6 Experimental Results B. Nonlinear Wave Effects

6.4 Experimental observation of symmetry-breaking nonlinear modes in an active ring S.O. Demokritov, A.A. Serga, V.E. Demidov, and B. Hillebrands1 Solitons are large-amplitude, spatially confined wave packets in nonlinear media. They occur in a wide range of physical systems, such as water surfaces, optical fibres, plasmas, Bose-Einstein condensates and magnetically ordered media [1, 2]. A distinguishing feature of soliton behavior, that is common to all systems, is that they propagate without a change in shape owing to the stabilizing effect of the particular nonlinearity involved [1,3]. When the propagation path is closed, modes consisting of one or several solitons may rotate around the ring, the topology of which imposes additional constraints on their allowed frequencies and phases [4, 5]. Here we measure the mode spectrum of spin-wave solitons in a nonlinear active ring constructed from a magnetic ferrite film. Several unusual symmetry-breaking soliton-like modes are found, such as “Möbius” solitons, which break the fundamental symmetry of 2π-periodicity in the phase change acquired per loop: a Möbius soliton needs to travel twice around the ring to meet the initial phase condition. Despite the numerous publications on nonlinear wave propagation [1–3,6,7], multi-soliton modes in confined nonlinear systems have received very little attention to date. Very recently Carr et al. have analyzed multi-soliton modes in a box with infinitely high walls and, equivalently, a ring [4, 5], and they find that the symmetry of these modes can differ from that of linear modes of the system. The linear modes of a box are sinusoidal standing waves enumerated by the number of half-wavelengths that satisfy the box size. There is a direct connection between the mode number of a linear mode and its mirror symmetry with respect to the center of the box: odd and even modes are symmetric and antisymmetric, respectively. It was shown [5] for the case of a so-called CW