Role of self-torques in transition metal dichalcogenide/ferromagnet bilayers

In recent years, transition metal dichalcogenides (TMDs) have been extensively studied for their efficient spin-orbit torque generation in TMD/ferromagnetic bilayers, owing to their large spin-orbit coupling, large variety of crystal symmetries, and pristine interfaces. Although the TMD layer was considered essential for the generation of the observed spin-orbit torques (SOTs), recent reports show the presence of a self-torque in single-layer ferromagnetic devices with magnitudes comparable to TMD/ferromagnetic devices. Here, we perform second-harmonic Hall SOT measurements on metal-organic chemical vapor deposition (MOCVD) grown ${\text{MoS}}_2$/permalloy/${\text{Al}}_2{\text{O}}_3$ devices and compare them to a single-layer permalloy/${\text{Al}}_2{\text{O}}_3$ device to accurately disentangle the role of self-torques, arising from the ferromagnetic layer, from contributions from the TMD layer in these bilayers. We report a fieldlike spin-torque conductivity of ${\sigma }_{FL}=(-2.8\pm 0.3)\times {10}^3\frac{\hslash }{2e}{\left(\mathrm{\Omega }\mathrm{m}\right)}^{-1}$ in a single-layer permalloy/${\text{Al}}_2{\text{O}}_3$ device, which is comparable to our ${\text{MoS}}_2$/permalloy/${\text{Al}}_2{\text{O}}_3$ devices and previous reports on similar TMD/ferromagnetic bilayers, indicating only a minor role of the ${\text{MoS}}_2$ layer. In addition, we observe a comparatively weak dampinglike torque in our devices, with a strong device-to-device variation. Finally, we find a linear dependence of the SOT conductivity on the Hall bar arm/channel width ratio of our devices, indicating that the Hall bar dimensions are of significant importance for the reported SOT strength. Our results accentuate the importance of delicate details, like device asymmetry, Hall bar dimensions, and self-torque generation, for the correct disentanglement of the microscopic origins underlying the SOTs, essential for future energy-efficient spintronic applications.

Figure 1

(a) Optical micrograph of an actual MOCVD ${\text{MoS}}_2\text{/}\text{Py}\text{/}{\text{Al}}_2{\text{O}}_3$ device. (b) A Raman spectrum of the MOCVD grown ${\text{MoS}}_2$ showing the characteristic $E_{2g}^1$ and $A_{1g}$ modes of ${\text{MoS}}_2$. The two insets on the right depict a white light (WL) and photoluminescence (PL) micrograph of a scratch in the MOCVD grown ${\text{MoS}}_2$ layer, indicating a strong PL from the monolayer ${\text{MoS}}_2$. (c) A schematic of a SOT device with the measurement geometry schematically depicted. A low frequency ac current $I$ (black arrow) is applied through the channel and the first- and second-harmonic Hall voltage ($V_{xy}^{\omega \left(2\omega \right)}$) are simultaneously measured while the magnetization of the permalloy $M$ (red arrow) is rotated in-plane by an external magnetic field. The current induced in-plane (dampinglike) and out-of-plane (fieldlike) SOTs are depicted with the green arrows ${\tau }_{\parallel }$ and ${\tau }_{\perp }$, respectively. (d) The measured first-harmonic and (e) second-harmonic Hall voltage versus in-plane angle of the applied magnetic field (40 mT). (d) A clear $cos\left(2\varphi \right)$ dependence is observed due to the planar Hall effect of the Py. (e) The second-harmonic Hall voltage (blue points) is fitted (black line) using Eq. (2). The dashed blue and red lines indicate the separate $cos\left(\varphi \right)cos\left(2\varphi \right)$ and $cos\left(\varphi \right)$ components from Eq. (2), related to the fieldlike and dampinglike torque, respectively.

Figure 2

A and B components from Eq. (2) versus the inverse magnetic field for a ${\text{MoS}}_2\text{/}\text{Py}\text{/}{\text{Al}}_2{\text{O}}_3$, (a) and (c), and single-layer $\text{Py}\text{/}{\text{Al}}_2{\text{O}}_3$, (b) and (d), device, respectively. The components were obtained by fitting the second-harmonic Hall voltage [as depicted in Fig. 1] to Eq. (2) for multiple external magnetic field strengths. A clear linear dependence is observed for the A component in both devices and is fitted to Eq. (3) to obtain the fieldlike torque ${\tau }_{FL}$. Especially for the ${\text{MoS}}_2\text{/}\text{Py}\text{/}{\text{Al}}_2{\text{O}}_3$ device, the B component deviates from the linear trend at low magnetic fields, which could be due to electron-magnon scattering. For the ${\text{MoS}}_2\text{/}\text{Py}\text{/}{\text{Al}}_2{\text{O}}_3$ devices, we therefore neglected the fields at low fields (10 mT, 20 mT, and 30 mT) to obtain a better linear fit. Furthermore, we corrected our data for a systematic offset of 15 mT in the applied field.

Figure 3

(a) Fieldlike and (b) dampinglike spin-torque conductivity for the ${\text{MoS}}_2\text{/}\text{Py}\text{/}{\text{Al}}_2{\text{O}}_3$ devices (circles) and the single-layer $\text{Py}\text{/}{\text{Al}}_2{\text{O}}_3$ device (squares) versus the arm width/channel width ratio of the Hall bar. The gray points correspond to the raw spin-torque conductivity and the colored points to the corrected spin-torque conductivity, according to Ref. [58]. The inset in (a) shows the voltage arm width ($a$) and the channel width ($w$). For these devices, the arm width is kept constant ($a=$ 2 $\mu \text{m}$), while the channel width is varied.

Figure 4

Antisymmetrized Hall voltage for the anomalous Hall measurement used to obtain the anomalous Hall resistance, $R_{\mathrm{AHE}}$, and the saturation magnetization, $M_s$, needed to determine ${\tau }_{DL}$ from Eq. (4). The data presented here are antisymmetrized to reduce any errors due to sample misalignment.