Anomalous sign inversion of spin-orbit torque in ferromagnetic/nonmagnetic bilayer systems due to self-induced spin-orbit torque

Self-induced spin-orbit torques (SI-SOTs) in ferromagnetic (FM) layers have been overlooked when estimating the spin Hall angle (SHA) of adjacent nonmagnetic (NM) layers. In this work, we observe anomalous sign inversion of the total SOT in the spin-torque ferromagnetic resonance due to the enhanced SI-SOT, and successfully rationalize the sign inversion through a theoretical calculation considering the SHE in both the NM and FM layers. The findings show that using an FM layer whose SHA sign is the same as that of the NM achieves efficient SOT-magnetization switching with the assistance of the SI-SOT. The contribution of the SI-SOT becomes salient for a weakly conductive NM layer, and conventional analyses that do not consider the SI-SOT can overestimate the SHA of the NM layer by a factor of more than 150.

Figure 1

(a) Schematic of the device structure and the electrical circuit. (b) ST-FMR spectra of (left panel) Ta(5)/Co(3), (middle panel) Ta(5)/Co(5), and (right panel) Ta(5)/Co(17.5) devices. Red and blue curves show the symmetric and the antisymmetric component obtained by fitting with Eq. (1). (c), (d) Measured θ dependence of $A$ of (c) Ta(5)/Co(5) and (d) Ta(5)/Co(17.5) devices. (e), (f) (Upper panel) Measured and (lower panel) expected θ dependence of $S$ of (e) Ta(5)/Co(5) and (f) Ta(5)/Co(17.5) devices. Solid lines are the total fitting (red), $sin2\theta cos\theta$ (blue), $sin2\theta$(green), $sin2\theta sin\theta$ (purple), and $sin\theta$ (brown) terms. (g), (h) Schematics of the spin injection into Co via the SHE in (g) Ta and (h) Co. In the ST-FMR measurements, frequency, $f$, was 13 GHz when $t_{\mathrm{FM}}=3\mathrm{nm}$ and 16 GHz when $t_{\mathrm{FM}}\ge 5\mathrm{nm}$. Signal output power was fixed to 13 dBm.

Figure 2

(a) ${\xi }_{\mathrm{FMR}}$ as a function of $t_{\mathrm{FM}}$ and (b) $1/{\xi }_{\mathrm{FMR}}$ as a function of $1/t_{\mathrm{FM}}$ for Ta/Co devices. (c) ${\theta }_{\mathrm{FM}}$ and (d) $l_{\mathrm{FM}}$ dependences of the ${\xi }_{\mathrm{FMR}}–t_{\mathrm{FM}}$ curve for case 1.

Figure 3

(a) ${\xi }_{\mathrm{FMR}}$ as a function of $t_{\mathrm{FM}}$ and (b) $1/{\xi }_{\mathrm{FMR}}$ as a function of $1/t_{\mathrm{FM}}$ for Py/Pt devices. (c) ${\theta }_{\mathrm{FM}}$ and (d) $l_{\mathrm{FM}}$ dependences of the ${\xi }_{\mathrm{FMR}}–t_{\mathrm{FM}}$ curve for case 2. $f=13$ GHz, 11 GHz, and 5 GHz when $t_{\mathrm{FM}}\ge 10\mathrm{nm}, 7\mathrm{nm}\ge t_{\mathrm{FM}}\ge 3\mathrm{nm}$, and $t_{\mathrm{FM}}=3\mathrm{nm}$, respectively. Signal output power was fixed to 13 dBm.

Figure 4

(a) ${\xi }_{\mathrm{FL}}/{\xi }_{\mathrm{DL}}$ dependence of the $1/{\xi }_{\mathrm{FMR}}–1/t_{\mathrm{FM}}$ curve for case 3. (b) ${\theta }_{\mathrm{NM}}$ and (c) ${\sigma }_{\mathrm{NM}}$ dependences of the ${\xi }_{\mathrm{FMR}}–t_{\mathrm{FM}}$ curve for case 4. The parameters for ${\xi }_{\mathrm{FL}}/{\xi }_{\mathrm{DL}}, {\theta }_{\mathrm{NM}}$, and ${\sigma }_{\mathrm{NM}}$ used in the calculations are shown in each graph. The parameter units are the same as those of Table 1.