Barrier-induced enhancement of Andreev reflection for minority-spin quasiparticles in ferromagnetic metal/insulator/superconductor ballistic junctions

A. Dimoulas

doi:10.1103/PhysRevB.61.9729

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Barrier-induced enhancement of Andreev reflection for minority-spin quasiparticles in ferromagnetic metal/insulator/superconductor ballistic junctions

A. Dimoulas

Institute of Materials Science, National Center for Scientific Research “DEMOKRITOS,” Athens, Greece

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Phys. Rev. B 61, 9729 – Published 1 April, 2000

DOI: https://doi.org/10.1103/PhysRevB.61.9729

Abstract

The Andreev reflection probability in ferromagnetic metal/superconductor ballistic junctions depends on the spin orientation of the incident quasiparticle when a barrier of low or moderate strength is present at the interface. In contrast to the common conception that a barrier always reduces Andreev reflection probability, this probability is enhanced for quasiparticles in the minority spin band only, due to a reduction in the phase shift of the wave function. Because of the Andreev reflection probability enhancement, which is predicted to be below the superconducting gap near the gap edge, the total subgap conductance exhibits characteristic weak but measurable features (maxima).

References (23)

G. A. Prinz, Science 282, 660 (1998).
M. Julliere, Phys. Lett. A54, 225 (1975).
J. C. Slonczewski, Phys. Rev. B 39, 6995 (1989).
A. F. Andreev, Zh. Eksp. Teor. Fiz. 46 1823 (1964) [ Sov. Phys. JETP 19, 1228 (1964)].
P. G. DeGennes, Superconductivity of Metals and Alloys (Benjamin, New York, 1966).
G. E. Blonder, M. Tinkham, and T. M. Klapwijk, Phys. Rev. B 25, 4515 (1982).
M. J. M. de Jong and C. W. J. Beenakker, Phys. Rev. Lett. 74, 1657 (1995).
The total exchange interaction energy is $E_{exch} = - (\frac{1}{2} {) N k}_{B} θ^{'} P^{2}$ [E. C. Stoner, Proc. R. Soc. London, Ser. A 165, 372 (1938)]. The energy per particle of given spin orientation is $\partial E_{exch} / \partial N_{↑} = - k_{B} θ^{'} P = - h_{0}$ and $\partial E_{exch} / \partial N_{↓} {= + k}_{B} θ^{'} {P = + h}_{0} .$ For $k_{B} θ^{'} \approx E_{F},$ in which case the Stoner criterion $k_{B} θ^{'} >~ (\frac{2}{3} {) E}_{F}$ for the onset of ferromagnetism is fulfilled, $h_{0} {/ E}_{F} {= (k}_{B} θ^{'} {/ E}_{F}) P \approx P .$
R. J. Soulen, Jr., J. M. Byers, M. S. Osofsky, B. Nadgorny, T. Ambrose, S. F. Cheng, P. R. Broussard, C. T. Tanaka, J. Nowak, J. S. Moodera, A. Barry, and J. M. D. Coey, Science 282, 85 (1998).
S. K. Upadhyay, A. Palasinami, R. N. Louie, and R. A. Buhrman, Phys. Rev. Lett. 81, 3247 (1998).
R. Meservey and P. M. Tedrow, Phys. Rep. 238, 173 (1994).
F. J. Jedema, B. J. van Wees, B. H. Hoving, A. T. Filip, and T. M. Klapwijk, Phys. Rev. B 60, 16 549 (1999); ibid.V. I. Fal’ko, A. F. Volkov, and C. Lambert, 60, 15 394 (1999).
J.-X. Zhu, B. Friedman, and C. S. Ting, Phys. Rev. B 59, 9558 (1999).
I. Zutic and O. T. Valls, Phys. Rev. B 61, 1555 (2000).
S. Kashiwaya, Y. Tanaka, N. Yoshida, and M. R. Beasley, cond-mat/9812160 (unpublished).
C. W. J. Beenakker, Rev. Mod. Phys. 69, 731 (1997).
C. J. Lambert, J. Phys.: Condens. Matter 3, 6579 (1991).
Y. Takane and H. Ebisawa, J. Phys. Soc. Jpn. 61, 1685 (1992).
C. W. J. Beenakker, Phys. Rev. B 46, 12 841 (1992).
See, for example, P. F. Bagwell, Phys. Rev. B 46, 12 573 (1992).
For normal reflection from a step barrier potential, $r = (k - i κ) / (k + i κ {) = e}^{- i 2 φ},$ $\tan φ = κ / k$ [see, e.g., G. Baym, Lectures on Quantum Mechanics (Benjamin/Cummings, London, 1969), p. 92; R. W. Robinett, Quantum Mechanics (Oxford University Press, New York, 1997), p. 256]. A factor of 2 in the phase appears because the particle acquires a phase shift -φ as it enters the barrier and an additional -φ as it returns in the opposite direction. In an Andreev reflection event of a spin-up quasiparticle, the corresponding phase shifts are $- φ_{↑}$ and $+ φ_{↓},$ resulting in a total phase shift of $δ φ = - (φ_{↑} - φ_{↓}) .$
B. J. van Wees, K.-M. H. Lenssen, and C. J. P. M. Harmans, Phys. Rev. B 44, 470 (1991).
U. Gunsenheimer, U. Schussler, and R. Kummel, Phys. Rev. B 49, 6111 (1994).

