

Fig. 3. Flux-¯ow voltage Vff dependence on the magnetic ®eld Bkb (a); corresponding dB=dVff Vff =N dependence (b). The resonance plateau features are marked by arrows. Solid line in (b) is guide to eye.


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that is seen in the derivative picture dB=dVff Vff where the peaks corresponding to the plateau features appear. At voltage scale reduced per one junction, Vff =N , one can see a big peak at 1.2 mV and two smaller peaks at 6 and 8 mV (Fig. 3b). From Eq. (3) that corresponds to 600 GHz, 3 and 4 THz. Recently resonance peaks at 6 and 8 mV have been observed as the subgap structure on the I ±V characteristics of Bi-2212 mesas [10,11] at zero magnetic ®eld. Later they have been interpreted as the resonance of the Josephson oscillations with caxis optical phonon modes [9]. The subgap structure at 6 and 8 mV has been reproduced then in many experiments on Bi-2212 [10±12] and Bi(Pb)2212 [13] mesa structures. We can conclude that peak structure at 6 and 8mV is well reproduced in our experiment, but as resonance of ¯ux-¯ow washboard frequency with the c-axis optical phonons. A big peak at 1.2 mV in our data has not been observed in subgap structure in previous tunneling experiments on mesas at zero magnetic ®eld. It can be therefore reasonable to consider it as a result of some excitations induced speci®cally by ¯ux-¯ow motion. One mechanism most likely related to our case have been proposed by Koyama and Tachiki [2]. They consider possibility of excitation of transverse Josephson plasma by Josephson ¯ux ¯ow. The estimate of plasma frequency from that model is in reasonable agreement with experimental value 600 GHz. Alternatively this peak might be attributed to the ¯ux-¯ow resonance on acoustic phonons [9,14] which probably has not been resolved in tunneling experiments. Further experiments on the temperature dependence of this peak and on its dependence on stack material need to be done to distinguish those alternatives. Note that the change of the slope of Vff B near B 1:5 T has been observed earlier [7], but has been interpreted as a crossover from a dilute to the dense vortex lattice. 3.2. Flux-¯ow resistivity The motion of the Josephson vortex lattice induces a dissipation in the layered structure mainly due to the quasiparticle current across the layers [15]. However, as it was shown recently by Kosh-

elev [3] for strong enough ®elds B > Bcr (Bcr U0 = pcs2 with c the anisotropy of London penetration depth) the contribution of in-plane dissipation becomes dominant. Even for low ®elds the inplane dissipation was shown to contribute to the Josephson ¯ux-¯ow resistivity when rab =rc ) c2 . The expression for ¯ux-¯ow resistivity qff has been obtained for both limits of low and high ®elds [3]: qff % 4: 4c s 2 B U0 rc 0:27rab =c2 B2 q; 2 B2 c B r at B < Bcr ; r rab U0 1 p ; rc 2 pc2 s2 6 5

qff

Br

at B > Bcr :

As it can be seen from Eqs. (5) and (6) the qff B is linear at low ®elds, then becomes quadratic and ®nally saturates to the value qc at ®elds higher than Br . Eqs. (5) and (6) provide the possibility to extract rab =rc and c from the measurements of ¯ux-¯ow resistance. Experimentally ¯ux-¯ow resistance has been measured only at low ®elds [4]. To verify the theoretical predictions [3] we have carried out measurements of the ¯ux-¯ow resistivity in Bi-2212 long stacked junctions in both limits of low and high ®elds. The ¯ux-¯ow resistance has been extracted from the experimental I ±V characteristics by the extrapolation of linear part of the ¯ux-¯ow step to the zero voltage bias. The most part of experiments has been carried out at liquid helium temperature. The results of our measurements are shown in Fig. 4. The data are ®tted well to Eq. (6) (solid line) with Br 1:85 T, rc 1:3 á 10þ3 Xþ1 cmþ1 . At low ®elds qff B dependence is linear in accordance with Eq. (5). Using the found value for Br we get from Eq. (5) rab =rc 1=2 =c2 10þ2 . Then from the ®t of linear dependence of qff B to Eq. (6) we get c 1300, rab =rc 3 á 108 . Finally we get for rab the value 4 á 105 Xþ1 cmþ1 . That is nearly expected values. For c we found earlier the similar value from the ®t to ®eld dependence of critical current across the layers [16]. The found value for rc is near the value rc 2 á 10þ3


