“…Up to now, it has been shown that the graded magnonic refractive index can be created by modification of the material properties, such as non-uniform saturation magnetization or exchange constant [ 44 , 45 , 46 , 47 ], the magnetic anisotropy [ 19 , 20 ] or the internal magnetic field [ 37 , 48 ]. This index can be also achieved by utilizing a non-uniform external magnetic field [ 39 , 49 , 50 , 51 ], electric field (voltage) [ 52 , 53 ] or temperature [ 54 , 55 ]. Therefore, graded-index magnonics are expected to overcome the current limitation of magnonics and pave feasible routes for the implementation of spin-wave devices.…”