Current-induced motion of a transverse magnetic domain wall in the presence of spin Hall effect

Abstract

We theoretically study the current-induced dynamics of a transverse magnetic domain wall in bi-layer nanowires consisting of a ferromagnet on top of a nonmagnet having strong spin-orbit coupling. Domain wall dynamics is characterized by two threshold current densities, WB th J and REV th J , where WB th J is a threshold for the chirality switching of the domain wall and REV th J is another threshold for the reversed domain wall motion caused by spin Hall effect. Domain walls with a certain chirality may move opposite to the electron-flow direction with high speed in the current range WB th REV th J J J   for the system designed to satisfy the conditions WB REV th th JJ  and    , where  is the Gilbert damping constant and  is the nonadiabaticity of spin torque. Micromagnetic simulations confirm the validity of analytical results. 1 t J SH J J WB J b and REV J b . When WB J J REV J b b b   , the DW can move against the electron-flow direction. Note that the existence of such b J range implicitly assumes WB J REV J b b  . When this inequality is not satisfied, the DW always moves along the electron-flow direction. For all cases, DW v can be larger than   J bdepending on the parameters (see Eq. (6)).Second, v DW is asymmetric against the initial tilt angle 0 for a fixed current polarity. A similar argument is also valid for a fixed 0  but with varying the current polarity; i.e., DW v is asymmetric with respect to the current polarity for a fixed 0  . This behavior follows because SHE-STT acts like a damping term for one sign of the current but acts like an antidamping term for the other sign. Therefore, although the condition of REV WB J J J of the analytical solutions; the DW moves along the current-flow direction at the limited range of the current (i.e., REV WB J J J

Angular dependence of spin-orbit spin-transfer torques

“…36,37 Comparing the measured and calculated angular dependence will provide clues to the mechanism of the spin-orbit torque. The detailed angular dependence also determines the magnetization dynamics and hence is important for device applications based on magnetization switching 1,3,10-13 , domain wall dynamics 2,[5][6][7][8][9]14,15 , and magnetic skyrmion motion 38 .…”

Threshold current for switching of a perpendicular magnetic layer induced by spin Hall effect

“…For the conventional CPP geometry with perpendicular free and fixed layers, the switching current density Rashba-type spin-orbit coupling is mainly responsible for spin torque resulting in the perpendicular switching induced by an in-plane current [18]. The existence of this Rashba effect in metallic ferromagnets is a subject under extensive discussion [36][37][38][39][40][41][42]. Although we do not consider the Rashba effect in this work, a further investigation about this possibility may be valuable.…”

Current-driven domain wall motion along high perpendicular anisotropy multilayers: The role of the Rashba field, the spin Hall effect, and the Dzyaloshinskii-Moriya interaction

“…These SOTs could, at least, be originated by two phenomena: the Rashba effect due to the large SOC and structure inversion asymmetry at the two different heavy-metal/ferromagnet and ferromagnet/oxide interfaces [10][11][12][13][14] and/or the spin Hall current generated from the heavy metal layer and injected in the thin ferromagnet. [15][16][17][18][19][20][21] On the other hand, a thin ferromagnetic layer in contact with a heavy-metal with strong SOC is expected to experience an interfacial anisotropic exchange due to the Dzyaloshinskii-Moriya interaction (DMI). [22][23][24][25][26][27][28][29] The DMI is a chiral spin-orbit interaction originating from relativistic effects that occur due to the lack of inversion symmetry of the atomic structure, and it can result in topologically rich magnetization patterns such as spiral, skyrmions 25,27,28 or chiral domain walls.…”

“…This spin current can be injected into the ferromagnetic layer, resulting in an additional SOT (3rd term in Eq. (5)), with amplitude H SH given by [18][19][20][21] …”