Generation of Spin-Wave Envelope Dark Solitons

Experimental study of nonlinear waves in different physical systems is an attractive area of research, not only from the fundamental point of view, but also for future ap- plications of nonlinear properties of solids. So far the most impressive results have been demonstrated in nonlinear guided-wave optics (see, e.g., Refs. (1,2)). In a sharp con- trast, the experimental study of nonlinear waves in solid- state systems has demonstrated much slower progress, in particular due to dissipative losses that make the ob- servation of large nonlinear effects in real systems dif- ficult. Nevertheless, spin-wave bright envelope solitons have been observed in magnetic films, for different ori- entations of the magnetic field and propagation direction (3,4). Similar results have been reported for other types of nonlinear waves in solids, e.g., acoustic envelope soli- tons generated in a quartz crystal (5). The first observation of microwave magnetic-envelope dark solitons was reported by Chen et al. (6), who gener- ated spin waves propagating perpendicularly to the direc- tion of a bias magnetic field in a tangentially magnetized single-crystal yttrium iron garnet (YIG) film. For such a geometry, the dispersion and nonlinear coefficients have the same sign (7) and, therefore, dark solitons can be gen- erated. The experimental results reported in Ref. (6) re- vealed unusual features of the soliton generation when the number of generated solitons was changing with the input power from even to odd. The purpose of this Letter is twofold. First, we demon- strate that in the case when an input pulse without any phase modulation enters a nonlinear dispersive medium at a certain point, the generated localized wave acquires an induced spatial phase shift accumulated during its gener- ation, the phase shift being inversely proportional to the wave group velocity. Such a phase shift is negligible for large group velocities, e.g., for optical solitons in fibers. However, for wave propagation in solids, the induced phase is no longer small, and its effect becomes important, as in the case of spin waves. Second, based on this general concept, we shed light on the experimental results reported in Ref. (6). We show that an arbitrary small phase shift across the initial pulse can change the character of the soli- ton generation, and both an odd and even number of dark solitons can emerge. For the same shape and duration of the input pulse, this effect is determined only by the pulse amplitude as observed in (6). First, we discuss the phenomenon of the phase shift accumulated during the pulse generation. We consider the evolution of a slowly varying wave envelope Asz, td described by the nonlinear Schrödinger (NLS) equation, i µ ›A