Current-induced out-of-plane torques in a single permalloy layer with lateral structural asymmetry

We investigated current-induced torques in a single permalloy layer connected to nonmagnetic electrodes with lateral inversion asymmetry by spin-torque ferromagnetic resonance. Considering the symmetry of the spin-torque ferromagnetic resonance spectrum with respect to the magnetic field direction, we successfully separated various types of torque. In addition to in-plane damping-like and field-like torques, we detected two additional components of out-of-plane (OOP) torques, the symmetries of which with respect to the magnetic field direction correspond to an OOP field-like torque and an OOP damping-like torque. We obtained the OOP torques in particular by breaking a lateral inversion symmetry of the nonmagnetic electrodes, and the sign of the torques is reversed by inverting the electrode structure. The microwave frequency dependence of the OOP torques indicates that the OOP torques are not attributable to a spin current but to the Oersted field generated by a nonuniform charge current, $B_{\mathrm{Oersted}}$, and an inductive field, $B_{\mathrm{induc}.}$ (which originates from $B_{\mathrm{Oersted}}$). We propose an external field-free and fast magnetization switching of a ferromagnetic layer with perpendicular magnetic anisotropy by using $B_{\mathrm{induc}.}$, which can be achieved only by fabricating the electrodes asymmetrically.

Figure 1

(a) Schematics of device structure and electrical circuit. (b) View of the device structure from the $z$-axis. ST-FMR spectra when $f=13\mathrm{GHz}$ for (c) $\mathrm{\Delta }l=0\mu \mathrm{m}$ and (d) $-20\mu \mathrm{m}$. Red and blue curves show the symmetric and antisymmetric Lorentzian components, respectively, obtained from the fitting of the ST-FMR spectrum. Insets show $f$ as a function of $B_{\mathrm{res}}$, and red curves are the fitting results by using the Kittel equation.

Figure 2

$\theta$ dependence of (a) $A$ and (b) $S$ for a device with $\mathrm{\Delta }l=0\mu \mathrm{m}$. Those of devices with (c and d) $\mathrm{\Delta }l=20\mu \mathrm{m}$ and (e and f) $-20\mu \mathrm{m}$ are also shown. $\theta$ dependences of $A$ are fitted by $sin2\theta cos\theta$ (blue), $sin2\theta$ (green), and $sin2\theta sin\theta$ (purple). $\theta$ dependences of $S$ are fitted by $sin2\theta cos\theta$ (blue), $sin2\theta$ (green), $sin2\theta sin\theta$ (purple), and $sin\theta$ (gold). Red curves are the sum of all of the components.

Figure 3

Torque efficiencies as a function of $\mathrm{\Delta }l$ for (a) IP DL torque, ${\xi }_{\mathrm{DL},y}$; (b) IP FL torque, ${\xi }_{\mathrm{FL},y}$; (c) OOP DL torque, ${\xi }_{\mathrm{DL},z}$; and (d) OOP FL torque, ${\xi }_{\mathrm{FL},z}$. Insets show the directions of the effective magnetic fields that correspond to each torque when the electric current is along the $x$ direction.

Figure 4

Microwave frequency $f$ dependence of (a) ${\xi }_{\mathrm{DL},z}$ and (b) ${\xi }_{\mathrm{FL},z}$ for $\mathrm{\Delta }l=20\mu \mathrm{m}$.

Figure 5

Results of the time evolution of the $z$-component of magnetization, $m_z$, by a micromagnetic simulation. The simulation conditions correspond to the SOT magnetization switching of a FM/NM bilayer structure with asymmetric NM electrodes. We applied $B_{\mathrm{Oersted}}$ or $B_{\mathrm{induc}.}$ along the OOP direction with or after application of the IP DL torque, respectively. Comparison of magnetization switching properties (a) under various amplitudes of $B_{\mathrm{induc}.}$ and (b) under application of $B_{\mathrm{Oersted}}$ and $B_{\mathrm{induc}.}$ with a magnitude of 2 μT. Result of $–z$ to $+z$ switching realized by inverting initial magnetization, injected spin orientation, and the sign of $B_{\mathrm{induc}.}$ is also shown in the inset. We injected a 100-ps-width spin-polarized current at $t=0$. We applied $B_{\mathrm{Oersted}}$ concomitantly with the spin-polarized current. We applied $B_{\mathrm{induc}.}$ at $t=100\mathrm{ps}$ (indicated as a dotted line), which exponentially decayed. The spin current was injected from the bottom surface, which might cause a slight difference in the magnetization switching properties between $–z$ to $+z$ and $+z$ to $–z$.