Quantification of spin accumulation causing spin-orbit torque in Pt/Co/Ta stack

Quantification of spin accumulation causing spin-orbit torque in Pt/Co/Ta stack Feilong Luo, Sarjoosing Goolaup, Christian Engel, and Wen Siang Lew* School of Physical and Mathematical Sciences, Nanyang Technological University,
21 Nanyang Link, Singapore 637371

Abstract Spin accumulation induced by spin-orbit coupling is experimentally quantified in stack with in-plane magnetic anisotropy via the contribution of spin accumulation to Hall resistances. Using a biasing direct current the spin accumulation within the structure can be tuned, enabling quantification. Quantification shows the spin accumulation can be more than ten percentage of local magnetization, when the electric current is 1011 Am−2. The spin accumulation is dependent of the thickness of Ta layer, the trend agrees with that of spin Hall angle indicating the capability of Ta and Pt in generating spins.

*Corresponding author: wensiang@ntu.edu.sg 2

Introduction Current-induced spin accumulation causes spin-orbit torque (SOT) on the magnetization of a ferromagnetic metal (FM) layer sandwiched by two heavy metal (HM) layers, via exchange interaction [1]. The spin accumulation originates from two spin-orbit coupling effects: Rashba effect and spin Hall effect [2-10]. The SOT is reflected in the revised Landau–Lifshitz–Gilbert equation by the term 0 J    M s , where 0  is the gyromagnetic coefficient, M is the magnetization of the FM layer, s is the spin accumulation, and J is a coefficient related to spin diffusion length of accumulated spins in the FM layer. The term 0 J    M s can be decomposed into a fieldlike torque F F H   τ M p and a dampinglike torque   D D H    τ M m p , where p represents the spin orientation of the electrons diffusing into the FM layer, and m is the unit vector of M [1, 10-14]. The corresponding effective fields arising from SOT can be written as the fieldlike term F F H  H p and dampinglike term D D H   H m p , alternatively, F D J H H    s p m p [6, 8, 10, 12, 15-20]. The effective field, Js, which is a combination of spin accumulation and a spin-diffusion related coefficient, has been widely characterized via current-induced domain wall motion [8, 21, 28-30], ferromagnetic resonance (FMR) techniques [31-38], and SOT-assisted magnetization switching [6, 20, 22, 35, 39]. Quantification of the spin accumulation, which plays a crucial role in the origins of the SOT, has remained elusive. In this letter, we provide a concise solution to quantify the spin accumulation in the sandwiched structure with in-plane magnetic anisotropy (IMA). We propose the spin accumulation s contributes to the second harmonic Hall resistance in the harmonic Hall 3

voltage scheme, in addition to the SOT effective field Js as expected. Applying a biasing direct current (DC) enables the extraction of the contribution of the spin accumulation from the second harmonic Hall resistances. Analogized to first harmonic Hall resistance which is induced by the magnetization, modulation of the second Hall resistance via DC current can be used to compute the spin accumulation. Results of the computation show the spin accumulation is dependent of the thickness of HM layers. This quantification allows us to understand the anatomy of Js and distinguish the roles of J and s.

Main body Following the transfer of momentum to the local magnetization, the accumulated spins s adopt similar polarization as the magnetization orientation of the FM layer. The structure comprises of Ta/Co/Pt multilayer, where the FM layer exhibits IMA. The initial polarization of s is induced by Rashba effect due to the asymmetric HM/FM interface and spin Hall effect within the Ta and Pt layers [2-10, 8, 15, 18, 19, 21-27]. The Rashba effect re-orientates the spin with in the conduction electrons of FM layer to provide a net resultant spin in the FM layer [5]. Additionally, the spin Hall effect induces a spin-selective separation of electrons in the HM layer; the spin polarized electrons then diffuses into the FM layer [10]. In the Co layer, the transfer of spin torque from the spin polarized electron to the FM layer occurs on the nanosecond time scale [5]. A schematic of the spin transfer process is depicted in Fig 1(a). At the end of the spin transfer, s is in relaxation state, hence it adopts the same orientation as the local magnetic moment Mm as depicted in Fig. 1(b). In experiment, within the low frequency regime of hundreds of Hertz, corresponding to period of oscillation of alternating current (AC) in millisecond scale, it is reasonable to 4

consider that the accumulated spins s follow the orientation of Mm. Similarly, extending to direct current (DC) bias regime, an identical approximation can be made and the spins s similarly aligns along m. Therefore, after the electron spins have transferred the mom

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