Control of out-of-plane anti-damping spin torque with a canted ferromagnetic spin source

Abstract

To achieve efficient anti-damping switching of nanoscale magnetic memories with perpendicular magnetic anisotropy using spin-orbit torque requires that the anti-damping spin-orbit torque have a strong out-of-plane component. The spin anomalous Hall effect and the planar Hall effect spin current produced by a ferromagnetic layer are candidate mechanisms for producing such an out-of-plane anti-damping torque, but both require that the magnetic moment of the spin source layer be canted partly out of the sample plane at zero applied magnetic field. Here we demonstrate such a canted configuration for a ferromagnetic SrRuO3 layer and we characterize all vector components of the torque that it produces, including non-zero out-of-plane anti-damping torques. We verify that the out-of-plane spin component can be tuned by the orientation of magnetic moment, with significant contributions from both the spin anomalous Hall effect and the planar Hall effect spin current.

Figures (11)

• Figure 1: Tilted spin currents produced by a canted magnetization. a, Illustration of the spin current allowed by symmetry for a non-magnetic material with high crystal symmetry, for which a spin current flowing in the $\hat{Z}$ direction must have spin polarization oriented in the $\pm \hat{Y}$ direction. b, Illustration of a tilted spin current originating from the planar Hall effect in a ferromagnet, relevant for the case in which an electric field ($\vec{E}$) is applied along the $\hat{X}$ direction and the magnetic moment is canted away from the $\hat{Z}$ direction into the $\hat{X}$ direction. c, Illustration of a tilted spin current originating from the spin anomalous Hall effect in a ferromagnet, relevant for the case in which the magnetic moment is canted away from the $\hat{Z}$ direction into the $\hat{Y}$ direction.
• Figure 1: Domain structure characterized using anomalous Hall effect measurements. a, The first derivative of anomalous Hall resistance as a function of external magnetic field for a single-layer $5$ nm SrRuO$_3$ thin film at $110$ K. 'A' denotes the dominant domain and 'M' denotes minor domains present in the sample. b, Anomalous Hall resistance for the same single-layer $5$ nm SrRuO$_3$ thin film at $110$ K. $R_A$ and $R_M$ are the contributions from the 'A' domain and the minor domain to the anomalous Hall resistance. c, The first derivative of anomalous Hall resistance as a function of external magnetic field for a $10$ nm SrRuO$_3$ thin film at $110$ K. d, Anomalous Hall resistance for the same $10$ nm SrRuO$_3$ film at $110$ K.
• Figure 2: Magnetic anisotropy of SrRuO$_3$ thin films. a, A side view showing the epitaxial relationship of SrRuO$_3$ grown on an $(001)$-oriented SrTiO$_3$ substrate, where the $[010]_{pc}$ axis points out of the page. $a$, $b$, and $c$ are the orthorhombic unit cell axes of SrRuO$_3$. In thin films, the direction of the magnetic easy axis ($\theta_C$) can differ from the $b$ axis. b, Device geometry for the angular-dependent magnetoresistance measurements. A longitudinal voltage ($V_{XX}$) is recorded while rotating the external magnetic field ($\vec{B}$) in a plane perpendicular to the applied current. $\theta$ is the external magnetic field angle from the surface normal ($[001]_{pc}$). c, An example angular dependent magnetoresistance measurement at 10 K, where longitudinal resistance ($R_{XX}$) is plotted as a function of magnetic field angle $\theta$ for a sample SrRuO$_3$(20 nm)/Py (5 nm). A d.c. current of 100 $\mu$A is applied along the $[010]_{pc}$ orientation and a magnetic field 6 T is rotated in the $(010)_{pc}$ plane. d, Summary of the easy-axis tilt angle ($\theta_C$) for SrRuO$_3$ films of various thicknesses ($t$) at 10 K.
• Figure 2: A check for exchange coupling between SrRuO$_3$ (10 nm) and Py (5 nm). a, Schematic illustration of the measurement geometry to test for exchange coupling along the [100]$_{pc}$ direction. Longitudinal voltage ($V_{XX}$) is measured while an external magnetic field is swept along the [100]$_{pc}$ direction. b, Measured longitudinal resistance as a function of external magnetic field at $80$ K for the geometry in panel a. Two dips are observed, at $8$ Oe and $-10$ Oe, indicating the absence of any significant exchange bias along the [100]$_{pc}$ direction. c, Measurement geometry to test for exchange coupling along the [010]$_{pc}$ direction. d, Measured longitudinal resistance as a function of external magnetic field at $80$ K for the geometry in panel c. Two dips are observed symmetrically located at $\pm 13$ Oe, indicating the absence of exchange bias along [010]$_{pc}$ direction.
• Figure 3: Spin torques characterized by spin-torque ferromagnetic resonance. a, A schematic of a SrRuO$_3$ (5 nm)/Py (5 nm) bilayer used in the ST-FMR measurements. Red layer: Py; Teal layer: SrRuO$_3$; $H_{RF}$: Oersted field produced by the applied microwave current; $\vec{B}$: external magnetic field; $\vec{E}$: electric field; $\varphi$: angle between external magnetic field and microwave current. b, Example ST-FMR spectrum, with the d.c. mixing voltage ($V_{mix}$) plotted as a function of external magnetic field ($B$). In this example, the ST-FMR measurement is done at 110 $K$ with $E$ along [010]$_{pc}$ and $\varphi = 45^\circ$. The red and orange curves represent the anti-symmetric ($V_A$) and symmetric ($V_S$) components of the mixing voltage respectively. c, Anti-symmetric mixing voltage as a function of magnetic field angle. X (purple), Y (blue), Z (red) components of the anti-symmetric mixing voltages are determined as the fit components proportional to $\sin(2\varphi)\sin\varphi$, $\sin(2\varphi)\cos\varphi$ and $\sin(2\varphi)$ respectively. d, Symmetric mixing voltage as a function of magnetic field angle. X (purple), Y (blue) and Z (red) components of the symmetric mixing voltages are determined as the fit components proportional to $\sin(2\varphi)\cos\varphi$, $\sin(2\varphi)\cos\varphi$ and $\sin(2\varphi)$ respectively. The electric field is applied approximately along the $[010]_{pc}$ crystallographic axis in the plane for c and d. e, f Anti-symmetric and symmetric mixing voltages as a function of magnetic field angle for an electric field applied approximately along the $[100]_{pc}$ crystallographic axis.