Design and construction of a spin-wave lens

Abstract

In this work, we present the focusing of a Damon-Eshbach wave in a Ni80Fe20 film by a shaped, discrete transition of the film thickness. We devised an algorithm to determine the required shape of a spin-wave lens. Due to the anisotropy three geometries qualify as plano-convex lenses. One lens geometry has been realized experimentally and the emitted spin-wave pattern is investigated by time-resolved scanning Kerr microscopy.

Figure 1

(a) Illustration of the refraction of a spin wave incident on a straight boundary of two Ni₈₀Fe₂₀ films with different thicknesses. The wave vectors of the incident wave and the refracted wave are marked as k₁ and k₂ respectively. (b) Isofrequency curves of spin waves in two differently thick (t₁ > t₂) Ni₈₀Fe₂₀ films. The transferred wave vector Δk due to refraction and the orientation of the step edge are marked by the dashed and solid black line, respectively. The group velocities are marked by v₁ and v₂. The solid black line denotes the direction of the edge.

Figure 2

(a,b) Illustration of the algorithm used to calculate the lens shape. A planar spin wave with wave vector k₀ in the layer with thickness t₁ is assumed to impinge from the left. The orange dots mark the iteration points at which the needed angle α_i of the group velocity v_i is calculated. (c) Angle of the group velocity on the isofrequency curve valid for t₂ as a function of k_z. (d) Final shape of the designed lens marked in red are parts of the structure which do not act as lens.

Figure 3

(a) Isofrequency curve for t₂ at μ₀H₀ = 10 mT and f = 5 GHz. The orange section repesents the wave vectors emitted be the derived lens. Wave vectors with group velocities parallel to that of the Damon-Eshbach direction are indicated as k_a and k_b. (b) Lens designs resulting in the choice of β_a (top) and β_b (bottom) as starting angles. The focal spot is marked by a black dot. The black lines mark sections of the lenses which do not contribute to focusing. (c) Wave vector intervals emitted by the kinked lenses. The wave vectors emitted at the lens center and termini are marked by circles and dashes, respectively.

Figure 4

(a) Illustration of the experimental arrangement. G1 and G2 mark the ground lines of the wave guide. S marks the signal line of the wave guide. (b) Top panel: Measurements of the out-of-plane component (M_y) of the spin-wave pattern at the lens, taken at an external magnetic field of μ₀H₀ = 10 mT. Bottom panel: Amplitude of the spin-wave pattern corresponding to the measurements on the left-hand side. The three patterns are recorded at different mw frequencies marked on the right hand side. (c,d) Scans of the amplitude at f₁ = 5016 MHz along the z and x axes, as indicated by the dashed lines in (b).

Figure 5

(a) Measured position x_f of the focal spot as a function of the frequency at μ₀H₀ = 10 mT (black dots) and μ₀H₀ = 20 mT (blue dots). The gray and green lines mark the calculated focal distances at 10 mT and 10 mT, respectively. (b) Measured width w of the focal spot as a function of the frequency at μ₀H₀ = 10 mT (black dots) and μ₀H₀ = 20 mT (blue dots).