Eavesdropping on spin waves inside the domain-wall nanochannel via three-magnon processes

One recent breakthrough in the field of magnonics is the experimental realization of reconfigurable spin-wave nanochannels formed by magnetic domain wall with a width of $10-100$ nm [Wagner \emph{et al}., Nat. Nano. \textbf{11}, 432 (2016)]. This remarkable progress enables an energy-efficient spin-wave propagation with a well-defined wave vector along its propagating path inside the wall. In the mentioned experiment, a micro-focus Brillouin light scattering spectroscopy was taken in a line-scans manner to measure the frequency of the bounded spin wave. Due to their localization nature, the confined spin waves can hardly be detected from outside the wall channel, which guarantees the information security to some extent. In this work, we theoretically propose a scheme to detect/eavesdrop on the spin waves inside the domain-wall nanochannel via nonlinear three-magnon processes. We send a spin wave in one magnetic domain to interact with the bounded mode in the wall. Two kinds of three-magnon processes, i.e., confluence and splitting, are expected to occur. The confluence process is conventional. We predict a stimulated three-magnon splitting (or "magnon laser") effect: the presence of a bound magnon propagating along the domain wall channel assists the splitting of the incident wave into two modes, one of which is identical to the bound mode in the channel. Micromagnetic simulations confirm our theoretical analysis. These results demonstrate that one is able to uniquely infer the spectrum of the spin-wave in the domain-wall nanochannel once we know both the injection and the transmitted waves.