Figure 1

Geometry. The thin film extends in the $y\text{−}z$ plane. The easy axis of each material coincides with the $z$ axis and an applied field is also in the $z$ direction. A Bloch domain wall has formed which is illustrated. Here $K_2>K_1$ such that the right film is “hard” and the left film is “soft.”Reuse & Permissions

Figure 2

$\mathrm{Fe}∕\mathrm{Co}$ spin waves $(K_{\mathrm{Co}}∕K_{\mathrm{Fe}}=10.6)$. (a) Spin wave frequencies for uniform magnetization, plotted as a function of in-plane wave vector. $\Gamma$ denotes $k_y=k_z=0$, $X$ denotes $a_0{k}_y=\pi ∕2$ and $k_z=0$ and $M$ denotes $a_0{k}_y=a_0{k}_z=\pi ∕2$ (the edge of the Brillouin zone). There is no clear separation into two spin wave bands. (b) Mode profiles with uniform magnetization. The amplitude $a_Y\left(x\right)$ is plotted as a function of depth (iron on the left and cobalt on the right). The frequencies are given in GHz above each plot. In contrast to the $\mathrm{Co}∕\mathrm{Sm}{\mathrm{Co}}_5$ bilayer (see Fig. 3), spin waves in this bilayer generally propagate through both materials.Reuse & Permissions

Figure 3

$\mathrm{Fe}∕\mathrm{Sm}{\mathrm{Co}}_5$ spin waves $(K_{\mathrm{Sm}\mathrm{Co}}∕K_{\mathrm{Co}}=32.4)$. (a) Spin wave frequencies for uniform magnetization, plotted as a function of in-plane wave vector. $\Gamma$ denotes $k_y=k_z=0$, $X$ denotes $a_0{k}_y=\pi ∕2$ and $k_z=0$ and $M$ denotes $a_0{k}_y=a_0{k}_z=\pi ∕2$ (the edge of the Brillouin zone). There is a separation into two spin wave bands corresponding to spin waves confined to either material. (b) Mode profiles with uniform magnetization. The amplitude $a_Y\left(x\right)$ is plotted as a function of depth (cobalt on the left and $\mathrm{Sm}{\mathrm{Co}}_5$ on the right). The frequencies are given in GHz above each plot. In contrast to the $\mathrm{Fe}∕\mathrm{Co}$ bilayer (see Fig. 2), spin waves in this bilayer generally do not propogate through both materials. (c) Mode profiles $a_Y\left(x\right)$ for a wall pinned at the interface. Note that all the resonant frequencies have decreased and there is an increase in the confinement of spin waves to one material or the other.Reuse & Permissions

Figure 4

A domain wall resonance appears below the spin wave bands in the frequency spectrum for the $\mathrm{Co}∕\mathrm{Sm}\mathrm{Co}$ bilayer. The mode amplitude $a_Y\left(x\right)$ is plotted as a function of position in the bilayer.Reuse & Permissions

Figure 5

Spin wave valve. For a cobalt/$\mathrm{Sm}{\mathrm{Co}}_5$ bilayer with $K_2∕K_1$ increased to 35, the lowest frequencies in the $\mathrm{Sm}{\mathrm{Co}}_5$ spin wave band (solid lines) and the highest frequencies in the cobalt spin wave band (dashed lines) are plotted as a function of applied field. It can be seen that the bands are separated in frequency space when the applied field is below around $0.03\mathrm{T}$ but above this threshold they overlap and spin waves may propagate through both materials.Reuse & Permissions

Figure 6

Two components of the susceptibility tensor, ${\chi }_{xx}\left(\omega \right)$ and ${\chi }_{yy}\left(\omega \right)$ for the $\mathrm{Co}∕\mathrm{Sm}{\mathrm{Co}}_5$ bilayer with $B=1\mathrm{T}$. The peaks at particular frequencies reveal the resonance frequencies of the system.Reuse & Permissions