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We investigated the spin-dependent transmission coefficient and tunneling magnetoresistance in symmetric parabolic-well with two ferromagnetic contacts (F/SPW/F). The quantum size effect and Rashba spin-orbit interaction are discussed simultaneously. The results indicate that the transmission coefficient and tunneling magnetoresistance are periodic function of the parabolic-well width. The oscillation frequencies of the transmission coefficient and tunneling magnetoresistance decrease with the increasing of the parabolic-well depth. The oscillation frequencies of the transmission coefficient and tunneling magnetoresistance increase with the increasing of the Rashba spin-orbit coupling strength. The amplitude and peak-to-valley ratio of the transmission coefficient and tunneling magnetoresistance are strongly dependent on the difference in orientations of the two magnetizations in the left and right ferromagnets.
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Keywords:
- magnetic tunneling junction /
- Rashba spin-orbit coupling /
- transmission coefficient /
- tunneling magnetoresistance
[1] Datta S, Das B 1990 Appl. Phys. Lett. 56 665
[2] Du J, Zhang P, Liu J H, Li J L, Li Y X 2008 Acta Phys. Sin. 57 7221 (in Chinese) [杜 坚、 张 鹏、 刘继红、 李金亮、 李玉现 2008 57 7221]
[3] Du J, Li C G, Qin F 2009 Acta Phys. Sin. 58 3448 (in Chinese) [杜 坚、 李春光、 秦 芳 2009 58 3448]
[4] Du J, Wang S X, Yang S M 2009 Acta Phys. Sin. 58 7926 (in Chinese) [杜 坚、 王素新、 杨淑敏 2009 58 7926]
[5] Du J, Wang S X, Yuan A G 2010 Acta Phys. Sin. 59 2760 (in Chinese) [杜 坚、 王素新、 袁爱国 2010 59 2760]
[6] Du J, Wang S X, Yuan A G 2010 Acta Phys. Sin. 59 2767 (in Chinese) [杜 坚、 王素新、 袁爱国 2010 59 2767]
[7] Moroz A V, Barnes C H W 1999 Phys. Rev. B 60 14272 Moroz A V, Samokhin K V, Barnes C H W 2000 Phys. Rev. Lett. 84 4164
[8] Mireles F, Kirczenow G 2002 Phys. Rev. B 66 214415 Mireles F, Kirczenow G 2001 Phys. Rev. B 64 024426
[9] Mireles F, Kirczenow G 2002 Europhys Lett. 59 107
[10] Schpers Th, Nitta J, Heersche H B, Takayanagi H 2001 Phys. Rev. B 64 125314
[11] Matsuyama T, Hu C M, Grundler D, Meier G, Merkt U 2002 Phys. Rev. B 65 155322
[12] Moser J, Zenger M, Gerl C, Schuh D, Meier R, Chen P, Bayreuther G, Wegscheider W, Weiss D, Lai C H, Huang R T, Kosuth M, Ebert H 2006 Appl. Phys. Lett. 89 162106
[13] Julliere M 1975 Phys. Lett. A 54 225
[14] Zhang X D, Li B Z, Sun G, Pu F C 1997 Phys. Rev. B 56 5484
[15] Zhang X D, Li B Z, Zhang W S, Pu F C 1998 Phys. Rev. B 57 1090
[16] Xie Z W, Li B Z 2002 Acta Phys. Sin. 51 399 (in Chinese) [谢征微、 李伯藏 2002 51 399]
[17] Jin L, Zhu L, Li L, Xie Z W 2009 Acta Phys. Sin. 58 8577 (in Chinese) [金 莲、 朱 林、 李 玲、 谢征微 2009 58 8577]
[18] Miller R C, Gossard A C, Kleinman D A, Munteanu O 1984 Phys. Rev. B 29 3740
[19] Shayegan M, Sajoto T, Santos M, Silvestre C 1988 Appl. Phys. Lett. 53 791
[20] Yuen W P 1993 Phys. Rev. B 48 17316
[21] Chiba D, Akiba N, Matsukura F, Ohno Y, Ohno H 2000 Appl. Phys. Lett. 77 1873
[22] Johnson M 1998 Phys. Rev. B 58 9635 Johnson M, Silsbee R H 1988 Phys. Rev. B 37 5326
[23] Hu C M, Matsuyama T 2001 Phys. Rev. Lett. 87 066803
[24] Herling G H, Rustgi M L 1992 J. Appl. Phys. 71 796
[25] Qi X H, Kong X J, Liu J J 1998 Phys. Rev. B 58 10578
[26] Wu H C, Guo Y, Chen X Y,Gu B L 2003 J. Appl. Phys. 93 5316
[27] Li Y X, GuoY, Li B Z 2005 Phys. Rev. B 71 012406
