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The influence of spin Hall effect on magnetization dynamics is one of the hottest topics in spintronics. In this paper, the magnetization dynamics driven by the spin Hall effect-induced torque in a ferromagnet /heavy metal bilayer structure has been investigated theoretically. By linearizing the Landau-Lifshitz-Gilbert equation which includes the spin Hall effect torque term, and taking stability analysis, the phase diagrams in the plane defined by the current density and external magnetic field have been obtained. Under the control of the current density and external magnetic field, several magnetic states, such as in-plane stable state, in-plane precession and bistable states can be realized. With the external magnetic field oriented within a certain range, the magnetization reversal and precession can be realized through adjusting the current density. In addition, the dynamic evolutions of these magnetic states are demonstrated by solving the temporal evolutive equations numerically.
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Keywords:
- magnetization reversal /
- spin Hall effect /
- stability analysis
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[2] Slonczewski J C 1996 J. Magn. Magn. Mater. 159 L1
[3] Myers E B, Ralph D C, Katine J A, Louie R N, Buhrman R A 1999 Science 285 867
[4] Katine J A, Albert F J, Buhrman R A, Myers E B, Ralph D C 2000 Phys. Rev. Lett. 84 3149
[5] Zhang L, Ren M, Hu J N, Deng N, Chen P Y 2008 Acta Phys. Sin. 57 2427 (in Chinese) [张磊, 任敏, 胡九宁, 邓宁, 陈陪毅 2008 57 2427]
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[7] Sun C Y, Wang Z C 2010 Chin. Phys. Lett. 27 077501
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[9] Bazaliy Ya B, B. A. Jones, Zhang S C 1998 Phys. Rev. B 57 R3213
[10] Zhang S, Li Z 2004 Phys. Rev. Lett. 93 127204
[11] Dyakonov M I, Perel V I 1971 Phys. Lett. 35 459
[12] Hirsch J E 1999 Phys. Rev. Lett. 83 1834
[13] Zhang S F 2000 Phys. Rev. Lett. 85 393
[14] Liu L Q, Pai C F, Li Y, Tseng H W, Ralph D C, Buhrman R A 2012 Science 336 555
[15] Liu L Q, Lee O J, Gudmundsen T J, Ralph D C, Buhrman R A 2012 Phys. Rev. Lett. 109 096602
[16] Pai C F, Liu L Q, Li Y, Tseng H W, Ralph D C, Buhrman R A 2012 Appl. Phys. Lett. 101 122404
[17] Lee K S, Lee S W, Min B C, Lee K J 2013 Appl. Phys. Lett. 102 112410
[18] Liu L Q, Pai C F, Ralph D C, Buhrman R A 2012 Phys. Rev. Lett. 109 186602
[19] Liu B Z, Peng J H 2005 Nonlinear Dynamics (Beijing: High Education Publishing) p34 (in Chinese) [刘秉正, 彭建华 2005 非线性动力学 (北京:高等教育出版社) 第34页]
[20] Bazaliy Ya B, Jones B. A., Zhang S C 2004 Phys. Rev. B 69 094421
[21] Grollier J, Cros V, Jaffrès H, Hamzic A, George J M, Faini G, Youssef J. Ben, Gall H Le, Fert A 2003 Phys. Rev. B 67 174402
[22] Smith N, Katine J A, Childress J R, Carey M J 2005 IEEE Trans. Magn. 41 2935
[23] Morise H, Nakamura S 2005 Phys. Rev. B 71 014439
