- Email: [email protected]
Collective Josephson vortex dynamics interacting with transverse Josephson plasma modes in intrinsic Josephson junctions
Physica B 284}288 (2000) 608}609
Collective Josephson vortex dynamics interacting with transverse Josephson plasma modes in intrinsic Josephson junctions Masahiko Machida *, Tomio Koyama, Masashi Tachiki Japan Atomic Energy Research Institute and CREST Japan Science and Technology Corporation(JST), Centre for Prom. of Computer Science and Engineering, 2-2-54 Nakameguro, Meguro-ku, Tokyo, 153-0061 Japan Institute for Materials Research, Tohoku University, Katahira 2-2-1, Aoba-ku, Sendai 980-77, Japan National Research Institute for Metals, Sengen 1-2-1, Tsukuba, Ibaraki 305, Japan
Abstract We perform large-scale numerical simulations for Josephson vortex dynamics interacting with transverse plasma modes in intrinsic Josephson junctions by employing the coupled Sine-Gordon (CSG) equation. The simulation results reveal that I}< characterisitics show three clear step-like structures, where structural transitions of Josephson vortex lattice #ow states occur due to resonances with transverse propagating Josephson plasma modes. We show that in-phase rectangular vortex lattice #ow states leading to strong electromagnetic wave radiations can appear in a wide region of the I}< characterisitics in intrinsic Josephson junctions. 2000 Elsevier Science B.V. All rights reserved. Keywords: Intrinsic Josephson E!ects; Josephson plasma; Josephson vortices; Vortex dynamics
Recently, intrinsic Josephson junctions (IJJs) in layered high-¹ superconductors have attracted much A interests. This is because single crystals of those materials are atomic-scale multi-stacked Josephson junctions and strong coherence between junctions can be expected. In conventional single Josephson junctions (SJJs), Josephson vortex dynamics has been intensively investigated [1]. Under the presence of the magnetic "eld, the Josephson vortices are driven unidirectionally under the transport current, and their motions couple with the transverse Josephson plasma mode leading to emission of electromagnetic waves. Thus, SJJs has been employed as useful #ux #ow oscillators. On the other hand, since IJJs are basically multi-stack of many junctions, strong radiations of the electromagnetic waves can be expected. However, it clearly requires coherent in-phase vortex dynamics over all junctions,
and not the common triangular #ux lattice #ow state but the rectangular one can satisfy the condition. Thus, explorations of such in-phase #ow state [2,3] and systematic understanding for the collective Josephson vortex dynamics [3] have been demanded. In this paper, we report numerical simulation results for the CSG equation which describe Josephson vortex dynamics in IJJs [3]. In the present simulations, the applied "eld is above 1T and collective vortex #ow states are invesitgated by changing the current from 0 to 2.2J . A The equation solved numerically is the CSG equation, RPl l RPl l RP > " > !sin Pl l !b l> l > Rt Rx Rt
j RPl l RPl l RPl l > > # \ !2 > # ?@ sD Rt Rt Rt
j # ?@ (sin Pl l #sin Pl l !2 sin Pl l ) > > \ > sD * Corresponding author. Tel.: #81-3-5723-2517; fax: #813-5723-2537. E-mail address: [email protected] (M. Machida)
j RPl l RP RP > > # l l\ !2 l> l , # b ?@ sD Rt Rt Rt
0921-4526/00/$ - see front matter 2000 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 9 9 ) 0 2 2 3 4 - 6
(1)
M. Machida et al. / Physica B 284}288 (2000) 608}609
Fig. 1. The I}< characteristics. The arrows indicate clear steplike structures, where the #ux #ow states are classi"ed into four regions from I to IV.
where s and D are thickness of the superconducting and insulating layers and j is the penetration depth in the ?@ ab-plane direction. The time and space is normalized by using the inverse plasma frequency 1/u and the c-axis penetration depth j . The simulated I}< characteristics A are shown in Fig. 1. Three clear step-like structures are observed and four regions are classi"ed by those structures. In region I, moving vortex velocities are slow and their motions are chaotic. In the low current region, it is considered that simulation boundaries work as e!ective pinning potentials. In region II, the vortices begin to align along the c-axis and the partially regular vortex #ow states give peak frequencies in the power spectrum for electric "eld oscillations (PSEO) measured at the sample edge. In region III, the vortex alignment along the c-axis becomes perfect and the in-phase rectangular #ux latttice #ow appear. Let us show the vortex con"guration in the region III in Fig. 2. This #ow states are stable in the wide range over the region III seen in Fig. 1. In this region, PSEO shows to be remarkably sharp and the power at the peak position is also very large. These states can lead to the radiation of strong coherent electromagnetic waves. In order to understand those simulation results, we com-
609
Fig. 2. The snapshot of the Josephson vortex con"guration with Josephson current distribution. The dots indicate the center of vortices and the lines represent the value of the normalized Josephson current in all junctions.
pare those with the eigen-mode analysis of Eq. (1). The analysis shows that the step-like structures observed in I}< characteristics are originated from resonances with some eigenplasma modes. In addition, the theoretical estimation reveals that the width of the useful region III is determined by the magnitude of a ratio j /sD and ?@ therefore IJJ systems can have very wide ranges in I}< characteristics [3]. In conlusion, we performed numerical simulations in order to explore the in-phase vortex #ow state in intrinsic Josephson junction systems. We clari"ed that the inphase oscillation can really emerge within accessible experimental conditions.
References [1] A. Barone, G. Paterno, Physics and Applications of the Josephson E!ect, Wiley, New York, 1982. [2] A.V. Ustinov, S. Sakai, Appl. Phys. Lett. 73 (1998) 686. [3] M. Machida, T. Koyama, A. Tanaka, M. Tachiki, Physica C 330 (2000) 85.
