Spin-wave wells revisited: From wavelength conversion and Möbius modes to magnon valleytronics

We have used micromagnetic simulations to model backward-volume dipole-exchange spin waves in graded profiles of the bias magnetic field. We demonstrate spin-wave wavelength conversion upon the wave's reflection from turning points due to the two characteristic minima (``$U$ points'') occurring in their dispersion at finite (nonzero) wave vectors. As a result, backward-volume dipole-exchange spin waves confined in ``spin-wave wells'' either form M\"obius modes, making multiple real-space turns for each reciprocal-space round trip, or split into pairs of degenerate modes in the valleys near the two $U$ points. The latter modes may therefore be assigned a pseudospin. We show that the pseudospin can be switched by scattering the spin wave from decreases of the bias magnetic field, while it is immune to scattering from field increases. Pseudospin creation and read-out can be accomplished using chiral spin-wave transducers, as described in Au et al. [Appl. Phys. Lett. 100, 182404 (2012)] and Au et al. [Appl. Phys. Lett. 100, 172408 (2012)], respectively. Taken together, the possibility of pseudospin creation, manipulation, and read-out suggests a path to development of a spin-wave version of valleytronics (``magnon valleytronics''), in which the pseudospin (rather than amplitude or phase) of spin waves would be used to encode data. Our results are not limited to graded bias magnetic field but can be generalized to other magnonic media with spatially varying characteristics, produced using the toolbox of graded index magnonics.