Figure 4
From: Control of Spin-Wave Propagation using Magnetisation Gradients

Micromagnetic calculations (left) and corresponding isofrequency curves (right). The numerical calculations are performed for f = 7.0 GHz. Two gradient shapes are analysed: a rectangle (a) and a triangle (b). Figure 4a is shown schematically in Fig. 1a. The isofrequency curves illustrate how the wavevector \(\overrightarrow{k}\) is transformed while the spin wave propagates (dotted line) into and through the magnetisation gradient region. The spin wave enters the gradient at a certain local value of the saturation magnetisation MS,in. The isofrequency curves visualise the 2-step conversion process: first, the spin waves are refracted at the interface. Next, the transformation inside the gradient takes place. The direction of \(\overrightarrow{k}\) can be directly compared to the micromagnetic simulations. Here, the spin wave is excited at the left of each picture and propagates to the right into the magnetisation gradient region (grey rectangle or triangle) where the conversion can take place. The dynamic magnetisation mz is colour coded (red: max, blue: min).