Figure 1
From: Control of Spin-Wave Propagation using Magnetisation Gradients
Scheme of the mode conversion and dispersion relations for different local values of the saturation magnetisation. (a) The mode conversion process transforms BVMSW (blue) to MSSW (red) modes. Both types of spin waves propagate in the sketched areas at different values of the saturation magnetisation MS. A magnetisation landscape – a temperature-induced arbitrary shaped magnetisation gradient \(\overrightarrow{\nabla }{M}_{{\rm{S}}}(x,y)\) – enables the mode conversion. A two–step process changes the direction of the wavevector \(\overrightarrow{k}\) and the group velocity \({\overrightarrow{v}}_{{\rm{gr}}}\). First, the spin-wave is refracted at the interface to the gradient decreasing the wavenumber. Next, a smooth transformation inside the magnetisation landscape occurs. The external magnetic field \({\overrightarrow{H}}_{{\rm{ext}}}\) is oriented parallel to the waveguide (in-plane orientation). (b) The dispersion relations of MSSW (propagating in the y direction) and BVMSW modes (propagating in the x direction) are shown versus the wavevector k. Due to the saturation magnetisation gradient, a wide band for both modes is realised. The intersection of these bands forms the conversion area (grey), where the mode conversion is allowed. The values MS,1 and MS,2 correspond to the temperatures T1 at antenna 1 and T2 at antenna 2 and are chosen according to the infrared camera measurements in Fig. 2. The conversion area is limited by the ferromagnetic resonance frequencies (FMR) for MS,1 and MS,2, respectively. A temperature-induced change in the minimal and maximal value of the saturation magnetisation leads to a shift of both frequencies and consequently of the conversion area. Thus, a similar behaviour of the conversion process is expected for different ranges of the saturation magnetisation. The maximal wavenumber of 500 rad/cm corresponds to the spin wave of the wavelength 125 µm. (c) The experimental set-up is shown schematically. A light pattern which creates a magnetisation gradient is formed close to the centre in x-direction of the waveguide at antenna 2 (illumination area). With respect to the externally applied magnetic field \({\overrightarrow{H}}_{{\rm{ext}}}\), antennas 1 and 3 can excite and detect BVMSWs. Antenna 2 is used for the detection of MSSWs. Thus, spin waves excited at MS,1 are converted and afterwards measured at MS,2.
