Competing spin wave emission mechanisms revealed by time-resolved x-ray microscopy

Spin wave emission and propagation in magnonic waveguides represent a highly promising alternative for beyond-CMOS computing. It is therefore all the more important to fully understand the underlying physics of the emission process. Here, we use time-resolved scanning transmission x-ray microscopy to directly image the formation process of the globally excited local emission of spin waves in a permalloy waveguide at the nanoscale. Thereby, we observe spin wave emission from the corner of the waveguide as well as from a local oscillation of a domain-wall-like structure within the waveguide. Additionally, an isofrequency contour analysis is used to fully explain the origin of quasicylindrical spin wave excitation from the corner and its concurrent nonreflection and nonrefraction at the domain interface. This study is complemented by micromagnetic simulations which perfectly fit the experimental findings. Thus, we clarify the fundamental question of the emission mechanisms in magnonic waveguides which lay the basis for future magnonic operations.

Figure 1

(a) XAS image of a magnonic Py waveguide. (b) XMCD image of the magnonic Py waveguide shown in (a). It demonstrates a homogeneous distribution of the XMCD contrast which excludes the existence of ripple domains. (c) Bright-field TEM cross section image of the waveguide sample. Besides the silicon nitride (${\mathrm{Si}}_3{\mathrm{Ni}}_4$) and the copper (Cu) of the CPW, the cross section of the Py waveguide is visible which shows no formation of significant grain structures with sufficient size which could also lead to an excitation.

Figure 2

(a) Schematic illustration of the Py waveguide (blue) below a CPW (gray) with the shown dimensions. The blue arrows represents the oscillating global RF field which is induced by the RF current $I_{\mathrm{RF}}$ (red arrow). (b) Micromagnetic simulation of the relaxed magnetization configuration of the Py waveguide. The color code shows the in-plane direction of the magnetization. The zoomed inset shows the area of interest where (1) a domain-wall-like structure and (2) a strong gradient in the magnetization direction can be observed. The black arrows indicate the magnetization direction. This area is used for further experiments and simulations in Figs. 3 and 5.

Figure 3

(a) Phase and amplitude map of the right lower corner of the magnonic waveguide during CW excitation. Amplitude and relative phase are encoded into brightness and color, respectively. The image shows clear quasicylindrical spin waves from the corner and straight spin wave emission from the domain-wall-like interface (dash-dotted line). (b) $k$-space image of (a) which provides information about two distinguishable wave vectors $k_a$ (green) and $k_b$ (red). (c) Three-dimensional representation of the $k$-selective imaging of $k_a$ and $k_b$ revealing the real-space images of the corresponding wave vector.

Figure 4

(a) Illustration of a burst signal with the total length of $l=7$ ns, a burst length of $l_{\mathrm{burst}}=1$ ns, and the carrier frequency $f_{\mathrm{burst}}=4.2$ GHz. (b) FFT spectrum of the time signal in (a).

Figure 5

(a) Demonstration of real-space simulations (top) and time-resolved STXM measurements (bottom) of the $m_z$ component at three different time steps $t_1=0$ ns, $t_2=0.29$ ns, and $t_3=0.57$ ns during the burst excitation. $t_1$ defines the starting point of the first detected magnonic response. $t_2$ shows one spin wave period for each emission process. After less than 0.6 ns two spin wave periods are visible. (b) Comparison between the simulated and the measured $k$-space images. These images were calculated by a 2D-FFT of the real-space images in (a). The $k$ space reveals the simultaneous excitation of two distinguishable $k$ vectors at $t_2$ which reinforce the observations in (a). At $t_3$ the wave vectors appear more clearly because of the development of the spin wave propagation. The experimental results perfectly match the micromagnetic simulations in real space and in $k$ space.

Figure 6

(a) Snapshot of the real-space simulation at $t_3$. (b) $k$-space image of the snapshot in (a). The IFCs for the magnetization applied along the $x$ axis and rotated by ${45}^{\circ }$ with respect to the $x$ axis are marked by the white and red “peanut”-like closed curves. In (a) and (b) the dash-dotted line marks the location of the domain-wall-like texture, the solid black arrows mark the directions of the wave vectors $k_a$ and $k_b$, and the dashed white arrow indicates the direction of the group velocity of the mode $k_b$. $k_{\parallel }$ denotes the tangential component of $k_b$ to the interface.