Graded-index magnonics

Abstract

The wave solutions of the Landau–Lifshitz equation (spin waves) are characterized by some of the most complex and peculiar dispersion relations among all waves. For example, the spin-wave (“magnonic”) dispersion can range from the parabolic law (typical for a quantum-mechanical electron) at short wavelengths to the nonanalytical linear type (typical for light and acoustic phonons) at long wavelengths. Moreover, the longwavelength magnonic dispersion has a gap and is inherently anisotropic, being naturally negative for a range of relative orientations between the effective field and the spin-wave wave vector. Nonuniformities in the effective field and magnetization configurations enable the guiding and steering of spin waves in a deliberate manner and therefore represent landscapes of graded refractive index (graded magnonic index). By analogy to the fields of graded-index photonics and transformation optics, the studies of spin waves in graded magnonic landscapes can be united under the umbrella of the graded-index magnonics theme and are reviewed here with focus on the challenges and opportunities ahead of this exciting research direction.