A sinusoidal magnetization distribution as an original way to generate a versatile magnonic crystal for magnon propagation

The manipulation of the magnetization in a film at the nanoscale is one of the best means for controlling spin-wave propagation in real time. In 3D Magnonics, the vertical or interfacial interaction with patterned layers can make the film magnetization depart from uniformity, which, in general, can introduce new spin-wave modes in the film, hence additional degrees of freedom for signal manipulation. In this paper, we suggest a sinusoidal distribution for the magnetization as an original and effective way to generate a magnonic crystal and control its magnon dynamics. Along with a uniform bias field, we introduce in the film layer a sinusoidal bias field, simulating the vertical/interfacial interaction with other layers: after relaxation, the film magnetization assumes a sinusoidal equilibrium distribution. Using micromagnetic simulations followed by Fourier analysis, we show how to control the magnon dynamics by tuning the magnetization undulation amplitude and symmetry. We compute the magnon dispersion curves and space profiles, we show the occurrence of new degrees of freedom for signal manipulation and the rise of localized and stationary magnon modes. We highlight the physical mechanisms governing the occurrence and variation of the frequency-gap at zone-boundary. Finally, we indicate how to practically implement a sinusoidal field (and consequent magnetization) when the vertical coupling is the inverse magnetoelastic interaction between ferroelectric and ferromagnetic films. Our results suggest a new mechanism for controlling magnon propagation, which appears extremely appealing for its really wide range of tunable effects on their dynamics, particularly interesting in the engineering of signal filtering, information storage and delivery, and sensing activity.