Stacked topological spin textures as emitters for multidimensional spin wave modes

Abstract

The investigation of propagating spin waves is a key topic of contemporary magnetism research [1]. For the excitation of spin waves with short wavelengths, it was typically necessary to either use transducers with sizes on the order of the desired wavelengths (striplines or point-contacts) or to generate those spin waves parametrically by a double-frequency spatially uniform microwave signal [2]. Only recently, a novel mechanism for the local excitation of spin waves, which overcomes the wavelength limit given by the minimum patterning size has been discovered. This method utilizes the translation of natural topological defects, namely the gyration of spin vortex cores [3]. A spin vortex is characterized by a planar, flux-closing magnetization curl, which tilts out of the plane in the central nanoscopic core region [cf. Fig. 1(a)]. Both, the in-plane rotation sense of the curl (circulation) and the orientation of the perpendicular core (polarity), are independently either positive or negative. The initial study [3] was carried out on a vortex pair system with opposite circulations and equal polarities, in which the two vortices were stacked via a nonmagnetic inter-layer [cf. Fig. 1(b) and 1(c)]. In such a system, spin waves can be generated by lateral magnetic field excitation at the vortex cores. Scanning transmission x-ray microscopy (STXM) was used to directly image these spin waves propagating to the rim of the sample in a spiraling manner [cf. Fig. 1(d)]. Thereby, the resulting spin wave length was found to be directly tunable by the excitation frequency. Moreover, the resulting spin waves were analytically calculated to exhibit a gapless, linear, and non-reciprocal dispersion relation with much shorter wave lengths compared to spin waves of the same frequency in corresponding single layer films.