[c1] G. A. Prinz, Science 282, 660 (1998).

[c2] M. Julliere, Phys. Lett. A54, 225 (1975).

[c3] J. C. Slonczewski, Phys. Rev. B 39, 6995 (1989).

[c4] A. F. Andreev, Zh. Eksp. Teor. Fiz. 46 1823 (1964) [ Sov. Phys. JETP 19, 1228 (1964)].

[c5] P. G. DeGennes, Superconductivity of Metals and Alloys (Benjamin, New York, 1966).

[c6] G. E. Blonder, M. Tinkham, and T. M. Klapwijk, Phys. Rev. B 25, 4515 (1982).

[c7] M. J. M. de Jong and C. W. J. Beenakker, Phys. Rev. Lett. 74, 1657 (1995).

[c8] The total exchange interaction energy is $E_{exch} = - (\frac{1}{2} {) N k}_{B} θ^{'} P^{2}$ [E. C. Stoner, Proc. R. Soc. London, Ser. A 165, 372 (1938)]. The energy per particle of given spin orientation is $\partial E_{exch} / \partial N_{↑} = - k_{B} θ^{'} P = - h_{0}$ and $\partial E_{exch} / \partial N_{↓} {= + k}_{B} θ^{'} {P = + h}_{0} .$ For $k_{B} θ^{'} \approx E_{F},$ in which case the Stoner criterion $k_{B} θ^{'} >~ (\frac{2}{3} {) E}_{F}$ for the onset of ferromagnetism is fulfilled, $h_{0} {/ E}_{F} {= (k}_{B} θ^{'} {/ E}_{F}) P \approx P .$

[c9] R. J. Soulen, Jr., J. M. Byers, M. S. Osofsky, B. Nadgorny, T. Ambrose, S. F. Cheng, P. R. Broussard, C. T. Tanaka, J. Nowak, J. S. Moodera, A. Barry, and J. M. D. Coey, Science 282, 85 (1998).

[c10] S. K. Upadhyay, A. Palasinami, R. N. Louie, and R. A. Buhrman, Phys. Rev. Lett. 81, 3247 (1998).

[c11] R. Meservey and P. M. Tedrow, Phys. Rep. 238, 173 (1994).

[c12] F. J. Jedema, B. J. van Wees, B. H. Hoving, A. T. Filip, and T. M. Klapwijk, Phys. Rev. B 60, 16 549 (1999); ibid.V. I. Fal’ko, A. F. Volkov, and C. Lambert, 60, 15 394 (1999).

[c13] J.-X. Zhu, B. Friedman, and C. S. Ting, Phys. Rev. B 59, 9558 (1999).

[c14] I. Zutic and O. T. Valls, Phys. Rev. B 61, 1555 (2000).

[c15] S. Kashiwaya, Y. Tanaka, N. Yoshida, and M. R. Beasley, cond-mat/9812160 (unpublished).

[c16] C. W. J. Beenakker, Rev. Mod. Phys. 69, 731 (1997).

[c17] C. J. Lambert, J. Phys.: Condens. Matter 3, 6579 (1991).

[c18] Y. Takane and H. Ebisawa, J. Phys. Soc. Jpn. 61, 1685 (1992).

[c19] C. W. J. Beenakker, Phys. Rev. B 46, 12 841 (1992).

[c20] See, for example, P. F. Bagwell, Phys. Rev. B 46, 12 573 (1992).

[c21] For normal reflection from a step barrier potential, $r = (k - i κ) / (k + i κ {) = e}^{- i 2 φ},$ $\tan φ = κ / k$ [see, e.g., G. Baym, Lectures on Quantum Mechanics (Benjamin/Cummings, London, 1969), p. 92; R. W. Robinett, Quantum Mechanics (Oxford University Press, New York, 1997), p. 256]. A factor of 2 in the phase appears because the particle acquires a phase shift -φ as it enters the barrier and an additional -φ as it returns in the opposite direction. In an Andreev reflection event of a spin-up quasiparticle, the corresponding phase shifts are $- φ_{↑}$ and $+ φ_{↓},$ resulting in a total phase shift of $δ φ = - (φ_{↑} - φ_{↓}) .$

[c22] B. J. van Wees, K.-M. H. Lenssen, and C. J. P. M. Harmans, Phys. Rev. B 44, 470 (1991).

[c23] U. Gunsenheimer, U. Schussler, and R. Kummel, Phys. Rev. B 49, 6111 (1994).

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Barrier-induced enhancement of Andreev reflection for minority-spin quasiparticles in ferromagnetic metal/insulator/superconductor ballistic junctions

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