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Spin-transfer torque-based magnetic random access memory is becoming more and more attractive in industry due to its non-volatility, fast switching speed and infinite endurance. However, it suffers energy and speed bottlenecks, so the magnetic tunnel junction urgently needs a new write scheme. Compared with the spin-transfer torque, emerging spin-orbit torque will replace spin-transfer torque as a new write scheme of magnetic storage technology for its faster writing speed and avoiding the barrier breakdown. A three-terminal magnetic tunnel junction consists of magnetic tunnel junction/heavy metal structure offers a promising perspective from a technological point of view in the design of new generation of magnetic random access memory, for it is possible to control the magnetization dynamics through two current densities of spin-transfer torque and the spin-orbit torque. In this paper, the stability of magnetic states in the three-terminal magnetic tunnel junction is studied theoretically. Through linearizing the Landau-Lifshitz-Gilbert equation including the spin-transfer torque and the spin-orbit torque defined in the spherical coordinates, the new equilibrium directions and linear differential equations are obtained. Performing linear stability analysis of the new equilibrium directions, the phase diagrams defined by the direction of pinned-layer magnetization vector and the current density of spin-orbit torque are obtained. Several magnetic states are distinguished in the phase diagram, such as in-plane precessional and stable states, out-of-plane precessional and stable states. When the pinned-layer magnetization vector rotates out of the film plane, through adjusting the direction of pinned-layer magnetization vector, the switching from stable state to precessional one can be realized. Orientating the pinned-layer magnetization vector in the film plane, neither the out-of-plane precession nor stable states emerges for the current density of spin-orbit torque and spin-transfer torque are relatively small. The instability current takes a minimum value with the pinned-layer magnetization vector nearly parallel or antiparallel to the easy axis of free layer and increases with the direction of pinned-layer magnetization vector deviating from these two locations. The magnetization reversal can be realized through adjusting the current density of spin-transfer torque, and the reversal time can decrease greatly under the assisting of spin-orbit torque. By showing the dependence of magnetization vector on the time of different magnetic states, the validity of phase diagram is confirmed. The selecting of the different directions of the pinned-layer magnetization vector provides an alternative way to control the current-driven magnetization dynamics. This will provide useful guide for the application of three-terminal magnetic tunnel junction.
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Zhao W S, Wang Z H, Peng S Z, Wang L Z, Chang L, Zhang Y G 2016 Sci. Sin.: Physica, Mechanica & Astronomica 46 107306
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Liu B Z, Peng J H 2005 Nonlinear Dynamics (Beijing: High Education Publishing) p34 (in Chinese)
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-
图 1 理论模型和坐标系
Figure 1. Theoretical mode and coordinate system.
图 2 以钉扎层磁化向量极角
$ \theta_{\rm p} $ 和自旋轨道矩电流密度$ J_{\rm SHE} $ 为控制参数的相图Figure 2. The phase diagram defined in parameter space spanned by the polar angle of pinned-layer magnetization vector
$ \theta_{\rm p} $ and the current density of spin-orbit torque$ J_{\rm SHE} $ 
图 3 对于图2中不同区域a, b, c,
$ a^{\prime} $ ,$ b^{\prime} $ ,$ c^{\prime} $ 六点, 自由层磁化向量随时间的演化轨迹 (a)和($ {\rm a}^{\prime} $ )准平行稳定态或平面内的进动态; (b)和($ {\rm b}^{\prime} $ )伸出膜面的进动态; (c)和($ {\rm c}^{\prime} $ )伸出膜面的稳定态Figure 3. The time evolutions of free-layer magnetization vector for six points a, b,
$ c, a^{\prime} $ ,$ b^{\prime} $ and$ c^{\prime} $ in different regions of Fig. 2. (a) and ($ {\rm a}^{\prime} $ ) quasi-P or IPP state; (b) and ($ {\rm b}^{\prime} $ ) OPP state; (c) and ($ {\rm c}^{\prime} $ ) OPS states.
