Direct observation of spin-wave focusing by a Fresnel lens

Spin waves are discussed as promising information carrier for beyond complementary metal-oxide semiconductor data processing. One major challenge is guiding and steering of spin waves in a uniform film. Here, we explore the use of diffractive optics for these tasks by nanoscale real-space imaging using x-ray microscopy and careful analysis with micromagnetic simulations. We discuss the properties of the focused caustic beams that are generated by a Fresnel-type zone plate and demonstrate control and steering of the focal spot. Thus, we present a steerable and intense nanometer-sized spin-wave source. Potentially, this could be used to selectively illuminate magnonic devices like nano-oscillators.

Figure 1

Sketch of the magnonic zone plate samples for x-ray microscopy. 50 nm of Py are deposited on top of an x-ray transparent $\mathrm{S}{\mathrm{i}}_3{\mathrm{N}}_4$ membrane. For rf excitation a 1.6-$\mu \mathrm{m}$-wide Cu stripline is deposited on top of the magnetic thin film as excitation source. The Fresnel zone plate is realized by an arrangement of holes at a distance of $6\mu \mathrm{m}$ from the excitation source. Additionally, an in-plane magnetic bias field is applied along the stripline. (a) shows the isofrequency contour and (b) shows the angle of the group velocity with respect to the bias field in this film for 3.6 GHz/12 mT (dashed red lines) and 5.7 GHz/18 mT (solid black lines).

Figure 2

Spin-wave amplitude for transmission through a hole-based Fresnel zone plate in a 50-nm Py thin film (a) at 3.6 GHz with an applied in-plane bias field of −12 mT and (b) at 5.7 GHz with an applied in-plane bias field of −18 mT. Additionally, cuts through the amplitude along the propagation direction and through the focal plane are shown. For (a) the focal spot is found 6 $\mu \mathrm{m}$ behind the lens and the spin waves are confined to 840-nm FWHM. Furthermore, the amplitude is increased by 23%, thus overcompensating for damping during spin-wave propagation.

Figure 3

Simulation of the spin-wave amplitude for transmission through a hole-based Fresnel zone plate in a 50-nm Py thin film at 5.7 GHz with an applied in-plane bias field of 22 mT. Qualitatively, the same spin-wave pattern as in the experiment (cf. Fig. 2) is found. Furthermore, a comparable focus distance and size is found.

Figure 4

(a), (d) The aperture functions $a\left(x\right)$ used in calculations. The solid black line represents the amplitude of the aperture function $\left|a\left(x\right)\right|$, whereas the dashed red line denotes its phase $\phi \left(x\right)$. (a) Presents function $a\left(x\right)=\mathrm{Rect}\left(\frac{x}{6\mu \mathrm{m}}\right),$ whereas (b) displays $a\left(x\right)=\left[0.51+0.49\mathrm{Rect}\left(\frac{x}{5.5\mu \mathrm{m}}\right)\right]\times exp\left[i\left(-{150}^{\circ }-{90}^{\circ }\mathrm{Rect}\left(\frac{x}{5.5\mu \mathrm{m}}\right)\right)\right].$ (b), (e) Profile of spin waves at frequency 5.7 GHz calculated with the application of the apertures shown in (a) and (d), respectively. The spin-wave profile in (e) is obtained for the interface located at $y=600$ nm. (c) Results of micromagnetic simulations of the diffraction of spin waves at frequency 5.7 GHz at the 6-$\mu \mathrm{m}$-long slit. The inset shows the zoomed-in region marked by the hatched black square, whereas the horizontal black line represents the location where the beam splits. The black solid horizontal lines in (c) and (e) represent the position of the interface used in calculations of the profile presented in (e). Green lines indicate the dominating direction of the group velocities along which spin-wave fronts align (viz., ±15° with respect to the $y$ axis).

Figure 5

Simulation of the magnetic behavior of the various slit widths (a) 6 $\mu \mathrm{m}$, (b) 0.9 $\mu \mathrm{m}$, and (c) 0.6 $\mu \mathrm{m}$ that constitute the zone plate structure in a 50-nm-thin Py film at 5.7 GHz with an applied in-plane bias field of 22 mT along the $x$ direction. For each slit the spin-wave transmission, the local static magnetization, and demagnetization fields are shown. It becomes evident that the magnetization is no longer independent when the slit width is reduced and the magnetostatic fields begin to overlap.

Figure 6

Simulation of the static magnetization and the magnetostatic fields of the full zone plate structure in a 50-nm-thin Py film at 5.7 GHz with an applied in-plane bias field of 22 mT along the $x$ direction. While the magnetization in the central slit is mostly undisturbed, the influence area of the demagnetization fields in the outer slits overlap and form a complex magnetization landscape.

Figure 7

Simulation of the magnetic behavior of the central slit of a zone plate structure in a 50-nm-thin Py film at 5.7 GHz with an applied in-plane bias field magnitude of 22 mT along the $x$ direction. The in-plane field is tilted to angles of (a) 5°, (b) 10°, and (c) 15° with respect to the $x$ axis. For each angle, the spin-wave amplitude after passing through the slit, the static magnetization of the slit edge, and the corresponding local magnetostatic field are shown.

Figure 8

Spin-wave amplitude and phase for transmission through a hole-based Fresnel zone plate in a 50-nm Py thin film at 5.7 GHz with applied in-plane bias fields. At field magnitudes below 6 mT (a) or above 40 mT (h) no spin-wave focusing occurs. At intermediate fields the focal spot moves inwards and downwards with increasing Damon-Eshbach-type spin-wave contribution, i.e., the wave length increases and the emission angle turns perpendicular to the external field. The central inset shows the focal positions (maximum lateral confinement) as green dots for fields ranging from −8 to −36 mT.

Figure 9

Spin-wave amplitude in transmission through a hole-based Fresnel zone plate in a 50-nm Py thin film at 5.7 GHz with applied in-plane bias fields of (a) −28 mT, (b) −14 mT, and (c) −10 mT. Additionally, (b), (d), and (f) show the respective $k$-space transformations of the observed spin waves and the analytic isofrequency contour at the respective field geometries. From the isofrequency contour the tilt angle of the in-plane bias field can be determined to be 0°, 3.5°, and 10°, respectively.