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The dominancy of damping like torque for the current induced magnetization switching in Pt/Co/W multilayers

Two classes of spin-orbit coupling (SOC) mechanisms have been considered as candidate sources for the spin orbit torque (SOT): the spin Hall Effect (SHE) in heavy metals with strong SOC and the Rashba effect arising from broken inversion symmetry at material surfaces and interfaces. In this work, we have investigated the SOT in perpendicularly magnetized Pt/Co/W films, which is compared with the results in Pt/Co/AlOx films. Theoretically, in the case of the asymmetric structure of trilayers with opposite sign of spin Hall angle, both damping like torque and field like torque due to the SHE and the Rashba effect will be enhanced. Using the harmonic measurements, we have characterized the effective fields corresponding to the damping like torque and the field like torque, but we have found the dominancy of damping like torque in the Pt/Co/W films. It is much different from the results in the Pt/Co/AlOx films, in which both the damping like torque and the field like torque are strong.


Introduction
Magnetization reversal by an electric current is crucial issue for spintronic memory and logic devices, such as spin transfer torque magnetic random access memory, in which magnetization switching are occurred in a spin valve structure [1]. Recently, another type of torques namely spin orbit torque (SOT) has attracted great interest as they can control the magnetization in heavy metal (HM)/ferromagnetic (FM) heterostructures with perpendicular magnetic anisotropy (PMA) [2][3][4][5][6][7][8][9][10][11][12][13]. Typically, in HM/FM/oxide trilayers with PMA, the charge current passing through the HM can produce pure spin current due to spin Hall effect (SHE), which exerts a torque on the magnetization. Hence, the sign and magnitude of SOT are essentially determined by the spin Hall angle in the HM. On the other hand, the SOT can also arise from the interfacial Rashba effect, for which the accumulated spins at the interface can force the moments to change its direction by direct exchange coupling. These two mechanisms are all related to strong spin orbit coupling (SOC) [14][15][16][17]. Recent theoretical studies showed that both the SHE and the Rashba effect can generate damping like torque and field like torque.
Correspondingly, the two kinds of torques yield to the damping like effective field H D~σ ×m and the field like effective field H F~σ , respectively, where m and σ are unit vectors of the magnetization in the FM layer and non-equilibrium spin polarization direction in the HMs.
Particularly, the direction of σ depends on the sign of spin Hall angle  SH of HMs.
Currently, most studies have focused on SOT in ultrathin FMs sandwiched between two HM layers, such as Pt/CoNiCo/Pt, Pt/Co/Ta, Pt/Co-Ni/W, and Pt/Co/Pt [18][19][20][21][22][23], in which both of the HM layers have contributions to the spin accumulation at the interfaces. Because the efficiency of SOT relates directly to the magnitude of effective spin Hall angle ( SH ), it is considered that the overall  SH will be enhanced if the sign of  SH in the top and bottom HM layer 3 is opposite. In this work, we studied the SOT in Pt/Co/W trilayers, in which the sign of  SH is positive in Pt while the value is negative in W. Theoretically, in the case of asymmetric structures with opposite sign of spin Hall angle, both the SHE and the Rashba effect will be enhanced. Correspondingly, the two kinds of torques will be increased. However, we found large damping like torque in the Pt/Co/W multilayers as compared with the field like torque.
The results were much different from the Pt/Co/AlO x films, in which both the damping like torque and the field like torque are comparable. (1)  We measured the SOT induced magnetization switching by applying a pulsed current with the width of 50 s, and the resistance was measured after a 16s delay under an external magnetic field along the x-direction. Figure 2  Reductions of the critical switching currents were observed as the external field increased for 4 both of the two samples. Furthermore, with applying appropriate field (~1000 Oe) the magnetizations are fully switched. It can be proved by the changes of the Hall resistance of the two samples, which are consistent with the results in R H -H measurements as shown in Figure   1(d). Considering the resistivity of the W layer is much larger than that of the Pt layer and the AlO x layer should be insulating, here we roughly took the thickness of Co and Pt layers into account when determining the switching current density (J c ) of the two samples. Therefore, with applying the magnetic field of 3000 Oe (fully magnetization switching), the J c in the Pt/Co/AlO x and Pt/Co/W films are (3.8±0.051)×10 11 Am −2 and (2.04±0.0044)×10 11 Am −2 , respectively.

Results and discussion
The harmonic measurements were determined by applying the sinusoidal AC current, for sample I the frequency is 365 Hz and the amplitude is ranged from 2.0 to 8.0 mA, for sample II the frequency is 315 Hz and the amplitude is ranged from 2.0 to 2.6 mA. The first (V  ) and second (V 2 ) harmonic Hall voltages are detected using two lock-in amplifier systems at the same time by sweeping the longitudinal (H x ) and transverse (H y ) fields. Before the harmonic measurements, we have applied a large out-of-plane external field to the two samples, which remain saturated after the field is turned off. Here, we will take the example of the harmonic measurements for sample I with 5.0 mA and for sample II with 2.0 mA respectively as shown in Figure 3 Where  defined as the ratio of planar Hall effect (PHE) resistance and anomalous Hall effect (AHE) resistance and ± sign is the direction of magnetization pointing ( ±M z ) along out-of-palne 5 axis [13,24]. The longitudinal (H L ) and transverse effective field (H T ) can be calculated using the following relation: To measure the PHE resistance R PHE , a 30000 Oe strong in-plane magnetic field is applied to saturate the magnetization of the samples [9,10,13,24]. Then, the R H was measured by rotating the magnetic field in the plane of sample to rotate the magnetization along the  direction. The  is applied current density, and  is reduced Planck constant [24]. The effective  SH up to 0.12 and 0.3004 were determined for sample I and sample II, respectively. Therefore, the effective  SH will be enhanced when the Co layer is sandwiched between two HM layers Pt and W with opposite signs of  SH , and the damping like torque play a dominant role.
In the previous studies on SOT of HM/FM/oxide trilayers, the spin density generated by the inverse spin galvanic effect exerts a torque on the magnetization, which is attributed to interfacial Rashba SOC [5][6][7][8][9]. A major difficulty to identify the physical origin of the SOT is that the SHE also plays an important role in magnetic multilayers. Recently, Haney et al. have developed semi-classical models for electron and spin transport in bilayer nanowires with a ferromagnetic layer and a nonmagnetic layer with strong SOC [25]. They have proved that the damping like torque is typically derived from the models describing the bulk SHE and the spin transfer torque, and the field like torque is typically derived from a Rashba model describing interfacial SOC. For the Rashba effect, an internal electric field gradient will arise at the interfaces along the direction of symmetry breaking. The direction of Rashba effect induced spin accumulation as well as an effective magnetic field will be along E×P, where E is the internal electric field, P is the electron momentum [26]. The direction of the E for a given interface can be obtained by considering the differences in the work function () of the two materials at the interface. The work functions of Pt, Co, W and AlO x are ~5.65 eV, 5.0 eV, 4.55 eV and 3.2 eV [27]. The smaller difference of work function in Pt/Co/W as compared with that in Pt/Co/AlO x films will decrease the spin accumulation from the Rashba effect. On the other hand, to obtain the -phase of W layer a dc sputtering power of 8 W was applied with the growth rate of 0.03nm/s, and the cubic lattice constant of -W is 0.5046 nm [28]. For the hexagonal lattice of Co, the inplane lattice constant is about 0.2507nm, which is almost half of that in -W. Therefore, we