图 4 以钉扎层磁化向量方位角
$ \phi_{\rm p} $ 和自旋轨道矩电流密度$ J_{\rm SHE} $ 为控制参数的相图Figure 4. The phase diagram defined in parameter space spanned by the azimuthal angle of pinned-layer magnetization vector
$ \phi_{\rm p} $ and the current density of spin-orbit torque$ J_{\rm SHE} $ .
图 5 对应图4中的“a”点, 自由层初始磁化沿x方向时磁化向量三个分量
$ m_{x} $ ,$ m_{y} $ 和$ m_{z} $ 在不同自旋矩驱动下随时间的演化 (a)自旋转移矩激发的平面内的稳定态; (b)自旋转移矩驱动磁化翻转; (c)自旋转移矩和自旋轨道矩共同激发的平面内的进动态; (d)自旋转移矩和自旋轨道矩共同驱动磁化翻转Figure 5. The time evolutions of three components
$ m_{x} $ ,$ m_{y} $ and$ m_{z} $ driven by different spin torque in free-layer magnetization vector for point ‘a’ of Fig. 4 with the initial magnetization along x direction: (a) IPS state excited by spin-transfer torque; (b) magnetization reversal driven by spin-transfer torque; (c) IPP state excited by spin-transfer torque and spin-orbit torque; (d) magnetization reversal driven by spin-transfer torque and spin-orbit torque. -
[1] Slonczewski J C 1996 J. Magn. Magn. Mater. 159 L1
Google Scholar
[2] Berger L 1996 Phys. Rev. B 54 9353
Google Scholar
[3] 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
Google Scholar
[4] Myers E B, Ralph D C, Katine J A, Louie R N, Buhrman R A 1999 Science 285 867
Google Scholar
[5] Katine J A, Albert F J, Buhrman R A, Myers E B, Ralph D C 2000 Phys. Rev. Lett. 84 3149
Google Scholar
[6] 张磊, 任敏, 胡九宁, 邓宁, 陈陪毅 2008 物理学报 57 2427
Google Scholar
Zhang L, Ren M, Hu J N, Deng N, Chen P Y 2008 Acta Phys. Sin. 57 2427
Google Scholar
[7] 包瑾, 徐晓光, 姜勇 2009 物理学报 58 7998
Google Scholar
Bao J, Xu X G, Jiang Y 2009 Acta Phys. Sin. 58 7998
Google Scholar
[8] Sun C Y, Wang Z C 2010 Chin. Phys. Lett. 27 077501
Google Scholar
[9] Huai Y, Albert F, Nguyen P, Pakala M, Valet T 2004 Appl. Phys. Lett. 84 3118
Google Scholar
[10] Yuasa S, Hono K, Hu G, Worledge D C 2018 MRS Bulletin 43 352
Google Scholar
[11] Sato N, Xue F, White R M, Bi C, Wang S X 2018 Nature Electronics 1 508
Google Scholar
[12] Cubukcu M, Boulle O, Mikuszeit N, Hamelin C, Brächer T, Lamard N, Cyrille M C, Buda-Prejbeanu L, Garello K, Miron I M, Klein O, de Loubens G, Naletov V V, Langer J, Ocker B, Pietro, Gaudin G 2018 IEEE Trans. Magn. 54 9300204
[13] Taniguchi T 2019 J. Magn. Magn. Mater. 483 281
Google Scholar
[14] 赵巍胜, 王昭昊, 彭守仲, 王乐知, 常亮, 张有光 2016 中国科学: 物理学 力学 天文学 46 107306
Zhao W S, Wang Z H, Peng S Z, Wang L Z, Chang L, Zhang Y G 2016 Sci. Sin.: Physica, Mechanica & Astronomica 46 107306
[15] Miron I M, Garello K, Gaudin G, Zermatten P J, Costache M V, Auffret S, Bandiera S, Rodmacq B, Schuhl A, Gambardella P 2011 Nature 476 189
Google Scholar
[16] Liu L Q, Lee O J, Gudmundsen T J, Ralph D C, Buhrman R A 2012 Phys. Rev. Lett. 109 096602
Google Scholar
[17] Liu L Q, Pai C F, Li Y, Tseng H W, Ralph D C, Buhrman R A 2012 Science 336 555