[28] Liu D, Kong X J 2008 J. Appl. Phys. 104 023707
[29] Liu D, Kong X J 2009 J. Appl. Phys. 105 043703
[30] Büttiker M 1993 J. Phys.: Condens Matter 5 9361
[31] Christen T, Büttiker M 1996 Phys. Rev. Lett. 77 143
[32] Zenger M, Moser J, Wegscheider W, Weiss D, Dietl T 2004 J. Appl. Phys. 96 2400
[33] Liu D, Zhang H M 2008 Mod. Phys. Lett. B 22 2667
[34] Shinobu Ohya, Pham Nam Hai, Masaaki Tanaka 2005 Appl. Phys. Lett. 87 012105
[35] Pham Nam Hai, Masafumi Yokoyama, Shinobu Ohya, Masaaki Tanaka 2006 Appl. Phys. Lett. 89 242106
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[1] Datta S, Das B 1990 Appl. Phys. Lett. 56 665
[2] Du J, Zhang P, Liu J H, Li J L, Li Y X 2008 Acta Phys. Sin. 57 7221 (in Chinese) [杜 坚、 张 鹏、 刘继红、 李金亮、 李玉现 2008 57 7221]
[3] Du J, Li C G, Qin F 2009 Acta Phys. Sin. 58 3448 (in Chinese) [杜 坚、 李春光、 秦 芳 2009 58 3448]
[4] Du J, Wang S X, Yang S M 2009 Acta Phys. Sin. 58 7926 (in Chinese) [杜 坚、 王素新、 杨淑敏 2009 58 7926]
[5] Du J, Wang S X, Yuan A G 2010 Acta Phys. Sin. 59 2760 (in Chinese) [杜 坚、 王素新、 袁爱国 2010 59 2760]
[6] Du J, Wang S X, Yuan A G 2010 Acta Phys. Sin. 59 2767 (in Chinese) [杜 坚、 王素新、 袁爱国 2010 59 2767]
[7] Moroz A V, Barnes C H W 1999 Phys. Rev. B 60 14272 Moroz A V, Samokhin K V, Barnes C H W 2000 Phys. Rev. Lett. 84 4164
[8] Mireles F, Kirczenow G 2002 Phys. Rev. B 66 214415 Mireles F, Kirczenow G 2001 Phys. Rev. B 64 024426
[9] Mireles F, Kirczenow G 2002 Europhys Lett. 59 107
[10] Schpers Th, Nitta J, Heersche H B, Takayanagi H 2001 Phys. Rev. B 64 125314
[11] Matsuyama T, Hu C M, Grundler D, Meier G, Merkt U 2002 Phys. Rev. B 65 155322
[12] Moser J, Zenger M, Gerl C, Schuh D, Meier R, Chen P, Bayreuther G, Wegscheider W, Weiss D, Lai C H, Huang R T, Kosuth M, Ebert H 2006 Appl. Phys. Lett. 89 162106
[13] Julliere M 1975 Phys. Lett. A 54 225
[14] Zhang X D, Li B Z, Sun G, Pu F C 1997 Phys. Rev. B 56 5484
[15] Zhang X D, Li B Z, Zhang W S, Pu F C 1998 Phys. Rev. B 57 1090
[16] Xie Z W, Li B Z 2002 Acta Phys. Sin. 51 399 (in Chinese) [谢征微、 李伯藏 2002 51 399]
[17] Jin L, Zhu L, Li L, Xie Z W 2009 Acta Phys. Sin. 58 8577 (in Chinese) [金 莲、 朱 林、 李 玲、 谢征微 2009 58 8577]
[18] Miller R C, Gossard A C, Kleinman D A, Munteanu O 1984 Phys. Rev. B 29 3740
[19] Shayegan M, Sajoto T, Santos M, Silvestre C 1988 Appl. Phys. Lett. 53 791
[20] Yuen W P 1993 Phys. Rev. B 48 17316
[21] Chiba D, Akiba N, Matsukura F, Ohno Y, Ohno H 2000 Appl. Phys. Lett. 77 1873
[22] Johnson M 1998 Phys. Rev. B 58 9635 Johnson M, Silsbee R H 1988 Phys. Rev. B 37 5326
[23] Hu C M, Matsuyama T 2001 Phys. Rev. Lett. 87 066803
[24] Herling G H, Rustgi M L 1992 J. Appl. Phys. 71 796
[25] Qi X H, Kong X J, Liu J J 1998 Phys. Rev. B 58 10578
[26] Wu H C, Guo Y, Chen X Y,Gu B L 2003 J. Appl. Phys. 93 5316
[27] Li Y X, GuoY, Li B Z 2005 Phys. Rev. B 71 012406
[28] Liu D, Kong X J 2008 J. Appl. Phys. 104 023707
[29] Liu D, Kong X J 2009 J. Appl. Phys. 105 043703
[30] Büttiker M 1993 J. Phys.: Condens Matter 5 9361
[31] Christen T, Büttiker M 1996 Phys. Rev. Lett. 77 143
[32] Zenger M, Moser J, Wegscheider W, Weiss D, Dietl T 2004 J. Appl. Phys. 96 2400
[33] Liu D, Zhang H M 2008 Mod. Phys. Lett. B 22 2667
[34] Shinobu Ohya, Pham Nam Hai, Masaaki Tanaka 2005 Appl. Phys. Lett. 87 012105
[35] Pham Nam Hai, Masafumi Yokoyama, Shinobu Ohya, Masaaki Tanaka 2006 Appl. Phys. Lett. 89 242106
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