Spin-Wave Excitation in Magnetic Insulators by Spin-Transfer Torque

We study the excitation of spin waves in magnetic insulators by the current-induced spin-transfer torque. We predict preferential excitation of surface spin waves induced by an easy-axis surface anisotropy with critical current inversely proportional to the penetration depth and surface anisotropy. The surface modes strongly reduce the critical current and enhance the excitation power of the current-induced magnetization dynamics.

Figure 1

An electrically insulating magnetic film of thickness $d$ with magnetization $\mathbf{m}$ ($\parallel \widehat{\mathbf{z}}$ at equilibrium) in contact with a normal metal. A spin current $J_s\parallel \widehat{\mathbf{z}}$ is generated in the normal metal and absorbed by the ferromagnet.

Figure 2

Spin wave band structure and magnetization profiles in YIG for $d=0.61\mu \mathrm{m}$ without surface anisotropy: $k_s=0$ at $\theta =\angle (\mathbf{m},\mathbf{q})=90°$. Top (from left to right): $\mathrm{Re}(\omega /{\omega }_M)$ vs. $qd$, $\mathrm{Im}(\omega /{\omega }_M)$ at $k_j=0$, $\mathrm{Im}(\omega /{\omega }_M)$ at $k_j=-0.2k_c$. Bottom: $m_x$ of the same 6 modes for $qd=0.09$ and 3.74 indicated by the dashed vertical lines in the top panels. The colors label different bands. The amplitude of the green mode (shaded [yellow] panel) is amplified.

Figure 3

Same as Fig. 2 but with $k_s=25/\mu \mathrm{m}$.

Figure 4

Top: Power spectrum (resolution $\delta \omega /{\omega }_M=0.01$) at various current levels ($k_j=0.2k_c$ from the top decreasing by $\Delta k_j=0.01k_c$) without (left: $k_s=0$) and with (right: $k_s=25.0/\mu \mathrm{m}$) surface anisotropy. Inset: the integrated power versus $k_j$.