Google Scholar
[18] Pai C F, Liu L Q, Li Y, Tseng H W, Ralph D C, Buhrman R A 2012 Appl. Phys. Lett. 101 122404
Google Scholar
[19] Cai K M, Yang M Y, Ju H L, Wang S M, Ji Y, Li B H, Edmonds K W, Sheng Y, Zhang B, Zhang N, Liu S, Zheng H Z, Wang K Y 2017 Nature Mater 16 712
Google Scholar
[20] Sheng Y, Li Y C, Ma X Q, Wang K Y 2018 Appl. Phys. Lett. 113 112406
Google Scholar
[21] Kwak W Y, Kwon J H, Grünberg P, Han S H, Cho B K 2018 Scientific Reports 8 382
Google Scholar
[22] Wang X, Wan C H, Kong W J, Zhang X, Xing Y W, Fang C, Tao B S, Yang W L, Huang L, Wu H, Irfan M, Han X F 2018 Adv. Mater. 30 1801318
Google Scholar
[23] Zhao X Z, Zhang X Y, Yang H W, Cai W L, Zhao Y L, Wang Z H, Zhao W S 2019 Nanotechnology 30 335707
Google Scholar
[24] Dyakonov M I, Perel V I 1971 Phys. Lett. 35 459
Google Scholar
[25] Hirsch J E 1999 Phys. Rev. Lett. 83 1834
Google Scholar
[26] Zhang S F 2000 Phys. Rev. Lett. 85 393
Google Scholar
[27] Tomasello R, Carpentieri M, Finocchio G 2013 Appl. Phys. Lett. 103 252408
Google Scholar
[28] Wang Z H, Zhao W S, Deng E, Klein J O, Chappert C 2015 Journal of Physics D: Applied Physics 48 065001
Google Scholar
[29] Grollier J, Cros V, Jaffrès H, Hamzic A, George J M, Faini G, Youssef J. Ben, Le Gall H , Fert A 2003 Phys. Rev. B 67 174402
Google Scholar
[30] Bazaliy Ya B, Jones B A, Zhang S C 2004 Phys. Rev. B 69 094421
Google Scholar
[31] Smith N, Katine J A, Childress J R, Carey M J 2005 IEEE Trans. Magn. 41 2935
Google Scholar
[32] Morise H, Nakamura S 2005 Phys. Rev. B 71 014439
Google Scholar
[33] 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
Liu B Z, Peng J H 2005 Nonlinear Dynamics (Beijing: High Education Publishing) p34 (in Chinese)
[34] Ebels U, Houssameddine D, Firastrau I, Gusakova D, Thirion C, Dieny B, Buda-Prejbeanu L D 2008 Phys. Rev. B 78 024436
Google Scholar
[35] Zhou Y, Bonetti S, Zha C L, Åkerman J 2009 New J. Phys. 11 103028
Google Scholar
[36] 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
Google Scholar
[37] Wang R X, He P B, Li Z D, Pan A L, Liu Q H 2011 J. Appl. Phys. 109 033905
Google Scholar
[38] Li Z D, He P B, Liu W M 2014 Chin. Phys. B 23 117502
Google Scholar
[39] 王日兴, 贺鹏斌, 肖运昌, 李建英 2015 物理学报 64 137201
Google Scholar
Wang R X, He P B, Xiao Y C, Li J Y 2015 Acta Phys. Sin. 64 137201
Google Scholar
[40] 王日兴, 叶华, 王丽娟, 敖章洪 2017 物理学报 66 127201
Google Scholar
Wang R X, Ye H, Wang L J, Ao Z H 2017 Acta Phys. Sin. 66 127201
Google Scholar
[41] Houssameddine D, Ebels U, Delaët B, Rodmacq B, Firastrau I, Ponthenier F, Brunet M, Thirion C, Michel J P, Buda-Prejbeanu L D, Cyrille M C, Redon O, Dieny B 2007 Nature Materials 6 447
Google Scholar
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