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Shapiro step response in Bi2Sr2CaCu2O8+δ in parallel and tilted magnetic field
Physica C 392–396 (2003) 319–322 www.elsevier.com/locate/physc
Shapiro step response in Bi2Sr2CaCu2O8þd in parallel and tilted magnetic field M.B. Gaifullin b
a,*
, Yu.I. Latyshev
b,c
, T. Yamashita c, Yuji Matsuda
a
a Institute for Solid State Physics, University of Tokyo, Kashiwanoha 5-1-5, Kashiwa, Chiba 277-8581, Japan Institute of Radio-Engineering and Electronics, Russian Academy of Sciences, Mokhovaya 11, GSP-9, Moscow 103907, Russia c Research Institute of Electrical Communications, Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai 980-8577, Japan
Received 13 November 2002; accepted 18 March 2003
Abstract We report the first observation of Shapiro step response in the Josephson flux-flow state of Bi2 Sr2 CaCu2 O8þd in strong magnetic field (Hk > 1 T) in ab plane. Phase of external microwave radiation and internal Josephson oscillation were locked in whole stack (N ¼ 67) of intrinsic Josephson junctions. Steps were observed at voltages Vst ¼ pNhm=2e, with p integer, m ¼ 45–142 GHz. As a matter of fact Vst remains constant and demonstrates that the Josephson vortices move at the same speed over the whole stack of junctions keeping the high special regularity. We also observed Shapiro steps at fields tilted with respect to the c-axis. The height of Shapiro steps and Josephson critical current increase sharply with increasing tilted angle and then both decrease at larger angle. We attribute this anomaly to the interaction between Josephson and pancake vortices. Ó 2003 Elsevier B.V. All rights reserved. PACS: 74.60.Ge; 74.50.+r; 74.72.Hs Keywords: Shapiro step; Intrinsic Josephson junctions; Josephson vortex flux-flow
1. Introduction It has been demonstrated in experiments that most anisotropic high-Tc superconductors such as Bi2 Sr2 CaCu2 O8þd act as a vertical c-axis stack of superconductor–insulator–superconductor Josephson junctions [1]. We study dynamics of Josephson vortex lattice (JVL) driven by steady current across the layers in long Josephson junctions. In
previous study the dynamical properties have been investigated by c-axis dc resistivity caused by Josephson vortex flux-flow [2] and by microwave emission experiments [3]. We use new method based on Shapiro step response [4] for studying coherent motion of dense JVL. In tilted magnetic fields we studied interaction between Josephson and pancake vortices by Shapiro step response.
2. Experimental *
Corresponding author. Tel.: +81-471-363242; fax: +81-471363243/363241. E-mail address: [email protected] (M.B. Gaifullin).
The stacked intrinsic long Josephson junctions have been fabricated by double-sided processing of
0921-4534/$ - see front matter Ó 2003 Elsevier B.V. All rights reserved. doi:10.1016/S0921-4534(03)00899-2
320
M.B. Gaifullin et al. / Physica C 392–396 (2003) 319–322
3. Results and discussion
Fig. 1. I–V characteristic of the stacked intrinsic Josephson junctions with microwave irradiation in magnetic field of 2.0 T applied parallel to the layers at temperature 5.0 K. The applied microwave frequency is 89.0 GHz. N , estimated from number of quasiparticle branches at H ¼ 0 T, is 67 3. Inset: Schematic view of the stacked intrinsic Josephson junction.
