Wannier-Stark ladder spectrum of Bloch oscillations of magneto-dipole spin waves in graded 1D magnonic crystals

Abstract

We have used the method of Wannier functions to calculate the frequencies and profiles of spin waves localised in one-dimensional (1D) magnonic crystals due to a gradient in the bias magnetic field. This localisation of spin waves is analogous to the phenomenon of Bloch oscillations of quantum-mechanical electrons in crystals in a uniform electric field. As a convenient yet realistic model, we consider backward volume magnetostatic spin waves (BVMSWs) in a film of yttriumiron garnet (YIG) in a bias magnetic field comprising spatially uniform, cosine and gradient contributions. The spin-wave spectrum is shown to have the characteristic form of a WannierStark ladder. The analytical results are verified using those obtained using numerical micromagnetic simulations. The physics of spin-wave Bloch oscillations combines the topics of magnonic crystals and graded magnonic index – the two cornerstones of modern magnonics.