Spin waves damping in nanometre-scale magnetic materials

Spin dynamics in magnetic nanostructured materials is a topic of great current interest. To describe spin motions in such magnetic systems, the phenomenological Landau–Lifshitz (LL), or the LL–Gilbert (LLG), equation is widely used. Damping term is one of the dominant features of magnetization dynamics and plays an essential role in these equations of motion. The form of this term is simple; however, an important question arises whether it provides a proper description of the magnetization coupling to the thermal bath and the related magnetic fluctuations in the real nanometre-scale magnetic materials. It is now generally accepted that for nanostructured systems the damping term in the LL (LLG) equation fails to account for the systematics of the magnetization relaxation, even at the linear response level. In ultrathin films and nanostructured magnets particular relaxation mechanisms arise, extrinsic and intrinsic, which are relevant at nanometre-length scales, yet are not so efficient in bulk materials. These mechanisms of relaxation are crucial for understanding the magnetization dynamics that results in a linewidth dependence on the nanomagnet’s size. We give an overview of recent efforts regarding the description of spin waves damping in nanostructured magnetic materials. Three types of systems are reviewed: ultrathin and exchange-based films, magnetic nanometre-scale samples and patterned magnetic structures. The former is an example of a rare case where consideration can be done analytically on microscopic footing. The latter two are typical samples when analytical approaches hardly have to be developed and numerical calculations are more fruitful. Progress in simulations of magnetization dynamics in nanometre-scale magnets gives hopes that a phenomenological approach can provide us with a realistic description of spin motions in expanding diverse of magnetic nanostructures.