Large Spin-Wave Bullet in a Ferrimagnetic Insulator Driven by the Spin Hall Effect

Because of its transverse nature, spin Hall effects (SHE) provide the possibility to excite and detect spin currents and magnetization dynamics even in magnetic insulators. Magnetic insulators are outstanding materials for the investigation of nonlinear phenomena and for novel low power spintronics applications because of their extremely low Gilbert damping. Here, we report on the direct imaging of electrically driven spin-torque ferromagnetic resonance (ST-FMR) in the ferrimagnetic insulator ${\mathrm{Y}}_3{\mathrm{Fe}}_5{\mathrm{O}}_{12}$ based on the excitation and detection by SHEs. The driven spin dynamics in ${\mathrm{Y}}_3{\mathrm{Fe}}_5{\mathrm{O}}_{12}$ is directly imaged by spatially resolved microfocused Brillouin light scattering spectroscopy. Previously, ST-FMR experiments assumed a uniform precession across the sample, which is not valid in our measurements. A strong spin-wave localization in the center of the sample is observed indicating the formation of a nonlinear, self-localized spin-wave “bullet”.

Figure 1

(a) Schematic of the ST-FMR experimental setup (b) ST-FMR mechanism in the $\mathrm{YIG}/\mathrm{Pt}$ bilayer. The alternating rf current drives an Oersted field $h_{\text{rf}}$ exerting a fieldlike torque ${\tau }_{\mathrm{H}}$ on the magnetization $\mathbf{M}$. At the same time a oscillatory transverse spin accumulation at the $\mathrm{YIG}/\mathrm{Pt}$ interface is generated by the SHE which results in a dampinglike torque ${\tau }_{\mathrm{STT}}$. (c) and (d) Typical dc voltage spectra recorded at in-plane angles of $\varphi =30°$ and $\varphi =240°$ and $P=+10\mathrm{dBm}$.

Figure 2

(a) Typical $V_{\mathrm{DC}}$ spectra at a constant frequency $f=4\mathrm{GHz}$ for various applied microwave powers. The inset shows the resonance peak at $P=+15\mathrm{dBm}$. Two modes are detected. (b) In-plane angular dependence of the symmetric portion to $V_{\mathrm{DC}}$. The purple curve is the $\sin 2\varphi \cos \varphi$ dependence from the ST-FMR model we use. The green curve shows an additional $\sin \varphi$ dependence in resonance. The sum of both signals is shown as blue curve. (c) Antisymmetric portion to $V_{\mathrm{DC}}$ as a function of the in-plane angle following the expected $\sin 2\varphi \cos \varphi$ dependence.

Figure 3

Resonance frequency as a function of bias magnetic field measured by BLS illustrated in a color-coded image. The laser spot was focused onto the center of the sample while the rf frequency and magnetic field were varied. As for the electrical measurements two modes are detected by BLS. The inset shows corresponding field dependence of the resonance measured by electrical means.

Figure 4

Spatially-resolved BLS map of the $5\times 5\mu {\mathrm{m}}^2$ large $\mathrm{YIG}/\mathrm{Pt}$ sample. The magnetic field $H=665\mathrm{Oe}$ is applied at $\varphi \sim 45°$. (a)—(d) Driving microwave frequency increases from 3.7 GHz to 3.85 GHz, microwave power $P=+17\mathrm{dBm}$.

Figure 5

Micromagnetic simulations: (a) The spectrum reveals two modes. Spatially-resolved magnetization distribution of the main mode, (b), and the less intense, subsidiary mode, (c). (d) The normalized integrated BLS intensity saturates at high excitation powers $P$, which is validated by micromagnetic simulations at large driving rf magnetic fields $h_{\text{rf}}$.