Collective Josephson vortex dynamics interacting with transverse Josephson plasma modes in intrinsic Josephson junctions Masahiko Machida *, Tomio Koyama, Masashi Tachiki Japan Atomic Energy Research Institute and CREST Japan Science and Technology Corporation(JST), Centre for Prom. of Computer Science and Engineering, 2-2-54 Nakameguro, Meguro-ku, Tokyo, 153-0061 Japan Institute for Materials Research, Tohoku University, Katahira 2-2-1, Aoba-ku, Sendai 980-77, Japan National Research Institute for Metals, Sengen 1-2-1, Tsukuba, Ibaraki 305, Japan
Abstract We perform large-scale numerical simulations for Josephson vortex dynamics interacting with transverse plasma modes in intrinsic Josephson junctions by employing the coupled Sine-Gordon (CSG) equation. The simulation results reveal that I}< characterisitics show three clear step-like structures, where structural transitions of Josephson vortex lattice #ow states occur due to resonances with transverse propagating Josephson plasma modes. We show that in-phase rectangular vortex lattice #ow states leading to strong electromagnetic wave radiations can appear in a wide region of the I}< characterisitics in intrinsic Josephson junctions. 2000 Elsevier Science B.V. All rights reserved. Keywords: Intrinsic Josephson E!ects; Josephson plasma; Josephson vortices; Vortex dynamics
Recently, intrinsic Josephson junctions (IJJs) in layered high-¹ superconductors have attracted much A interests. This is because single crystals of those materials are atomic-scale multi-stacked Josephson junctions and strong coherence between junctions can be expected. In conventional single Josephson junctions (SJJs), Josephson vortex dynamics has been intensively investigated [1]. Under the presence of the magnetic "eld, the Josephson vortices are driven unidirectionally under the transport current, and their motions couple with the transverse Josephson plasma mode leading to emission of electromagnetic waves. Thus, SJJs has been employed as useful #ux #ow oscillators. On the other hand, since IJJs are basically multi-stack of many junctions, strong radiations of the electromagnetic waves can be expected. However, it clearly requires coherent in-phase vortex dynamics over all junctions,
and not the common triangular #ux lattice #ow state but the rectangular one can satisfy the condition. Thus, explorations of such in-phase #ow state [2,3] and systematic understanding for the collective Josephson vortex dynamics [3] have been demanded. In this paper, we report numerical simulation results for the CSG equation which describe Josephson vortex dynamics in IJJs [3]. In the present simulations, the applied "eld is above 1T and collective vortex #ow states are invesitgated by changing the current from 0 to 2.2J . A The equation solved numerically is the CSG equation, RPl l RPl l RP > " > !sin Pl l !b l> l > Rt Rx Rt
j RPl l RPl l RPl l > > # \ !2 > # ?@ sD Rt Rt Rt
j # ?@ (sin Pl l #sin Pl l !2 sin Pl l ) > > \ > sD * Corresponding author. Tel.: #81-3-5723-2517; fax: #813-5723-2537. E-mail address: [email protected] (M. Machida)
j RPl l RP RP > > # l l\ !2 l> l , # b ?@ sD Rt Rt Rt
0921-4526/00/$ - see front matter 2000 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 9 9 ) 0 2 2 3 4 - 6
(1)
M. Machida et al. / Physica B 284}288 (2000) 608}609
Fig. 1. The I}< characteristics. The arrows indicate clear steplike structures, where the #ux #ow states are classi"ed into four regions from I to IV.
where s and D are thickness of the superconducting and insulating layers and j is the penetration depth in the ?@ ab-plane direction. The time and space is normalized by using the inverse plasma frequency 1/u and the c-axis penetration depth j . The simulated I}< characteristics A are shown in Fig. 1. Three clear step-like structures are observed and four regions are classi"ed by those structures. In region I, moving vortex velocities are slow and their motions are chaotic. In the low current region, it is considered that simulation boundaries work as e!ective pinning potentials. In region II, the vortices begin to align along the c-axis and the partially regular vortex #ow states give peak frequencies in the power spectrum for electric "eld oscillations (PSEO) measured at the sample edge. In region III, the vortex alignment along the c-axis becomes perfect and the in-phase rectangular #ux latttice #ow appear. Let us show the vortex con"guration in the region III in Fig. 2. This #ow states are stable in the wide range over the region III seen in Fig. 1. In this region, PSEO shows to be remarkably sharp and the power at the peak position is also very large. These states can lead to the radiation of strong coherent electromagnetic waves. In order to understand those simulation results, we com-
609
Fig. 2. The snapshot of the Josephson vortex con"guration with Josephson current distribution. The dots indicate the center of vortices and the lines represent the value of the normalized Josephson current in all junctions.
pare those with the eigen-mode analysis of Eq. (1). The analysis shows that the step-like structures observed in I}< characteristics are originated from resonances with some eigenplasma modes. In addition, the theoretical estimation reveals that the width of the useful region III is determined by the magnitude of a ratio j /sD and ?@ therefore IJJ systems can have very wide ranges in I}< characteristics [3]. In conlusion, we performed numerical simulations in order to explore the in-phase vortex #ow state in intrinsic Josephson junction systems. We clari"ed that the inphase oscillation can really emerge within accessible experimental conditions.
References [1] A. Barone, G. Paterno, Physics and Applications of the Josephson E!ect, Wiley, New York, 1982. [2] A.V. Ustinov, S. Sakai, Appl. Phys. Lett. 73 (1998) 686. [3] M. Machida, T. Koyama, A. Tanaka, M. Tachiki, Physica C 330 (2000) 85.