Selective behaviour of spin wave propagation in asymmetrically modulated ferromagnetic nanowires

Investigation of magnetic domain wall (DW) motion and spin wave (SW) propagation in ferromagnetic nanowires has garnered attention due to the potential applications in future information communication. Particular in patterned ferromagnetic nanowires, the DW and SW propagation are controllable by geometrical modulation generally use notches or artificial imperfections extensively. Recently, diode-like ratchet behaviour of DW motion has been reported in ferromagnetic nanowires with asymmetrically modulated geometry under the drive of alternating magnetic field^[1,2]. The DW ratchet effect was experimentally observed in ferromagnetic wires with asymmetric notches by applying spin-polarized pulsed current or static magnetic field. These works have demonstrated that a proper introduction of the asymmetric pinning potential can be used to selectively control the DW propagation direction. Therefore, the diode-like dynamic behaviour as a kind of asymmetric stray field effect, should also apply to the SW propagation in ferromagnetic nanowires. However, very few studies have been devoted to the diode-like behaviour in SW propagations. In particular, a demonstration of SW propagation along the ferromagnetic nanowires are still lacking. In this work, we have investigated a selective behaviour of SW propagation under a static and alternating magnetic field in asymmetrically triangular-shaped notched Permalloy nanowires by means of the micromagnetic simulation^[3]. The degree of geometrical notch asymmetry in nanowire has been systematically varied by modulating the geometric ratio of the notch width and height, as shown in Fig. 1a. The SW was generated by the DW oscillation under alternating field at centre of the nanowire or periodic change of the DW width during the DW propagation. By simulations, It has been observed that a diode-like behaviour in SW propagations in the nanowires with variation of the driving field strength and frequency, as illustrated i- Fig 1b. By the introduction of asymmetric energy potentials in the ferromagnetic nanowire, we believe that a kind of effective method of controlling SW propagations is found under alternating driving field.