high quality Bi2 Sr2 CaCu2 O8þd (Tc ¼ 80 K) whiskers using a focusing ion beam technique [5]. The oxygen doping level was d 0:25, indicating the slightly overdoped regime. The inset of Fig. 1 shows schematically the arrangement of the junctions. The length of the junction is L ¼ 30 lm with a width of W ¼ 2:0 lm in ab plane. The critical current density Jc at 4.2 K in the absence of magnetic field was 1–2 103 A/cm2 . A microwave from the backward-wave-oscillators at the frequencies ranging from 45 to 142 GHz was transmitted through the set of rectangular waveguides for different bands. In experiments the microwave frequency was always much higher than frequency of the Josephson plasma resonance with low damping in Bi2 Sr2 CaCu2 O8þd at a chosen magnetic field and temperature [6]. The thin sample at the center of the rectangular waveguide produced an inductive susceptance. The microwave inductive coupling and power were strong enough to completely suppress critical current in the sample. The magnetic field H P 1 T was rotated in plane perpendicular to the long dimension L using split pair superconducting magnets with fine goniometer having angular resolution 0.01°. The I–V characteristics were measured at several tenths of Hz using a low noise oscilloscope.
Fig. 1 shows the I–V characteristics in the strong ab plane field Hk P U0 =cs2 , where U0 ¼ h=2e, s is the spacing between adjacent CuO2 double layers. At this field a distance between two vortices equal to the core of Josephson vortex. As a result the critical current is strongly suppressed to 1/30 of Jc at H ¼ 0 in the absence of microwave irradiation. The linear slope with slight upturn in the I–V characteristics at finite voltage corresponds to the Josephson flux-flow state. One can see multiple Josephson flux-flow branches above 45 mV. Shapiro steps appeared on the first flux-flow branch when the junction is irradiated by microwaves. In the present case Shapiro effect is markedly different from conventional one because dc voltage appears due to Josephson vortices fluxflow. Therefore the dc voltages of the Shapiro steps are closely related to Josephson vortex dynamics. If the Josephson vortices move at different speed in some layers, it induces changes in voltage position of step Vst . Because Vst remains constant, it follows that the Josephson vortices move at the same speed over the whole stack of junctions. The observation of sharp enough Shapiro steps indicates that the Josephson vortices move keeping the high spatial regularity [4]. Excess width of steps is caused by internal degrees of freedom. Under various field angles to the b-axis, h, we find collectively phase locked Shapiro steps shown in Figs. 1 and 2. The steps occurred at the same voltages given by Vst ¼ pNhm=2e, where N is the whole number of the junctions in the stack. The height of Shapiro steps DIn increases very rapidly at small angles and has a maximum at h < 0:6° in Fig. 2. Josephson critical current has the same angular dependence as seen in Fig. 3. Height of steps is proportional to Josephson critical current Ic . Therefore height of the Shapiro steps is very sensitive to vortex state. Because Ic is proportional to the interlayer phase coherence [7], Jc ðB; T Þ ¼ J0 ð0; T Þhcos un;nþ1 ðrÞi;
ð1Þ
where hcos un;nþ1 ðrÞi presents the thermal and disorder averages of the cosine of gauge invariant phase difference between adjacent CuO2 double layers. At small angles h < 0:6° the sharp increase
M.B. Gaifullin et al. / Physica C 392–396 (2003) 319–322
321
Fig. 2. The angular dependence of the Shapiro step response for h from 0° to 90°.
of both Ic and DIn to be related with pinning of the Josephson vortices by pancake vortices [8], the latter being pinned by crystal much stronger because of normal vortex core. At the higher angles the reduction of Ic is caused by the Josephson strings that are created by the deviation from the straight alignment of the pancakes along the c-axis. Magnetic field has effect on the gauge invariant phase difference as un;nþ1 ! un;nþ1 þ 2psHk x=U0 in our geometry. In high temperature expansion in the vortex liquid state U0 EJ =kB TH? 1 [9,10], the height of step is expressed ! ps2 Hk2 U0 EJ ð0Þ ; ð2Þ exp DI / kB TH? H? U0
Fig. 3. The angular dependence of the critical current for h from 0° to 90°.
4. Conclusion We have observed Shapiro steps in the Josephson flux-flow regime of Bi2 Sr2 CaCu2 O8þd stacked junctions and in tilted magnetic field in the case of the interaction of Josephson vortices with pancake vortices. Observation of Shapiro steps in the Josephson flux-flow state provide strong evidence of the coherent motion of the JVL. Pancake vortices have effect on the height of Shapiro steps with tilting magnetic field.
