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基于自由电子近似和Winful的隧穿时间模型，研究了普通金属/自旋过滤层/非磁绝缘层/自旋过滤层/普通金属（NM/SF/I/SF/NM）双自旋过滤隧道结中自旋相关的居留时间（dwell time）和相位时间（phase time）.分别以居留时间和相位时间随入射电子能量、势垒高度和势垒宽度、以及分子场大小的变化情况做了讨论.计算结果表明：在低能隧穿区域（入射电子的能量小于势垒高度），由于自旋相关的自相干项的影响，不同自旋方向电子的相位时间总是大于居留时间；在高能隧穿区域（入射电子的能量大于势垒高度），自旋相关的自相干项的影响减小，不同自旋方向电子的相位时间和于居留时间趋于一致.NM/SF/I/SF/NM双自旋过滤隧道结中的居留时间和相位时间基本不受非磁绝缘层势垒高度和宽度变化的影响，该现象不同于常规的铁磁金属/非磁绝缘层/铁磁金属（FM/I/FM）隧道结.但当非磁绝缘层势垒高度低于自旋过滤层势垒高度时，改变非磁绝缘层的势垒高度和宽度会使居留时间和相位时间出现相峰值，该峰值的出现与不同自旋方向电子的共振隧穿有关.自旋过滤层的势垒高度的变化对NM/SF/I/SF/NM双自旋过滤隧道结中的居留时间和相位时间影响大，但宽度变化的影响较小.自旋过滤层中分子场的变化对不同自旋方向的电子的居留时间和相位时间有明显影响，且上自旋电子的居留时间和相位时间随分子场的增大而减少，而下自旋电子的情况刚好相反.Based on the free electronic model and Winful's theory about tunneling times, the dwell times and the phase times in NM/SF/I/SF/NM double spin filter junctions are investigated, where the NM denotes the normal metal, SF the insulator barrier with spin filter effects and I the nonmagnetic insulator barrier. There are three different cases which are analyzed in detail:1) the dependences of dwell time and phase time on the energy of the incident electron; 2) the dependences of dwell time and phase time on the heights of the barrier; 3) the dependences of dwell time and phase time on the width of the barrier and the molecular field in the spin filter layer. The numerical results show that for the first case, when the electrons have low incident energy (smaller than the barrier height), as the influence of the spin-dependent self-interfere term, the phase times are always larger than the dwell times for electrons with different spinorientations. But when the electrons have high incident energy (higher than the barrier heights), the influence of the self-interfere term disappears and the differences between the phase time and dwell time for electrons with different spin orientations disappear also. For case 2, the numerical results show that the variation of nonmagnetic insulator barrier height has little influence on the dwell time and phase time in NM/SF/I/SF/NM double spin filter junctions. But when the nonmagnetic insulator barrier height is lower than the barrier height of spin filter layer, the quantum well will appear and the resonant tunneling can be induced to lead to the peaks in the dependences of dwell and phase times on the insulator barrier height. The variation of spin-filter barrier height has obvious influence on the dwell time and phase time in NM/SF/I/SF/NM double spin filter junction. With increasing the height of spin-filter barrier, the dwell times and phase time both first increase and then decrease. For case 3, the influences of the widths of the nonmagnetic insulator barrier layer and spin filter layer on the dwell time and phase time are little. But when the barrier height of nonmagnetic insulator barrier is lower than that of spin-filter layer, the variation of width of insulator barrier can lead to the resonant tunneling and the peaks in dwell and phase times. Unlike the influence of width of barrier, the influences of molecular field in the spin filter layer on the dwell time and phase time are obvious. For the up-spin electrons, dwell time and phase time decrease with increasing the molecular fields, which is contrary to the scenario for the down-spin electrons.
