We have used the method of Wannier functions to calculate the frequencies and profiles of spin waves localized in one-dimensional magnonic crystals due to a gradient in the bias magnetic field. This localization 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 in a film of yttrium-iron garnet 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 Wannier–Stark 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.
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