Spin-wave dynamics controlled by tunable ac magnonic crystal

The magnonic crystal, which has a spatial modulation wave vector $q$, couples the spin wave with wave vector $k$ to the one with wave vector $k-q$. For a conventional magnonic crystal with direct current (dc) supply, the spin waves around $q/2$ are resonantly coupled to the waves near $-q/2$, and a band gap is opened at $k=\pm q/2$. If instead of the dc current the magnonic crystal is supplied with an alternating current (ac), then the band gap is \emph{shifted} to $k$ satisfying $|\omega_{s}(k)-\omega_{s}(k-q)|=\omega_{ac}$; here $\omega_{s}(k)$ is the dispersion of the spin wave, while $\omega_{ac}$ is the frequency of the ac modulation. The resulting gap in the case of the ac magnonic crystal is the half of the one caused by the dc with the same amplitude of modulation. The time evolution of the resonantly coupled spin waves controlled by properly suited ac pulses can be well interpreted as the motion on a Bloch sphere. The tunability of the ac magnonic crystal broadens the perspective of spin-wave computing.