Observation of Spin Splitting Torque in a Collinear Antiferromagnet ${\mathrm{RuO}}_2$

Current-induced spin torques provide efficient data writing approaches for magnetic memories. Recently, the spin splitting torque (SST) was theoretically predicted, which combines advantages of conventional spin transfer torque (STT) and spin-orbit torque (SOT) as well as enables controllable spin polarization. Here we provide the experimental evidence of SST in collinear antiferromagnet ${\mathrm{RuO}}_2$ films. The spin current direction is found to be correlated to the crystal orientation of ${\mathrm{RuO}}_2$ and the spin polarization direction is dependent on (parallel to) the Néel vector. These features are quite characteristic for the predicted SST. Our finding not only presents a new member for the spin torques besides traditional STT and SOT, but also proposes a promising spin source ${\mathrm{RuO}}_2$ for spintronics.

Figure 1

(a) Crystal and magnetic structure of the rutile ${\mathrm{RuO}}_2$. Gray and red spheres represent Ru and O atoms, respectively. Purple arrows mark the Ru local moments. (b) Schematic of the anisotropic spin band splitting in ${\mathrm{RuO}}_2$. Oxygen octahedrons of two sublattices are rotated by 90°. The Ru atoms of two magnetic sublattices feel anisotropic octahedral crystal field (wavy black lines), leading to the anisotropic spin band splitting, as displayed by blue and red ellipses. (c) For the (100)-oriented ${\mathrm{RuO}}_2$ film, transversal spin current ($J_T$) flowing along the [100] axis (out-of-plane) can be induced by the charge current along the $[0\overline{1}0]$ axis. The spin polarization is parallel to the Néel vector ([001] axis). (d) For the (110)-oriented ${\mathrm{RuO}}_2$ film, spin polarized current ($J_L$) flowing along longitudinal direction can be generated by the charge current along the $[1\overline{1}0]$ axis. The spin polarization is also parallel to the Néel vector.

Figure 2

(a),(b) Schematic of ST-FMR measurements for the (a) ${\mathrm{RuO}}_2(100)/\mathrm{Py}$ and the (b) ${\mathrm{RuO}}_2(110)/\mathrm{Py}$ samples. For the ${\mathrm{RuO}}_2(100)$ film, both spin splitting torque (SST) and spin-orbit torque (SOT) exist, giving rise to a strong spin torque. For the ${\mathrm{RuO}}_2(110)$ film, SST is absent, only SOT contributes to a weak spin torque. The angle between the charge current ($J_C$) and the external magnetic field ($H_{\mathrm{ext}}$) is termed as $\phi$. (c),(d) ST-FMR spectra of the (c) ${\mathrm{RuO}}_2(100)/\mathrm{Py}$ and the (d) ${\mathrm{RuO}}_2(110)/\mathrm{Py}$ samples measured at $\phi =45°$ and $f=6\mathrm{GHz}$. The input power $P_{\mathrm{in}}=15\mathrm{dBm}$. Circles are the raw data; red and blue lines represent the symmetric ($V_S$) and the antisymmetric ($V_A$) components, respectively. (e),(f) The calculated (e) spin torque efficiency ${\theta }_{\mathrm{SH}}^{\mathrm{eff}}$ and the (f) spin torque conductivity ${\sigma }_{\mathrm{SH}}^{\mathrm{eff}}$ at different microwave frequencies in ${\mathrm{RuO}}_2(100)$ and ${\mathrm{RuO}}_2(110)$ films. The error bars are from three repetitive measurements.

Figure 3

(a),(c),(e) Schematic of spin current generation in (100)-oriented ${\mathrm{RuO}}_2$ with (a) $J_C\perp H_{\mathrm{FA}}$, (c) $J_C//H_{\mathrm{FA}}$, or (e) $⟨J_C,H_{\mathrm{FA}}⟩=\beta$ (The angle between $J_C$ and $H_{\mathrm{FA}}$ is $\beta$). $J_C$ and $H_{\mathrm{FA}}$ represent the charge current and the annealing field, respectively. (b),(d) Angle-dependent $V_S$ of ST-FMR data for configurations of (b) $J_C\perp H_{\mathrm{FA}}$ and (d) $J_C//H_{\mathrm{FA}}$. Orange lines are fitted by the Eq. (S3) [25]. Red, blue, and green lines represent angle-dependent voltage signals contributed by the dampinglike torque of ${\sigma }_x$, ${\sigma }_y$ as well as the fieldlike torque of ${\sigma }_z$, respectively. ${\sigma }_i$ represents the $i$-axis spin polarization. (f) Ratios of $|{\theta }_x^{\mathrm{eff}}/{\theta }_y^{\mathrm{eff}}|$ as a function of $\beta$. ${\theta }_i^{\mathrm{eff}}$ represents the spin torque efficiency of ${\sigma }_i$. Red line is fitted by the expression of $|\cos \beta /(\sin \beta +C)|$. The specific positions of $J_C\perp H_{\mathrm{FA}}$ and $J_C//H_{\mathrm{FA}}$ for $\beta =90°$ and 180°, respectively, are highlighted. The error bars are from three repetitive measurements.

Figure 4

ST-FMR measurement results for the samples with 2 nm thick Cu insertion. (a),(b) ST-FMR spectra of (a) ${\mathrm{RuO}}_2(100)/\mathrm{Cu}/\mathrm{Py}$ and (b) ${\mathrm{RuO}}_2(110)/\mathrm{Cu}/\mathrm{Py}$ samples. Red and blue lines are the symmetric ($V_S$) and the antisymmetric ($V_A$) components. (c) Calculated ${\theta }_{\mathrm{SH}}^{\mathrm{eff}}$ at different microwave frequencies for the ${\mathrm{RuO}}_2(100)/\mathrm{Cu}/\mathrm{Py}$ and the ${\mathrm{RuO}}_2(110)/\mathrm{Cu}/\mathrm{Py}$ samples.