Coherent THz Transient Spin Currents by Spin Pumping

The generation of short spin current pulses is the basis for fast spintronic devices. In thin bilayer systems consisting of a nonmagnetic metal and a ferromagnet, a pure spin current is induced by a precessing magnetization into the nonmagnetic layer by spin pumping. This effect has been experimentally demonstrated at ferromagnetic resonance at GHz frequencies. Here, it is theoretically shown that transient magnetization dynamics efficiently generates short spin current pulses that exhibit two transient contributions. An effective coherent spin current generation is found far above the ferromagnetic resonance up to THz frequencies although dynamic magnetization amplitudes are very small in this regime. The results provide a concept for coherent THz spin current generation.

Figure 1

Scheme of a bilayer system of a ferromagnet (FM) and a non-magnetic metal (NM) typically used in experiments. The transient magnetization is shown in red. The pumped spin current is indicated by $j_s$, with a spin polarization given by the spin current vector ${\overrightarrow{I}}_s$. The spin polarization of ${\overrightarrow{I}}_s^l$ oscillates in the plane perpendicular to the equilibrium magnetization. The spin polarization of ${\overrightarrow{I}}_s^n$ is parallel to the static magnetization. Both exhibit different time dependencies.

Figure 2

Spin current in a thin film system for harmonic excitation. The magnetization lies in plane along an external field of 5 mT. The excitation field of 0.1 mT in plane and perpendicular to the magnetization. The amplitudes of the spin current components are given. (a) dc spin current polarized along the equilibrium magnetization (black line), (b) ac spin current polarized out of plane (blue line), (c) ac spin current polarized in plane (red line). (d) All components for frequencies up to THz frequencies. The inset shows the coordinate system with respect to the thin film (gray).

Figure 3

Transient spin current in a thin film system for resonant wavelet excitation. (a) Excitation field pulse with $\mathrm{\Omega }={\omega }_r$, $\sigma =1\mathrm{ns}$, $h_{\phi }=0.1\mathrm{mT}$, $t_0=3\mathrm{ns}$, and ${\varphi }_h=0$. (b) Out-of-plane (blue line) and in-plane polarized (red line) components of $I_s^l$. The scale of the in-plane component is magnified by a factor of 10. (c) The spin current $I_s^n$ is polarized along the static magnetization direction.

Figure 4

Coherent spin current generation at THz frequencies. (a) Excitation field pulse with $\mathrm{\Omega }/2\pi =1\mathrm{THz}$, $\sigma =1\mathrm{ps}$, $h_{\phi }=0.1\mathrm{mT}$, $t_0=4\mathrm{ps}$. (b) Out-of-plane (blue line) and in-plane polarized (red line) components of $I_s^l$.