Acknowledgements where EJ is the Josephson energy. Since U0 =ps2 100T , the exponential factor is about unity at large angles tilting magnetic field out of ab plane and the height is well scaled by DI ¼ const= H sin h.
M.B.G. acknowledges support from JSPS, Y.I.L. acknowledges support from the CRDF grant no. RP-12397-MO-02 and grant of Russian
322
M.B. Gaifullin et al. / Physica C 392–396 (2003) 319–322
Ministry of Science and Industry no. 40.012.1.1. 11.46.
References [1] R. Kleiner, P. Muller, Phys. Rev. B 49 (1994) 1327. [2] J.U. Lee, J. Nordman, G. Hohenwarter, Appl. Phys. Lett. 67 (1995) 1471. [3] G. Hechtfischer, R. Kleiner, K. Schlenda, W. Walkenhorst, P. Muller, Phys. Rev. B 55 (1997) 14638.
[4] Yu.I. Latyshev, M.B. Gaifullin, T. Yamashita, M. Machida, Y. Matsuda, Phys. Rev. Lett. 87 (2001) 247007. [5] Yu.I. Latyshev, S.-J. Kim, T. Yamashita, IEEE Trans. Appl. Supercond. 9 (1999) 4312. [6] M.B. Gaifullin, Y. Matsuda, N. Chikumoto, J. Shimoyama, K. Kishio, Phys. Rev. Lett. 84 (2000) 2945. [7] L.N. Bulaevskii, M. Maley, M. Tachiki, Phys. Rev. Lett. 74 (1995) 801. [8] Latyshev, A.F. Volkov, Physica C 182 (1991) 47. [9] L.N. Bulaevskii, M. Maley, H. Safar, D. Dominguez, Phys. Rev. B 53 (1996) 6634. [10] A. Koshelev, Phys. Lett. 77 (1996) 3901.
Shapiro step response in Bi2Sr2CaCu2O8þd in parallel and tilted magnetic field M.B. Gaifullin b
a,*
, Yu.I. Latyshev
b,c
, T. Yamashita c, Yuji Matsuda
a
a Institute for Solid State Physics, University of Tokyo, Kashiwanoha 5-1-5, Kashiwa, Chiba 277-8581, Japan Institute of Radio-Engineering and Electronics, Russian Academy of Sciences, Mokhovaya 11, GSP-9, Moscow 103907, Russia c Research Institute of Electrical Communications, Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai 980-8577, Japan
Received 13 November 2002; accepted 18 March 2003
Abstract We report the first observation of Shapiro step response in the Josephson flux-flow state of Bi2 Sr2 CaCu2 O8þd in strong magnetic field (Hk > 1 T) in ab plane. Phase of external microwave radiation and internal Josephson oscillation were locked in whole stack (N ¼ 67) of intrinsic Josephson junctions. Steps were observed at voltages Vst ¼ pNhm=2e, with p integer, m ¼ 45–142 GHz. As a matter of fact Vst remains constant and demonstrates that the Josephson vortices move at the same speed over the whole stack of junctions keeping the high special regularity. We also observed Shapiro steps at fields tilted with respect to the c-axis. The height of Shapiro steps and Josephson critical current increase sharply with increasing tilted angle and then both decrease at larger angle. We attribute this anomaly to the interaction between Josephson and pancake vortices. Ó 2003 Elsevier B.V. All rights reserved. PACS: 74.60.Ge; 74.50.+r; 74.72.Hs Keywords: Shapiro step; Intrinsic Josephson junctions; Josephson vortex flux-flow
1. Introduction It has been demonstrated in experiments that most anisotropic high-Tc superconductors such as Bi2 Sr2 CaCu2 O8þd act as a vertical c-axis stack of superconductor–insulator–superconductor Josephson junctions [1]. We study dynamics of Josephson vortex lattice (JVL) driven by steady current across the layers in long Josephson junctions. In
previous study the dynamical properties have been investigated by c-axis dc resistivity caused by Josephson vortex flux-flow [2] and by microwave emission experiments [3]. We use new method based on Shapiro step response [4] for studying coherent motion of dense JVL. In tilted magnetic fields we studied interaction between Josephson and pancake vortices by Shapiro step response.
