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Current–voltage relation for Josephson junctions with ferromagnetic insulator
Physica B 284}288 (2000) 511}512
Current}voltage relation for Josephson junctions with ferromagnetic insulator Nobukatsu Yoshida *, Yukio Tanaka , Satoshi Kashiwaya, Junichiro Inoue Department of Applied Physics, Nagoya University, Nagoya, 464-8603, Japan Electrotechnical Laboratory, Umezono, Tsukuba, Ibaraki, 305-8568, Japan
Abstract We calculate the current}voltage relation for planar superconducting d-wave junctions including a ferromagnetic insulating layer. The height of the current peak near zero-bias voltage due to the formation of zero energy states is reduced with the increase of the magnitude of the exchange interaction in ferromagnetic insulator. 2000 Elsevier Science B.V. All rights reserved. Keywords: Exchange interaction; Ferromagnetic insulator; Josephson junctions
It is well known that the zero energy state (ZES) [1] which is formed on surface/interface of d-wave superconductor in#uences signi"cantly the transport properties of d-wave superconducting junctions [2}7]. Recently, it was clari"ed for superconducting junctions including ferromagnetic insulator that the exchange interaction in#uences signi"cantly both, the tunneling conductance [8] and DC Josephson e!ect [9]. We can naturally expect that the bias voltage (eV) dependence of the Josephson current is also in#uenced signi"cantly as the change of the magnitude of the exchange interaction. In this paper, we investigate the quasiparticle current and the "rst Fourier component of the AC Josephson current in d-wave superconductor/ferromagnetic insulator/dwave superconductor (D/FI/D) junction by extending previous theories [7,10]. The model used here is a two-dimensional junction with perfectly #at interface. We model the ferromagnetic insulator as a d-function and introduce parameters Z "Z !(#)Z for up (down) spin injection, with ts K Z "2mH / and Z "2mH / , where H and H K K K are the ordinary barrier potential and exchange interac-
* Corresponding author. E-mail address: [email protected] (N. Yoshida)
tion, respectively. We choose the pair potential in the left (right) superconductor as D (h)"D cos(2h!2a) * [D (h)"D cos(2h!2b)] where h is the incidental angle 0 of a quasiparticle to the interface and a (b) is the orientation of left (right) d-wave superconductors with respect to the normal to the interface. In the following, we will consider the mirror type junction i.e., a"!b"p/4 and "x Z "5. The spatial dependence of pair potential and all dynamical spin processes are neglected for simplicity, then, the current component is calculated numerical in a similar way based on the scattering theory [5}7,10]. To avoid an unphysical divergence and introduce the junction broadening e!ect, phenomenological smearing factor is introduced into the calculation. From the "gures, normalized current component is plotted as a function eV, where explicit normalization factor is given in Eq. (4) of Ref. [7]. Fig. 1 shows the current}voltage relations for the normalized quasiparticle current through the junction for several values of Z at zero temperature. The K origin of this peak near the zero-bias is due to the zero energy resonating state at the interface [1] and is enhanced with the increase of the magnitude of Z for ! Z "0 [2]. For "xed Z , with the increasing of the K magnitude of Z , the height of the peak is reduced and K the peak splits into two peaks. In this case, an electron (hole) with down spin does not feel the resonating state at the interface seriously. As Z becomes larger than K
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 1 0 4 - 3
512
N. Yoshida et al. / Physica B 284}288 (2000) 511}512
Z ("5), the sign of Z changes and the peak appears K near zero bias voltage again. Fig. 2 shows the imaginary parts of the "rst Fourier component of the AC current. The strong enhancement of the AC current is the manifestation of the formation of zero energy states at the interface [4]. At zero voltage, with the increase of Z , the transition of the position of K the free energy minima as a function of the phase di!erence of the two superconductors occurs [9]. Consequently, the sign of the current is reversed (see curve d in Fig. 2). We hope such properties will be observed in experiments in the near future. Fig. 1. Quasiparticle current for various Z . Z is a: Z "0, b: K K K Z "1, c: Z "3, d: Z "10. K K K
References [1] C.R. Hu, Phys. Rev. Lett. 72 (1994) 1526. [2] Y. Tanaka, S. Kashiwaya, Phys. Rev. Lett. 74 (1995) 3451. [3] S. Kashiwaya et al., Phys. Rev. B 51 (1995) 1350. [4] Y. Tanaka, S. Kashiwaya, Phys. Rev. B 53 (1996) 11957. [5] M. Hurd, T. LoK fwander, G. Johansson, G. Wendin, Phys. Rev. B 59 (1999) 4412. [6] T. LoK fwander, G. Johansson, M. Hurd, G. Wendin, Phys. Rev. B 57 (1998) R3225. [7] N. Yoshida, Y. Tanaka, S. Kashiwaya, Adv. Superconduct. XI (1999) 339. [8] S. Kashiwaya, Y. Tanaka, N. Yoshida, M.R. Beasley, Phys. Rev. B, to appear. [9] Y. Tanaka, S. Kashiwaya, Physica C 274 (1997) 357. [10] D. Averin, A. Bardas, Phys. Rev. Lett. 75 (1995) 1831.
