Nonlinear nanoscale localization of magnetic excitations in atomic lattices

Reviewed here is the nonlinear intrinsic localization expected for large amplitude spin waves in a variety of magnetically ordered lattices. Both static and dynamic properties of intrinsic localized spin wave gap modes and resonant modes are surveyed in detail. The modulational instability of extended nonlinear spin waves is discussed as a mechanism for dynamical localization of spin waves in homogeneous magnetic lattices. The interest in this particular nonlinear dynamics area stems from the realization that some localized vibrations in perfectly periodic but nonintegrable lattices can be stabilized by lattice discreteness. However, in this rapidly growing area in nonlinear condensed matter research the experimental identification of intrinsic localized modes is yet to be demonstrated. To this end the study of spin lattice models has definite advantages over those previously presented for vibrational models both because of the importance of intrasite and intersite nonlinear interaction terms and because the dissipation of spin waves in magnetic materials is weak compared to that of lattice vibrations in crystals. Thus, both from the theoretical and the experimental points of view, nonlinear magnetic systems may provide more tractable candidates for the investigation of intrinsic localized modes which display nanoscale dimensions as well as for the future exploration of the quantum properties of such excitations.