2. Experimental *
Corresponding author. Tel.: +81-471-363242; fax: +81-471363243/363241. E-mail address: [email protected] (M.B. Gaifullin).
The stacked intrinsic long Josephson junctions have been fabricated by double-sided processing of
0921-4534/$ - see front matter Ó 2003 Elsevier B.V. All rights reserved. doi:10.1016/S0921-4534(03)00899-2
320
M.B. Gaifullin et al. / Physica C 392–396 (2003) 319–322
3. Results and discussion
Fig. 1. I–V characteristic of the stacked intrinsic Josephson junctions with microwave irradiation in magnetic field of 2.0 T applied parallel to the layers at temperature 5.0 K. The applied microwave frequency is 89.0 GHz. N , estimated from number of quasiparticle branches at H ¼ 0 T, is 67 3. Inset: Schematic view of the stacked intrinsic Josephson junction.
high quality Bi2 Sr2 CaCu2 O8þd (Tc ¼ 80 K) whiskers using a focusing ion beam technique [5]. The oxygen doping level was d 0:25, indicating the slightly overdoped regime. The inset of Fig. 1 shows schematically the arrangement of the junctions. The length of the junction is L ¼ 30 lm with a width of W ¼ 2:0 lm in ab plane. The critical current density Jc at 4.2 K in the absence of magnetic field was 1–2 103 A/cm2 . A microwave from the backward-wave-oscillators at the frequencies ranging from 45 to 142 GHz was transmitted through the set of rectangular waveguides for different bands. In experiments the microwave frequency was always much higher than frequency of the Josephson plasma resonance with low damping in Bi2 Sr2 CaCu2 O8þd at a chosen magnetic field and temperature [6]. The thin sample at the center of the rectangular waveguide produced an inductive susceptance. The microwave inductive coupling and power were strong enough to completely suppress critical current in the sample. The magnetic field H P 1 T was rotated in plane perpendicular to the long dimension L using split pair superconducting magnets with fine goniometer having angular resolution 0.01°. The I–V characteristics were measured at several tenths of Hz using a low noise oscilloscope.
Fig. 1 shows the I–V characteristics in the strong ab plane field Hk P U0 =cs2 , where U0 ¼ h=2e, s is the spacing between adjacent CuO2 double layers. At this field a distance between two vortices equal to the core of Josephson vortex. As a result the critical current is strongly suppressed to 1/30 of Jc at H ¼ 0 in the absence of microwave irradiation. The linear slope with slight upturn in the I–V characteristics at finite voltage corresponds to the Josephson flux-flow state. One can see multiple Josephson flux-flow branches above 45 mV. Shapiro steps appeared on the first flux-flow branch when the junction is irradiated by microwaves. In the present case Shapiro effect is markedly different from conventional one because dc voltage appears due to Josephson vortices fluxflow. Therefore the dc voltages of the Shapiro steps are closely related to Josephson vortex dynamics. If the Josephson vortices move at different speed in some layers, it induces changes in voltage position of step Vst . Because Vst remains constant, it follows that the Josephson vortices move at the same speed over the whole stack of junctions. The observation of sharp enough Shapiro steps indicates that the Josephson vortices move keeping the high spatial regularity [4]. Excess width of steps is caused by internal degrees of freedom. Under various field angles to the b-axis, h, we find collectively phase locked Shapiro steps shown in Figs. 1 and 2. The steps occurred at the same voltages given by Vst ¼ pNhm=2e, where N is the whole number of the junctions in the stack. The height of Shapiro steps DIn increases very rapidly at small angles and has a maximum at h < 0:6° in Fig. 2. Josephson critical current has the same angular dependence as seen in Fig. 3. Height of steps is proportional to Josephson critical current Ic . Therefore height of the Shapiro steps is very sensitive to vortex state. Because Ic is proportional to the interlayer phase coherence [7], Jc ðB; T Þ ¼ J0 ð0; T Þhcos un;nþ1 ðrÞi;
ð1Þ
where hcos un;nþ1 ðrÞi presents the thermal and disorder averages of the cosine of gauge invariant phase difference between adjacent CuO2 double layers. At small angles h < 0:6° the sharp increase
M.B. Gaifullin et al. / Physica C 392–396 (2003) 319–322
321
Fig. 2. The angular dependence of the Shapiro step response for h from 0° to 90°.