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Keywords:
- dwell time /
- phase time /
- magnetic tunneling junction /
- spin filter effect
[1] Moodera J S, Santos T S, Nagahama T 2007J. Phys.:Condens. Matter 19 165202
[2] Meservey R, Tedrow P M 1994Phys. Rep. 238 173
[3] Saffarzadeh A 2004J. Magn. Magn. Mater. 269 327
[4] Nagahana T, Santos T S, Moodera J S 2009Phys. Rev. Lett. 99 016602
[5] Jin D F, Ren Y, Li Z Z, Xiao M W, Jin G J, Hu A 2006Phys. Rev. B 73 012414
[6] He P B, Liu W M 2005Phys. Rev. B 72 064410
[7] Li Y, Li B Z, Zhang W S, Dai D S 1998Phys. Rev. B 57 1079
[8] Worledge D C, Geballe T H 2000J. Appl. Phys. 88 5277
[9] Miao G X, Mller M, Moodera J S 2009Phys. Rev. Lett. 102 076601
[10] Miao G X, Chang J Y, Assaf Badih A, Donald H 2014Nat. Comms. 5 3682
[11] Miao G X, Moodera J S 2012Phys. Rev. B 85 144424
[12] Lders U, Bibes M, Fusil S, Bouzehouane K, Jacquet E, Sommers C B, Contour J P, Bobo J F, Barthélémy A, Fert A, Levy P M 2007Phys. Rev. B 76 134412
[13] Lders U, Barthélémy A, Bibes M, Bouzehouane K, Fusil S, Jacquet E, Contour J P, Bobo J F, Fontcuberta J, Fert A 2006Adv. Mat. 18 1733
[14] Condon E U, Morse P M 1931Rev. Mod. Phys. 3 43
[15] Wigner E P 1955Phys. Rev. 98 145
[16] Smith F T 1960Phys. Rev. 118 349
[17] Bttiker M 1983Phys. Rev. B 27 6178
[18] Bttiker M, Landauer R 1982Phys. Rev. Lett. 49 1739
[19] Landauer R, Martin Th 1994Rev. Mod. Phys. 66 217
[20] Winful H G 2003Phys. Rev. Lett. 91 260401
[21] Guo Y, Shang C E, Chen X Y 2005Phys. Rev. B 72 045356
[22] Wang B, Guo Y, Gu B L 2002J. Appl. Phys. 91 1318
[23] Wu H C, Guo Y, Chen X Y, Gu B L 2003J. Appl. Phys. 93 5316
[24] Zhang Y T, Li Y C 2006J. Appl. Phys. 99 013907
[25] Du J, Zhang P, Liu J H, Li J L, Li Y X 2008Acta Phys. Sin. 57 7221(in Chinese)[杜坚, 张鹏, 刘继红, 李金亮, 李玉现2008物理学报57 7221]
[26] Slonczewski J C 1989Phys. Rev. B 39 6995
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[1] Moodera J S, Santos T S, Nagahama T 2007J. Phys.:Condens. Matter 19 165202
[2] Meservey R, Tedrow P M 1994Phys. Rep. 238 173
[3] Saffarzadeh A 2004J. Magn. Magn. Mater. 269 327
[4] Nagahana T, Santos T S, Moodera J S 2009Phys. Rev. Lett. 99 016602
[5] Jin D F, Ren Y, Li Z Z, Xiao M W, Jin G J, Hu A 2006Phys. Rev. B 73 012414
[6] He P B, Liu W M 2005Phys. Rev. B 72 064410
[7] Li Y, Li B Z, Zhang W S, Dai D S 1998Phys. Rev. B 57 1079
[8] Worledge D C, Geballe T H 2000J. Appl. Phys. 88 5277
[9] Miao G X, Mller M, Moodera J S 2009Phys. Rev. Lett. 102 076601
[10] Miao G X, Chang J Y, Assaf Badih A, Donald H 2014Nat. Comms. 5 3682
[11] Miao G X, Moodera J S 2012Phys. Rev. B 85 144424
[12] Lders U, Bibes M, Fusil S, Bouzehouane K, Jacquet E, Sommers C B, Contour J P, Bobo J F, Barthélémy A, Fert A, Levy P M 2007Phys. Rev. B 76 134412
[13] Lders U, Barthélémy A, Bibes M, Bouzehouane K, Fusil S, Jacquet E, Contour J P, Bobo J F, Fontcuberta J, Fert A 2006Adv. Mat. 18 1733
[14] Condon E U, Morse P M 1931Rev. Mod. Phys. 3 43
[15] Wigner E P 1955Phys. Rev. 98 145
[16] Smith F T 1960Phys. Rev. 118 349
[17] Bttiker M 1983Phys. Rev. B 27 6178
[18] Bttiker M, Landauer R 1982Phys. Rev. Lett. 49 1739
[19] Landauer R, Martin Th 1994Rev. Mod. Phys. 66 217
[20] Winful H G 2003Phys. Rev. Lett. 91 260401
[21] Guo Y, Shang C E, Chen X Y 2005Phys. Rev. B 72 045356
[22] Wang B, Guo Y, Gu B L 2002J. Appl. Phys. 91 1318
[23] Wu H C, Guo Y, Chen X Y, Gu B L 2003J. Appl. Phys. 93 5316
[24] Zhang Y T, Li Y C 2006J. Appl. Phys. 99 013907
[25] Du J, Zhang P, Liu J H, Li J L, Li Y X 2008Acta Phys. Sin. 57 7221(in Chinese)[杜坚, 张鹏, 刘继红, 李金亮, 李玉现2008物理学报57 7221]
[26] Slonczewski J C 1989Phys. Rev. B 39 6995
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