Time-Domain Measurement of Current-Induced Spin Wave Dynamics

The performance of spintronic devices critically depends on three material parameters, namely, the spin polarization in the current ($P$), the intrinsic Gilbert damping ($\alpha$), and the coefficient of the nonadiabatic spin transfer torque ($\beta$). However, there has been no method to determine these crucial material parameters in a self-contained manner. Here we show that $P$, $\alpha$, and $\beta$ can be simultaneously determined by performing a single series of time-domain measurements of current-induced spin wave dynamics in a ferromagnetic film.

Figure 1

The principle of the current-induced spin wave dynamics. (a) The spin wave generated by a microwave pulse is subject to a stream of STT introduced by an electric current $j$, resulting in the variations of both group velocity $v_g$ and amplitude $A$. Upstream and downstream spin waves change their velocities into $v_g-\Delta v_{\mathrm{STT}}$ and $v_g+\Delta v_{\mathrm{STT}}$, respectively, and their amplitudes into $A-\Delta A_{\mathrm{STT}}$ and $A+\Delta A_{\mathrm{STT}}$, respectively. (b) Electric signals of the spin wave for different gap distances $x$, demonstrating the propagation of spin wave packets.

Figure 2

Experimental data of the current-induced modulations. (a) The spin wave Doppler shift induced by electric current ($x=20\mu \mathrm{m}$). (b) Spin polarization $P$ measured for several devices with different gap distances. (c) The spin wave attenuation induced by electric current ($x=20\mu \mathrm{m}$). (d) Nonadiabaticity of STT ($\beta$) deduced from the attenuation of SW amplitude.

Figure 3

Current-induced modulation of the SW amplitude and the nonadiabaticity $\beta$ (micromagnetic simulation). (a) Current-induced modulation of the SW amplitude in the absence of the Oersted field effect ($\beta =3\alpha$). (b) Current-induced modulation of the SW amplitude in the presence of the Oersted field effect ($\beta =3\alpha$). The solid triangles and open squares represent the case of forward propagating SWs ($+k$) and backward propagating SWs ($-k$), respectively. The black and red symbols represent the case of the detection position $x=20$ and $40\mu \mathrm{m}$, respectively. (c) Comparison of the current-induced modulation of the SW amplitude evaluated from the subtraction method as Eq. (S15) [21]($\Delta {\tilde{A}}_{\mathrm{STT}}$, open triangles) and that estimated in the absence of the Oersted field ($\tilde{A}$, solid squares) ($\beta =3\alpha$). (d) $\beta$ (input) vs $\beta$ (fitting). The red symbols correspond to the case in the presence of the Oersted field effect, and the solid line corresponds to $\mathrm{\text{slope}}=1$ meaning $\beta (\mathrm{\text{input}})=\beta (\mathrm{\text{fitting}})$. The inset shows the difference of $\beta$ (input) and $\beta$ (fitting).