of both Ic and DIn to be related with pinning of the Josephson vortices by pancake vortices [8], the latter being pinned by crystal much stronger because of normal vortex core. At the higher angles the reduction of Ic is caused by the Josephson strings that are created by the deviation from the straight alignment of the pancakes along the c-axis. Magnetic field has effect on the gauge invariant phase difference as un;nþ1 ! un;nþ1 þ 2psHk x=U0 in our geometry. In high temperature expansion in the vortex liquid state U0 EJ =kB TH? 1 [9,10], the height of step is expressed ! ps2 Hk2 U0 EJ ð0Þ ; ð2Þ exp DI / kB TH? H? U0
Fig. 3. The angular dependence of the critical current for h from 0° to 90°.
4. Conclusion We have observed Shapiro steps in the Josephson flux-flow regime of Bi2 Sr2 CaCu2 O8þd stacked junctions and in tilted magnetic field in the case of the interaction of Josephson vortices with pancake vortices. Observation of Shapiro steps in the Josephson flux-flow state provide strong evidence of the coherent motion of the JVL. Pancake vortices have effect on the height of Shapiro steps with tilting magnetic field.
Acknowledgements where EJ is the Josephson energy. Since U0 =ps2 100T , the exponential factor is about unity at large angles tilting magnetic field out of ab plane and the height is well scaled by DI ¼ const= H sin h.
M.B.G. acknowledges support from JSPS, Y.I.L. acknowledges support from the CRDF grant no. RP-12397-MO-02 and grant of Russian
322
M.B. Gaifullin et al. / Physica C 392–396 (2003) 319–322
Ministry of Science and Industry no. 40.012.1.1. 11.46.
References [1] R. Kleiner, P. Muller, Phys. Rev. B 49 (1994) 1327. [2] J.U. Lee, J. Nordman, G. Hohenwarter, Appl. Phys. Lett. 67 (1995) 1471. [3] G. Hechtfischer, R. Kleiner, K. Schlenda, W. Walkenhorst, P. Muller, Phys. Rev. B 55 (1997) 14638.
[4] Yu.I. Latyshev, M.B. Gaifullin, T. Yamashita, M. Machida, Y. Matsuda, Phys. Rev. Lett. 87 (2001) 247007. [5] Yu.I. Latyshev, S.-J. Kim, T. Yamashita, IEEE Trans. Appl. Supercond. 9 (1999) 4312. [6] M.B. Gaifullin, Y. Matsuda, N. Chikumoto, J. Shimoyama, K. Kishio, Phys. Rev. Lett. 84 (2000) 2945. [7] L.N. Bulaevskii, M. Maley, M. Tachiki, Phys. Rev. Lett. 74 (1995) 801. [8] Latyshev, A.F. Volkov, Physica C 182 (1991) 47. [9] L.N. Bulaevskii, M. Maley, H. Safar, D. Dominguez, Phys. Rev. B 53 (1996) 6634. [10] A. Koshelev, Phys. Lett. 77 (1996) 3901.