Wave-vector-dependent spin pumping as a probe of exchange-coupled magnons

We demonstrate that short-wavelength exchange-coupled magnons can be identified electrically through the combination of their spin-pumping and damping properties in a metal/magnetic insulator heterostructure. We present clear wave-vector dependence of the spin pumping from parametrically excited exchange-coupled magnons in the heterostructure. The efficiency of spin pumping by dipole-exchange magnons was measured to be sensitive to their wave numbers and propagation angles, while the efficiency was found to be almost constant in the exchange limit. This dependence enabled us to uncover nontrivial dual bistability in the system originating from drastic change in dominant nonequilibrium magnon modes. These findings pave a path for direct electric access to short-wavelength spin dynamics that cannot be probed by optical techniques.

Figure 1

(a) Magnetic field ${\mu }_{0}H$ dependence of the inverse spin Hall voltage $V_{\text{ISHE}}$ at microwave excitation powers $P=80\mathrm{mW}$ and $240\mathrm{mW}$. Onset of the parametric excitation was $P=86$ mW [see also Fig. 3]. (b) The magnon dispersion for the YIG film with a schematic of three-magnon splitting. (c) and (d) ${\mu }_{0}H$ dependencies of $V_{\text{ISHE}}$ and the microwave absorption intensity $P_{\text{abs}}$ at various $P$.

Figure 2

(a) ${\mu }_{0}H$ dependence of the spin-pumping efficiency $\kappa =V_{\text{ISHE}}/P_{\text{abs}}$ at various $P$. When $V_{\text{ISHE}}=P_{\text{abs}}=0, \kappa$ is set to zero. (b) The ${\mu }_{0}H$ dependence of the wave number $k$ and the angle ${\theta }_k$ of the primary excited magnon calculated with the measured saturation magnetization ${\mu }_0{M}_{\text{s}}=198\mathrm{mT}$ and the exchange interaction constant $D=5.94\times {10}^{-10}\mathrm{mT}{\mathrm{cm}}^2$.

Figure 3

(a) ${\mu }_{0}H$ dependence of $V_{\text{ISHE}}$ at $P=282$ mW. The red (black) curve was measured with increasing (decreasing) ${\mu }_{0}H$. The dotted line shows ${\mu }_{0}H=26$, 46 and $86\mathrm{mT}$. (b) $V_{\text{ISHE}}$ as a function of ${\mu }_{0}H$ and $P$, measured with increasing ${\mu }_{0}H$ under various $P$. The red (blue) solid (dashed) curve shows the threshold magnetic field ${\mu }_0{H}_{\text{th,l}}^{+(-)}, {\mu }_0{H}_{\text{th,m}}^{+(-)}$, and ${\mu }_0{H}_{\text{th,r}}^{+(-)}$ with increasing (decreasing) ${\mu }_{0}H$. (c), (d), (e) $V_{\text{ISHE}}$ as a function of $P$ at ${\mu }_{0}H=28$, 86, and 48 mT. The red (black) curve was measured with increasing (decreasing) $P$.

Figure 4

(a) $P$ dependence of $P_{\text{abs}}$ and $V_{\text{ISHE}}$ at ${\mu }_{0}H=46\mathrm{mT}$. The red (black) curve was measured with increasing (decreasing) $P$. (b) $P$ dependence of $\kappa =V_{\text{ISHE}}/P_{\text{abs}}$. (c) $P$ dependence of $n_{\text{dip}}/(n_{\text{ex}}+n_{\text{dip}})$, where $n_{\text{ex}}$ and $n_{\text{dip}}$ denote the number of exchange and dipole-exchange magnons, respectively. The blue (red) circle represents the primary excited exchange (secondary excited dipole-exchange) magnons.