  Generation of second-harmonic waves is one of the universal nonlinear
phenomena that have found numerous technical applications in many modern
technologies, in particular, in photonics. This phenomenon also has great
potential in the field of magnonics, which considers the use of spin waves in
magnetic nanostructures to implement wave-based signal processing and
computing. However, due to the strong frequency dependence of the phase
velocity of spin waves, resonant phase-matched generation of second-harmonic
spin waves has not yet been achieved in practice. Here, we show experimentally
that such a process can be realized using a combination of different modes of
nano-sized spin-wave waveguides based on low-damping magnetic insulators. We
demonstrate that our approach enables efficient spatially-extended energy
transfer between interacting waves, which can be controlled by the intensity of
the initial wave and the static magnetic field. The demonstrated approach can
be used for the generation of short-wavelength spin waves that are difficult to
excite directly, as well as for the implementation of novel devices for
magnonic logic and unconventional computing.
