Localized domain-wall excitations in patterned magnetic dots probed by broadband ferromagnetic resonance

We investigate the magnetization dynamics in circular Permalloy dots with spatially separated magnetic vortices interconnected by domain walls (double vortex state). We identify a novel type of quasi one-dimensional (1D) localised spin wave modes confined along domain walls, connecting each of two vortex cores with two edge half-antivortices. Variation of the mode eigenfrequencies with the dot size is in quantitative agreement with the developed model, which considers a dipolar origin of the localized 1D spin waves or so-called Winter\'s magnons [J.M. Winter, Phys.Rev. 124, 452 (1961)]. These spin waves are analogous to the displacement waves of strings, and could be excited in a wide class of patterned magnetic nanostructures possessing domain walls, namely in triangular, square, circular or elliptic magnetic dots.