Intrinsic Spin-Orbit Torque Arising from the Berry Curvature in a Metallic-Magnet/Cu-Oxide Interface

We report the observation of the intrinsic dampinglike spin-orbit torque (SOT) arising from the Berry curvature in metallic-$\text{magnet}/{\mathrm{CuO}}_x$ heterostructures. We show that a robust dampinglike SOT, an order of magnitude larger than a fieldlike SOT, is generated in the heterostructure despite the absence of the bulk spin-orbit effect in the ${\mathrm{CuO}}_x$ layer. Furthermore, by tuning the interfacial oxidation level, we demonstrate that the fieldlike SOT changes drastically and even switches its sign, which originates from oxygen-modulated spin-dependent disorder. These results provide important information for a fundamental understanding of the physics of the SOTs.

Figure 1

(a) An optical image of the sample geometry including contact pads, with the circuit and a 45° tilt of an in-plane magnetic field ${\mathbf{H}}_{\text{ext}}$ with respect to the strip length direction used for the STFMR measurements. The $H_{\text{ext}}$ dependence of the dc voltage $V_{\mathrm{mix}}$ for the ${\mathrm{Ni}}_{81}{\mathrm{Fe}}_{19}(7.5\mathrm{nm})/{\mathrm{CuO}}_x$ (10 nm) bilayers with (b) $Q=3.0\%$ and (c) 5.5% measured at the rf current frequencies of 4–9 GHz.

Figure 2

(a) The fitting curves of $V_{\mathrm{mix}}$ as a function of the field for the ${\mathrm{Ni}}_{81}{\mathrm{Fe}}_{19}(7.5\mathrm{nm})/{\mathrm{CuO}}_x(10\mathrm{nm})$ bilayers with $Q=3.0\%$ and 5.5% at 7 GHz. The red and blue curves correspond to the symmetric and antisymmetric Lorentzian fitting, respectively. (b) The $Q$ dependence of the electrical resistivity $\rho$ of ${\mathrm{CuO}}_x(10\mathrm{nm})$ single-layer films, capped with a 4-nm-thick ${\mathrm{SiO}}_2$ protective layer. The resistivity was measured by the four-probe method. (c) The $V_{\mathrm{mix}}$ as a function of the field for the ${\mathrm{Ni}}_{81}{\mathrm{Fe}}_{19}(7.5\mathrm{nm})/{\mathrm{CuO}}_x(10\mathrm{nm})$ bilayers with various $Q$ measured at 7 GHz.

Figure 3

(a) The estimated SOT efficiency per unit electric field ${\xi }_{\mathrm{DL}(\parallel )}^E$ for the ${\mathrm{Ni}}_{81}{\mathrm{Fe}}_{19}(7.5\mathrm{nm})/{\mathrm{CuO}}_x(10\mathrm{nm})$ bilayers with various $Q$ values. The open squares are the in-plane torque efficiency ${\xi }_{\parallel (\mathrm{PHE})}^E$ evaluated from the second harmonic Hall voltage measurements. The red and black solid circles are ${\xi }_{\parallel }^E$ and ${\xi }_{\mathrm{DL}}^E$, respectively, estimated from the STFMR measurements. (b) The ${\mathrm{Ni}}_{81}{\mathrm{Fe}}_{19}$-layer-thickness $t_{\mathrm{FM}}$ dependence of $H_{\mathrm{DL}}^E=H_{\mathrm{DL}}/E$ for the ${\mathrm{Ni}}_{81}{\mathrm{Fe}}_{19}(t_{\mathrm{FM}})/{\mathrm{CuO}}_x(10\mathrm{nm})$ bilayer at $Q=3\%$, where $H_{\mathrm{DL}}$ is the DL spin-orbit effective field. The solid circles are the experimental data, and the dashed curve is a function proportional to $1/t_{\mathrm{FM}}$. (c) Curves fitting Cu $2p_{3/2}$ XPS spectra for ${\mathrm{CuO}}_x(10\mathrm{nm})$ single-layer films with various $Q$ values. The red fitting curves are the merged $\mathrm{Cu}/{\mathrm{Cu}}_2\mathrm{O}$ (blue curves) and CuO (green curves) $2p_{3/2}$ peaks, and the gray curves are the Shirley background.