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contribution of in-plane dissipation to the ¯ux¯ow resistivity. Acknowledgements We are thankful to A.M. Nikitina for providing us with Bi-2212 single crystal whiskers and to A.E. Koshelev, Ch. Helm, L.N. Bulaevskii and N.F. Pedersen for fruitful discussions. This work was supported by the Russian State Program on HTS under grant no. 99016. References
[1] L.N. Bulaevskii, et al., Phys. Rev. B 53 (1996) 14601. [2] T. Koyama, M. Tachiki, Solid State Commun. 96 (1995) 367. [3] A.E. Koshelev, Phys. Rev. B 62 (2000) R3616. [4] J.U. Lee, J.E. Norman, G. Hohenwarter, Appl. Phys. Lett. 67 (1995) 1471. [5] Yu.I. Latyshev, P. Monceau, V.N. Pavlenko, Physica C 293 (1997) 174. [6] G. Hecht®scher, R. Kleiner, K. Schlenga, W. Walkenhorst, P. Muller, H.L. Johnson, Phys. Rev. B 55 (1997) 14638. [7] G. Hecht®scher, R. Kleiner, A.V. Ustinov, P. Muller, Phys. Rev. Lett. 79 (1997) 1365. [8] Yu.I. Latyshev, S.J. Kim, T. Yamashita, IEEE Trans. Appl. Supercond. 9 (1999) 4312. [9] Ch. Helm, Ch. Preis, F. Forsthofer, J. Keller, K. Schlenga, R. Kleiner, P. Muller, Phys. Rev. Lett. 79 (1997) 737. [10] A. Yurgens, D. Winkler, N. Zavaritsky, T. Claeson, Proceedings of the Conference on Oxide Superconductor Physics and Nano-Engineering II, SPIE Proceedings, vol. 2697, SPIE, Bellingham, WA, 1996. [11] K. Schlenga, G. Hecht®scher, R. Kleiner, W. Walkenhorst, P. Muller, H.L. Johnson, M. Veith, W. Brodkorb, E. Steinbeiss, Phys. Rev. Lett. 76 (1996) 4943. [12] Ya.G. Ponomarev, et al., Solid State Commun. 111 (1999) 513. [13] G. Oya, A. Irie, Physica C 362 (2001) 138. [14] C. Preis, C. Helm, K. Schmalzl, J. Keller, R. Kleiner, P. Muller, Physica C 362 (2001) 51. [15] J.R. Clem, M.W. Coey, Phys. Rev. B 42 (1990) 6209. [16] Yu.I. Latyshev, J.E. Nevelskaya, P. Monceau, Phys. Rev. Lett. 77 (1996) 932. [17] Yu.I. Latyshev, T. Yamashita, L.N. Bulaevskii, M.J. Graf, A.V. Balatsky, M.P. Maley, Phys. Rev. Lett. 82 (1999) 5345. [18] S.-F. Lee, et al., Phys. Rev. Lett. 77 (1996) 735. [19] H. Kitano, et al., J. Low Temp. Phys. 117 (1999) 1241. [20] Yu.I. Latyshev, I.G. Gorlova, A.V. Nikitina, V.U. Antokhina, S.G. Zybtsev, N.P. Kukhta, V.N. Timofeev, Physica C 216 (1993) 471.

Fig. 4. Normalized ¯ux-¯ow resistivity qff =qc vs applied magnetic ®eld Bkb. Lines are ®t of Eqs. (5) and (6) to the experimental data with parameters: Br 1:85 T, qc 770 X cm, c 1300, rab =rc 3 á 108 . Inset shows the close-up of the linear region at low ®elds.

Xþ1 cmþ1 obtained from interlayer tunneling experiments on small Bi-2212 stacks [17]. The found value for rab is several times higher than value found from the microwave measurements [18,19]. The corresponding value for qab is %2:5 á 10þ6 X cm. This is about ®ve times less than expected value from linear extrapolation of qab T of our whiskers to T 3 0 [20] and may be an indication of faster than linear drop of qab T at low temperatures. 4. Conclusions We studied Josephson ¯ux-¯ow features on the I ±V characteristics of long Bi-2212 stacks fabricated from single crystal whiskers by FIB technique. We found plateau like features on fdependence of maximum ¯ux-¯ow voltage on magnetic ®elds, corresponding to washboard frequencies 600 GHz, 3 and 4 THz. We consider that as resonance features for excitation of transverse Josephson plasma and c-axis optical phonons by Josephson ¯ux-¯ow oscillations. We found also that experimental data on ¯ux-¯ow resistivity are well described by the recent theory [3] considering