Inelastic scattering of spin wave beam at the edge localized spin waves and second harmonic generation of spin waves

Abstract

Spin waves (SWs) are precessional magnetization disturbances propagating in magnetic media in the form of waves at microwave frequencies [1] that are the most commonly used frequencies range for wireless communication. Wavelengths of SWs are several orders of magnitude shorter than the lengths of electromagnetic waves of corresponding frequencies. The dynamics of SWs even in uniformly magnetized films is extraordinarily rich. It is easy to obtain effects difficult to be achived for other type of waves, such as nonreciprocity, excitation caustic-beam that are characteristic for hyperbolic media, easy external control over propagation (e.g., by inhomogeneous magnetic field) [2]. Non-linear phenomena are also easily available[1,3]. All these make SWs to be a promising candidate for information carriers, especially in the context of beyond-CMOS applications [4].SWs may be confined to certain areas of the thin film, e.g., in a potential well created by an inhomogeneity of the static demagnetizing field in the vicinity of film’s edge. Such localized modes are called edge SWs (E-SWs). Usually, the frequencies of E-SWs are downshifted with respect to bulk-type SWs (B-SWs), i.e., SWs propagating far from the edge where the static effective field is practically homogenous.Here, we theoretically study by means of micromagnetic simulations [5] and analytical modelling the dynamics of the E-SWs localized at the edge of thin permalloy film and their interaction with B-SWs. Firstly, we focus on the utilization of the E-SWs to excite short B-SWs propagating in the form of plane waves. Secondly, we study the inelastic non-linear scattering of B-SW beam by the E-SWs.We consider propagation of the E-SW along the edge of 10 nm thick permalloy film that is uniformly magnetized by the external field of value 300 mT directed perpendicularly to the film’s edge (see Fig. 1a, where the system is presented along with exemplary result of a simulation). The E-SW is excited by the point-source-like microwave field of frequency 12 GHz located at the film’s edge. There are visible two prominent peaks in the simulated spectrum (Fig. 1b). The first one corresponds to the frequency of the microwave field (12 GHz) and propagation of the E-SWs, whereas the second peak has doubled frequency (24 GHz) and corresponds to the B-SWs propagating obliquely outwards the edge in the form of plane waves. It indicates excitation of the B-SWs by the propagating E-SWs in the process of second harmonic generation. Noteworthy, the wavelength of the B-SWs is over twice shorter than the wavelength of the E-SWs shown in Fig. 1a. The B-SW of wavelength equal to 78 nm is excited by the 285 nm long E-SW.For the same sample, we analytically and numerically analyze the interaction of an obliquely incident B-SW beam (at frequency f) with an E-SWs at frequency n. We find that due to the inelastic scattering the secondary B-SW beams with up- and down-shifted frequency (f-n, f+n) can be excited. In Fig. 2 an exemplary result of simulation for a B-SW beam incident at the films edge where E-SW propagates and the resulting secondary scattered beam with frequency (f+ν)=42 GHz are shown. Moreover, we observe angular shifts between the primary incident and the scattered beams with shifted frequencies and analyze the efficiency of the scattering process. Finally, we present an application of this effect for SW demultiplexing.Acknowledgments. The research was supported by the National Science Centre of Poland, project no. 2019/35/D/ST3/03729 (P.G. and M.K.); COST action under project CA17123 MAGNETOFON (I.L.); the Spanish MCIU grant PID2019-108075RB-C3-3 (K.G.). K.G. acknowledges support by IKERBASQUE (the Basque Foundation for Science). The simulations were performed at the Poznan Supercomputing and Networking Center (Grant No. 398). **