[24] Ebels U, Houssameddine D, Firastrau I, Gusakova D, Thirion C, Dieny B, Buda-Prejbeanu L D 2008 Phys. Rev. B 78 024436
[25] Zhou Y, Bonetti S, Zha C L, Åkerman J 2009 New J. Phys. 11 103028
[26] He P B, Wang R X, Li Z D, Liu Q H, Pan A L, Wang Y G, Zou B S 2010 Eur. Phys. J. B 73 417
[27] Wang R X, He P B, Li Z D, Pan A L, Liu Q H 2011 J. Appl. Phys. 109 039905
[28] Wang R X, Zhao J L, He P B, Gu G N, Li Z D, Pan A L, Liu Q H 2013 J. Magn. Magn. Mater. 327 132
[29] Li Z D, He P B, Liu W M 2014 Chin. Phys. B 23 117502
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[1] Berger L 1996 Phys. Rev. B 54 9353
[2] Slonczewski J C 1996 J. Magn. Magn. Mater. 159 L1
[3] Myers E B, Ralph D C, Katine J A, Louie R N, Buhrman R A 1999 Science 285 867
[4] Katine J A, Albert F J, Buhrman R A, Myers E B, Ralph D C 2000 Phys. Rev. Lett. 84 3149
[5] Zhang L, Ren M, Hu J N, Deng N, Chen P Y 2008 Acta Phys. Sin. 57 2427 (in Chinese) [张磊, 任敏, 胡九宁, 邓宁, 陈陪毅 2008 57 2427]
[6] Bao J, Xu X G, Jiang Y 2009 Acta Phys. Sin. 58 7998 (in Chinese) [包瑾, 徐晓光, 姜勇 2009 58 7998]
[7] Sun C Y, Wang Z C 2010 Chin. Phys. Lett. 27 077501
[8] Kiselev S I, Sankey J C, Krivorotov I N, Emley N C, Schoelkopf R J, Buhrman R A, Ralph D C 2003 Nature 425 380
[9] Bazaliy Ya B, B. A. Jones, Zhang S C 1998 Phys. Rev. B 57 R3213
[10] Zhang S, Li Z 2004 Phys. Rev. Lett. 93 127204
[11] Dyakonov M I, Perel V I 1971 Phys. Lett. 35 459
[12] Hirsch J E 1999 Phys. Rev. Lett. 83 1834
[13] Zhang S F 2000 Phys. Rev. Lett. 85 393
[14] Liu L Q, Pai C F, Li Y, Tseng H W, Ralph D C, Buhrman R A 2012 Science 336 555
[15] Liu L Q, Lee O J, Gudmundsen T J, Ralph D C, Buhrman R A 2012 Phys. Rev. Lett. 109 096602
[16] Pai C F, Liu L Q, Li Y, Tseng H W, Ralph D C, Buhrman R A 2012 Appl. Phys. Lett. 101 122404
[17] Lee K S, Lee S W, Min B C, Lee K J 2013 Appl. Phys. Lett. 102 112410
[18] Liu L Q, Pai C F, Ralph D C, Buhrman R A 2012 Phys. Rev. Lett. 109 186602
[19] Liu B Z, Peng J H 2005 Nonlinear Dynamics (Beijing: High Education Publishing) p34 (in Chinese) [刘秉正, 彭建华 2005 非线性动力学 (北京:高等教育出版社) 第34页]
[20] Bazaliy Ya B, Jones B. A., Zhang S C 2004 Phys. Rev. B 69 094421
[21] Grollier J, Cros V, Jaffrès H, Hamzic A, George J M, Faini G, Youssef J. Ben, Gall H Le, Fert A 2003 Phys. Rev. B 67 174402
[22] Smith N, Katine J A, Childress J R, Carey M J 2005 IEEE Trans. Magn. 41 2935
[23] Morise H, Nakamura S 2005 Phys. Rev. B 71 014439
[24] Ebels U, Houssameddine D, Firastrau I, Gusakova D, Thirion C, Dieny B, Buda-Prejbeanu L D 2008 Phys. Rev. B 78 024436
[25] Zhou Y, Bonetti S, Zha C L, Åkerman J 2009 New J. Phys. 11 103028
[26] He P B, Wang R X, Li Z D, Liu Q H, Pan A L, Wang Y G, Zou B S 2010 Eur. Phys. J. B 73 417
[27] Wang R X, He P B, Li Z D, Pan A L, Liu Q H 2011 J. Appl. Phys. 109 039905
[28] Wang R X, Zhao J L, He P B, Gu G N, Li Z D, Pan A L, Liu Q H 2013 J. Magn. Magn. Mater. 327 132
[29] Li Z D, He P B, Liu W M 2014 Chin. Phys. B 23 117502
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