Fig. 2. Imaginary part of the "rst Fourier component of the AC Josephson current for various Z . Z is a: Z "0, b: Z "1, c: K K K K Z "3, d: Z "10. K K
Current}voltage relation for Josephson junctions with ferromagnetic insulator Nobukatsu Yoshida *, Yukio Tanaka , Satoshi Kashiwaya, Junichiro Inoue Department of Applied Physics, Nagoya University, Nagoya, 464-8603, Japan Electrotechnical Laboratory, Umezono, Tsukuba, Ibaraki, 305-8568, Japan
Abstract We calculate the current}voltage relation for planar superconducting d-wave junctions including a ferromagnetic insulating layer. The height of the current peak near zero-bias voltage due to the formation of zero energy states is reduced with the increase of the magnitude of the exchange interaction in ferromagnetic insulator. 2000 Elsevier Science B.V. All rights reserved. Keywords: Exchange interaction; Ferromagnetic insulator; Josephson junctions
It is well known that the zero energy state (ZES) [1] which is formed on surface/interface of d-wave superconductor in#uences signi"cantly the transport properties of d-wave superconducting junctions [2}7]. Recently, it was clari"ed for superconducting junctions including ferromagnetic insulator that the exchange interaction in#uences signi"cantly both, the tunneling conductance [8] and DC Josephson e!ect [9]. We can naturally expect that the bias voltage (eV) dependence of the Josephson current is also in#uenced signi"cantly as the change of the magnitude of the exchange interaction. In this paper, we investigate the quasiparticle current and the "rst Fourier component of the AC Josephson current in d-wave superconductor/ferromagnetic insulator/dwave superconductor (D/FI/D) junction by extending previous theories [7,10]. The model used here is a two-dimensional junction with perfectly #at interface. We model the ferromagnetic insulator as a d-function and introduce parameters Z "Z !(#)Z for up (down) spin injection, with ts K Z "2mH / and Z "2mH / , where H and H K K K are the ordinary barrier potential and exchange interac-
* Corresponding author. E-mail address: [email protected] (N. Yoshida)
tion, respectively. We choose the pair potential in the left (right) superconductor as D (h)"D cos(2h!2a) * [D (h)"D cos(2h!2b)] where h is the incidental angle 0 of a quasiparticle to the interface and a (b) is the orientation of left (right) d-wave superconductors with respect to the normal to the interface. In the following, we will consider the mirror type junction i.e., a"!b"p/4 and "x Z "5. The spatial dependence of pair potential and all dynamical spin processes are neglected for simplicity, then, the current component is calculated numerical in a similar way based on the scattering theory [5}7,10]. To avoid an unphysical divergence and introduce the junction broadening e!ect, phenomenological smearing factor is introduced into the calculation. From the "gures, normalized current component is plotted as a function eV, where explicit normalization factor is given in Eq. (4) of Ref. [7]. Fig. 1 shows the current}voltage relations for the normalized quasiparticle current through the junction for several values of Z at zero temperature. The K origin of this peak near the zero-bias is due to the zero energy resonating state at the interface [1] and is enhanced with the increase of the magnitude of Z for ! Z "0 [2]. For "xed Z , with the increasing of the K magnitude of Z , the height of the peak is reduced and K the peak splits into two peaks. In this case, an electron (hole) with down spin does not feel the resonating state at the interface seriously. As Z becomes larger than K
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 1 0 4 - 3
512
N. Yoshida et al. / Physica B 284}288 (2000) 511}512
Z ("5), the sign of Z changes and the peak appears K near zero bias voltage again. Fig. 2 shows the imaginary parts of the "rst Fourier component of the AC current. The strong enhancement of the AC current is the manifestation of the formation of zero energy states at the interface [4]. At zero voltage, with the increase of Z , the transition of the position of K the free energy minima as a function of the phase di!erence of the two superconductors occurs [9]. Consequently, the sign of the current is reversed (see curve d in Fig. 2). We hope such properties will be observed in experiments in the near future. Fig. 1. Quasiparticle current for various Z . Z is a: Z "0, b: K K K Z "1, c: Z "3, d: Z "10. K K K
References [1] C.R. Hu, Phys. Rev. Lett. 72 (1994) 1526. [2] Y. Tanaka, S. Kashiwaya, Phys. Rev. Lett. 74 (1995) 3451. [3] S. Kashiwaya et al., Phys. Rev. B 51 (1995) 1350. [4] Y. Tanaka, S. Kashiwaya, Phys. Rev. B 53 (1996) 11957. [5] M. Hurd, T. LoK fwander, G. Johansson, G. Wendin, Phys. Rev. B 59 (1999) 4412. [6] T. LoK fwander, G. Johansson, M. Hurd, G. Wendin, Phys. Rev. B 57 (1998) R3225. [7] N. Yoshida, Y. Tanaka, S. Kashiwaya, Adv. Superconduct. XI (1999) 339. [8] S. Kashiwaya, Y. Tanaka, N. Yoshida, M.R. Beasley, Phys. Rev. B, to appear. [9] Y. Tanaka, S. Kashiwaya, Physica C 274 (1997) 357. [10] D. Averin, A. Bardas, Phys. Rev. Lett. 75 (1995) 1831.
Fig. 2. Imaginary part of the "rst Fourier component of the AC Josephson current for various Z . Z is a: Z "0, b: Z "1, c: K K K K Z "3, d: Z "10. K K